JP2007200281A - Multidimensional information processor, medium storing multidimensional information processing program, multidimensional information display device, and multidimensional information processing method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a technology about multidimensional information processing capable of displaying a list of a plurality of pieces of multidimensional information on a two-dimensional plane when variables of the multidimensional information has a plurality of combinations. <P>SOLUTION: Samplings constructed of the multidimensional information are arranged on the two-dimensional plane while paying attention to their similarity and center of gravity, and their list can be displayed. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to processing and display of multidimensional information, and more particularly to a technique for presenting information understandable to a designer in an optimization technique using a computer.

Conventionally, a technique described in Patent Document 1 has been disclosed as a technique for presenting multidimensional information. In this publication, regardless of the number of dimensions, all quadrants whose vertices are any one point in the multidimensional space are developed on one plane, so that any point on each quadrant can be handled on the plane. It corresponds to one point in the area to be performed. This makes it possible to intuitively grasp the increase / decrease state of the function value in the multidimensional space.
Japanese Patent No. 2732711.

  However, in the above prior art, since the multidimensional information determined as the domain of the multivariable function is displayed on one plane, that is, in two dimensions, when the values of a plurality of variables constituting the multidimension change, It is not possible to intuitively understand how the relative relationship between the two has changed.

  For example, if the above-mentioned conventional technology is applied to meet the need to understand the range of combinations of multivariables that can be taken realistically by a combination of many variables, There is a problem that it is necessary to create a two-dimensional plane for each combination and compare them side by side, making it difficult to intuitively grasp the relative relationship between different multivariables.

  The present invention has been made paying attention to the above-mentioned problem. When there are a plurality of combinations of multidimensional information whose variables have changed, the plurality of multidimensional information can be displayed in a list on a two-dimensional plane. An object is to provide a technology related to multidimensional information processing.

  To achieve the above object, in the multidimensional information processing apparatus according to the first aspect of the present invention, for a system having responses to a plurality of variables, there are a plurality of samplings composed of combinations of the variables and / or the responses of the system. , An inter-sampling distance calculation means for calculating the Euclidean distance between the samplings as an inter-sampling distance, and an initial position setting means for selecting any one of the samplings as a first sampling and arranging it as an initial position on a two-dimensional plane And the second sampling arrangement means for selecting the sampling with the shortest sampling distance as the second sampling, and arranging the sampling at a position corresponding to the sampling distance on the basis of the initial position on the two-dimensional plane. And a sample already placed on the two-dimensional plane. A reference centroid calculating means for calculating a reference centroid which is a centroid of the second sampling, a sampling having the shortest distance between the second sampling and the sampling is selected as a third sampling, and the position of the second sampling on the two-dimensional plane and the reference A third sampling in which the third sampling is arranged at a position corresponding to a sampling distance between the third sampling and the second sampling and a sampling distance between the third sampling and the reference centroid with respect to the position of the center of gravity. Arrangement means, and after the fourth sampling, newly selected sampling is regarded as the third sampling, previous sampling is regarded as the second sampling, the second sampling arrangement means and the reference centroid calculation means And the repetition of implementing the third sampling arrangement means. It means return, characterized by comprising a.

  In the multidimensional information processing device of the second invention, when there are a plurality of processing target clusters having a plurality of samplings composed of combinations of the variables and / or the responses of the system for a system having responses to a plurality of variables, Center-of-gravity calculating means for calculating the center of gravity for each of the plurality of processing target clusters, distance between center of gravity calculating means for calculating the distance between the centers of gravity of the plurality of processing target clusters, and maintaining the distance between the centers of gravity of the plurality of processing target clusters. First arrangement means for arranging the respective processing target clusters so as to select any one of the samplings within the processing target clusters for each of the plurality of processing target clusters, and arranging the selected initial positions on a two-dimensional plane And an initial position setting unit that performs sampling in the processing target cluster for each of the plurality of processing target clusters. A shortest distance sampling extraction means for calculating a Euclidean distance between the two groups and extracting a sampling having the smallest Euclidean distance, and the shortest distance sampling in the processing target cluster for each of the plurality of processing target clusters on the two-dimensional plane. Second sampling means for positioning at a position corresponding to the Euclidean distance with the initial position as a reference, and moving sampling according to the Euclidean distance between the samplings existing on the boundary surface of each processing target cluster, Cluster combining means for combining processing target clusters; and notation means for notifying the variables and / or the responses of the sampling on the two-dimensional plane.

  In the multidimensional information processing device of the third invention, when there are a plurality of samplings composed of combinations of a plurality of variables, the attribute axes are set on the two-dimensional plane so that the axes corresponding to the variables do not overlap in the traveling direction. Corresponding to the plurality of sampling, setting means, shaping means for plotting the variable on the attribute axis, and shaping the sampling based on the plotted variable, centroid calculating means for calculating the centroid of the shape And a notation means for notifying the center of gravity of the shape on one two-dimensional plane.

  In the first, second, and third inventions, it is possible to display a list of relative relationships with variables and responses that constitute multidimensional information on a two-dimensional plane, and intuitively understand the relative relationships of multidimensional information. Can grasp.

  Hereinafter, the best mode for realizing a multidimensional information processing system of the present invention will be described based on an embodiment shown in the drawings.

  FIG. 1 is a system diagram illustrating the configuration of a multidimensional information processing system according to the first embodiment. Connected to the arithmetic processing device 1 are a display device 2 (corresponding to display means) for displaying the arithmetic results of the arithmetic processing device 1 and a keyboard 3 for inputting information to the arithmetic processing device 1. Information input is not limited to a keyboard, and data may be input from various devices such as a simulator. The arithmetic processing device 1 is provided with a storage device 1a for storing various data and calculation results, and an arithmetic device 1b for processing data stored in the storage device 1a.

  FIG. 2 is a flowchart showing the flow of the technical concept of the first embodiment. In the multidimensional information processing system of the first embodiment, in order to make it possible to grasp multidimensional information of the system intuitively, quantitatively, and efficiently, the multidimensional information obtained by combining information in a self-organized manner based on the Euclidean distance of each sampling. We propose a three-dimensional information processing system.

  In step 101, sampling is prepared. Sampling, when there is a system defined by a plurality of limiting elements, can define a relationship between a combination of the limiting elements and a response (for example, evaluation characteristics) as a set of combinations. At this time, the Euclidean distance between all the samplings is calculated in advance as the inter-sampling distance (inter-sampling distance calculating means). Details of the Euclidean distance will be described later.

  In step 102, one arbitrary sampling is selected as the first sampling, and the first sampling is arranged as an initial position on the two-dimensional plane (initial position setting means).

  In step 103, the sampling with the shortest distance between the first sampling and the sampling is selected as the second sampling, and the sampling is arranged at a position corresponding to the sampling distance with the initial position on the two-dimensional plane as a reference (second sampling arrangement means). .

  In step 104, a reference centroid that is a centroid of sampling already arranged on the two-dimensional plane is calculated. In the first embodiment, the center of gravity of the first sampling position and the second sampling position is calculated as the reference center of gravity (reference center of gravity calculating means). When a plurality of samplings are already arranged, the centroid calculated from the plurality of arranged samplings may be calculated as the reference centroid, and there is no particular limitation.

  In step 105, the sampling with the shortest distance between the second sampling and the sampling is selected as the third sampling, and the third sampling and the second sampling are performed based on the position of the second sampling and the position of the reference centroid on the two-dimensional plane. The third sampling is arranged at a position corresponding to the sampling distance between the third sampling and the sampling distance between the third sampling and the reference centroid (third sampling arrangement means).

  In step 106, it is determined whether or not the number of samplings has become zero. If there are unallocated samplings, the next sampling selected is the fourth sampling, and the newly selected sampling is the third sampling. Assuming that the sampling selected immediately before is regarded as the second sampling, Step 103, Step 104, and Step 105 are repeated and sequentially arranged on the two-dimensional plane (repetition means). When 0 is reached, the routine proceeds to step 107.

  In step 107, variables, characteristics, and the like constituting each sampling are described at each sampling position determined by the above processing.

  It is comprised from the process. Hereinafter, each component will be described while being applied to a specific design problem.

(Determination of optimal spring-S / ABS specifications for sedan vehicles in light bottoming)
Applying the above concept to the optimization process when determining the optimal spring-S / ABS specification for a sedan vehicle in light bottoming driving will be explained. Note that light bottoming means that the vehicle nose-dives during braking, and “optimum spring-S / ABS specification” is a combination of the spring constant of the coil spring of the suspension and the damping characteristics of the shock absorber. Represents a decision. As a response model, a sedan vehicle model with a suspension was constructed, and each design variable was set.

(Preparation for sampling)
FIG. 3 shows a sampling data set by a combination of evaluation characteristics and design parameters stored in the storage device 1a. Evaluation characteristics include vertical displacement of the center of gravity (Characteristic 1), front seat vertical acceleration (Characteristic 2), rear seat vertical acceleration (Characteristic 3), pitch angle (Characteristic 4), front wheel ground load (Characteristic 5), and rear wheel grounding. Load (characteristic 6). In addition, as the design parameters, the valve characteristic inclination expansion side, the valve characteristic inclination reduction side, the blow-by expansion side, the blow-by expansion side, the spring load, and the stabilizer roll rigidity are taken up as front wheels and rear wheels, respectively. Each design parameter is defined from the values shown in the characteristic diagram showing the characteristics of the suspension in FIG.

  FIG. 4 shows the suspension characteristics, and the horizontal axis represents the piston speed and the vertical axis represents the damping force. The design parameter “blow-by” represents the piston speed when the slope of this relationship changes (point B). The “valve characteristic gradient” represents the gradient of the area expressed by a linear function (point C). For convenience, the standard deviation of the vertical displacement of the center of gravity of the vehicle is set as the characteristic 1, the standard deviation of the vertical acceleration of the front seat is set as the characteristic 2, the standard deviation of the vertical acceleration of the rear seat is set as the characteristic 3, and the standard deviation of the vehicle pitch angle is set as the characteristic. 4, the standard deviation of the front wheel ground load is characteristic 5, and the standard deviation of the rear wheel ground load is characteristic 6. N pieces of data (sampling) including a combination of these evaluation characteristics 1 to 6 and 12 design parameters are prepared and stored in the storage device 1a.

  These data are configured to generate a design parameter using an orthogonal table or a random number, and to perform a structural analysis based on the generated design parameter. Specifically, a response model to be subjected to structural analysis is incorporated. This response model is equipped with a simulator capable of outputting evaluation characteristics based on input design variables. In addition, it may be the data collected by experiment etc. and is not specifically limited.

(Placement on a two-dimensional plane)
FIG. 5 and FIG. 6 are schematic explanatory diagrams showing a procedure for arranging on a two-dimensional plane. The procedure will be described in detail below.

  First, one arbitrary first sampling is selected (hereinafter point A). Next, the selected sampling is placed on a two-dimensional plane. In addition, as long as it is on a two-dimensional plane, it may be arranged at any position and may be set arbitrarily. Then, the Euclidean distance between the points (first sampling: data 1) arranged on the two-dimensional plane and other points (multiple samplings: data 2 to data n) is calculated.

本事案の場合、個体x_iを構成するp個の要素とは、12個の各設計変数及び6個の評価特性を構成するｎ個のデータセットのうち、適宜選択された値である。よって、距離の計算で取り上げる対象は、変数同士（設計変数同士）、あるいは、応答同士（評価特性同士）、応答と変数を会わせたもの、の何れでもよい。 Here, the distance calculation method is based on the similarity based on the distance in the Euclidean space. That is, if the value of the k-th element among the p elements constituting the individual x _i is x _i ^k , the Ward distance between the individuals x _{i and} x _j is expressed by Expression (3.4). Here, the element is a value included in the individual x _i .
(3.4)

In the case of this case, the p elements constituting the individual x _i are values appropriately selected from the t data sets constituting the twelve design variables and the six evaluation characteristics. Therefore, the object taken up in the calculation of the distance may be any of variables (design variables), responses (evaluation characteristics), or a combination of responses and variables.

  Next, the second sampling data (hereinafter referred to as point B), which is the shortest distance among the calculated distances between all samplings, is selected and calculated from the initial position placed in step 102 on the two-dimensional plane. They are arranged at positions separated by a distance corresponding to the shortest distance (see FIG. 5). The shortest distance means that the calculated value is the smallest value. At this time, the selected sampling may be anywhere on the circumference having the radius corresponding to the calculated shortest distance with the point selected first as the center.

  Next, the center of gravity of the points A and B is calculated, and this center of gravity is set as the reference center of gravity. Then, the distance of the response between point B and all other samplings is calculated, and the point closest to point B (point C) is selected. Here, the distance between the newly selected point and the reference centroid (reference centroid and point C, point B and point C) is also calculated and arranged at a position that also represents this relative distance (see FIG. 6). The above distance calculation and arrangement processing are repeatedly executed until sampling becomes zero. As described above, a diagram in which responses are displayed on a two-dimensional plane can be created. At this time, a circle with a radius that is half of the minimum value of the distance between two points is defined for each sampling, and by setting a color according to the value of the design variable and evaluation characteristics, even in the area where sampling does not exist, the color It is possible to display.

  In a multidimensional Euclidean space, regardless of the number of samplings, all samplings can be arranged while maintaining the Euclidean distance between samplings. However, since a person cannot recognize position information in a multidimensional space of four or more dimensions, it is desired to arrange all samplings while maintaining the Euclidean distance between the samplings in the two-dimensional space that is most easily recognized. However, if sampling having information of four or more dimensions is arranged on a two-dimensional plane, there is a problem that information loss due to dimensional reduction occurs, and it cannot be arranged with accuracy that can withstand practical use. Thus, in the first embodiment, as a method of arranging multidimensional information on a two-dimensional plane while minimizing the effect of information loss due to dimensional reduction, focusing on the center of gravity of already arranged sampling, It is the one that has been arranged.

  Next, variables, characteristics, and the like constituting each sampling are described at each sampling position determined by the above processing. FIG. 7 is a contour map in which the evaluation characteristics and design variables with the sampling are expressed in shades at the sampling positions determined by the above processing. FIG. 7A is a contour map in which values corresponding to the front wheel contact load (characteristic 5) are expressed in shades, and FIG. 7B is a contour map in which values corresponding to Fr spring loads are expressed in shades. FIG. 7C is a contour map in which values corresponding to the Fr blow-by compression side are expressed in shades. Each contour map position corresponds to the same sampling, and it can be seen that the values constituting each sampling are different.

  In the contour map of FIG. 7, spaces (hereinafter referred to as voids) are formed between the response points. There are two reasons why this void is formed: when the system cannot output a response to the void, or when there is no sampling.

  If the system cannot output a response to the void, it is synonymous with expressing the capacity limit of the target system. That is, it becomes possible to grasp the capacity of the system by the void, and reference information for creating a new system for obtaining the response of the void portion can be obtained from the two-dimensional plan view of the variable. Incidentally, since the existing self-organizing map and the like develop similar responses around, there is no concept of void.

  On the other hand, when there is no sampling, the response of the void portion and the variable to be realized can be predicted by approximating the existing response to a curved surface. It is also possible to check the response by generating a model in the part corresponding to the void with reference to the variables that make up the two points that sandwich the void. A distance model generation method is proposed as a specific model generation method in this case.

(Distance model generation method)
The distance model generation method is a method for newly generating a model similar to a design variable (hereinafter, a limiting element) that constitutes an existing response. Here, the Euclidean distance, which makes it easy to imagine the similarity between individuals and is easy to handle, is taken up. FIG. 8 is a schematic explanatory diagram showing the distance model generation process.

The Euclidean distance defines the distance d between individuals (x _i −x _j ), ^where x _i ^k is the value of the kth element among the p elements that make up the individual x _i To do. Here, the element is a value included in the individual x _i .
(4.1)

The model is generated using uniform random numbers. Therefore, a model generated by uniform random numbers is d _rand , a model expressed by a limiting element that constitutes two points sandwiching the void or one point adjacent to the void (hereinafter referred to as a principle model), x _c , and a threshold value If the model that is not satisfied is x _o , the newly generated model and these distances are expressed by equation (4.2).
(4.2)

Then, to apply the limitation rule not to adopt an extremely similar model principles model x _c. For example, when the Euclidean distance is 0.01 or less and you want to recognize that the two individuals are almost the same, the newly generated model x _rand uses the one that follows the restriction law of equation (4.3) for the principle model x _c To do. The new model adopted here adopts one model of the minimum distance that satisfies the equation (4.3). In addition, since the generation of the model can be greatly changed by changing the value of the restriction rule, the designer can decide according to the purpose. In addition, when there are several principle models, in order to prevent the generation of the same model, the equation (4.3) is calculated using the other principle models and the generated model, and is not adopted if it does not match.
(4.3)

Hereinafter, a model generation algorithm will be described based on the distance model generation process of FIG.
(i) Prepare a principle model.
(ii) A model is generated using random numbers, the distance is calculated according to equation (4.2), and a model satisfying equation (4.3) is selected. The distance between the model generated at this time and the principle model is stored.
(iii) Generate a model again using random numbers based on the principle model, and calculate the distance using equation (4.2). Replace the minimum distance, which is the restriction law of equation (4.3), with the distance of (ii), and select a model that satisfies this. Here, the distance between the selected model and the principle model is stored.
(iv) Thereafter, the above (i) to (iii) are repeated.

  FIG. 9 is a diagram showing the relationship between the contour map and the design variable pattern (corresponding to sampling pattern notation means). For example, on the contour map describing a certain characteristic, when the position α on the contour map is changed to the position γ via the position β as shown in FIG. 9A, the combination of design variables is as shown in FIG. As shown in (b), it can be understood that the design pattern has changed. In this way, by designating the pattern of the design variable together with the contour map on the two-dimensional plane, the influence of the variable shape on the response can be confirmed.

Hereinafter, the effects of the first embodiment will be listed below.
(1) For a system having responses to a plurality of variables, when there are a plurality of samplings composed of combinations of the variables and / or the responses of the system, the Euclidean distance between the samplings is calculated as the sampling distance (sampling An inter-distance calculation means), an arbitrary one of the samplings is selected as the first sampling, arranged as an initial position on a two-dimensional plane (initial position setting means), and the sampling with the shortest distance between the first sampling and the sampling Is selected as the second sampling, and is arranged at a position corresponding to the distance between the samplings with the initial position on the two-dimensional plane as a reference (second sampling arrangement means), and the sampling already arranged on the two-dimensional plane A reference centroid which is a centroid of the reference (reference centroid calculation means), The sampling having the shortest distance between two samplings and the sampling is selected as the third sampling, and the third sampling and the second sampling are performed on the basis of the position of the second sampling and the position of the reference centroid on the two-dimensional plane. The third sampling is arranged at a position corresponding to the sampling distance between the third sampling and the sampling distance between the third sampling and the reference centroid (third sampling arrangement means). After the fourth sampling, a newly selected sampling is arranged. The third sampling is considered, the sampling selected immediately before is considered as the second sampling, and the second sampling arrangement means, the reference centroid calculation means, and the third sampling arrangement means are executed (repetition means). Then, a contour map (corresponding to the notation means) that represents the design variables and / or evaluation characteristics of sampling on a two-dimensional plane is provided.

  Therefore, it is possible to display a list of multidimensional information on a two-dimensional plane by using the contour map, so that the tendency of the system can be recognized intuitively. That is, information in a multidimensional space can be arranged on a two-dimensional plane with minimal loss.

  Also, by creating a contour map according to the distance, it is possible to intuitively understand how much each sampling differs.

  In addition, there may be a region (void) where sampling does not exist. At this time, it is possible to generate sampling efficiently by generating a distance model based on sampling values around this region and performing curved surface interpolation.

  If sampling cannot be output to the void, the capacity of the target system can be grasped.

  (2) A variable for each sampling and / or a combination with the response is shown. (Sampling pattern notation means).

  Therefore, by describing the pattern of the design variable on the two-dimensional plane together with the contour map, the influence of the shape of the variable on the response (change tendency of the design pattern, etc.) can be confirmed. In the first embodiment, the change of the design variable is represented. However, the change of the evaluation characteristic (response) may be represented together with the design variable, or both the design variable and the evaluation characteristic may be represented.

  Further, by introducing a threshold value into the contour map and displaying only an effective area, it is possible to display only an area realizing a certain response. At this time, by displaying the design pattern of the effective region, it becomes possible to grasp the design pattern that realizes a certain response, and the influence of the shape of the variable on the response can be confirmed.

  In addition, by confirming the design pattern around the void, reference information for creating a new system for obtaining the void response can be obtained. In other words, by proposing a system that can set a value that cannot be obtained in the surrounding design pattern, it is estimated that the response to the void can be output, and it becomes possible to examine a new system that realizes this design pattern. .

  (3) The variable and / or the response value is displayed in color. Specifically, the contour map displayed design variables and / or evaluation characteristic values in shades. Therefore, it is possible to display a three-dimensional concept on a two-dimensional plane, and it is possible to recognize the tendency of the system more intuitively. In addition, it is not limited to shading, and the maximum value to the minimum value may be defined and displayed with a color tone such as RGB, or may be displayed with contour lines.

(Implementation using a medium on which a multidimensional information processing program is recorded)
In the above embodiment, the multidimensional information processing system has been described. However, all the above-described actions may be provided in a state described in a program or the like that can be read by the arithmetic device. Specifically, for a system having responses to a plurality of variables, when there are a plurality of samplings composed of combinations of the variables and / or the responses of the system, the Euclidean distance between the samplings is calculated as the inter-sampling distance. An inter-sampling distance calculation command unit that outputs a command, an initial position setting command unit that outputs a command to select any one of the samplings as a first sampling and place it as an initial position on a two-dimensional plane; A second sampling arrangement command that selects one sampling and a sampling with the shortest sampling distance as the second sampling, and outputs a command to arrange at a position corresponding to the sampling distance on the basis of the initial position on the two-dimensional plane. And sampling already placed on the two-dimensional plane A reference center of gravity calculation command unit that outputs a command for calculating a reference center of gravity, which is a center of gravity, and a sampling having the shortest sampling distance between the second sampling and the second sampling are selected as the third sampling, and the second sampling on the two-dimensional plane is selected. The third sampling is arranged at a position corresponding to a sampling distance between the third sampling and the second sampling and a sampling distance between the third sampling and the reference centroid with reference to the position and the position of the reference centroid. A third sampling arrangement command unit that outputs a command to perform, and after the fourth sampling, the newly selected sampling is regarded as the third sampling, the previous sampling selected as the second sampling, and the second sampling Sampling arrangement command unit, reference centroid calculation command unit and first By repeating command section for outputting a command to implement a sampling arrangement command unit, a medium multidimensional information processing program is recorded, characterized in that it comprises a, it is possible to improve the distribution of.

  In the medium on which the multidimensional information processing program is recorded, the reference centroid calculation command unit calculates a centroid between the first sampling position and the second sampling position on the two-dimensional plane as a reference centroid. The repetition command unit regards the newly selected sampling as the third sampling, the previous sampling selected as the second sampling, and the second sampling after the fourth sampling. The selected sampling may be regarded as the first sampling, and a command unit that performs the second sampling arrangement unit, the reference centroid calculation unit, and the third sampling arrangement unit may be used.

  Further, in the medium on which the multi-dimensional information processing program is recorded, a sampling pattern notation command unit that outputs a command that indicates the combination of the variable and / or the response for each sampling may be provided.

  In the medium on which the multidimensional information processing program is recorded, the notation command unit may be a command unit that outputs a command to display the variable and / or the response value in color tone.

(Implementation as a multidimensional information display device)
In the first embodiment, the multi-dimensional information processing system has been described. However, when the multi-dimensional information processing is executed, the above-described operation is a system having responses to a plurality of variables as display means for the designer. When there is a plurality of samplings composed of combinations of the variables and / or the responses of the system, the inter-sampling distance is calculated to output a command to calculate the Euclidean distance between the samplings as the inter-sampling distance, and the sampling Any one of the first sampling is selected as the first sampling, the initial position setting means arranged as the initial position on the two-dimensional plane, and the sampling with the shortest sampling distance is selected as the second sampling, Sampling based on the initial position on a two-dimensional plane Second sampling arrangement means arranged at a position corresponding to the distance; reference centroid calculation means for outputting a reference centroid that is a centroid of sampling already arranged on the two-dimensional plane; and the second sampling; Sampling with the shortest sampling distance is selected as the third sampling, and sampling of the third sampling and the second sampling is performed with reference to the position of the second sampling and the position of the reference centroid on the two-dimensional plane. A third sampling arrangement means for arranging the third sampling at a position corresponding to a distance and a sampling distance between the third sampling and the reference centroid; and after the fourth sampling, a newly selected sampling is selected from the third sampling. The second sampling is the sampling previously selected Assuming that the second sampling arrangement means, the reference centroid calculation means, and the third sampling arrangement means are implemented, the repetition means for arranging the plurality of samplings, and the repetition means arranged on the two-dimensional plane. By providing a multi-dimensional information display device characterized by including a display means for displaying the result, the design easiness of the designer can be further improved. As a display means, it may divide and display on a monitor screen etc., and may display on a separate monitor screen. Thereby, the tendency of the system can be easily grasped visually.

  In the multidimensional information display device, the reference centroid calculating unit is a unit that calculates a centroid between the position of the first sampling and the position of the second sampling on the two-dimensional plane as a reference centroid. The means regards the newly selected sampling as the third sampling after the fourth sampling, regards the sampling selected immediately before as the second sampling, and designates the sampling selected two times before as the first sampling. In view of this, the second sampling arrangement means, the reference centroid calculation means, and the third sampling arrangement means may be implemented.

  In the multidimensional information display device, sampling pattern display means for displaying a combination of the variable and / or the response for each sampling may be provided.

  In the multidimensional information display device, the display unit may display the variable and / or the response value in color.

  Next, Example 2 will be described. Even in the second embodiment, description will be made based on a specific design object, but since this design object is the same as that in the first embodiment, only different points will be described.

  FIG. 10 is a flowchart showing the flow of the technical concept of the second embodiment. In the multidimensional information processing system of the second embodiment, in order to make it possible to grasp multidimensional information of the system intuitively, quantitatively, and efficiently, the multidimensional information is combined in a self-organized manner based on the Euclidean distance of each sampling. We propose a three-dimensional information processing system.

  In step 201, sampling is prepared. Since this is basically the same as step 101 in the first embodiment, a description thereof will be omitted.

  In step 202, sampling is clustered hierarchically. Hierarchical clustering is a method in which clusters are sequentially generated based on the distance between two points, and finally repeated until one cluster is obtained, and details will be described later.

  In step 203, an arbitrary hierarchy is selected and the cluster is divided. Step 202 and step 203 correspond to a dividing unit. This divided cluster is defined as a cluster to be processed.

  In step 204, each processing target cluster is maintained such that one sampling in the cluster closest to the centroid of each cluster maintains the distance between the centroids of each processing target cluster (the distance between selected responses of two different clusters). Are arranged on a two-dimensional plane (first arrangement means and initial position setting means).

  In step 205, using the result calculated in step 202, the Euclidean distance between the samplings in the processing target cluster is calculated for each divided processing target cluster, and the sampling having the smallest Euclidean distance is extracted (shortest distance sampling extraction). means). Then, for each of the plurality of processing target clusters, the shortest distance sampling in the processing target cluster is arranged at a position corresponding to the Euclidean distance with the initial position on the two-dimensional plane as a reference (second arrangement means).

  In step 206, step 205 is repeated until all sampling arrangements in the processing target cluster are completed.

  In step 207, in order to combine the processing target clusters divided in step 203, a cluster pair having a short distance from the tree diagram is selected.

  In step 208, in the selected cluster pair, the distance between the sampling existing on the boundary surface of the cluster arranged on the two-dimensional plane and the sampling existing on the boundary surface of the different cluster is extracted from the result calculated in step 202. The closest samplings are moved so that they are lined up close to each other while maintaining the distance between the centers of gravity between the two points.

  In step 209, multiple response points are also moved by the movement of step 208.

  In Step 210, Steps 207 to 209 are repeated, and when the movement is completed, two clusters are defined as one cluster. Steps 207 to 210 correspond to cluster combining means.

  In step 211, variables, characteristics, etc. constituting each sampling are described at the positions of each sampling determined by the above processing (notation means).

  Hereinafter, each component will be described while being applied to a specific design problem.

(Determination of optimal spring-S / ABS specifications for sedan vehicles in light bottoming)
Applying the above concept to the optimization process when determining the optimal spring-S / ABS specification for a sedan vehicle in light bottoming driving will be explained. Since the sampling is the same as in the first embodiment, the description thereof is omitted.

(Placement on a two-dimensional plane)
The arrangement on the two-dimensional plane in the second embodiment can be roughly divided into descriptions of hierarchical clustering, cluster division and combination, variables, and / or characteristics. Each will be described in detail below.

(Hierarchical clustering)
11 and 12 are schematic explanatory diagrams showing the hierarchical clustering process. Here, the background to which hierarchical clustering is applied will be described. First, define the word “system”. A system is a processing system or order that exists between input results that produce a specific result when there is a specific input. A specific event (phenomenon) is realized by defining a specific system to a certain value (corresponding to a system defined by a plurality of limiting elements). And the unique system works in a limited number, range, and nature, not processing everything or giving order to everything. Therefore, even if the types of events are the same, if there are various types with different limitations, there is a system corresponding to each. Furthermore, there are host systems that handle these uniformly according to the type of event.

  For example, in an automobile suspension, the abstract system is a suspension, the individual system is a multi-link or torsion beam, the concrete system is a specific multi-link or torsion beam determined by the specific geometry value or bush stiffness value taken by the individual system, etc. It is.

  However, this classification is not intended to specifically understand systems in the same hierarchy or upper and lower systems. As the analysis (understanding) of the events shown by the lowest-level system progresses (matures), in order to make new efforts and discoveries, it is necessary to accurately understand the relationships between systems and the commonality that defines the overall system. Must be used. When a complex event (phenomenon) is considered to be realized as a result of a combination of several events (phenomena), the characteristic of a complex event (phenomenon) is the characteristic of a certain event (phenomenon) It is thought that the characteristics of the combination have an influence.

  In view of the above idea, in the second embodiment, in order to understand complicated phenomena, hierarchical clustering is used to classify complex phenomena while systematizing them. Clustering is an object of gathering groups that are similar to each other to create a community (hereinafter referred to as a cluster) in order to efficiently organize a meaningful system from a group of people with different characteristics. It is a general term for the method of classifying. Among these, hierarchical clustering is a method of generating hierarchies so that groups are nested. In the second embodiment, “similar” is clustered on the basis of “distance between samplings”.

  Hierarchical clustering was adopted in the second embodiment because, as described above, the system originally targeted by us is based on hierarchical classification (that is, the most understandable system) This is because it is not known in advance how many hierarchies and clusters exist in a trend system for understanding the relationship of hierarchic systems.

  For example, when non-hierarchical clustering is performed, a threshold value or the like is set in advance for the degree of similarity, and tasks within this threshold value are clustered. This threshold value leads to the introduction of an existing concept. There is a fear. This is because when an existing concept is introduced, only a result confined to the existing concept is obtained, and the system cannot be classified correctly.

  Further, when complex phenomena are classified hierarchically, a cluster in a certain hierarchy can be handled as a unit that is organized according to the classification criteria when expressing the system. Therefore, once clustering is performed hierarchically, a unit having a unit is formed according to the classification criteria, and the unit is arranged on the two-dimensional plane, whereby an arrangement having a certain tendency can be obtained. In addition, it is possible to systematize more complex phenomena in a form that is easier to understand by laying out based on the loose rules of what kind of tendency they have as a whole rather than focusing on individual parameters. Conceivable.

In hierarchical clustering, clusters are generated by joining individuals one by one based on similarity or dissimilarity, and gradually increasing from a small cluster to a larger cluster. Therefore, the cluster generation procedure is divided into two stages: definition of similarity (dissimilarity) and cluster generation. Here, the set of individuals x _i (1 ≦ i ≦ n), the set of all individuals X = {x ₁ , x ₂ , x ₃ ,..., X _n }, the similarity between individuals x _i and x _j Degrees d (x _i , x _j ) [1 ≦ x _i , x _j ≦ n, x _i ≠ x _j , x _i , x _j ∈X] are defined. Further, when an individual x _i is a cluster G _i , a cluster g including all the clusters is g = {G ₁ , G ₂ ,..., G _n }. At this time, the hierarchical clustering algorithm (Agglomerative Hierarchal Clustering: hereinafter referred to as AHC) is as follows.

(I) Define the following for the initial n clusters (individuals).
(3.2)

ここでG_qとG_rをgから取り除き、G'=G_q∪G_rをgに追加する。この際、クラスター数を一つ減らす。 (II) The cluster pair having the maximum similarity (or the minimum similarity) is combined.
(3.3)

Here, G _q and G _r are removed from g, and G ′ = G _q ∪G _r is added to g. At this time, the number of clusters is reduced by one.

(III) Recalculate the similarity d (G ′, G _i ) between clusters for all G _i ∈g and G _i ≠ G ′.

  (IV) Thereafter, (II) and (III) are repeated until the number of clusters becomes 1.

  Various similarities (dissimilarities) taken up in (II) of the AHC have been proposed. Therefore, the center of gravity method (Centroid Method) and the Ward method (Ward's Method) are taken up.

[Centroid Method]
This method is based on the similarity based on the distance in the Euclidean space. That is, if the value of the k-th element among the p elements constituting the individual x _i is x _i ^k , the distance between the individuals x _{i and} x _j is expressed by equation (A.16). Here, the element is a value included in the individual x _i .
(A.16)

When the center of gravity M (G) = (M1 (G),..., Mp (G)) with respect to the cluster G is expressed by the equation (A.17).
(A.17)

Therefore, the calculation of similarity follows equation (A.18).
(A.18)

（A.19）

Here, considering a two-dimensional plane passing through three points M (Gq), M (Gr), and M (Gi) in the Euclidean space where the individual exists, a coordinate system shown in FIG. Each coordinate in the coordinate system shown in FIG. (A) is M (Gq) = (0, 0), M (Gr) = (z, 0), and M (Gi) = (x, y). When G '= Gq∪Gr, M (G') also exists on this plane. If α = | Gq | / (| Gq | + | Gr |), the coordinates of M (G ') are M (G ′) = ((1−α) z, 0). Therefore, if the distance between M (G ′) and M (Gi) on this plane is δ, the recalculation of the similarity d (G ′, Gi) is expressed by the equation (A.19).
(A)

(A.19)

(Ward's Method)
This method is based on the similarity based on the Euclid distance. That is, assuming that the value of the k-th element among the p elements constituting the individual x _i is x _i ^k , the Ward distance between the individuals x _{i and} x _j is expressed by Expression (A.20). Here, the element is a value included in the individual x _i .
(A.20)

At this time, the center of gravity M (G) = (M1 (G),..., Mp (G)) with respect to the cluster G is expressed by the equation (A.21).
(A.21)

Here, the sum of squares E (G) of the difference in the distance between the center of gravity in cluster G and each individual is defined as in equation (A.22).
(A.22)

Therefore, the difference in distance between two different clusters G _i and G _j can be expressed as shown in equation (A.23).
(A.23)

From this, G _q and G _r that minimize ΔE are selected, as represented by the equation (A.24), for the coupling rule of the cluster of AHC (II).
(A.24)

従って、ΔE(Gi,Gj)は式（A.26）のように展開できる。
（A.26）

Next, a threshold (A.25) is defined for an arbitrary set part G⊆X.
(A.25)

Therefore, ΔE (Gi, Gj) can be expanded as shown in equation (A.26).
(A.26)

従って、式の右辺の||M(Gi∪Gj)||2は、α＝|Gi|/(|Gi|＋|Gj|)とおくと式（A.28）のように表される。
（A.28）

Here, M (Gi∪Gj) is expressed by equation (A.27).
(A.27)

Therefore, || M (Gi∪Gj) || 2 on the right side of the equation is expressed as equation (A.28) when α = | Gi | / (| Gi | + | Gj |).
(A.28)

From the above, equation (A.26) is expressed as equation (A.29).
(A.29)

Here, when G ′ = Gq∪Gr, if the recalculation formula of the centroid method is used for ΔE (G ′, Gi), it can be expressed as Eq. (A.30).
(A.30)

従って、式（A.31）を式（A.30）に代入するとΔE(G',Gi)は式（A.32）のようになる。ここで、|G'|＝|Gq|＋|Gr|である。
（A.32）

したがって、G'＝Gq∪Grのときd（Gi,Gj）＝ΔE(Gi,Gj)と定義すると、AHC(III)の類似度d(G',Gi)の再計算は、結合する前のd(Gq,Gi)，d(Gr,Gi)を用いて式（A.33）で表される。
（A.33）

Here, a relationship such as Equation (A.29) to Equation (A.31) is expressed.
(A.31)

Therefore, if equation (A.31) is substituted into equation (A.30), ΔE (G ′, Gi) becomes equation (A.32). Here, | G ′ | = | Gq | + | Gr |.
(A.32)

Therefore, if we define d (Gi, Gj) = ΔE (Gi, Gj) when G ′ = Gq∪Gr, the recalculation of the similarity d (G ′, Gi) of AHC (III) It is expressed by equation (A.33) using d (Gq, Gi) and d (Gr, Gi).
(A.33)

  As described above, the recalculation formula for the similarity of AHC (III) is recalculated using only the similarity between clusters without referring to the similarity between individuals. Therefore, it can be said that it is efficient to store only the similarity between clusters according to the recalculation formula, so that the clusters are combined and it is not necessary to refer to many similarities.

FIG. 11 shows a cluster generation method based on the above algorithm, and FIG. 12 shows an example of hierarchical clustering. Here, the cluster generation method is summarized as follows based on FIG.
(A) Sampling is clustered to generate clusters p, qr. In FIG. 11, it corresponds to a small circle.
(B) Calculate the center of gravity of each cluster.
(C) Combine clusters with small similarity (close distance). In FIG. 11, cluster p and cluster q are combined to generate a new cluster t.
(D) Calculate the center of gravity of the combined cluster t.
(E) Combine clusters with small similarity (close distance).
(F) Repeat (C) to (E) until there is one cluster.
In the step (A), the point information before clustering may be used instead of the cluster, and there is no particular limitation.

[Split and join clusters]
Next, the division and combination of clusters shown in step 203 to step 210 will be described.

  FIG. 12 is a tree diagram showing clusters formed by hierarchical clustering. This tree diagram represents the Euclidean distance on the vertical axis. First, an arbitrary hierarchy is selected and the cluster is divided. In FIG. 12, a cluster surrounded by a dotted line is represented. Each cluster is numbered as cluster 1 to cluster 4.

  Next, one sampling in the cluster closest to the centroid of each cluster is placed on a two-dimensional plane so as to maintain the distance between each cluster centroid (the distance between selected responses of two different clusters). FIG. 13 is a diagram illustrating a state in which each cluster is located on a two-dimensional plane so as to maintain the distance between the centers of gravity. In FIG. 13, the center of gravity 1 of the cluster 1 and the center of gravity 2 of the cluster 2 are arranged, and for example, the distance between the centers of gravity is 0.3.

  At this time, the position of the sampling closest to the center of gravity (response close to the center of gravity 1) arranged on the plane first may be arbitrary. A two-dimensional plane has no concept of vertical and horizontal axes and represents only the distance between clusters. Therefore, the second and subsequent samplings arranged on the plane are arranged at arbitrary positions in a circular arc centered on the sampling before the reference or the center of gravity of the cluster. Note that the area on the two-dimensional plane of all samplings is kept constant. In the second embodiment, sampling is represented as a circle having the same radius.

  Next, when the placement of the centroid points is completed, using the distance information calculated by hierarchical clustering, sampling in the same cluster (similar to the distance) similar to each sampling placed on the two-dimensional plane, Arrange at any position separated by the distance between the center of gravity. FIG. 14 is a diagram showing a concept of work for arranging sampling in a cluster around sampling corresponding to the center of gravity. This operation is repeated until all the sampling arrangements in the divided clusters are completed.

  Next, in order to join the divided clusters, a cluster pair having a short distance is selected from the dendrogram. In Example 2, since cluster 1 and cluster 2 are adjacent as shown in FIG. 12, for example, these are selected as a cluster pair. Then, in the selected cluster pair, the result of calculating the distance between the sampling existing on the boundary surface of the clusters arranged on the two-dimensional plane and the sampling existing on the boundary surface of different clusters by hierarchical clustering (ie, between samplings) And move the nearest samplings so that they are lined up close together while maintaining the distance between the centers of gravity between the two points. FIG. 15 is a schematic explanatory diagram showing how the closest response (sampling) is moved.

  At this time, each sampling is arranged on the two-dimensional plane so that the distances between the samplings coincide with each other. Disagreement. Therefore, as the sampling is moved, a number of samplings are also moved so that the mutual relationships of the distances coincide with each other. FIG. 16 is a schematic explanatory diagram showing how another sampling is moved.

  This operation is repeated until all sampling moves are completed, and when the move is completed, two clusters are defined as one cluster. Repeat for other clusters until you finally get one cluster.

  Through the above operation, each sampling is arranged on a two-dimensional plane, and a characteristic contour map or a parameter contour map is created by expressing each design variable and / or each evaluation characteristic on the arranged two-dimensional plane. Note that the specific notation method is the same as that in the first embodiment, and a description thereof will be omitted.

  Note that, when the arrangement is completed on the two-dimensional plane, the cluster boundary of the selected hierarchy may be displayed. FIG. 17 is a diagram illustrating a change in the boundary line on the two-dimensional plane when different layers are selected. In addition, as a contour map, what overlapped the contour map of all the evaluation characteristics was used, However, It does not specifically limit.

  For example, when a certain hierarchy A is specified, the boundaries of clusters corresponding to that hierarchy are displayed, and it can be understood that the hierarchy is composed of relatively few clusters. Next, when the lower hierarchy B is specified, the boundaries of the clusters corresponding to that hierarchy are displayed, and it can be understood that the cluster is composed of many clusters. Once placed on a two-dimensional plane by the above processing, each sampling is placed on the basis of distance, so a new boundary line appears as it goes to the lower layer, and how the boundary line appears. I can understand. Thus, it is possible to recognize the change of the boundary by displaying the boundary of the cluster when the hierarchy is moved up and down, and it is possible to grasp the distribution tendency of the response and the variable.

Hereinafter, effects of the second embodiment will be listed.
(4) For a system having responses to a plurality of variables, when there are a plurality of processing target clusters having a plurality of samplings composed of combinations of the variables and / or the responses of the system, the center of gravity for each of the plurality of processing target clusters Is calculated (centroid calculation means), the distance between the centers of gravity of the plurality of processing target clusters is calculated (inter-centroid distance calculation means), and each processing target cluster is arranged so as to maintain the distance between the centroids of the plurality of processing target clusters. (First arrangement means). Next, an arbitrary one is selected from the samplings within the processing target cluster for each of the plurality of processing target clusters, and arranged as an initial position on the two-dimensional plane (initial position setting means). Next, the Euclidean distance between the samplings in the processing target cluster is calculated for each of the plurality of processing target clusters, the sampling having the shortest Euclidean distance is extracted (shortest distance sampling extracting means), and the processing target is processed for each of the plurality of processing target clusters. The shortest distance sampling in the cluster is arranged at a position corresponding to the Euclidean distance with the initial position on the two-dimensional plane as a reference (second arrangement means). Sampling is moved according to the Euclidean distance between the samplings existing on the boundary surface of each processing target cluster, and a plurality of processing target clusters are combined (cluster combining means). Then, a contour map is created by representing sampling variables and / or responses on a two-dimensional plane (corresponding to a notation means).

  Therefore, it becomes possible to arrange multidimensional information on a two-dimensional plane, and it is possible to obtain the same operational effects as in the first embodiment. Further, by combining the processing target clusters, the entire system can be grasped intuitively.

  A cluster is formed hierarchically using a hierarchical clustering method, and a plurality of clusters are formed by designating an arbitrary hierarchy of the formed hierarchy. Therefore, it becomes possible to use the connection information between clusters obtained as a result of hierarchical clustering, and it is possible to efficiently arrange response points (sampling) on the two-dimensional plane.

  Further, for example, the configuration may be such that the boundaries of each cluster can be displayed on the two-dimensional plane when the arrangement on the two-dimensional plane is completed. For example, when a certain hierarchy is specified, the boundary of the cluster corresponding to the hierarchy is displayed, and when the lower hierarchy is specified, the boundary of the cluster corresponding to the hierarchy is displayed. Thus, it is possible to recognize the change of the boundary by displaying the boundary of the cluster when the hierarchy is moved up and down, and it is possible to grasp the distribution tendency of the response and the variable.

(Implementation using a medium on which a multidimensional information processing program is recorded)
In the second embodiment, the multi-dimensional information processing system has been described. However, all of the above-described actions may be provided in a state described in a program or the like that can be read by the arithmetic device. Specifically, for a system having responses to a plurality of variables, when there are a plurality of processing target clusters having a plurality of samplings composed of combinations of the variables and / or the responses of the system, for each of the plurality of processing target clusters A center-of-gravity calculation command unit that outputs a command to calculate the center of gravity of the plurality of clusters, a distance calculation command unit between center of gravity that outputs a command to calculate the distance between the centers of gravity of the plurality of processing target clusters, and the center of gravity of the plurality of processing target clusters A placement command unit that outputs a command to place each processing target cluster so as to maintain a distance; and an arbitrary one from the sampling in the processing target cluster for each of the plurality of processing target clusters; A first placement command unit arranged as an initial position on the processing target class for each of the plurality of processing target clusters; An Euclidean distance between the samplings in the sampler, an extraction command unit that outputs a command to extract a sampling with the smallest Euclidean distance, and the shortest distance sampling in the processing target cluster for each of the plurality of processing target clusters, A second placement command unit that outputs a command to place at a position corresponding to the Euclidean distance with the initial position on the two-dimensional plane as a reference, and a Euclidean distance between samplings existing on a boundary surface of each processing target cluster And a cluster combination command unit that outputs a command to combine the plurality of clusters to be processed, and a command that outputs the command indicating the variables and / or the response of the sampling on the two-dimensional plane. A multi-dimensional information processing program characterized by comprising a command section The can be improved distribution of by the media.

  Further, in a medium on which a multidimensional information processing program is recorded, a system having responses to a plurality of variables is divided into a plurality based on the Euclidean distance between samplings composed of combinations of the variables and / or the responses of the system. A cluster formation command unit that outputs a command to form a cluster may be provided, and the plurality of processing target clusters may be clusters formed by the cluster formation command unit.

  Further, in the medium on which the multidimensional information processing program is recorded, the cluster formation command unit forms a cluster hierarchically using a hierarchical clustering method, and specifies a plurality of arbitrary layers of the formed hierarchy. It is good also as a command part which forms a cluster.

  Further, in the medium on which the multi-dimensional information processing program is recorded, a sampling pattern notation command unit that outputs a command that indicates the combination of the variable and / or the response for each sampling may be provided.

  In the medium on which the multidimensional information processing program is recorded, the notation command unit may be a command unit that outputs a command to display the variable and / or the response value in color tone.

(Implementation as a multidimensional information display device)
In the second embodiment, the multi-dimensional information processing system has been described. However, the above-described operation is a system having responses to a plurality of variables as display means for the designer when the multi-dimensional information processing is executed. When there are a plurality of processing target clusters having a plurality of samplings composed of combinations of the variables and / or the responses of the system, a center of gravity is calculated for each of the plurality of processing target clusters, and Calculating a distance between centroids, arranging each of the processing target clusters so as to maintain the distance between the centroids of the plurality of processing target clusters, and arbitrarily sampling from the sampling in the processing target cluster for each of the plurality of processing target clusters Select one and place it as an initial position on the two-dimensional plane, for each of the plurality of processing target clusters The Euclidean distance between the samplings in the processing target cluster is calculated, the sampling having the smallest Euclidean distance is extracted, and the shortest distance sampling in the processing target cluster is calculated on the two-dimensional plane for each of the plurality of processing target clusters. Is arranged at a position corresponding to the Euclidean distance with reference to the initial position, and the sampling is moved according to the Euclidean distance between the samplings existing on the boundary surface of each processing target cluster, and the plurality of processing target clusters are combined. There is provided a multi-dimensional information display device comprising: an arrangement state display means for displaying the result obtained; and a display means for displaying the sampling variable and / or the response on the two-dimensional plane. It is good as well. Thereby, the user can grasp | ascertain the tendency of a system easily. As a display means, it may divide and display on a monitor screen etc., and may display on a separate monitor screen. Thereby, the tendency of the system can be easily grasped visually.

  Further, in the multidimensional information display device, the plurality of processing target clusters may have a system having responses to a plurality of variables, based on a Euclidean distance between samplings composed of combinations of the variables and / or the responses of the system. A plurality of clusters formed by division may be used.

  Further, in the multidimensional information display device, the plurality of processing target clusters may have a system having responses to a plurality of variables, based on a Euclidean distance between samplings composed of combinations of the variables and / or the responses of the system. A cluster may be formed hierarchically using a hierarchical clustering technique, and a plurality of clusters may be formed by designating an arbitrary hierarchy of the formed hierarchy.

  Moreover, you may provide the sampling pattern display means which displays the combination with the said variable and / or the said response for every said sampling as said multidimensional information display apparatus.

  As the multidimensional information display device, the display means may display the variable and / or the response value in color.

  Next, Example 3 will be described. Even in the third embodiment, description will be made based on a specific design object. Since this design object is the same as that in the first embodiment, only different points will be described.

  FIG. 18 is a flowchart showing the flow of the technical concept of the third embodiment. In the multidimensional information processing system according to the third embodiment, in order to make it possible to grasp the multidimensional information of the system intuitively, quantitatively, and efficiently, each sampling is shaped and self-organized based on the center of gravity position of this shape. We propose a multi-dimensional information processing system that combines information.

  In step 301, sampling is prepared. Since this is basically the same as step 101 in the first embodiment, a description thereof will be omitted.

  In step 302, an attribute axis indicating the attribute of the design variable or evaluation characteristic that constitutes sampling is set, and the value of each design variable or evaluation characteristic is plotted on each attribute axis to shape the sampling.

  In step 303, the centroid of the shaped sampling is calculated.

  In step 304, variables, characteristics, and the like constituting each sampling are described in the respective sampling positions determined by the above processing (the center of gravity of each sampling).

Hereinafter, each component will be described while being applied to a specific design problem.
(Determination of optimal spring-S / ABS specifications for sedan vehicles in light bottoming)
Applying the above concept to the optimization process when determining the optimal spring-S / ABS specification for a sedan vehicle in light bottoming driving will be explained. Since the sampling is the same as in the first embodiment, the description thereof is omitted.

(Placement on a two-dimensional plane)
In the arrangement on the two-dimensional plane in the third embodiment, it can be roughly divided into a part for setting and shaping an attribute axis, a part for describing variables and / or characteristics, and the like. Each will be described in detail below.

[Set and shape attribute axis]
FIG. 19 is a schematic explanatory diagram showing attribute axes and shaping. In Example 3, six variables were selected as design variables, and axes extending radially from the center were set as attribute axes corresponding to the variables. At this time, the axes corresponding to the variables are set on the two-dimensional plane so as not to overlap in the traveling direction. This is because, by setting in this way, each attribute axis does not have an intersection in the traveling direction, and the combination of variables can be reliably expressed by the shape. Next, plot the value of the variable on the attribute axis to shape the sampling.

  FIG. 20 is a conceptual diagram illustrating a state in which the centroid is calculated for each sampling and the centroids are displayed in an overlapping manner. For example, the centroids corresponding to data 1 to data 3 in the database shown in FIG. 3 are calculated and plotted on a two-dimensional plane. This operation is performed for all the samplings, and they are displayed in a superimposed manner.

  The position of each center of gravity represents the relative relationship between design variables constituting each sampling. In other words, it can be said that the relative relationship of design variables represents the characteristics of sampling. From this, it is possible to grasp how the characteristics of each sampling are distributed when the centroids of each sampling are displayed in an overlapping manner.

  In other words, the relative relationship between a plurality of pieces of multidimensional information cannot normally be recognized by humans, but by displaying a list on a two-dimensional plane as described above, it is possible to intuitively recognize system trends. . Therefore, when there are multiple combinations of design variables and evaluation characteristics, it is possible to identify at a glance data that shows similar or dissimilar trends, and design the desired trend. A combination of parameters can be easily extracted.

  FIG. 21 is a diagram showing an example in which sampling evaluation characteristics or design variables are represented by bar graphs at each center of gravity. In this way, by grasping the characteristics of each sampling relatively on the two-dimensional plane and noting the design parameters and evaluation characteristics of each sampling at that position, the relationship between the relative relationship and each value can be grasped simultaneously. can do.

  Next, a fourth embodiment that is a modification of the third embodiment will be described. In the fourth embodiment, an example in which the level of the design variable and the value of the evaluation characteristic is displayed in color at the center of gravity position is shown. FIG. 22 is a diagram showing an example in which all the design variables shown in FIG. 3 are set as attribute axes. A shape formed by a solid line is represented by a design variable of data 1, and the evaluation characteristic of data 1 is indicated by a color at the position of the center of gravity. For example, in the case of FIG. 22, it is displayed in red. Similarly, the shape formed by the one-dot chain line is displayed by the design variable of data 2, and the evaluation characteristic of data 2 is shown in green at this barycentric position. Also, the shape formed by the dotted line is displayed by the design variable of data 3, and the evaluation characteristic of data 3 is shown in blue at the center of gravity.

  FIG. 23 is a diagram showing a characteristic contour map and a parameter contour map in which each evaluation characteristic and design variable are written at the center of gravity as described above for each sampling. FIG. 24 is a diagram showing an integrated characteristic contour map obtained by superimposing characteristic contour maps that describe each evaluation characteristic. Hereinafter, the contour map will be described in detail.

(Advantages of introducing contour maps)
Here, the superiority of the introduction of the contour map will be described in detail in comparison with various techniques of optimization methods that have been proposed in the past. Conventionally, Document 1 (Transaction of JSCES, Paper No. 20000019, Japan Society for Computing Technology (issued on May 24, 2000)) is disclosed as a technique using a response phase model as an optimization method. In this system, structural analysis is performed based on design parameters created using an orthogonal table or random numbers, and the estimation formula is calculated by least square approximation for the number of characteristics to be evaluated from the relationship between the design parameters and the obtained response model. create. Next, design constraint conditions are set, and a design parameter that maximizes or minimizes all estimation formulas created under the constraint conditions is obtained. The design parameter obtained here is the optimum value to be obtained.

In this way, the relationship between the design parameter and the response model is estimated, and only the estimation formula needs to be handled until the optimum design value is obtained. Therefore, the input box (design parameter) and the output (optimum design value) are black boxed ( Mathematical processing in the system: solving simultaneous equations of estimation equations). Therefore, the merits of the optimization method using the response phase method can be enumerated as follows.
(A1) An estimation formula can be created from the relationship between a large number of design parameters and a response model, and the optimization calculation is efficient because only the estimation formula needs to be handled.
(A2) Optimal design values can be obtained without knowing the design.
(A3) The optimum design value can be obtained without knowledge of the optimization method using the response phase method.

  Reference 2 (Japan Opportunity Association 2001 Annual Conference (2001. 8.27-30)) is disclosed as a technique that uses a genetic algorithm as an optimization method. In this method, a structural analysis is performed based on a design parameter created using an orthogonal table or a random number, and a direction in which a maximum value or a minimum value (that is, an optimum value) is likely to exist is searched from the response model. Next, the structural analysis is repeated until the optimum value is obtained while changing the design parameters so that the response appears in the direction in which the optimum value exists. Here, a genetic algorithm is used to search for a direction in which an optimum value is likely to exist and to create a new design parameter.

Since changes in design parameters are made discretely using a genetic algorithm, the input parameters (design parameters) and outputs (optimal value design) are black boxed (discrete numerical processing in the system: design parameters based on the genetic algorithm) Can be discretized). Therefore, the merit of the optimization method using the genetic algorithm can be enumerated as follows.
(A4) If an optimization system using a genetic algorithm is left to the system, an almost optimal design value can be obtained.
(A5) Optimal design values can be obtained without knowing the design.
(A6) Optimal design values can be obtained without knowing an optimization system using a genetic algorithm.

  However, the techniques described in Documents 1 and 2 have the following problems. That is, in any of the techniques described in Reference 1 and Reference 2, the validity of the accuracy of the estimation formula is unknown, and if the multi-modality is strong, a truly optimum design value is obtained. I do n’t know. Further, since the optimization calculation is black boxed (mathematical numerical processing), the optimal physical meaning (design meaning) is not known.

In other words, the optimization system using the response phase method (see Document 1) has the following problems although there are merits (a1) to (a3).
(b1) Since the accuracy of the estimation formula depends on the number of relationships between the design parameters and the response model, many structural analyzes are required to improve accuracy. Also, it is not known in advance how many structural analyzes are appropriate.
(b2) It is not known whether the optimum design value is truly obtained by braking the estimation equation.
(b3) Optimization calculation is black-boxed (mathematical numerical processing), but the effects shown in (2) and (3) above are obtained, but the optimal physical meaning (design meaning) is unknown. .

Further, the technique described in Document 2 has the following problems although there are merits (a4) to (a5).
(b4) In the case of a phenomenon that exhibits very multimodality (strong non-linearity), it requires an extremely large amount of structural analysis before obtaining the optimum design value, which is inefficient.
(b5) If the multimodality is very strong, there is a possibility of falling into LocalMinimum (or LocalMaximum), and there is a possibility of finding an answer that is not truly the optimum design value, so it is not known whether it is really optimal. This is because there is no means for confirming the entire design space. Note that LocalMinumum or LocalMaximum represents a local minimum value or maximum value, and is different from the true minimum value or maximum value.
(b6) Since the optimization calculation is black boxed (discrete numerical processing), the effects shown in (5) and (6) above can be obtained, but the optimal physical meaning (design meaning) is not known. Absent.

That is, when the above problems are arranged, the conventional techniques include the following problems.
-It requires a lot of calculations to improve accuracy and is inefficient.
・ I can't figure out the entire design space, so I don't know if it's really optimal.
-Since the optimization process is black-boxed (mathematical and discrete), the physical meaning of the relationship between the optimal design value and the response model is unknown.

  Therefore, in the fourth embodiment, a characteristic contour map for recording each evaluation characteristic at a corresponding position on the two-dimensional plane or a variable for recording each design variable is arranged on the two-dimensional plane according to the similarity of a plurality of parameters. The contour map was used to grasp the entire design space and to find the physical meaning of the relationship between the optimum design value (or simply the design value) and the response model.

(Function of contour map)
For example, the contour map of the front wheel contact load characteristic represents the entire design region as a contour map based on the quantitative value of the evaluation characteristic value. Therefore, the user (designer) can confirm the magnitude of the evaluation characteristic value by viewing the characteristic contour map. The optimum value of the evaluation characteristic is the minimum value or the maximum value as referred to in the characteristic contour map, and in FIG. Since each contour map does not necessarily have a true optimum value, it is an “area where an optimum value is likely to exist” at this stage (since it cannot be said that sufficient sampling is ensured).

  Further, all response models (evaluation characteristic values) are displayed so as to be at the same position in all characteristic contour maps. This is because the position of the center of gravity does not change. For example, in order to reduce the front wheel ground contact load (change in the arrow direction in FIG. 23), the design parameter may be changed in the same direction. For example, from the contour map, Fr is greatly changed from large to small on the blow-by compression side, and Rr remains small, and Fr is largely changed from large to small on the valve characteristic inclination compression side, and Rr remains small. Understandable.

  Since the contour map can also be grasped by a quantitative value, if the target evaluation characteristic value is set on the evaluation characteristic contour map, the value on the parameter contour map corresponding to the same place may be read.

(Overlapping effect)
FIG. 24 is a diagram illustrating the effect of superimposing the characteristic contour maps. By superimposing characteristic contour maps of independent evaluation characteristics, places where values are low (low density) are small (density is low), and places where values are high (high density) are large (density) The non-common places are averaged, and the common places are emphasized. Therefore, it can be seen that the region where the optimum value (minimum value or maximum value) is likely to exist is a place where the density of the contour map as a result of superimposition is low or a place where the density is high.

  For example, even when it is necessary to consider a trade-off relationship in which one characteristic is good and the other characteristic is deteriorated, there is a case where it is desired to consider a certain evaluation characteristic with particular emphasis. At this time, by assigning a weight to the value of the evaluation characteristic to be regarded as important, the density of the contour map becomes clearer, and the evaluation characteristic regarded as important when superimposed can be emphasized. In addition, what is necessary is just to judge the area | region where the optimal value is likely to exist from light and shade.

(Extraction of areas where optimal values are likely to exist)
Further, the contour maps of the respective evaluation characteristics are overlapped to extract a region where an optimum value is likely to exist, and it can be seen that the design parameter pattern satisfying this region has a certain tendency (see FIG. 25). For example, in the case of the above spring-S / ABS specifications, the user (designer) knows what the current specifications tend to be, what the other vehicle's specifications tend to be, In many cases, the specifications of the developed vehicle are determined. In the optimization system as shown in the background art, the entire region could not be shown. Therefore, in such a case, an analysis model was created from the beginning and calculation was performed.

  On the other hand, in Example 4, since the entire area of the evaluation characteristics and the entire area of the design parameter are indicated by the contour map, and each contour map is displayed on the same design parameter pattern, the optimum value is It is possible to instantly obtain design parameter patterns and trends in a region that is likely to exist.

  It should be noted that all the characteristic contour maps may be overlaid, an area estimated to be the optimum value may be extracted, and an optimization process may be performed, for example, a desired evaluation characteristic among a plurality of evaluation characteristics Alternatively, only the evaluation characteristics selected by superimposing them may be extracted.

  In addition, although the design pattern corresponding to the characteristic contour map is extracted, the characteristic value corresponding to the parameter contour map may be extracted to see the change in the characteristic value due to the change in the design pattern.

  FIG. 26 is a diagram illustrating Example 5 in which the attribute axes of Example 3 are arranged in parallel. As shown in FIG. 26, when the attribute axes are arranged in parallel, the attribute axes do not overlap, and the center of gravity can be made to represent the sampling tendency by shaping. In addition, since the concept about other superimposition etc. is the same, description is abbreviate | omitted.

  As described above, in Examples 3, 4, and 5, the following effects can be obtained.

  (5) When there are multiple samplings consisting of combinations of multiple variables, set the axes corresponding to each variable on the 2D plane so that they do not overlap in the direction of travel (equivalent to attribute axis setting means) Variables are plotted and sampling is shaped based on the plotted variables (corresponding to shaping means). Then, the centroid of the shaped sampling is calculated (corresponding to the centroid calculating means), and the centroid of the shape corresponding to the plurality of samplings is expressed on one two-dimensional plane (corresponding to the notifying means).

  In other words, the relative relationship between a plurality of pieces of multidimensional information cannot normally be recognized by humans, but by displaying a list on a two-dimensional plane as described above, it is possible to intuitively recognize system trends. . Therefore, when there are multiple combinations of design variables and evaluation characteristics, it is possible to identify at a glance data that shows similar or dissimilar trends, and design the desired trend. A combination of parameters can be easily extracted.

(Implementation using a medium on which a multidimensional information processing program is recorded)
In the third to fifth embodiments, the multidimensional information processing system has been described. However, all the above-described actions may be provided in a state described in a program or the like that can be read by the arithmetic device. Specifically, when there are a plurality of samplings composed of combinations of a plurality of variables, an attribute axis setting command unit that outputs a command to set the axes corresponding to each of the variables on the two-dimensional plane so as not to overlap in the traveling direction. A shaping command unit that plots the variable on the attribute axis, and outputs a command to shape the sampling based on the plotted variable, and a centroid calculation command unit that outputs a command to calculate the centroid of the shape And a notation command unit that outputs a command to mark the center of gravity of the shape corresponding to the plurality of samplings on one two-dimensional plane, a medium on which a multidimensional information processing program is recorded By doing so, the dispersibility can be improved.

  Further, in the medium on which the multi-dimensional information processing program is recorded, a sampling pattern notation command unit that outputs a command that indicates the combination of the variable and / or the response for each sampling may be provided.

  In the medium on which the multidimensional information processing program is recorded, the notation command unit may be a command unit that outputs a command to display the variable and / or the response value in color tone.

(Implementation as a multidimensional information display device)
Moreover, although Example 3-5 demonstrated the multidimensional information processing system, when performing the said multidimensional information processing, the above-mentioned effect | action is based on the combination of a some variable as a display means with respect to a designer. When there are a plurality of samplings, the axes corresponding to the variables are set on a two-dimensional plane so as not to overlap in the traveling direction, the variables are plotted on the attribute axes, and the sampling is performed based on the plotted variables. And a display unit for calculating the center of gravity of the shape and displaying the center of gravity of the shape corresponding to the plurality of samplings on one two-dimensional plane. It is good also as providing the multidimensional information display apparatus characterized by this. Thereby, the user can grasp | ascertain the tendency of a system easily. As a display means, it may divide and display on a monitor screen etc., and may display on a separate monitor screen. Thereby, the tendency of the system can be easily grasped visually.

  Moreover, you may provide the sampling pattern display means which displays the combination with the said variable and / or the said response for every said sampling as said multidimensional information display apparatus.

  As the multidimensional information display device, the display means may display the variable and / or the response value in color.

  Next, Example 6 will be described. In the sixth embodiment, the candidate solution space is visualized by introducing the concept of threshold using the contour map created by any of the methods described in the above embodiments. FIG. 27 is a flowchart illustrating a candidate solution space visualization process according to the sixth embodiment.

In step 601, a contour map of each evaluation characteristic is created.
In step 602, a contour map for overall evaluation of the overall performance is created by superimposing the contour maps of the respective evaluation characteristics.

In step 603, a threshold value is introduced into each evaluation characteristic.
In step 604, the candidate solution space is visualized.

  FIG. 28 is a schematic explanatory diagram showing the operation of the sixth embodiment. MapA is a contour map of a certain evaluation characteristic, and only the area that satisfies the threshold is displayed by the introduction of the threshold (in FIG. 28, the dark area does not meet the threshold, the thin area Is the area where the threshold is met.) Similarly, for MapB, MapC, and the entire map, only areas that satisfy the threshold values set for each evaluation characteristic and comprehensive evaluation are displayed.

  Therefore, many candidate solutions can be visualized. Incidentally, although the optimization method in the prior art was able to obtain one optimal candidate solution, it was not possible to obtain a plurality of candidates that satisfy the conditions. Moreover, it was impossible to look down on the relationship between multiple candidates. However, in Example 6, in addition to being able to visualize many candidate solutions, as shown in FIG. 9 and FIG. 25, it is possible to grasp the design pattern of the region where the candidate solution exists or does not exist.

  In addition, for example, there is a region that satisfies a threshold value as a comprehensive evaluation in the entire map and does not satisfy the threshold value in MapC. By comparing these areas, it is possible to grasp the trade-off relationship that an area having good MapC characteristics is inappropriate as an overall characteristic. This relationship can also be examined between evaluation characteristics.

  In addition, although the candidate solution spaces display areas that satisfy the threshold value as comprehensive evaluations, it is necessary to determine which area is preferable among them. At this time, even if the highest value is obtained as the characteristic, it can be said that the design flexibility is low and the design capacity is low when the region where the candidate solution exists is small. That is, by introducing a threshold value and visualizing a region that satisfies the threshold value, it is possible to grasp the design capacity.

  As described above, in the invention described in the sixth embodiment, the following effects can be obtained in addition to the effects of the first to fifth embodiments.

  (6) When there is a sampling composed of a combination of a design variable (variable) and a characteristic (response), a threshold is set for the characteristic (threshold setting means). Then, only sampling having a response larger than the threshold (or sampling having a small response) is represented on the contour map (two-dimensional plane) (candidate solution space notation means).

  Therefore, it is possible to visualize the design space (candidate solution space) in which the characteristics desired by the designer can be obtained. In particular, since a large number of candidate solutions are displayed at the same time, the degree of freedom in design can be easily improved.

  (7) Of the plurality of characteristics (responses), only an arbitrarily selected characteristic (response) is described on the contour map (two-dimensional plane) (arbitrary response notation means).

  Therefore, it is possible to instantly grasp which one of the plurality of characteristics is low.

  (8) A plurality of contour maps (two-dimensional planes) in which only arbitrarily selected characteristics (responses) are described are superimposed (superimposing means).

  In the first place, the position indicated by the contour map represents the same combination of design variables. Therefore, the overall characteristics can be evaluated by superimposing the contour maps of the characteristics. In addition, by displaying only the area that satisfies the threshold, it is possible to compare between contour maps of each characteristic, or between the superimposed contour map and the contour map of each characteristic. It is possible to grasp the capacity or characteristics of solution spaces that cannot be candidates.

(Implementation using a medium on which a multidimensional information processing program is recorded)
In the sixth embodiment, the multidimensional information processing system has been described. However, all the above-described actions may be provided in a state described in a program or the like that can be read by the arithmetic device. Specifically, the sampling is composed of a combination of a variable and a response, and a threshold value setting command unit for setting a threshold value for the response, and a sampling having a response larger than the threshold value or a small value. By providing a candidate solution space notation command unit for notifying only sampling having a response on the two-dimensional plane, a medium on which a multidimensional information processing program is recorded is provided. Can be planned.

  Moreover, you may provide the arbitrary response description command part which describes on the said two-dimensional plane only the response selected arbitrarily among these responses.

  Moreover, you may provide the superimposition command part which superimposes the several two-dimensional plane displayed by the said arbitrary response description command part.

(Implementation as a multidimensional information display device)
Further, in the sixth embodiment, the multidimensional information processing system has been described. However, the above-described operation can be performed by setting a threshold value for characteristics as display means for the designer when the multidimensional information processing is executed. Multidimensional information display comprising threshold setting means for setting and candidate solution space display means for displaying only sampling having characteristics larger than the threshold (or sampling having small characteristics) on the contour map An apparatus may be provided. Thereby, the user can grasp | ascertain the candidate solution space of a system easily. As a display means, it may divide and display on a monitor screen etc., and may display on a separate monitor screen. Thereby, the tendency of the system can be easily grasped visually.

  Moreover, you may provide the arbitrary response display means which displays on the contour map only the characteristic selected arbitrarily among several characteristics.

  Further, a superimposing unit that superimposes a plurality of contour maps displayed by the arbitrary response display unit may be provided.

  Next, Example 7 will be described. Example 7 basically shows a specific example in which the technique of Example 6 is introduced to shorten the industrial product development process. When developing industrial products such as automobiles, each development department designs and evaluates the design parts that are given to them, such as suspension design, steering design, brake design, engine design, powertrain design, and interior design. These are combined as a total to complete the final car. In other words, it can be said that the final industrial product form is a system product because it is composed of a plurality of parts.

  When developing these system products, because one system is in a relationship that interacts with each other, just because each development department has achieved optimal performance, the final product is not necessarily an attractive product. Not exclusively. That is, it is essential to link each department, and it is very important for each development department to understand the development direction of other development departments and the trade-off relationship with other development departments. However, in the past, it was often necessary to spend a lot of time on adjustment work, such as designing at a certain level in each development department, examining problems between each department, and making adjustments again. was there.

  Therefore, in the seventh embodiment, a contour map including all design parameters necessary for the design of the automobile is created in advance, and characteristics that each development department must evaluate and an evaluation characteristic map as a total vehicle are created. We propose a development system that can update information between development departments in real time.

FIG. 29 is a flowchart showing the development system of the seventh embodiment.
In step 701, each performance evaluation department performs an optimum design, and creates a contour map using the history (information on all experiments and analysis).

  In step 702, the maps of all the departments are overlapped to extract an area that is currently optimal (optimum value). At this time, the performance to be regarded as important is weighted on the map and adapted to the needs of the market. For example, in the case of the Luxuary preference, the sound / vibration performance is mainly evaluated, and in the case of the Sporty preference, the steering stability is mainly evaluated.

  In step 703, it is determined whether or not the optimum value has reached the target. If not, the process proceeds to step 703, and if it has reached, the control flow ends.

  In step 704, the characteristics that have not reached the target are grasped, the trade-off characteristics associated with the movement of the characteristics are extracted, the performance degradation due to the movement of the characteristics is estimated, and the variable movement allowance is calculated. The result is notified to the relevant department and examined in the relevant department. Based on the result of this examination, it is determined whether or not the target has been reached again.

  As a specific example, a process in which the aerodynamic performance evaluation department, the steering stability evaluation department, and the sound / vibration evaluation department that share the suspension geometry as a design variable determine the final geometry will be described.

  First, design variables related to suspension geometry are arranged on the horizontal axis, and optimal design is performed using the values of each geometry. Here, in the aerodynamic performance evaluation department, aerodynamic characteristic data when each geometry is used is accumulated by experiment and analysis. The Steering Stability Evaluation Department accumulates steering stability evaluation characteristic data when using each geometry by experiment and analysis. The sound and vibration evaluation department accumulates sound and vibration characteristics data when using each geometry through experiments and analysis.

  Since each performance evaluation department obtains a relationship between each combination of design variables and each evaluation characteristic, a contour map is created based on each combination of these design variables.

  Since a position corresponding to each combination of design variables is determined by creating the contour map, a characteristic contour map is created by plotting aerodynamic characteristics, steering stability characteristics, and sound / vibration characteristics corresponding to the combination of design variables. By superimposing these characteristic contour maps, an optimum value that is optimum at the present time is extracted.

  Here, when the extracted optimum value does not reach the target characteristic, it is grasped which characteristic has the lowest performance at the position on the contour map corresponding to the present optimum value. Next, when a characteristic with low performance is moved on the contour map in a direction in which high performance can be obtained, which characteristic is deteriorated, that is, a trade-off characteristic is extracted. Then, notify the department that has the trade-off characteristics of the estimated performance degradation due to movement, the movement cost of variables, etc., and urge the examination again.

  As described above, in the seventh embodiment, in addition to the operational effects of the sixth embodiment, the following operational effects can be obtained.

  (9) A multi-dimensional information processing device that is applied to a development system that develops products by each of the plurality of performance evaluation departments evaluating one of the plurality of characteristics (responses). Only the characteristics to be displayed are described on the contour map (two-dimensional plane) (departmental response notation means). Next, a plurality of contour maps in which the characteristics for each department are described are overlapped to display the overall characteristics of the product (total response display means). The candidate solution space of the overall characteristic and the candidate solution space of the departmental characteristic are compared, and the comparison result information is notified to each performance evaluation department (notification means).

  By mapping all the evaluation performance, you can understand how to respond to the request. Here, “request” is, for example, a new vehicle concept, etc., and “how to respond” is the evaluation characteristics necessary to ensure performance in accordance with the concept, which design pattern should be selected. Indicates whether it can be improved.

  Moreover, market values can be expressed by weighting evaluation performance.

  By creating a contour map for each characteristic, it is possible to grasp the trade-off relationship, and it is possible to immediately grasp what is the problem that has deteriorated other performance.

  When designing a new vehicle, the vehicle design pattern that achieves the new concept can be temporarily designed from the contour map and weighting. Here, the “provisional design” is an area in which an optimum value corresponding to the weight is obtained by using a weight corresponding to a new concept, and a design area corresponding to the optimum value includes a desired design pattern. Extraction of the area means that it has been provisionally designed.

  When it is desired to improve the performance, it is possible to grasp which variable should be handled while considering other performance.

  In addition, by making each map and characteristics into a database, an existing database can be used even when the vehicle type is different, such as when the same platform is used.

(Implementation using a medium on which a multidimensional information processing program is recorded)
In the seventh embodiment, the multi-dimensional information processing system has been described. However, all the above-described actions may be provided in a state described in a program or the like that can be read by the arithmetic device. Specifically, a medium on which a multi-dimensional information processing program applied to a development system that performs product development by each of a plurality of performance evaluation departments evaluating one of the plurality of characteristics is recorded. Comprehensive response display that displays the overall characteristics of the product by overlaying the departmental response notation means that displays only the responses evaluated by the evaluation department on the contour map and the multiple contour maps indicated by the departmental response notation means A multi-dimensional information processing program comprising: a means for comparing a candidate solution space for a comprehensive characteristic and a candidate solution space for a departmental characteristic, and notifying each performance evaluation department of comparison result information By using a medium on which is recorded, the dispersibility can be improved.

(Implementation as a multidimensional information display device)
In the seventh embodiment, the multi-dimensional information processing system has been described. However, when the multi-dimensional information processing is executed, a plurality of performance evaluation departments each serve as a display unit for the designer. Is a multi-dimensional information display device applied to a development system that develops products by evaluating any one of the responses of each section, and displays only the responses evaluated by each performance evaluation section on the contour map And a plurality of contour maps displayed by the departmental response display means, and a comprehensive response display means for displaying the overall response of the product, and a candidate solution space for the overall response and a candidate solution space for the departmental response. It is good also as providing the multidimensional information display apparatus characterized by including the notification means which compares and notifies comparison result information to each performance evaluation department. Thereby, the user can grasp | ascertain the whole image of product development easily. As a display means, it may divide and display on a monitor screen etc., and may display on a separate monitor screen. Thereby, the progress and tendency of product development can be easily grasped visually.

  Next, Example 8 will be described. When designing an industrial product, if a product is manufactured by determining design variables, variations always occur. When the design variables vary, if the characteristics vary greatly, it cannot be realized as a product, so it is necessary to manage variations.

  Therefore, in actual design work, the distribution width of the design variable is determined so that the entire distribution of characteristics or the set distribution range (for example, ± 3σ) satisfies the required level, and the distribution width of the design variable is set to the design value. (The design variable distribution is controlled so that the characteristic distribution falls within the target value.)

  The above-mentioned “determining the distribution width of a design variable so that the entire distribution of characteristics or a set distribution range (for example, ± 3σ) satisfies the required level” can be obtained by inputting various values and trends to the design variable. It is an iterative process to check whether the characteristic value to be satisfied satisfies the required level. Therefore, the number of combinations of design variables to be input becomes enormous, and it is almost impossible to grasp the distribution range of design variables for the characteristic distribution to satisfy the required level without omission.

  Therefore, in the eighth embodiment, a combination of a plurality of design variables is expressed as a position on the contour map, and the size (dispersion) of the distribution of product characteristics is expressed by, for example, color tone at that position. At this time, if a position where the distribution of product characteristics satisfies the required value is found on the contour map, the combination of design variables corresponding to the surrounding positions is also highly likely that the distribution of product characteristics satisfies the required value. If additional calculation is performed for the surroundings, the “distribution range of design variables for the characteristic distribution to satisfy the required level” can be grasped efficiently and without omission.

  Therefore, first, a certain design variable is determined, and sampling corresponding to the manufacturing variation is generated in a normal distribution. At this time, it was decided to verify whether or not the variation in characteristics for each design variable was within a predetermined range. When the variation in characteristics falls within the predetermined range, the design variable is a candidate solution with high reliability (design variable), and when there is a variation larger than the predetermined range, the design variable is determined as a candidate solution with low reliability. It is possible to confirm the reliability. Hereinafter, this process is referred to as a reliability candidate solution extraction process.

  In the reliability candidate solution extraction process, design variables are determined with relatively few calculation points, a distance model is further generated around the value extracted as a new correct candidate solution, and the reliability candidate solution extraction process is performed again. I decided to do it.

FIG. 30 is a flowchart illustrating the contents of the reliability candidate solution extraction process according to the eighth embodiment.
In step 801, sampling according to the variable probability distribution is generated. Specifically, centering on sampling of a certain design variable, new sampling according to a normal distribution is generated, and characteristics for each design variable are prepared.

ここで、x₁，x₂，・・・，x_mは設計変数、U は特性関数ｆから決まる特性、ρは自己相関係数である。尚、このステップ７０１，７０２は、各サンプリングに対して行われ、各サンプリングの特性の分散がデータとして記憶される。 In step 802, a variation distribution is calculated. Specifically, the characteristic variance Var [U] is calculated using the following estimation formula for variation.

Here, x ₁ , x ₂ ,..., X _m are design variables, U is a characteristic determined from the characteristic function f, and ρ is an autocorrelation coefficient. The steps 701 and 702 are performed for each sampling, and the dispersion of the characteristics of each sampling is stored as data.

In step 803, the similarity is calculated. Specifically, the hierarchical clustering described in the second embodiment is performed.
In step 804, the contour map is created by sequentially combining the samplings based on the similarity. Steps 803 and 804 are steps for expressing each sampling as a contour map, and the contour map creation method described in the above embodiments may be applied as appropriate.

  In step 805, a confidence interval is set. The confidence interval is a variance value of the characteristic, and by setting the confidence interval, it can be determined whether or not the characteristic variation with respect to the design variable variation is within the confidence interval.

  In step 806, reliability candidate solutions are extracted. Specifically, out of each sampling, those whose variance is smaller than the confidence interval are extracted. Only sampling satisfying this condition is displayed on the contour map, and processing is performed so that the rest are not displayed. After extracting the reliability candidate solution, a new sampling is generated around the reliability candidate solution, and the reliability candidate solution is searched for more efficiently by searching for the reliability candidate solution.

  In step 807, it is determined whether or not there is a request for resetting the confidence interval. If there is a reset request, the process proceeds to step 805; otherwise, the process ends.

  Next, the operation based on the above processing will be described. FIG. 31 is a schematic diagram showing a normal distribution of design variables and a probability distribution of characteristics corresponding to design variables based on the normal distribution. When design variables are determined, the design variables always vary. In general, this variation follows a normal distribution. In other words, it can be said that variations in design variables are not controllable and always exist.

  On the other hand, there are cases where the variation in characteristics with respect to the variation in each design variable varies greatly and when the variation is small. At this time, it is possible to select a design variable having a small variation in characteristics. In other words, it can be said that the variation in characteristics can be controlled.

  That is, a large dispersion of characteristic values is synonymous with a large variation in obtained characteristics, and is a design variable with low reproducibility of characteristics when design variables vary and low reliability. On the other hand, a small dispersion of the characteristic value is synonymous with a small variation in the obtained characteristic, and even if the design variable varies somewhat, the characteristic is highly reproducible and highly reliable.

  Therefore, for each design variable, a variance Vari [U] of characteristics when sampling is generated with a normal distribution is stored, and a confidence interval (= a desirable value as variance) is set. Among the values of the variance Var [U] of each sampling, sampling smaller than the confidence interval is displayed as a highly reliable design variable, that is, a reliability candidate solution. Thereby, a candidate solution can be easily extracted only by the characteristic variance Var [U].

  FIG. 32 is a characteristic variation map in which only the reliability candidate solutions are displayed. The dark area in FIG. 32 is an area where the characteristic variation is large, and the thin area is the reliability candidate solution area. Thus, by expressing a highly reliable candidate solution, it is possible to intuitively grasp the reliability of the design area. For example, if only the reliability candidate solutions are displayed on the characteristic variation map, and further, the characteristic values are displayed in color tone on each candidate solution, it is possible to easily extract candidate solutions having high characteristics and high reliability.

  Further, for example, by comparing design patterns of a candidate solution with high reliability and a candidate solution with low reliability, it is possible to easily grasp which design pattern has a correlation with reliability.

  As described above, the effects listed below can be obtained in the eighth embodiment.

  (10) A new variable is generated with a predetermined probability distribution with respect to the design variable (variable generating means). In addition, since general dispersion follows a normal distribution, it is desirable to generate a normal distribution. Next, the variance of the characteristic (response) corresponding to each generated design variable is calculated (dispersion calculation means). Then, the variance is written on the contour map (reliability candidate solution writing means). In addition, what is necessary is just to express with a color tone display etc. as a description of dispersion | distribution.

  Thereby, the spread of reliability in the design space can be grasped at a glance.

  (11) A confidence interval is set for the variance (confidence interval setting means). Only sampling having a variance within the set confidence interval is described on the contour map.

  Thereby, a highly reliable candidate solution can be easily extracted only by the characteristic variance Var [U].

  (12) A new sampling may be generated in the vicinity of the sampling having a variance within the confidence interval (boundary sampling generating means).

  As a result, the candidate solution space can be efficiently clarified by reducing the number of initial samplings, assigning a certain amount of candidate solution space, and intensively searching the vicinity of the region.

(Implementation using a medium on which a multidimensional information processing program is recorded)
In the eighth embodiment, the multi-dimensional information processing system has been described. However, all the above-described actions may be provided in a state described in a program or the like that can be read by the arithmetic device. Specifically, a variable generation command unit that generates a new variable with a predetermined probability distribution for the variable, a dispersion calculation command unit that calculates a variance of responses corresponding to each variable generated by the variable generation command unit, a contour Dispersibility can be improved by using a medium on which a multi-dimensional information processing program characterized by including a dispersion notation command unit that expresses dispersion on a map is recorded.

  In addition, a confidence interval setting command unit that sets a confidence interval for variance and a reliability candidate solution notation command unit that describes only sampling having a variance within the confidence interval set by the confidence interval setting command unit may be provided. .

  In addition, a boundary sampling generation command unit that generates new sampling may be provided in the vicinity of sampling having a variance within the confidence interval.

(Implementation as a multidimensional information display device)
In the eighth embodiment, the multi-dimensional information processing system has been described. However, when the multi-dimensional information processing is executed, the above-described operation is performed as a display unit for the designer with a predetermined probability distribution with respect to variables. Variable generating means for generating a new variable, dispersion calculating means for calculating a variance of a response corresponding to each variable generated by the variable generating means, reliability candidate solution displaying means for displaying the variance on a contour map, It is good also as providing the multidimensional information display apparatus characterized by having provided. Thereby, the user can grasp | ascertain the reliability of a candidate solution easily. As a display means, it may divide and display on a monitor screen etc., and may display on a separate monitor screen. Thereby, the tendency of the system can be easily grasped visually.

  Alternatively, a confidence interval may be set for the variance, and reliability candidate solution display means may be provided only for sampling having a variance that falls within the set confidence interval.

  Further, boundary sampling generation means for generating new sampling in the vicinity of sampling having variance within the confidence interval may be provided.

  Next, Example 9 will be described. In each of the above embodiments, the relationship between the design variable and the characteristic is grasped using the contour map. On the other hand, in the ninth embodiment, after selecting a region by introducing a threshold value, the design region is identified by hierarchical clustering, and the relationship between the design variable and the characteristic in the design region is grasped.

  The design region can be regarded as individual peaks existing in the direction satisfying the threshold, which are separated by the threshold that the characteristic should satisfy at the minimum in the phenomenon showing multimodality. Each design area can simultaneously represent a characteristic range (characteristic area) realized by each design and a design variable range (design variable area) realizing the characteristic.

  Therefore, the characteristic region and the design variable region corresponding to the characteristic region can be regarded as a design region, and each range can be considered as a design capacity. It is thought that the design area tends to gather things with similar characteristics of design variables. Therefore, it is considered that each design area has a typical design pattern that characterizes the area.

  From the above, in order to identify the design area, it is necessary to obtain a set of sample points having similar design patterns and satisfying threshold values. As a method of collecting similar design patterns, the classification methods described in the above embodiments can be cited.

  That is, the similarity is measured with reference to the design variable pattern of each sample point, and those having a high similarity are grouped. On the other hand, since the design region is regarded as a set of sample points that satisfy the threshold value, in order to specify the range of the design region, information on sample points that do not satisfy the threshold value must be used.

  Hierarchical clustering is considered to be able to identify a design area by following a hierarchy and finding a group of hierarchies that include sample points that satisfy a threshold below a sample point that does not satisfy the threshold. The design area identification method using hierarchical clustering is described below.

ここで、EはクラスターGの重心と各現象個体との距離の二乗和、gは全てのクラスターを含むクラスターである。 Of the n sample points, if one sample individual is defined as x _i (1 ≦ i ≦ n) and G _i is a cluster of x _i , the coupling rule of the cluster is expressed by equation (4.10).
(4.10)

Here, E is the sum of squares of the distances between the center of gravity of cluster G and each phenomenon individual, and g is a cluster including all clusters.

Next, a method for identifying the design region from the data clustered by the equation (4.10) will be described. When two clusters including only individuals that satisfy the threshold are defined as G _ci (1 ≦ i ≦ n) and G _cj (1 ≦ j ≦ n), the cluster G that satisfies the closest threshold The coupling rule for _q and G _r is as shown in Equation (4.11).
(4.11)

Next, a cluster that serves as a design area is searched from clusters that satisfy a threshold value in the closest relationship. A cluster including individuals that do not satisfy the threshold is defined as G _oi (1 ≦ i ≦ n). When the cluster composed of Gq and Gr combined in equation (4.11) and the cluster that does not satisfy the threshold value are in the closest relationship, these relationships are expressed in equation (4.12).
(4.12)

図３４に設計領域を特定するためのG_p,G_q，G_rの関係を示す。 The design area can be said to be a group consisting of one layer below the lowest layer satisfying Equation (4.12), ie, cluster G _q ∪ G _r , with the hierarchized clusters going from the upper layer to the lower layer . Therefore, if the design region is G _DSK (1 ≦ k ≦ n), the design region is expressed by Equation (4.13).
(4.13)

FIG. 34 shows the relationship between G _p , G _q and G _r for specifying the design area.

  From the above, the algorithm for identifying the design area is as follows. FIG. 33 is a flowchart for identifying the design area and grasping the relationship between the characteristics and the design area.

  In step 901, preparation for sampling is performed. Here, sampling is data composed of a combination of design variables and characteristics.

  In step 902, a characteristic threshold value is set.

  In step 903, an area that satisfies the threshold is selected.

  In step 904, a distance model is generated. The generation of the distance model has been described with reference to FIG.

  In step 905, it is determined whether or not the distance model has been generated a specified number of times.

  In step 906, hierarchical clustering is performed. Since hierarchical clustering has been described in the second embodiment, the description thereof is omitted.

  In step 907, the relationship between characteristics and areas is grasped.

  The design area identified by this method has the capacity of the design variable and the capacity that it realizes. The design capacity has a feature that, in any design area, the characteristics to be realized fall within the capacity of the corresponding characteristics no matter what design is performed within the capacity of the design variable. In addition, when a design object shows a complicated phenomenon in a wide area, a very large number of design areas can be obtained. From the characteristics of clustering, each design area is considered to have a completely different design capacity.

  Therefore, it is possible to understand the difference in design by comparing the individual design areas using the design capacity. Also, in this method, the design area is a complicated and difficult to explain phenomenon divided into simple phenomena, and the design area is composed of many similar design variable patterns. It is possible to create a simple curved surface approximate expression, and by solving this, it is possible to obtain a highly accurate optimum value in a certain design region.

  As shown in FIG. 34, the design area is defined as a set of sample points that satisfy all threshold values below the sample points that do not satisfy the threshold value by following the hierarchy of the dendrogram. be able to.

  If the multi-peak phenomenon is divided on the basis of the threshold value, and the direction that satisfies the threshold is a mountain and the direction that does not satisfy the valley is a valley, the set of sample points that satisfy the threshold and the threshold are satisfied. Each sample point is nothing but a multimodal mountain-valley relationship. In other words, if this relationship is used, it is possible to investigate that there is a dangerous design area that does not satisfy the threshold even if the design variable pattern is a wide design area, for example, by following the hierarchy. .

  The design area must be a cluster composed of two or more sample points. A cluster with one sample point can be interpreted as either a distance model generation where a model close to that sample point could not be generated, or a very dangerous area with no design variable capacity (small) Because.

  When the Euclidean distance between the cluster and the cluster that does not satisfy the threshold value closest to the cluster is large, the former is used, and when the distance is small, the latter is used. is there.

  In addition, the threshold is met by comparing the representative design pattern that characterizes the extracted design area and the design pattern of the model that does not satisfy the threshold that is closest to this design area. It becomes possible to investigate the characteristics of the design variables to be eliminated.

  This captures the characteristics of design variables whose characteristics to be realized have a negative direction, and it is possible to grasp in advance from hierarchical information problems that are likely to fall into actual design.

  From the above, by applying hierarchical clustering, we have developed a method for identifying a design region that has both the range of a specific design variable classified by the design pattern and the characteristic width realized by it.

  By looking at the identified design areas, it is possible to understand representative design patterns that realize design capacity and characteristics. In addition, by tracing the hierarchy of the tree diagram by hierarchical clustering, investigate the relationship between the design pattern and the change in the characteristics to be realized, and the design risk area in the representative design pattern due to the appearance of a model that does not meet the threshold Became possible.

  FIG. 35A shows the locations of the identified design areas in the overall model distribution, taking two example design areas. In this specific example, when the design variables are X and Y, and the characteristic determined by these two design variables is Z, sampling is plotted on a plane determined by the X axis and the Y axis, and the value of Z is set in this sampling. Appropriate colors are added. The dendrogram shown in FIG. 33 represents a part of the result of hierarchical clustering of each of these samplings, and defines a region that continuously satisfies characteristic values as a design region.

  Also, the design capacities of the design areas of the two examples taken up here are shown in FIGS. 35 (b) and 35 (c), respectively. 35 (b) and 35 (c), the vertical axis represents the design variable capacity, and the horizontal axis represents the design variables X and Y. 35B and 35C, the vertical axis represents the capacity of the evaluation characteristic value, and the horizontal axis represents the characteristic Z. Also, in the right diagrams of FIGS. 35B and 35C, the threshold value is indicated by a thick solid line. Since the characteristic value level is a normalized value with the threshold value being 1.0 and the maximum characteristic value being 0.0, the closer the value is to 0.0, the better the characteristic value can be obtained. The design region shown in FIG. 35B is a region including the maximum value of the characteristic, and the design region shown in FIG. 35C is a region near the threshold boundary.

  There were 38 sample points constituting the design area 79 (DesingSpace 79) shown in FIG. The design area 79 is an area having a wide range of design variables and a wide range of possible characteristic values. This can be said to be highly stable as a design area. This is because the designer can freely handle the design variables, and the value of the characteristic value is guaranteed to some extent no matter how much it is changed. That is, it can be said that the design region 79 is a design region having a high degree of freedom in design and high stability.

  A design area 16 (DesingSpace 16) shown in FIG. 35B is a design area located near the boundary line of the threshold value. There are only two models. Therefore, the design area is an area that has low stability as the design area and is likely to be excluded. This is because if the value of the design variable is slightly outside the design area, there is a high possibility that the value will deviate from the threshold value. As a general designer, it is considered that an area having a large design capacity such as the design area 79 is preferred.

  As described above, according to the ninth embodiment, the following effects can be obtained.

  (13) New sampling is generated around the candidate solution space (boundary sampling generating means).

  Therefore, information in the vicinity of the boundary of the region of the candidate solution space can be obtained intensively.

  (14) Of the new samplings that have been generated, only the samplings that satisfy the threshold value are represented, and the boundary of the candidate solution space is specified (boundary specifying means).

  Therefore, the candidate solution space region can be identified efficiently.

  (15) The relationship between the sampling variable and the response in the identified candidate solution space is described (relation notation means).

  Therefore, it is possible to indicate the range of design variables and evaluation characteristic values that can be realized in the design area. Here, each displayed design area has design information such as the width of the design variable and the range of characteristics. The designer can select these by looking at these figures and comparing and examining the design areas used for the design.

(Implementation using a medium on which a multidimensional information processing program is recorded)
In the ninth embodiment, the multi-dimensional information processing system has been described. However, all the above-described actions may be provided in a state described in a program or the like that can be read by the arithmetic device. Specifically, a medium on which a multi-dimensional information processing program is recorded, characterized in that a boundary sampling generation command unit for generating new sampling is provided around the candidate solution space described by the candidate solution space description command unit As a result, the dispersibility can be improved.

  In addition, a boundary specifying command unit may be provided that specifies only the sampling satisfying the threshold among the new samplings generated by the boundary sampling generation command unit and specifies the boundary of the candidate solution space.

  In addition, a relationship notation command unit that indicates the relationship between the sampling variable and the response in the identified candidate solution space may be provided.

(Implementation as a multidimensional information display device)
In the ninth embodiment, the multidimensional information processing system has been described. However, the above-described operation is displayed by the candidate solution space display means as a display means for the designer when the multidimensional information processing is executed. It is also possible to provide a multidimensional information display device characterized by providing boundary sampling generation display means for generating and displaying new sampling around the candidate solution space. Thereby, the user can grasp | ascertain the area | region of candidate solution space easily. As a display means, it may divide and display on a monitor screen etc., and may display on a separate monitor screen. Thereby, a candidate solution space area | region can be grasped | ascertained easily visually.

  In addition, among the new samplings generated by the boundary sampling generation display means, only the sampling satisfying the threshold value may be displayed, and boundary specific display means for specifying and displaying the boundary of the candidate solution space may be provided.

  Further, a relationship display means for displaying the relationship between the sampling variable and the response in the identified candidate solution space may be provided.

  As described above, the description has been made based on each of the first to ninth embodiments. However, the specific configuration may be changed as appropriate except for the part related to the essence of the invention. For example, in the above embodiments, the specification determination of the sedan vehicle is shown as an example, but similar characteristic contour maps and parameter contour maps are created in other vehicle types (for example, one-box vehicles), and these contour maps are superimposed. Thus, it is possible to obtain a specification corresponding to the middle between the sedan vehicle and other vehicle types without calculating from the beginning.

  In the first embodiment, an example in which an optimization program is incorporated in the arithmetic processing unit 1 has been described. However, the optimization program may be distributed in the market using a program medium in which the optimization program is stored. Alternatively, the program may be stored in a server or the like, and the user may install the arithmetic processing apparatus 1 as appropriate by downloading or the like.

  In the first embodiment, the response model is applied to a system including a suspension coil spring and a shock absorber. However, the response model is not limited to this, and may be applied to an electric circuit, an economic model, a program, and the like. .

  In the present specification, “notation” includes, for example, writing to a memory such as an arithmetic device, writing to an external storage device, outputting to an interface such as a screen, and printing out. The display represents a state in which the image can be output in a state that can be seen by a human.

1 is a system diagram illustrating a multidimensional information processing system according to a first embodiment. 3 is a flowchart illustrating an arithmetic processing structure in the arithmetic processing apparatus according to the first embodiment. It is a figure which shows the data set of the design variable and evaluation characteristic of the suspension of Example 1. FIG. 6 is a characteristic diagram illustrating characteristics of the suspension of Example 1. FIG. FIG. 3 is a schematic explanatory diagram illustrating a procedure of arranging on a two-dimensional plane according to the first embodiment. FIG. 3 is a schematic explanatory diagram illustrating a procedure of arranging on a two-dimensional plane according to the first embodiment. FIG. 6 is a contour map in which evaluation characteristics and design variables having the sampling are expressed in shades at each sampling position determined by the arrangement processing of the first embodiment. It is a schematic explanatory drawing showing the distance model production | generation process of Example 1. FIG. It is a figure showing the change on the characteristic contour map of Example 1, and the change of a design pattern. 10 is a flowchart showing the flow of a technical concept of Example 2. FIG. 10 is a schematic explanatory diagram illustrating hierarchical clustering processing according to the second embodiment. It is a figure showing the dendrogram by the hierarchical clustering process of Example 2. FIG. It is a figure showing the state arrange | positioned on a two-dimensional plane so that the distance between each cluster gravity center of Example 2 may be maintained. It is a figure showing the concept of the operation | work which arrange | positions the sampling in the cluster of Example 2 around the sampling corresponded to a gravity center. It is a schematic explanatory drawing showing a mode that the response (sampling) of the nearest neighbor of Example 2 is moved. It is a schematic explanatory drawing showing a mode that the other sampling of Example 2 is moved. It is a figure showing the change of the boundary line on a two-dimensional plane at the time of selecting the different hierarchy of Example 2. FIG. 10 is a flowchart showing the flow of a technical concept of Example 3. It is a schematic explanatory drawing showing the attribute axis and shaping of Example 3. It is a conceptual diagram showing the state which calculates a gravity center with respect to each sampling of Example 3, and displays each gravity center overlappingly. It is a figure which shows the example which expressed the evaluation characteristic of sampling, the design variable, etc. in the barycenter of Example 3 with the bar graph, respectively. It is a figure which shows the example which set all the design variables shown in FIG. 3 of Example 4 to the attribute axis. It is a figure showing the characteristic contour map and parameter contour map which described each evaluation characteristic and the design variable in the gravity center as mentioned above with respect to each sampling of Example 4. It is a figure showing the integrated characteristic contour map which overlap | superposed the characteristic contour map which described each evaluation characteristic of Example 4. FIG. It is a figure showing the design pattern in the optimal area | region of the contour map of Example 4. FIG. It is a figure which shows the example which has arrange | positioned the attribute axis of Example 5 in parallel. 18 is a flowchart illustrating a candidate solution space visualization process according to the sixth embodiment. FIG. 10 is a schematic explanatory diagram illustrating the operation of the sixth embodiment. 10 is a flowchart illustrating a development system according to a seventh embodiment. 20 is a flowchart showing the contents of reliability candidate solution extraction processing according to an eighth embodiment. It is the schematic showing the probability distribution of the characteristic corresponding to the normal distribution of a design variable, and the design variable based on a normal distribution. This is a characteristic variation map in which only reliability candidate solutions are displayed. It is a flowchart for identifying the design area | region of Example 9, and grasping | ascertaining the relationship between a characteristic and a design area | region. G _p for specifying a design region in Example 9, G _q, is a diagram showing the relationship between G _r. FIG. 5 is a diagram illustrating the location of an identified design area in the overall model distribution and the design capacity of two example design areas taken here.

Explanation of symbols

1 arithmetic processing unit 2 display unit 3 keyboard

Claims (72)

For a system having responses to multiple variables, when there are multiple samplings of combinations of the variables and / or the responses of the system,
An inter-sampling distance calculating means for calculating the Euclidean distance between the samplings as an inter-sampling distance;
An initial position setting means for selecting any one of the samplings as a first sampling and arranging the selected one as an initial position on a two-dimensional plane;
A second sampling arrangement means for selecting the sampling with the shortest sampling distance as the second sampling, and arranging the sampling at a position corresponding to the sampling distance on the basis of the initial position on the two-dimensional plane;
A reference centroid calculating means for calculating a reference centroid that is a centroid of sampling already arranged on the two-dimensional plane;
The sampling having the shortest distance between the second sampling and the sampling is selected as the third sampling, and the third sampling and the second sampling are selected based on the position of the second sampling and the position of the reference centroid on the two-dimensional plane. A third sampling arrangement means for arranging the third sampling at a position corresponding to a sampling distance between two samplings and a sampling distance between the third sampling and the reference centroid;
After the fourth sampling, the newly selected sampling is regarded as the third sampling, the previous sampling is regarded as the second sampling, the second sampling arrangement means, the reference centroid calculating means, and the third sampling Repetitive means for implementing the sampling arrangement means;
A multidimensional information processing apparatus comprising: The multidimensional information processing apparatus according to claim 1,
The reference centroid calculating means is a means for calculating a centroid between the first sampling position and the second sampling position on the two-dimensional plane as a reference centroid,
After the fourth sampling, the repetition means regards the newly selected sampling as the third sampling, regards the sampling selected immediately before as the second sampling, and determines the sampling selected two times before as the first sampling. A multi-dimensional information processing apparatus that is regarded as sampling and is means for implementing the second sampling arrangement means, the reference centroid calculation means, and the third sampling arrangement means. For a system having responses to a plurality of variables, when there are a plurality of processing clusters having a plurality of samplings composed of combinations of the variables and / or the responses of the system,
Centroid calculating means for calculating a centroid for each of the plurality of processing target clusters;
A center-of-gravity distance calculating means for calculating a distance between centers of gravity of the plurality of processing target clusters;
First arrangement means for arranging each of the processing target clusters so as to maintain the distance between the centers of gravity of the plurality of processing target clusters;
Selecting an arbitrary one from the sampling within the processing target cluster for each of the plurality of processing target clusters, and placing an initial position on a two-dimensional plane; and
A shortest distance sampling extraction means for calculating a Euclidean distance between samplings in the processing target cluster for each of the plurality of processing target clusters, and extracting a sampling having the smallest Euclidean distance;
Second arrangement means for arranging the shortest distance sampling in the processing target cluster for each of the plurality of processing target clusters at a position corresponding to the Euclidean distance with respect to the initial position on the two-dimensional plane;
Cluster coupling means for moving the sampling according to the Euclidean distance between the samplings existing on the boundary surface of each processing target cluster, and combining the plurality of processing target clusters;
Notation means for indicating the variables and / or the responses of the sampling on the two-dimensional plane;
A multidimensional information processing apparatus comprising: The multidimensional information processing apparatus according to claim 3,
A system having a response to a plurality of variables is provided with a dividing unit that forms a plurality of clusters by dividing on the basis of the Euclidean distance between samplings composed of a combination of the variable and / or the response of the system.
The multi-dimensional information processing apparatus, wherein the plurality of processing target clusters are clusters formed by the dividing unit. The multidimensional information processing apparatus according to claim 4,
The division means is means for forming a cluster in a hierarchical manner using a hierarchical clustering technique and forming a plurality of clusters by designating an arbitrary hierarchy of the formed hierarchy. Processing equipment. When there are multiple samplings consisting of combinations of multiple variables,
Attribute axis setting means for setting on the two-dimensional plane so that the axes corresponding to each of the variables do not overlap in the direction of travel;
Shaping means for plotting the variable on the attribute axis and shaping the sampling based on the plotted variable;
Centroid calculating means for calculating the centroid of the shape;
Notation means for notifying the center of gravity of the shape corresponding to the plurality of samplings on one two-dimensional plane;
A multidimensional information processing apparatus comprising: The multidimensional information processing apparatus according to any one of claims 1 to 6,
A multi-dimensional information processing apparatus comprising sampling pattern notation means for notifying a combination of the variable and / or the response for each sampling. In the multidimensional information processor according to any one of claims 1 to 7,
The multi-dimensional information processing apparatus, wherein the notation means displays the variable and / or the response value in color. The multidimensional information processing apparatus according to any one of claims 1 to 8,
The sampling consists of a combination of variables and responses,
Threshold setting means for setting a threshold for the response;
Candidate solution space notation means for notifying on the two-dimensional plane only sampling having a response larger than the threshold or sampling having a small response;
A multidimensional information processing apparatus comprising: The multidimensional information processing apparatus according to claim 9,
A multidimensional information processing apparatus comprising boundary sampling generation means for generating new sampling around a candidate solution space described by the candidate solution space notation means. The multidimensional information processing apparatus according to claim 10,
Among the new samplings generated by the boundary sampling generation means, there is provided a boundary specifying means for specifying only the sampling satisfying the threshold and specifying the boundary of the candidate solution space. apparatus. The multidimensional information processing apparatus according to claim 11,
A multidimensional information processing apparatus comprising a relationship notation means for notifying a relationship between a sampling variable and a response in the identified candidate solution space. The multidimensional information processing apparatus according to any one of claims 1 to 12,
The sampling is composed of a combination of a variable and a plurality of responses,
A multi-dimensional information processing apparatus, comprising: an arbitrary response notation unit that displays on the two-dimensional plane only an arbitrarily selected response among the plurality of responses. The multidimensional information processing apparatus according to claim 13,
A multidimensional information processing apparatus comprising superimposing means for superimposing a plurality of two-dimensional planes represented by the arbitrary response notation means. The multidimensional information processing apparatus according to any one of claims 12 to 14,
A multi-dimensional information processing apparatus that is applied to a development system that performs product development by each of a plurality of performance evaluation departments evaluating one of the plurality of responses,
A departmental response notation means for notifying only the response evaluated by each performance evaluation department on the two-dimensional plane;
A plurality of two-dimensional planes represented by the departmental response notation means, and a comprehensive response display means for notifying the overall response of the product;
A notification means for comparing the candidate solution space of the overall response and the candidate solution space of the sector-specific response, and notifying each performance evaluation department of the comparison result information;
A multidimensional information processing apparatus characterized by comprising: The multidimensional information processing apparatus according to any one of claims 1 to 15,
The sampling consists of a combination of variables and responses,
Variable generating means for generating a new variable with a predetermined probability distribution with respect to the variable;
Dispersion calculation means for calculating a variance of responses corresponding to each variable generated by the variable generation means;
A dispersion notation means for expressing the dispersion on the two-dimensional plane;
A multidimensional information processing apparatus characterized by comprising: The multidimensional information processing apparatus according to claim 16,
Confidence interval setting means for setting a confidence interval for the variance;
Reliability candidate solution notation means for noting only sampling having variance within the confidence interval set by the confidence interval setting means;
A multidimensional information processing apparatus characterized by comprising: The multidimensional information processing apparatus according to claim 17,
A multidimensional information processing apparatus comprising boundary sampling generating means for generating new sampling in the vicinity of sampling having variance within the confidence interval. For a system having responses to multiple variables, when there are multiple samplings of combinations of the variables and / or the responses of the system,
An inter-sampling distance calculation command unit that outputs a command for calculating the Euclidean distance between the samplings as the inter-sampling distance;
An initial position setting command unit that selects any one of the samplings as the first sampling and outputs a command to place the initial position on the two-dimensional plane;
Second sampling that selects the sampling with the shortest distance between the first sampling and the second sampling as the second sampling, and outputs a command to be placed at a position corresponding to the sampling distance on the basis of the initial position on the two-dimensional plane. A placement command section;
A reference centroid calculation command unit that outputs a command to calculate a reference centroid that is a centroid of sampling already arranged on the two-dimensional plane;
The sampling having the shortest distance between the second sampling and the sampling is selected as the third sampling, and the third sampling and the second sampling are selected based on the position of the second sampling and the position of the reference centroid on the two-dimensional plane. A third sampling arrangement command unit that outputs a command to arrange the third sampling at a position corresponding to a sampling distance between two samplings and a sampling distance between the third sampling and the reference centroid;
After the fourth sampling, the newly selected sampling is regarded as the third sampling, the previous sampling is regarded as the second sampling, the second sampling arrangement command unit, the reference centroid calculation command unit, and the A repeat command unit for outputting a command for executing the third sampling arrangement command unit;
A medium on which a multidimensional information processing program is recorded. The multidimensional information processing apparatus according to claim 19,
The reference center-of-gravity calculation command unit is a command unit that calculates a center of gravity between the position of the first sampling and the position of the second sampling on the two-dimensional plane as a reference center of gravity,
The repetition command unit regards the newly selected sampling as the third sampling after the fourth sampling, regards the sampling selected immediately before as the second sampling, and determines the sampling selected two times before as the second sampling. A medium on which a multi-dimensional information processing program is recorded, which is a command section that implements the second sampling arrangement means, the reference centroid calculation means, and the third sampling arrangement means, assuming that one sampling is performed. For a system having responses to a plurality of variables, when there are a plurality of processing clusters having a plurality of samplings composed of combinations of the variables and / or the responses of the system,
A center-of-gravity calculation command unit that outputs a command to calculate the center of gravity for each of the plurality of processing target clusters;
A center-of-gravity distance calculation command unit that outputs a command for calculating a distance between the centers of gravity of the plurality of processing target clusters;
An arrangement command unit that outputs an instruction to arrange each of the processing target clusters so as to maintain the distance between the centers of gravity of the plurality of processing target clusters;
A first placement command unit that selects any one of the samplings within the processing target cluster for each of the plurality of processing target clusters, and places the initial placement on a two-dimensional plane;
An extraction command unit that calculates a Euclidean distance between samplings in the processing target cluster for each of the plurality of processing target clusters, and outputs a command to extract a sampling having the smallest Euclidean distance;
A second placement command that outputs a command to place the shortest distance sampling in the processing target cluster at a position corresponding to the Euclidean distance with reference to the initial position on the two-dimensional plane for each of the plurality of processing target clusters. And
A cluster combination command unit that outputs a command to move the sampling according to the Euclidean distance between the samplings existing on the boundary surface of each processing target cluster and to combine the plurality of processing target clusters;
A notation command unit for outputting a command for notifying the variable and / or the response of the sampling on the two-dimensional plane;
A medium on which a multidimensional information processing program is recorded. In the medium on which the multidimensional information processing program according to claim 21 is recorded,
For a system having responses to a plurality of variables, a cluster formation command unit that outputs a command to form a plurality of clusters by dividing the Euclidean distance between samplings composed of combinations of the variables and / or the responses of the system Provided,
The medium on which a multidimensional information processing program is recorded, wherein the plurality of processing target clusters are clusters formed by the cluster formation command unit. In the medium on which the multidimensional information processing program according to claim 22 is recorded,
The cluster formation command unit is a command unit that forms a cluster in a hierarchical manner using a hierarchical clustering technique and forms a plurality of clusters by designating an arbitrary hierarchy of the formed hierarchy. A medium on which a multidimensional information processing program is recorded. When there are multiple samplings consisting of combinations of multiple variables,
An attribute axis setting command unit that outputs a command to set the axis corresponding to each of the variables on the two-dimensional plane so as not to overlap in the traveling direction;
A shaping command unit that plots the variable on the attribute axis and outputs a command to shape the sampling based on the plotted variable;
A center-of-gravity calculation command unit that outputs a command to calculate the center of gravity of the shape;
A notation command unit that outputs a command to mark the center of gravity of the shape corresponding to the plurality of samplings on one two-dimensional plane;
A medium on which a multidimensional information processing program is recorded. A medium on which the multidimensional information processing program according to any one of claims 19 to 24 is recorded,
A medium on which a multi-dimensional information processing program is recorded, comprising a sampling pattern notation command unit that outputs a command that represents a combination of the variable and / or the response for each sampling. A medium on which the multidimensional information processing program according to any one of claims 19 to 25 is recorded,
The medium on which a multidimensional information processing program is recorded, wherein the notation command unit is a command unit that outputs a command to display the variable and / or the response value in color tone. 27. A medium on which the multidimensional information processing program according to any one of claims 19 to 26 is recorded.
The sampling consists of a combination of variables and responses,
A threshold value setting command unit for setting a threshold value for the response;
A candidate solution space notation command unit for notifying on the two-dimensional plane only sampling having a response larger than the threshold or sampling having a small response;
A medium on which a multidimensional information processing program is recorded. A medium on which the multidimensional information processing program according to claim 27 is recorded.
A medium on which a multi-dimensional information processing program is recorded, wherein a boundary sampling generation command unit for generating new sampling is provided around the candidate solution space described by the candidate solution space notation command unit. A medium on which the multidimensional information processing program according to claim 28 is recorded,
Among the new samplings generated by the boundary sampling generation command unit, only a sampling satisfying the threshold value is described, and a multidimensional dimension specifying command unit for specifying a boundary of the candidate solution space is provided. A medium on which an information processing program is recorded. 30. A medium on which the multidimensional information processing program according to claim 29 is recorded.
A medium on which a multi-dimensional information processing program is recorded, comprising a relation notation command unit for notifying a relation between a sampling variable and a response in the identified candidate solution space. A medium on which the multidimensional information processing program according to any one of claims 19 to 30 is recorded,
The sampling is composed of a combination of a variable and a plurality of responses,
An arbitrary response notation command unit that displays on the two-dimensional plane only a response arbitrarily selected from the plurality of responses;
A medium on which a multidimensional information processing program is recorded. A medium on which the multidimensional information processing program according to claim 31 is recorded,
A medium on which a multidimensional information processing program is recorded, comprising a superimposition command unit that superimposes a plurality of two-dimensional planes displayed by the arbitrary response notation command unit. A medium on which the multidimensional information processing program according to any one of claims 30 to 32 is recorded,
A medium on which a multi-dimensional information processing program applied to a development system for developing a product by evaluating one of the plurality of responses is recorded by a plurality of performance evaluation departments,
A section-specific response notation command section that displays on the two-dimensional plane only the response evaluated by each performance evaluation section;
A plurality of two-dimensional planes written by the departmental response notation command unit, and a comprehensive response display command unit for expressing the overall response of the product;
A notification command unit that compares the candidate solution space of the overall response and the candidate solution space of the sector-specific response, and notifies each performance evaluation department of the comparison result information;
A medium on which a multidimensional information processing program is recorded. A medium in which the multidimensional information processing program according to any one of claims 19 to 33 is recorded,
The sampling consists of a combination of variables and responses,
A variable generation command unit for generating a new variable with a predetermined probability distribution with respect to the variable;
A dispersion calculation command unit for calculating a variance of responses corresponding to each variable generated by the variable generation command unit;
A dispersion display command unit for expressing the dispersion on the two-dimensional plane;
A medium on which a multidimensional information processing program is recorded. A medium on which the multidimensional information processing program according to claim 34 is recorded.
A confidence interval setting command unit for setting a confidence interval for the variance;
A medium on which a multi-dimensional information processing program is recorded, wherein the medium is a reliability candidate solution notation command unit that represents only sampling having variance within a confidence interval set by the confidence interval setting command unit. 36. A medium on which the multidimensional information processing program according to claim 35 is recorded.
A medium on which a multi-dimensional information processing program is recorded, wherein a boundary sampling generation command section for generating new sampling is provided in the vicinity of sampling having variance within the confidence interval. For a system having responses to multiple variables, when there are multiple samplings of combinations of the variables and / or the responses of the system,
An inter-sampling distance that outputs a command for calculating the Euclidean distance between the samplings as an inter-sampling distance is calculated, an arbitrary one is selected from the samplings as a first sampling, and an initial position is set on a two-dimensional plane Position setting means;
A second sampling arrangement means for selecting the sampling with the shortest sampling distance as the second sampling, and arranging the sampling at a position corresponding to the sampling distance on the basis of the initial position on the two-dimensional plane;
A reference centroid calculating means for outputting a command for calculating a reference centroid that is a centroid of sampling already arranged on the two-dimensional plane;
The sampling having the shortest distance between the second sampling and the sampling is selected as the third sampling, and the third sampling and the second sampling are selected based on the position of the second sampling and the position of the reference centroid on the two-dimensional plane. A third sampling arrangement means for arranging the third sampling at a position corresponding to a sampling distance between two samplings and a sampling distance between the third sampling and the reference centroid;
After the fourth sampling, the newly selected sampling is regarded as the third sampling, the previous sampling is regarded as the second sampling, the second sampling arrangement means, the reference centroid calculating means, and the third sampling Repetitive means for arranging the plurality of samplings by implementing sampling arrangement means;
Display means for displaying results arranged on the two-dimensional plane by the repeating means;
A multidimensional information display device characterized by comprising: The multidimensional information display device according to claim 37,
The reference centroid calculating means is a means for calculating a centroid between the first sampling position and the second sampling position on the two-dimensional plane as a reference centroid,
After the fourth sampling, the repetition means regards the newly selected sampling as the third sampling, regards the sampling selected immediately before as the second sampling, and determines the sampling selected two times before as the first sampling. A multi-dimensional information display device that is regarded as sampling and is means for implementing the second sampling arrangement means, the reference centroid calculation means, and the third sampling arrangement means. For a system having responses to a plurality of variables, when there are a plurality of processing target clusters having a plurality of samplings composed of combinations of the variables and / or the responses of the system, a center of gravity is calculated for each of the plurality of processing target clusters. Calculating the distance between the centers of gravity of the plurality of processing target clusters, arranging the processing target clusters so as to maintain the distance between the center of gravity of the plurality of processing target clusters, and performing the processing for each of the plurality of processing target clusters. Select any one of the samplings in the target cluster, place it as an initial position on the two-dimensional plane, calculate the Euclidean distance between the samplings in the processing target cluster for each of the plurality of processing target clusters, and select the most Euclidean A sampling with a small distance is extracted, and the plurality of processing target clusters are extracted. The shortest distance sampling in the processing target cluster is arranged at a position corresponding to the Euclidean distance with the initial position on the two-dimensional plane as a reference, and samplings existing on the boundary surface of each processing target cluster The arrangement state display means for moving the sampling according to the Euclidean distance and displaying the result of combining the plurality of processing target clusters,
Display means for displaying the sampling variables and / or the response on the two-dimensional plane;
A multidimensional information display device characterized by comprising: The multidimensional information display device according to claim 39,
The plurality of clusters to be processed are a plurality of clusters formed by dividing a system having responses to a plurality of variables based on a Euclidean distance between samplings composed of combinations of the variables and / or the responses of the system. A multidimensional information display device characterized by The multidimensional information display device according to claim 39,
The plurality of clusters to be processed are hierarchically defined using a hierarchical clustering method based on a Euclidean distance between samplings composed of combinations of the variables and / or the responses of the system with respect to a system having responses to a plurality of variables. A multi-dimensional information display device, which is a plurality of clusters formed by forming clusters on the screen and designating an arbitrary layer of the formed layers. When there are a plurality of samplings composed of combinations of a plurality of variables, the axes corresponding to the variables are set on a two-dimensional plane so as not to overlap in the direction of travel, the variables are plotted on the attribute axes, and the plotted Shaped display means for displaying the result of shaping the sampling based on a variable;
Display means for calculating the center of gravity of the shape and displaying the center of gravity of the shape corresponding to the plurality of samplings on one two-dimensional plane;
A multidimensional information display device characterized by comprising: The multidimensional information display device according to any one of claims 37 to 42,
A multi-dimensional information display device comprising sampling pattern display means for displaying a combination of the variable and / or the response for each sampling. The multidimensional information display device according to any one of claims 37 to 43,
The multi-dimensional information display device, wherein the display means displays the variable and / or the response value in color. In the multidimensional information display device according to any one of claims 37 to 44,
The sampling consists of a combination of variables and responses,
A candidate solution space display means for setting a threshold for the response and displaying only a sampling having a response larger than the threshold or a sampling having a small response on the two-dimensional plane;
A multidimensional information display device characterized by comprising: In the multidimensional information display device according to claim 45,
A multidimensional information display device comprising boundary sampling display means for generating and displaying new sampling around the candidate solution space displayed by the candidate solution space display means. The multidimensional information display device according to claim 46,
Of the new samplings generated by the boundary sampling display means, only the sampling satisfying the threshold value is displayed, and boundary specifying display means for specifying and displaying the boundary of the candidate solution space is provided. Multidimensional information display device. The multidimensional information display device according to claim 47,
Relationship notation means for notifying the relationship between sampling variables and responses in the identified candidate solution space;
Relationship display means for displaying the expressed relationship;
A multidimensional information display device characterized by comprising: The multidimensional information display device according to any one of claims 37 to 48,
The sampling is composed of a combination of a variable and a plurality of responses,
An arbitrary response display means for displaying only an arbitrarily selected response on the two-dimensional plane among the plurality of responses;
A multidimensional information display device characterized by comprising: The multidimensional information display device according to claim 49,
A multi-dimensional information display device comprising superimposing display means for superimposing and displaying a plurality of two-dimensional planes displayed by the arbitrary response display means. The multidimensional information display device according to any one of claims 48 to 50,
A multi-dimensional information display device applied to a development system that performs product development by each of a plurality of performance evaluation departments evaluating one of the plurality of responses,
Department-specific response display means for displaying only the response evaluated by each performance evaluation department on the two-dimensional plane;
A plurality of two-dimensional planes displayed by the departmental response display means, and a comprehensive response display means for displaying a comprehensive response of the product;
A notification means for comparing the candidate solution space of the overall response and the candidate solution space of the sector-specific response, and notifying each performance evaluation department of the comparison result information;
A multidimensional information display device characterized by comprising: The multidimensional information display device according to any one of claims 37 to 51,
The sampling consists of a combination of variables and responses,
A variable display means for generating a new variable with a predetermined probability distribution for the variable, calculating a variance of a response corresponding to each generated variable, and displaying the variance on the two-dimensional plane;
A multidimensional information display device characterized by comprising: The multidimensional information display device according to claim 52,
A multi-dimensional information display device, which is a reliability candidate solution display means for setting a confidence interval for the variance and displaying only sampling having a variance within the confidence interval. The multidimensional information display device according to claim 53,
A multidimensional information display device comprising boundary sampling generation display means for generating and displaying a new sampling in the vicinity of sampling having a variance within the confidence interval. For a system having responses to multiple variables, when there are multiple samplings of combinations of the variables and / or the responses of the system,
An inter-sampling distance calculating step for outputting a command for calculating the Euclidean distance between the samplings as an inter-sampling distance;
An initial position setting step of selecting an arbitrary one from the samplings as the first sampling and outputting a command to place it as an initial position on a two-dimensional plane;
Second sampling that selects the sampling with the shortest distance between the first sampling and the second sampling as the second sampling, and outputs a command to be placed at a position corresponding to the sampling distance on the basis of the initial position on the two-dimensional plane. A placement step;
A reference centroid calculating step for outputting a command to calculate a reference centroid that is a centroid of sampling already arranged on the two-dimensional plane;
The sampling having the shortest distance between the second sampling and the sampling is selected as the third sampling, and the third sampling and the second sampling are selected based on the position of the second sampling and the position of the reference centroid on the two-dimensional plane. A third sampling arrangement step of outputting a command to arrange the third sampling at a position corresponding to a sampling distance between two samplings and a sampling distance between the third sampling and the reference centroid;
After the fourth sampling, the newly selected sampling is regarded as the third sampling, the previous sampling is regarded as the second sampling, the second sampling arrangement step, the reference centroid calculating step, and the third sampling A repetition step for outputting a command for performing the sampling arrangement step;
A multidimensional information processing method characterized by comprising: The multidimensional information processing method according to claim 55,
The reference centroid calculating step is a step of calculating a centroid of the first sampling position and the second sampling position on the two-dimensional plane as a reference centroid,
In the repetition step, after the fourth sampling, the newly selected sampling is regarded as the third sampling, the previous sampling is regarded as the second sampling, and the second previous sampling is regarded as the first sampling. A multidimensional information processing method characterized by being regarded as sampling and performing the second sampling arrangement step, the reference centroid calculation step, and the third sampling arrangement step. For a system having responses to a plurality of variables, when there are a plurality of processing clusters having a plurality of samplings composed of combinations of the variables and / or the responses of the system,
Calculating a center of gravity for each of the plurality of processing target clusters;
Calculating a distance between centroids of the plurality of processing target clusters;
Arranging each of the processing target clusters so as to maintain the distance between the centers of gravity of the plurality of processing target clusters;
Selecting an arbitrary one from the sampling in the processing target cluster for each of the plurality of processing target clusters, and arranging as an initial position on a two-dimensional plane;
Calculating a Euclidean distance between samplings in the processing target cluster for each of the plurality of processing target clusters, and extracting a sampling having the smallest Euclidean distance;
Arranging the shortest distance sampling in the processing target cluster for each of the plurality of processing target clusters at a position corresponding to the Euclidean distance with reference to the initial position on the two-dimensional plane;
Moving the sampling according to the Euclidean distance between the samplings existing on the boundary surface of each processing target cluster, and combining the plurality of processing target clusters;
Marking the variables and / or the response of the sampling on the two-dimensional plane;
A multidimensional information processing method characterized by comprising: The multidimensional information processing method according to claim 57,
The plurality of processing target clusters is a cluster formed by dividing a system having responses to a plurality of variables based on a Euclidean distance between samplings composed of combinations of the variables and / or the responses of the system. A multidimensional information processing method characterized by being. The multidimensional information processing method according to claim 57,
The plurality of clusters to be processed are hierarchically defined using a hierarchical clustering method based on a Euclidean distance between samplings composed of combinations of the variables and / or the responses of the system with respect to a system having responses to a plurality of variables. A multi-dimensional information processing method, characterized in that a plurality of clusters are formed by forming clusters in and specifying an arbitrary hierarchy of the formed hierarchies. When there are multiple samplings consisting of combinations of multiple variables,
Setting an axis corresponding to each of the variables on the two-dimensional plane so as not to overlap in the direction of travel;
Plotting the variable on the attribute axis and shaping the sampling based on the plotted variable;
Calculating the center of gravity of the shape;
Expressing the center of gravity of the shape corresponding to the plurality of samplings on one two-dimensional plane;
A multidimensional information processing method characterized by comprising: The multidimensional information processing method according to any one of claims 55 to 60,
A multidimensional information processing method comprising a step of notifying a combination of the variable and / or the response for each sampling. A multidimensional information processing method according to any one of claims 55 to 61,
A multidimensional information processing method, wherein when the variable and / or the response of the sampling are expressed on the two-dimensional plane, the value of the variable and / or the response is displayed in color. The multidimensional information processing method according to any one of claims 55 to 62,
The sampling consists of a combination of variables and responses,
Setting a threshold for the response;
Noting on the two-dimensional plane as a candidate solution space only samples having a response greater than the threshold or samples having a small response;
A multidimensional information processing method characterized by comprising: The multidimensional information processing method according to claim 63,
A multidimensional information processing method, comprising the step of generating a new sampling around the candidate solution space. The multidimensional information processing method according to claim 64,
A multi-dimensional information processing method comprising: a step of notifying only sampling satisfying the threshold value among new samplings generated in the vicinity of the candidate solution space, and specifying a boundary of the candidate solution space . The multidimensional information processing method according to claim 65,
A multidimensional information processing method comprising: a step of notifying a relationship between a sampling variable and a response in the identified candidate solution space. In the multidimensional information processing method according to any one of claims 55 to 66,
The sampling is composed of a combination of a variable and a plurality of responses,
A multidimensional information processing method, comprising: a step of notifying the arbitrarily selected response of the plurality of responses on the two-dimensional plane. The multidimensional information processing method according to claim 67,
A multidimensional information processing apparatus, comprising: a step of superimposing a plurality of two-dimensional planes on which only the arbitrary response is described. The multidimensional information processing apparatus according to any one of claims 66 to 68,
A multi-dimensional information processing method applied to a development system that performs product development by each of a plurality of performance evaluation departments evaluating each of the plurality of responses,
Noting only the response evaluated by each performance evaluation department on the two-dimensional plane;
Overlaying a plurality of two-dimensional planes represented by each performance evaluation department, and notifying the overall response of the product;
Comparing the candidate solution space of the overall response with the candidate solution space of the departmental response, and notifying each performance evaluation department of comparison result information;
A multidimensional information processing method characterized by comprising: The multidimensional information processing method according to any one of claims 55 to 69,
The sampling consists of a combination of variables and responses,
Generating a new variable with a predetermined probability distribution for the variable;
Calculating a variance of responses corresponding to each of the generated variables;
Expressing the variance on the two-dimensional plane;
A multidimensional information processing method characterized by comprising: The multidimensional information processing method according to claim 70,
Setting a confidence interval for the variance;
Noting only sampling with variance within the set confidence interval;
A multidimensional information processing method characterized by comprising: The multidimensional information processing method according to claim 71,
A multidimensional information processing method, comprising the step of generating a new sampling in the vicinity of a sampling having a variance within the confidence interval.

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