JP2008059106A - Apparatus for generating sampling, medium recorded with sampling generation program, and method for generating sampling - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a sampling generation technique capable of enhancing accuracy in limited computing time. <P>SOLUTION: An apparatus for generating samplings includes: a restriction element model generating means for generating new restriction element models that differ by a set Euclidian distance with reference to restriction elements that make up samplings, when there is a set of samplings consisting of combinations of a plurality of restriction elements and characteristics indicating the relationship between inputs and outputs to a system defined by the restriction elements; and a sampling generating means for generating new samplings consisting of combinations with the characteristics defined by the new restriction element models. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a technique for reproducing a design object as a computer model and generating sampling using a computer.

  Conventionally, there has been a method of grasping the relationship between design variables and characteristics by computing the computer model characteristics while changing the design variables (for example, structural dimensions and rigidity) while making the design object a computer model on a computer. Are known. However, since the types of design variables that can be changed among a plurality of design variables are limited, there is a problem that the relationship between the design variables and characteristics cannot be grasped with sufficient accuracy.

Therefore, in the technique described in Patent Document 1, an approximate expression (hereinafter referred to as a response surface) of the relationship between the design variable and the characteristic is created based on the discrete data of the combination of the relationship between the small design variable and the characteristic. ing. Thus, accuracy is improved by obtaining an approximate value even in a range where there is no data between discrete data. Specifically, an optimization method is disclosed in which a response surface is created and a design variable whose characteristic has an optimum value is obtained based on the response surface.
JP 2003-16114 A

  In the conventional technique for creating a response surface, since the response surface is an approximate expression, the accuracy decreases as the number of discrete data as a basis thereof decreases. However, increasing the number of discrete data means that the design time is increased as it is, and it is difficult to obtain an optimum value with high accuracy in a limited time. That is, there is a trade-off relationship between calculation time and accuracy.

  The present invention has been made paying attention to the above-described problems, and an object of the present invention is to provide a sampling generation technique capable of improving accuracy with a small calculation time.

  In order to achieve the above object, in the sampling generation apparatus of the present invention, a sampling set composed of a combination of a plurality of limiting elements and characteristics representing the relationship between an input and an output with respect to a system defined by these limiting elements is provided. At a certain time, a new limiting element model that differs by a set Euclidean distance is generated on the basis of the limiting element, and a combination with the characteristic defined by the new limiting element model is generated as a new sampling.

  In the present invention, when there are a plurality of system samples defined by the limiting element, it is possible to generate a new sampling in the vicinity of the existing sampling, and the sampling density can be increased efficiently.

  Hereinafter, the best mode for realizing the sampling generation technique 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 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.

  Note that the sampling generation technique in the embodiment may be incorporated in advance in the arithmetic processing unit 1, or the sampling generation program may be stored in a medium such as a CD-ROM, or the sampling generation program may be stored in a server or the like. You may memorize | store and use it, downloading suitably.

  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 the multidimensional information of the system intuitively, quantitatively, and efficiently, the horizontal axis arranged based on the Euclidean distance of each sampling, The characteristic is expressed using the vertical axis and the horizontal axis as the design space.

As shown in FIG. 2, this system is roughly divided into the following steps.
In step S1, an initial model is generated (initial model generation unit).
In step S2, the characteristics of the initial model are calculated (calculation unit).
In step S3, the complex phenomenon is divided (complex phenomenon dividing unit).
In step S4, a hierarchical response surface approximation formula is created (hierarchical response surface approximation formula creation unit)
In step S5, it is determined whether or not steps S2 to S4 have been executed a predetermined number of times, and if executed, this control flow is terminated, and otherwise, the process proceeds to step S6.
In step S6, a new model is generated in the divided local phenomenon space (sampling generation unit), and steps S2 to S4 are repeatedly executed.

  In the initial model generation unit in step S1, model generation using random numbers may be performed. The model places control variables (limit elements) that make up the structure. However, when dealing with a very complicated phenomenon, the initial model generation using random numbers has the following two problems. The first problem is that at the stage of creating a hierarchical response surface approximation formula after division of complex phenomena, it affects the accuracy of the hierarchy and approximation formula for creating the approximation formula from the difference in the density of the design pattern with respect to the design area. That is. The second problem is that the difference in the density of the model in the initial model generation also affects the efficiency in step S6 for improving the accuracy of the approximate expression.

  Such a problem becomes prominent when the phenomenon to be handled is complicated. Therefore, when dealing with complex phenomena, a method using an orthogonal table that can investigate a wide area is recommended. In addition, when a very large number of models need to be generated, it is possible to generate a model that is uniform over a wide area by using model generation by rotation of orthogonal coordinates in the orthogonal table.

  In the calculation unit in step S2, a characteristic value is extracted by calculation using general-purpose structural analysis software based on the structure generated by the initial model.

  The complex phenomenon dividing unit in step S3 hierarchically divides the complex phenomenon for each feature of the phenomenon by applying hierarchical clustering and performing clustering based on the design pattern (combination of a plurality of limiting elements). Details will be described later.

  The hierarchical response surface approximation formula creation unit in step S4 creates a response surface approximation formula for the characteristics corresponding to the design pattern for each phenomenon space divided in step S3. This is because the approximation accuracy is improved as it goes from the uppermost cluster representing the complex phenomenon itself to the lower cluster.

  The model generation unit in the local phenomenon space in step S6 generates a model that matches the target cluster when it is desired to improve the approximation accuracy with the lowermost cluster. Steps S2, S3, and S4 are performed again based on the model generated here.

Below, the background which comprised the said step is demonstrated.
The detailed design stage is a design stage in which the completeness is maximized based on the basic structure of the product determined in the concept design stage and the basic design stage. In this design stage, the design is conventionally performed using CAE (Computer Aided Engineering) technology. In other words, detailed design is performed by CAD (Computer Aided Design), structural analysis such as FEM (Finite Element Method) for structural verification, and Response Surface Method (RSM) for structural optimization. A representative optimization method is used.

  The basics of these technologies have already been established, and with the recent development of computer technology, it has become possible to easily simulate even very complex phenomena that are close to reality, dramatically improving design productivity and efficiency. It is improving. These techniques improve the efficiency by handling discrete numerical information, and the effect is particularly great in the optimization technique.

  For example, the response surface method, which is one of the optimization techniques, creates an approximate function between design variables and characteristic values by using several points of analysis or experimental results to satisfy various design constraints. The optimal design variable is derived by solving the created approximation function. In addition, it can be said that the use of such an approximate function has a great advantage in design such that approximate sensitivity calculation can be easily performed.

  In recent years, many techniques for improving the efficiency have been proposed, such as a method using an experimental design method for efficiently setting parameters of analysis and experimental points. In this way, by replacing an actual complex physical phenomenon with an approximate function composed of discrete numerical information that is easy to handle, it is possible to efficiently derive optimal values using existing mathematical solutions. It becomes possible.

  However, since such technology replaces physical information with discrete numerical information, it does not provide the designer with a physical description of the actual physical phenomenon, only the relationship between input and output. Cannot be provided.

  Therefore, for example, when a design change occurs in the detailed design stage, it is often impossible to establish a design guideline from the information provided, and the design routine for design / verification / optimization is performed again. The efficiency of this will be reduced.

  In order to solve this problem, it is necessary to provide the designer with physical design information that exists between the structure and the physical phenomenon that it represents. Such design information enables the designer to physically understand the relationship between the structure of the design object and the phenomenon. Since it is possible to understand the design derived through the black box of the existing CAE technology using discrete numerical information, it is considered that the reliability of the designer's design is improved. . From this understanding, it can be considered that a guideline for redesign can be established to some extent when a design change occurs. However, with existing CAE technology, there is no method that can provide such design information.

  In the first embodiment, in a detailed design stage for determining a detailed part of a product, a structure using physical design information and a complex physical phenomenon indicated by the structure are used for the purpose of physical understanding of a design object and efficiency at the time of design change. We propose a method that can provide an accurate relationship with.

  Two major features of this method are the division of complex physical phenomena and the exact approximation of the individual physical phenomena that have been divided. In the detailed design stage, as the various functions are combined, that is, the structure is complicated, the physical phenomenon represented by the functions is often complicated.

  However, complex physical phenomena are expressed as a result of a combination of simple physical phenomena exhibited by various features of individual functions and structures. Hierarchical structures based on the characteristics of complex phenomena to individual simple phenomena It is thought that Here, hierarchical clustering is applied based on physical design information (design patterns) to divide complex physical phenomena.

  In addition, as the complex phenomenon space in the uppermost layer goes to the individual phenomenon space in the lower layer, the design patterns that compose it become more similar for each feature, so the approximation created in the lower layer phenomenon space has high accuracy. Is expected to have In this method, the approximation by the response surface method was used to create the approximate expression for each layer.

  The method developed in this way is a method of hierarchically clustering a set of physical design information-physical phenomena with a design pattern and creating a response surface approximation formula for each clustered layer. Surface Method: H-RSM) By clustering with design patterns using this method, the influence of outliers can be eliminated even when the estimation range is wide, and cases can be classified with similar design patterns. can do. When updating the response surface approximation formula, necessary data can be known from the clustered design pattern.

[Hierarchical response surface methodology]
Hierarchical response surface concept In the conventional response surface method, in order to derive an optimal structure, a design variable constituting the structure is generally assigned to a predictive variable. However, here, physical phenomena are assigned to predictive variables in order to extract an accurate relationship between the physical design information and the characteristics of the structure in a complex phenomenon. From this, it becomes possible to derive the relationship between the physical phenomenon and the characteristic of the structure in a certain structure. Here, a variable string of physical phenomena (corresponding to a plurality of limiting elements) assigned to a predictive variable is referred to as a “design pattern”.

  The response surface approximation formula used in the response surface method is created by using some analysis or sample points of experimental results as an approximation function between design variables and characteristic values. Therefore, the regression accuracy of the response surface approximation formula is strongly influenced by the sample points as the phenomenon becomes more complex.

  Conventional methods for creating highly accurate response surface approximation formulas include methods that devise combinations of sample points so as to increase accuracy, and methods that update response surfaces sequentially during the optimization process. Has been studied.

  In any case, since the estimation accuracy depends on the data amount for creating the response surface approximation formula, the data amount increases as the estimation range widens. In addition, it is difficult to examine what kind of data is necessary when updating the response surface approximation formula for higher accuracy. However, considering the physical phenomenon of the structure, the characteristic phenomenon shown for each feature of the physical phenomenon may be different. That is, the conventional response surface method takes into account the physical phenomenon and the characteristic phenomenon of all the structures at the same time, and therefore requires a large number of sample points to create an approximate expression for explaining all of them.

  On the other hand, if a complex phenomenon is divided into features of structural physical phenomena, each divided phenomenon space is composed of sample points with similar physical phenomenon characteristics, that is, design patterns. It is conceivable that the approximation in the phenomenon space is highly accurate.

  Since complex phenomena have a hierarchical structure that gradually changes into simple phenomena for each feature of the structure, hierarchical clustering analysis (HCA) is applied to divide the complex phenomenon.

  In this method, a set of control variables (limit elements) -characteristic values (characteristics) is hierarchically clustered with a design pattern that is the shape of a control variable, and a response surface approximation formula is created for each clustered hierarchy.

  By using the hierarchical clustering described here, various design patterns composed of many sample points can be classified and considered as a set of similar patterns. It can be expressed by a combination of simple response surfaces, and the approximation becomes easy.

  Further, by hierarchizing, it is possible to approximate from a global response surface to a response surface of a local group with high approximation accuracy. Further, when the approximation accuracy of the response surface is further improved, the design pattern of sample points necessary for the update can be easily estimated from the cluster.

  An outline of the hierarchical response surface methodology is shown in FIG. As described in the flowchart of FIG. 2, the hierarchical response surface method is divided into four main parts: data generation for the initial cluster, hierarchical clustering, creation of a hierarchical response surface approximation formula, and update of the cluster and response surface. It is configured.

  By using the hierarchical response surface approximation formula obtained by this method, it becomes possible to provide the designer with the relationship between the design pattern, which is physical design information that can accurately explain complex phenomena, and the characteristics of the structure. It is thought that it will be possible to promote understanding of, and it will be possible to give design hints for design reuse.

[Data generation for initial cluster]
In order to perform hierarchical clustering, a design pattern is first generated. Here, in order to create a globally equivalent combination, an orthogonal table of an experimental design method is used. The orthogonal table has been widely used as a method for efficiently analyzing the influence of factors on characteristic values with a small number of calculations, focusing mainly on quality control. One characteristic of the orthogonal table is that all two factors in the table are orthogonal. That is, the degree of influence of the design factor on the characteristic value can be obtained independently for each factor without being influenced by other design factors.

  The orthogonal condition requires that the number of repetitions of the level of each factor is the same, and that the inner product is zero for any two columns of each factor. Currently, there are several types of orthogonal tables in which combinations of the number of factors and levels that satisfy these conditions are set. Here, a globally equivalent combination is created using an orthogonal table. However, when performing cluster analysis, a large combination is often required to some extent. In this case, by using the orthogonal relationship described above and rotating the orthogonal coordinates, it is possible to obtain a globally uniform and substantially non-overlapping combination.

(Hierarchical clustering)
4 and 5 are schematic explanatory diagrams showing the processing of hierarchical clustering. 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 first embodiment, in order to understand complicated phenomena, hierarchical clustering is used to classify complex phenomena while systematizing them. Clustering is an object of creating a community (hereinafter referred to as a cluster) by gathering similar things together in order to efficiently organize into a meaningful system from a group of different properties mixed together. 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 is adopted in the first embodiment, as described above, that 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 the trend system for understanding the relationship of the hierarchical systems.

  For example, when non-hierarchical clustering is performed, a threshold value or the like is set in advance, and operations within this threshold value are clustered. This threshold value may lead to the introduction of an existing concept. 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.

  In addition, when complex phenomena are classified hierarchically, a cluster in a certain hierarchy can be handled as a unit of unit 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 on the basis of similarity or dissimilarity, and gradually becoming smaller clusters. 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).

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、クラスタ数を一つ減らす。 (II) Combine cluster pairs with maximum similarity (or minimum similarity).

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 .

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

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

Here, a two-dimensional plane passing through three points M (Gq), M (Gr), and M (Gi) in the Euclidean space where the individual exists is considered, and 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).

(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 .

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

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

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

従って、ΔE(Gi,Gj)は式（A.26）のように展開できる。

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

Therefore, ΔE (Gi, Gj) can be expanded as shown in equation (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。

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

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

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。

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。

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

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

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).

  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, by storing only the similarity between clusters according to the recalculation formula, it can be said that it is efficient because the clusters are combined and it is not necessary to refer to many similarities.

FIG. 4 shows a cluster generation method based on the above algorithm, and FIG. 5 shows an example of hierarchical clustering. Here, the cluster generation method is summarized as follows based on FIG.
(A) The 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) Join 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, cluster division and combination will be described.

  FIG. 5 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. 5, a cluster surrounded by a dotted line is represented. Each cluster is numbered as cluster 1 to cluster 4.

  Hierarchical clustering is performed on the initial sample points based on the design pattern according to the AHC described above. As a result, the lower the cluster, the more the cluster composed of samples that do not include outliers or heterogeneous design patterns. Therefore, it is considered that the approximation using the sample points included in the target cluster has higher accuracy as the lower cluster is reached.

[Creation of hierarchical response surface approximation formula]
A response surface approximation formula is created using data of each cluster classified by hierarchical clustering.

  The response surface method is a method of obtaining an approximate function and using it for optimization regardless of the function shape, but the function of a linear function or a function that can be linearized and transformed can be statistically calculated using the least square method. Can be estimated.

ただし、kは制御変数の数、x_iは制御変数、βは多項式係数である。また２次の多項式を作成するために必要なサンプル点の個数Sは式(3.13)となる。

したがって、階層的クラスタリングによって階層化したデータを用いて、各階層で応答曲面近似式を作成する場合、Sを基準とし、Sを満たす階層以上の各層で応答曲面近似式を作成する。 When a quadratic polynomial is adopted as the response function, the response surface approximation formula is expressed as equation (3.12).

Here, k is the number of control variables, x _i is a control variable, and β is a polynomial coefficient. In addition, the number S of sample points necessary to create a second-order polynomial is expressed by Equation (3.13).

Therefore, when a response surface approximation formula is created in each layer using data hierarchized by hierarchical clustering, a response surface approximation formula is created in each layer higher than the level satisfying S with S as a reference.

  FIG. 6 shows an outline of the relationship between sample points arranged in a wide area and groups clustered as a result of hierarchical clustering. Here, it is assumed that each sampling design pattern is arranged on a plane according to the Euclidean distance. Then, it is assumed that a third axis in the vertical direction is set on the plane, and a characteristic value is set on the third axis.

  While the cluster in the uppermost layer is a group representing all phenomena, the complexity of the phenomenon is differentiated as the features of the design pattern are grouped in the lower layers. Therefore, from this relationship, the more complicated the phenomenon represented by the characteristic, the worse the approximation accuracy in the upper-layer cluster that explains the phenomenon of the wide-area characteristic with the wide-area design pattern. However, in the lower layer direction, since the division of the complex phenomenon proceeds, both the characteristic region and the design pattern region are narrowed, so that the approximation accuracy is considered to be improved. Using this relationship, that is, the relationship between the hierarchical differentiation of complex phenomena and the response surface approximation formula of each layer, the complexity of the phenomenon can be increased by examining the relationship between the complex characteristic phenomenon and the design pattern by tracing the hierarchy from the lower layer. The cause of this can be explained in detail from the characteristics of the design pattern.

  That is, as shown by the arrow A in FIG. 6, the design pattern changes when the first layer is raised from the lowermost layer. However, there is a difference between the characteristic phenomenon caused by raising the hierarchy and the characteristic phenomenon of the lowermost layer. This is the effect of changing the design pattern. Differences in design patterns can be quantitatively determined by comparing the design patterns of the lowest layer and the upper layer, and differences in characteristic phenomena can be solved by solving response surface approximation formulas of the lower layer and the upper layer and comparing them. To understand.

  Similarly, when completely different design patterns are combined as in Cluster B of FIG. 6, the cause of the complicated phenomenon can be described in detail from the design features. The conventional response surface approximation formula corresponds to the top layer approximation formula of the hierarchical response surface approximation formula, but these relationships that could not be explained in the phenomenon space in the same dimension are represented by complex phenomena for each physical feature based on the design pattern. It became possible by dividing into two.

誤差２乗和を最小化することから、係数βの不偏推定量bは式(3.15)で表される。

ここから残差平方和SSEは式(3.16)で表される。

また、応答ｙの平均値まわりの変動Syyは式(3.17)で表される。

以上から、自由度調整済み決定係数R²は式(3.18)となる。

[Model generation to improve approximation accuracy]
The hierarchical response surface method is a method in which a set of control variables and characteristic values is clustered with a design pattern, and a response surface approximation formula is created for each clustered layer. Accordingly, the closer to the lower cluster in FIG. 6, the higher the approximation accuracy is because the influence of the outlier and the extraneous pattern can be removed. Here, the determination coefficient R ² adjusted for the degree of freedom is taken as an index representing the suitability of the regression model. The determination coefficient R ^{2 with} adjusted degrees of freedom compares the residuals per unit degree of freedom. The closer the R ² is to 1, the smaller the residuals are. In other words, the fitness of the regression model is high. Equation (3.12) can be linearized into a multivariable linear equation by replacing a higher order variable with a primary variable. When the total number of sample points used for estimating the coefficient β of the regression equation is n and the number of variables is k, Equation (3.12) can be displayed in a matrix in the linear regression model shown in Equation (3.14). Where ε is an error.

Since the error sum of squares is minimized, the unbiased estimation amount b of the coefficient β is expressed by Equation (3.15).

From this, the residual sum of squares SSE is expressed by equation (3.16).

Further, the fluctuation Syy around the average value of the response y is expressed by the equation (3.17).

From the above, the degree of freedom adjusted coefficient of determination R ² is a formula (3.18).

In order to improve the model fit of the lowermost response surface (closer to R ² to 1) is shown in FIG. 6, increasing the sample points, it is necessary to create a further lower possible surface approximation. Thereby, it becomes possible to consider separately the design pattern which has deteriorated the approximation accuracy.

  The model is generated with random numbers based on the combined Ward distance d (Gp) of the clusters located in the lowermost cluster composed of the minimum number of samples S. FIG. 7 is a diagram showing the relationship between the sampling design pattern included in the lowermost layer cluster Gp, a random distance model, and the adopted distance model.

In other words, as shown in Equation (3.19), when the Ward distance d (Gx, Gp) between the model Gx to be generated and the target lowermost cluster Gp is within the combined Ward distance d (Gp) of the target cluster, it is certain. It is possible to generate a model belonging to the target cluster.

  Therefore, when a design pattern is generated with random numbers, the Ward distance d (Gx, Gp) with the lowest layer cluster Gp is calculated, and this distance is within the combined Ward distance d (Gp) of the target cluster Determines that this design pattern is a new design pattern belonging to the lowermost cluster Gp, and calculates a characteristic corresponding to this design pattern to generate a new sampling. As a result, a plurality of samplings can be generated only in an area desired by the designer, and the calculation time can be reduced.

  When the approximation accuracy is improved, for example, when there is an optimum value in the peak portion of the approximate expression, the optimum value can be easily extracted by extracting the design pattern corresponding to the peak portion.

As described above, the effects listed below can be obtained in the first embodiment.
(1) When there is a set of samplings composed of a combination of multiple limiting elements and characteristics representing the relationship between the input and output for the system defined by these limiting elements, the design pattern that constitutes the sampling (the limiting elements) ) As a reference, a new design pattern (restriction element model) that differs by the set Euclidean distance is generated, and a new sampling composed of a combination with the characteristics defined by the new design pattern is generated.

  Therefore, new sampling can be generated in the vicinity of existing sampling, and the sampling density can be increased efficiently.

  (2) Arranging sampling based on the Euclidean distance between design patterns (between limiting elements), selecting an arbitrary range from the arranged sampling, and generating a new sampling within the selected range. did.

  Since the arranged sampling is arranged according to the degree of similarity of the design pattern, when an arbitrary range is selected, a set of design patterns that are similar in the range is selected. By generating new sampling in this range, it is possible to efficiently generate sampling only in the region focused on by the designer.

  (3) Specifically, sampling is classified hierarchically into a plurality of clusters based on the Euclidean distance between the limiting elements. Then, an arbitrary hierarchical cluster is selected from the plurality of clusters, an approximate expression is created for the characteristics of the selected hierarchical cluster, and an optimum value is extracted based on the approximate expression.

  Complex phenomena are divided into simple phenomena as they follow the hierarchy. Therefore, design patterns for a certain characteristic are extracted based on the Euclidean distance range by designating an approximate expression by designating a hierarchy. By generating new sampling that approximates the extracted design pattern, it is possible to extract the peak of characteristics with high accuracy, and to calculate an optimum value with higher accuracy.

  Next, Example 2 will be described. In Example 1, the initial sampling is clustered hierarchically, a response surface approximation formula is created for each layer, and a response surface approximation formula with higher accuracy is created as the hierarchy goes to the lower layer. At this time, in order to further improve the accuracy of the response surface approximation formula of the lowest layer, a design pattern is generated with random numbers, and a design pattern within the Euclidean distance constituting the lowest layer cluster is newly sampled among these design patterns. It was adopted as.

  On the other hand, in the second embodiment, the concept of “threshold value” is introduced, and the design space is divided to generate sampling more efficiently for the target area.

  FIG. 8 is a flowchart showing the flow of the technical concept of the second embodiment. Since Steps S1 to S3 are the same as those in the first embodiment, only different steps will be described.

In step S11, a characteristic threshold value is set. This threshold value is the minimum value that realizes the characteristics desired by the designer.
In step S12, a local model creation process is executed. This local model creation process will be described later.
In step S13, it is determined whether or not the local model creation process has been executed a prescribed number of times. If the local model creation process has been executed a prescribed number of times, the process proceeds to step S14. Otherwise, step S12 is repeatedly executed.

  In step S14, an area (design space) that satisfies the threshold is selected.

In step S15, an approximate expression is created for each region.
In step S16, the optimum value calculation is executed based on the created approximate expression.
It is comprised from the process. Hereinafter, the above steps will be described.

  Complex phenomena in the basic design stage can be defined as a wide design space that contains various values and has trade-offs between characteristics. Therefore, the design space to be handled is considered to be a complicated phenomenon that exhibits multimodality.

  On the other hand, a design candidate, which is one piece of information required in the basic design stage, can be defined as a design that satisfies the characteristic restrictions set by the designer as a minimum. If defined in this way, design candidates scattered in a wide design space can be divided into features of several design variables. This means that a complex phenomenon of a wide and complex design space is decomposed based on the characteristics of design variables.

  Therefore, when decomposing based on the characteristics of design variables, the Euclidean distance between the design variables of each sampling is calculated, and the complex phenomenon is expressed as a combination of individual phenomena by arranging based on this Euclidean distance. Express the design space with

  In this case, each phenomenon can be defined as a design set including several design candidates whose design variable features are similar (design candidates belonging to a predetermined range in which the Euclidean distance is close). Therefore, if the decomposition is performed based on the characteristics of the design variable until the characteristic constraint is satisfied, it can be considered that it becomes a design candidate with a design capacity.

  In the second embodiment, the restriction on characteristics set by the designer is defined as “Threshold”. In order to extract design candidates and their design capacities efficiently and accurately from complex design spaces, thresholds are introduced into the design space, focusing on areas where there is a high possibility of design candidates, and design candidates The precise range of design capacity, that is, the design boundary of the design candidate is grasped. Focused investigation of areas where design candidates exist does not investigate areas that are unlikely to be design candidates, and is considered to be very efficient at the basic design stage in which a wide design space is handled.

  As a result, a large number of design candidates such as design candidate 1 (DesignSpace 1), design candidate 2 (DesignSpace 2), design candidate 3 (DesignSpace 3),... As shown in FIG. The design candidates obtained in this trial are design candidates that only satisfy the threshold value. Therefore, in order to extract a design candidate that matches the designer's values, it is only necessary to extract the design area that best fits from the many design areas found in this trial.

  From the above, (i) introduction of threshold values, (ii) generation and calculation of initial models, (iii) in order to extract design areas that match the values that are the design information required in the basic design stage, Five steps are taken: generation and calculation of a model that satisfies the threshold, (iv) identification of the design area, and (v) extraction of the design area that matches the designer's values.

  Hereinafter, a method for generating a model intensively for a design area divided by a threshold and a method for extracting a design area that matches the designer's values will be described in detail.

(Local model creation processing)
By introducing a threshold value into the multimodal phenomenon, the entire wide design space can be divided into several design areas. In order to accurately grasp the characteristic shape of these design areas, a model is intensively generated for the divided design areas. As a result, the calculation efficiency when the design space is divided is calculated as compared with the curved surface approximation method represented by the conventional response surface method, which requires a large number of calculations to improve the approximation accuracy. Since it is possible to know in advance what does not need to be done, it is thought that it will be greatly improved. Here, we describe a model creation method using uniform random numbers for region identification.

[Local model creation algorithm using uniform random numbers]
As shown in FIG. 9, the set of design variables constituting one design area often shows a similar tendency. This is the same when the design variable is multidimensional. Therefore, in order to generate a model in the design area, a method for newly generating a similar model is required based on pre-calculated sample points in the design area. Here, the sample points calculated in advance use a model generated using a random number or an orthogonal table.

  As described above, in the second embodiment, as a method for generating a new multidimensional model in the design area, a method using a measure of distance between individuals used in a clustering grouping algorithm has been developed. In the clustering grouping algorithm, the distance between individuals is used as a measure for measuring the similarity (dissimilarity) between individuals. Various kinds of such scales have been proposed. In Example 2, the Euclidean distance, which makes it easy to imagine the degree of similarity between individuals and is easy to handle, is taken up.

Euclidean distance, when the value of k-th element of p elements constituting the individual x _i and x _i ^k, the distance d between individuals x _i -x _j, is defined by the equation (4.1) . Here, the element is a value included in the individual x _i .

The model is generated using uniform random numbers. Therefore, if x _{rand is} a model generated with uniform random numbers, x _c is a model that satisfies a pre-calculated threshold value, and x _o is a model that does not satisfy the threshold value, then the newly generated model and these distances are It is expressed by equations (4.2) and (4.3).

  Next, it is determined whether or not calculation is possible. This is because the generation of a model with uniform random numbers does not take into account any reference to a model in advance, so a model extremely similar to a model that satisfies the threshold may be generated. There are two problems that deteriorate the calculation efficiency, such as the possibility of generating a model closer to a model that does not satisfy the threshold than a model that satisfies the value.

Two restriction rules are provided to determine whether the model generated here is a good model or not, that is, whether or not it is actually calculated. First, the newly created model x _rand, already searched the calculated most Euclidean distance is smaller similar model in the model, if the closest model x _c satisfying the threshold, the new model It adopted, not in the case of model x _o that do not meet the threshold adopted. This restriction law is expressed by equation (4.4).

Then, to apply the limitation rule not to adopt an extremely similar model to the model x _c satisfying the threshold. For example, if the Euclidean distance is less than 0.01 and the two individuals are recognized to be almost the same, the newly generated model x _rand will follow the restriction law of equation (4.5) for the model that satisfies the threshold. Is adopted.

  In the following, a model generation algorithm will be described. Moreover, the image figure of the procedure in which a model is produced | generated was shown to FIG.10 (a) to (d).

  (a) For a design space including a model calculated in advance, as shown in FIG. In FIG. 10A, ● and x are values obtained by plotting the characteristic values of the initial model. On the other hand, ◯ is a model generated by random numbers, and since characteristic values and the like have not been calculated, it cannot be plotted in practice, but the points that are intentionally plotted are displayed for easy understanding.

  (b) Perform a primary determination as to whether to calculate the generated model. The determination is made using equation (4.4). As shown in FIG. 10B, Euclidean distances with all models already calculated are calculated. If it falls within the area indicated by the dark hatching in FIG. 10B, the closest model satisfies the threshold value. A model that falls within the thin hatching range indicates that the closest model does not satisfy the threshold value.

  (c) A secondary determination is made as to whether or not calculation is possible for the model adopted in (b). The determination is made using equation (4.5). Pay attention to the nearest model, and determine whether it is possible to calculate based on the closest distance. FIG. 10 (c) shows the result of classification as to whether to calculate the generated model.

  (d) Characteristic values are calculated for the remaining models, and models with uniform random numbers are generated again. In FIG. 10 (d), the calculated result is compared with the threshold value, the model that cleared the threshold value is indicated by ●, and the model that did not clear the threshold value is indicated by ○.

  By adopting the model according to the above generation rule and restriction rule and performing calculations, models that satisfy the threshold with a high probability gradually gather. By repeating the above operations a predetermined number of times set in advance, a large number of models can be generated only in the necessary design area, and the design area can be accurately grasped. Note that when there are many models calculated in advance, the number of models employed in the algorithm (b) increases, so that the efficiency of model generation for specifying a region is improved.

  In this way, by introducing the threshold value, the design space can be divided into a region that satisfies the threshold value and a region other than that. Select an area that meets this threshold, generate sampling intensively in this area, create a response surface using the existing response surface approximation method, and extract the peaks of the response surface to efficiently optimize the value. Can be extracted.

  As described above, in the configuration of the second embodiment, the same effects as those of the first embodiment can be obtained. In the first embodiment, when a new model is generated, a design pattern is generated by generating a random number in the selected cluster. Therefore, when the characteristic value is actually calculated, the case where the characteristic value is not satisfied is also included. There was a possibility. In other words, there is no problem if all of the selected clusters satisfy certain characteristics, but even if multi-peak valleys exist in the clusters, sampling is generated uniformly and efficiency is reduced. There was a problem to do.

  On the other hand, in the second embodiment, since it is determined whether or not to calculate the characteristic value of the model generated based on the Euclidean distance between the sampling that satisfies the threshold and the sampling that does not satisfy the threshold, the characteristic value is not satisfied. The calculation of the model (design pattern) can be suppressed as much as possible, and the occurrence of sampling that does not satisfy the characteristic value can be further suppressed.

  Next, Example 3 will be described. Since the basic configuration is the same as that of the second embodiment, only different points will be described. In the second embodiment, a threshold value is set, and local sampling generation processing is executed a specified number of times to generate sampling intensively in an area that satisfies the threshold value, and an existing response surface approximation to this area. A response surface was calculated by the method, and an optimum value was extracted based on the response surface. On the other hand, in the third embodiment, the optimum value is extracted without using the existing response surface approximation method by sequentially updating the threshold value.

  FIG. 11 is a flowchart showing the flow of the technical concept of the third embodiment. Since Step S1 to Step S12 are the same as those in the second embodiment, only different points will be described.

In step S21, the threshold value is increased by a predetermined value.
In step S22, it is determined whether or not the remaining number of samplings satisfying the threshold value is 1. If it is 1, it is determined that the calculation has been completed, and the process proceeds to step S23. Otherwise, steps S12 to S21 are performed. repeat.
In step S23, the last remaining sampling is extracted as an optimum value.

  FIG. 12 is a diagram illustrating the operation of the third embodiment. First, the design area 1 (DesignSpace1), the design area 2 (DesignSpace2), and the design area 3 (DesignSpace3) remain in the area that satisfies the threshold value set first. At this time, if the threshold value is raised, the design regions 1 and 3 are excluded from the design object because they do not satisfy the threshold value. Next, when the local model creation process is executed again in the design area 2 and the threshold value is further increased, the number of samplings is gradually reduced.

  By repeating the above steps, there is finally one sampling that satisfies the threshold value, which corresponds to the optimum value. In this way, by simply repeating the local sampling creation process while raising the threshold value, it is possible to easily extract the optimum value without creating a response surface approximation formula or the like.

  As described above, in the third embodiment, the following operational effects can be obtained. First, a threshold value of characteristics (first target) is set, and sampling having characteristics satisfying the threshold value is extracted from sampling characteristics.

  Next, a new design pattern (combination of a plurality of limiting elements) is generated by random numbers, and the Euclidean distance between this design pattern and the design pattern corresponding to the extracted sampling and the sampling not extracted is measured and close. Are considered to have the same attributes as the other design pattern. If it is close to the extracted sampling, it is determined that there is a high possibility that the threshold value is satisfied, and if it is close to the sampling that is not extracted, it is determined that there is a high possibility that the threshold value is not satisfied.

  That is, in step S12, the design pattern generated by random numbers is discriminated based on the Euclidean distance as to whether or not it is worth calculating the characteristic, and finally determined to be worth calculating the characteristic. The characteristic value is calculated using the limited element model. And the new sampling comprised from the combination with the characteristic value prescribed | regulated by this produced | generated new limiting element model is produced | generated (1st sampling production | generation step execution means).

  Next, the threshold value is raised (a second target is set) in a more optimal direction with respect to the initially set threshold value (first target) (second target setting means). Then, sampling having characteristics satisfying the raised threshold is extracted from the characteristics of the set including the new sampling generated in step S12 (second target reaching set extraction means).

  Step S12 is repeatedly executed for the extracted sampling (second sampling generation step execution means and repetition means), and finally the remaining sampling is extracted as an optimum value.

  As a result, it is possible to search for optimum values for all design regions as compared with the case where a designer extracts a specific region, and it is possible to extract optimum values with high reliability.

  Next, Example 4 will be described. Since the basic configuration is the same as that of the second embodiment, only different points will be described. In the second embodiment, a threshold value is set, and local sampling generation processing is executed a specified number of times to generate sampling intensively in an area that satisfies the threshold value, and an existing response surface approximation to this area. A response surface was calculated by the method, and an optimum value was extracted based on the response surface.

  That is, there is no problem when an optimum value is extracted as in the second embodiment, as long as the peak portion needs to be accurately grasped. However, when it is desired to grasp the capacity of the design space (DesignSpace), it is important to accurately grasp the boundary of the space that satisfies the threshold. The capacity of the design space is an index indicating how much the design space has a margin.

  Thus, in the fourth embodiment, sampling for identifying the boundary of the design space is efficiently generated. FIG. 13 is a flowchart illustrating the flow of the technical concept of the fourth embodiment. Since steps S1 to S11 are the same as those in the second embodiment, only different points will be described.

  In step S31, boundary local model creation processing is executed. Details of this processing will be described later.

  In step S32, it is determined whether or not a model that does not satisfy the threshold value has appeared. If it appears, this control flow is terminated, and if it does not appear, step S31 is repeatedly executed.

[Boundary local model creation processing]
In the basic design stage, it is required to accurately represent the design area and capture the features of the design area. On the other hand, in order to accurately grasp the design capacity, it is necessary to consider what the boundary of the design area, that is, the design boundary (Boundary of Design) is. In the fourth embodiment, a model generation method based on the Euclidean distance described in the second embodiment is applied to generate a model near the boundary in order to investigate the design boundary in detail.

  In Example 2, model generation using uniform random numbers was performed. In this case, since the model is generated without distinction between the design boundary and the design area, there is no guarantee that the design boundary can be accurately captured. Therefore, we developed a method for generating models intensively between the model that satisfies the closest threshold value across the design boundary and the model that does not satisfy the threshold value.

  As shown in FIG. 14, a model that satisfies the closest threshold value and a model that does not satisfy the threshold value are searched from pre-calculated models. It is considered that there is always a design boundary between these two points. Next, a model close to a model satisfying the threshold is generated from the models in the closest relationship. By repeating this, a model can be generated gradually from the region satisfying the threshold toward the design boundary. As a method of actively generating a model close to the threshold, a method of generating a design boundary random number model according to the Weibull distribution was devised.

The Weibull distribution is a nonlinear function that is used to approximate the time change of the failure rate with a small number of parameters. The phenomenon occurrence probability P (x) at a certain time x is defined as in Expression (4.6) using the occurrence pattern m.

Assuming that x in Equation (4.6) is the Euclidean distance of the model generation region that is set within the closest range, the model generation position is controlled by changing the m value in Equation (4.6) as shown in FIG. Is possible. Model generation based on the Euclidean distance of the model generation area facilitates handling of generation of a multidimensional model. Probability of the width d _w of the model generation region determined by Weibull random numbers, where x _{c is} the model that satisfies the threshold and x _o is the model that does not satisfy the threshold between the two closest models The density distribution is as shown in equation (4.7).

When the design boundary is specified from the model side that satisfies the threshold value, a new model can be generated with high probability in the vicinity of x _c by increasing the m value in Equation (4.7). Note that the m value in equation (4.7) must be set to an appropriate value in consideration of the closest distance and calculation efficiency. Next, a restriction rule for generating a model from the model side that satisfies the threshold value between the closest points toward the boundary is provided. The newly generated model x _w-rand is located within the model generation area width d _w obtained by the Weibull random number among the models generated by the uniform random number, and on the boundary side existing between the nearest two points. You must adopt what is located. Therefore, a newly generated model x _w-rand that conforms to the restriction law of equation (4.8) is adopted.

  According to this model generation method, model generation is performed in a state in which Expression (4.4), which is the restriction law of Example 2, is always satisfied. Therefore, it is necessary to generate a model that satisfies the restriction law equations (4.5) and (4.8). Also, the model generation end condition is that the model is generated from the region that satisfies the threshold toward the boundary, so when the generated model is calculated and the threshold is no longer satisfied, the design boundary is It is determined that it has been identified, and model generation is terminated. From the above, the model generation algorithm for obtaining the design boundary is as follows. Moreover, the image figure of model generation was shown to Fig.15 (a) to (d).

  (a) In a design space including a model calculated in advance, a model satisfying a threshold value in the closest relation and a model not satisfying the threshold value are searched. In the figure, a model that satisfies the threshold is indicated by ●, and a model that does not satisfy the threshold is indicated by ×.

  (b) A new model is generated on the model side that satisfies the nearest threshold value according to the generation rule of equation (4.7). A newly generated model is indicated by a circle.

  (c) It is determined whether the model generated in (b) can be calculated. Judgment uses formulas (4.5) and (4.8). In the figure, ◎ indicates a model that is determined to be the same by the formula (4.5) and is omitted, and ◯ indicates a model that actually calculates the characteristic value.

  (d) The above-described calculations (a) and (b) are performed again with the model that has passed the determination in (c) having undergone the calculation of the characteristic value as a model that satisfies the threshold value.

  By repeatedly performing the above steps, a model can be efficiently generated for the design boundary of the design region, and the design boundary can be specified. Note that when there are many models calculated in advance, the number of models employed in the algorithm (b) increases, so that the efficiency of model generation for specifying a region is improved.

  As described above, in the fourth embodiment, a threshold (characteristic target) is set, and sampling having characteristics that satisfy the threshold and sampling having characteristics that do not satisfy the threshold are extracted. Then, the design pattern is generated so as to be directed to the sampling design pattern that does not satisfy the threshold with reference to the sampling design pattern (limit element) that satisfies the threshold (Euclidean distance setting means and limit element model generation means). .

  Specifically, the design pattern is generated using a probability density distribution that generates a larger number of design patterns as the Euclidean distance is closer to a model that satisfies the threshold value. At this time, it is a condition that the generated design pattern is a predetermined distance away from the model satisfying the threshold, and exists between the model satisfying the threshold and the model not satisfying the threshold. Then, the characteristic value of the generated design pattern is calculated and repeated until the generated characteristic value of the design pattern does not satisfy the threshold value.

  As a result, the boundary of the design area can be accurately grasped, and the design range (design capacity) that can be designed can be grasped with high accuracy, so that the robustness of the design can be improved and the degree of freedom of design can be increased. .

  Next, Example 5 will be described. In the second embodiment, it is effective when the peak portion only needs to be accurately grasped in extracting the optimum value. In the fourth embodiment, a threshold value is introduced, and the boundary of the space that satisfies the threshold value, In other words, it is effective when it is desired to grasp the design capacity.

  However, if both of these can be estimated accurately, there is no need to rely on both methods, and if the entire design space is to be estimated accurately, consider improving the accuracy of the response surface approximation formula efficiently. It may be useful to do so. When creating a response surface approximation formula, the factor that lowers the estimation accuracy is lack of information on peaks and inflection points. That is, if the point where the characteristic changes is unknown, the response surface approximation formula is created based on the steady point. Therefore, if the information on peaks and inflection points can be increased efficiently, the accuracy of the response surface approximation formula inevitably improves.

  Here, as described in the first embodiment, when hierarchical clustering is executed, each cluster is an aggregate of similar ones. Therefore, at a cluster connection point, a characteristic peak (including a mountain valley) or a variable is always present. I found that there was a music point.

  Therefore, in the fifth embodiment, focusing on this cluster connection point, sampling is concentrated in the vicinity of the cluster connection point, thereby improving the accuracy of the cluster connection point and improving the accuracy of the response surface approximation formula. It is something to be made.

  FIG. 16 is a flowchart illustrating the flow of the technical concept of the fifth embodiment. Since steps S1 to S3 are the same as those in the first embodiment, only different points will be described.

  In step S41, a response surface approximation formula is created.

  In step S42, the accuracy of the approximate expression is calculated. For example, the deviation of the characteristic value between the created response surface approximation formula and sampling is calculated, and a value obtained by dividing the absolute value of this deviation by the sampling number is used as the degree of deviation.

  In step S43, it is determined whether or not the aiming accuracy is obtained. When the aiming accuracy is obtained, the present control flow is terminated, and when the aiming accuracy is not obtained, the process proceeds to step S44. Here, the target accuracy is determined, for example, as to whether or not the deviation calculated in step S42 is less than a predetermined value.

  In step S44, cluster connection points are extracted. Specifically, sampling between the ends of adjacent clusters is extracted.

  In step S45, cluster extraction point local model creation processing is executed using the extracted sampling, and the process proceeds to step S3. Details of this processing will be described later.

  Therefore, Step S44 → Step S45 → Step S2 → Step S3 → Step S41 → Step S42 is repeatedly executed until the target accuracy is obtained.

[Cluster connection point local model creation processing]
In the fifth embodiment, a model generation method based on the Euclidean distance described in the second embodiment is applied, and a method of generating a model in the vicinity of the boundary in order to investigate the cluster connection point in detail will be described.

  In Example 2, model generation using uniform random numbers was performed. In this case, since sampling is generated as a whole, it cannot be generated intensively at the cluster connection point, and the calculation man-hour increases as a whole. Therefore, we developed a method to generate new models intensively between the models that are closest to each other across the cluster connection points.

As shown in FIG. 17, a model closest to the cluster connection point is searched from models calculated in advance. Here, the cluster connection point means a point where clusters including two or more samplings are combined. If a sampling located at the right end in FIG. 17 of a cluster is x ₁ and a sampling located at the left end in FIG. 17 of an adjacent cluster is x ₂ , there is always an inflection point or peak between these two points. Conceivable. Next, a new model is generated within the range of the Euclidean distance of the closest model.

As the newly generated model x _rand, a model that is located in a region sandwiched between models x ₁ and x ₂ that sandwich the cluster connection point among the models generated by uniform random numbers is adopted. Note that according to this model generation method, the model generation is performed in a state where Expression (4.4), which is the restriction law of the second embodiment, is always satisfied.

In the fifth embodiment, a distance model generation method is proposed in order to generate a new sampling.
[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. 18 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 .

The model is generated using uniform random numbers. Therefore, a model generated by uniform random numbers is d _rand , a model (hereinafter referred to as a principle model) expressed by a limiting element that constitutes sampling of two points sandwiching a cluster connection point is expressed as x _c , and sampling of two points is performed. Assuming that a model having a Euclidean distance equal to or greater than the constituent limiting elements is x _o , the newly generated model x _rand and these distances are expressed by Equation (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.

Hereinafter, a model generation algorithm will be described based on the distance model generation process of FIG.
(i) Prepare a principle model. In the case of the fifth embodiment, this corresponds to a design pattern (restriction element) that constitutes sampling of two points across the cluster connection point.
(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.

  When the model is generated, the characteristic value of the generated model is calculated, and a new sampling is added to perform hierarchical clustering again. In this case, a new cluster may be generated due to a new sampling occurring at the boundary, or the sampling included in the existing cluster may increase. When a new cluster is formed at the boundary of the cluster of the initial sampling, an inflection point and a peak that can be detected as the accuracy is improved appear, and the estimation accuracy is further improved.

  A response surface approximation formula in which sampling of the cluster connection points is increased is created. By repeating the above operation until the accuracy of the response surface approximation formula becomes the target accuracy, the accuracy of creating the response surface approximation formula can be improved.

  As described above, in the fifth embodiment, hierarchical clustering is performed (classification means), and a new design pattern (limitation element model) is within the Euclidean distance between sampling restriction elements located at the boundaries of the classified clusters. Is generated. A characteristic value corresponding to the new design pattern is calculated to generate a new sampling. Next, the new set obtained by adding a new sampling to the initial model is hierarchically clustered again, and an approximate expression is created for the sampling characteristics that constitute the new set.

  Therefore, it becomes possible to centrally secure inflection points and peaks of the response surface, and improve the estimation accuracy of the response surface approximation formula with a small number of samplings.

  Next, Example 6 will be described. In the second embodiment, a threshold value is introduced, a local model creation process is performed to select a region, and then an approximate expression for each region is created for the selected region. Therefore, although sampling can be efficiently generated in a region that satisfies the threshold value, there may be a peak or inflection point in the vicinity of the existing sampling because the distance to the existing sampling may be close or remote. In some cases, the accuracy of the response surface approximation formula may vary. On the other hand, the sixth embodiment is different in that after selecting a region, a distance model close to the existing model is generated in the region and then an approximate expression for each region is created.

  FIG. 19 is a flowchart showing the flow of the technical concept of the sixth embodiment. Since Step S1 to Step S3 and Step S11 are the same as those in the second embodiment, only different points will be described.

  In step S51, a cluster configured only by sampling that satisfies the threshold is selected as a region to be noted.

In step S52, a distance model generation process is executed using the existing sampling design pattern in the cluster as a principle model. Since the distance model generation process is the same as that described in the fifth embodiment, the description thereof is omitted.
In step S53, it is determined whether the distance model has been generated a specified number of times. If the specified number of times has been generated, the process proceeds to step S54. Otherwise, the distance model generation is repeated.

In step S54, a response surface approximation formula is created for each region.
In step S55, an optimum value is extracted based on the response surface approximation formula.

  FIG. 20 shows a part of the result of hierarchically clustering existing samplings, ◯ for samplings that satisfy the threshold, and x for samplings that do not satisfy the threshold. As shown in FIG. 20, it can be seen that the design space 31 (DesingSpace 31) and the design section 37 (DesingSpace 37) exist as a cluster in which samplings with ◯ are continuous. Since such a design space can be a design candidate, it is called a design candidate solution space. Therefore, since a set of design patterns satisfying the threshold exists in the design space 31 and the design space 37 which are design candidate solution spaces, it is desired to create a response surface approximation formula with high accuracy for this region.

  Therefore, a design pattern (restriction element) corresponding to the existing sampling in each design space is adopted as a principle model, and a random model is generated by a distance model generation method. Among the random models, the Euclidean distance is closest to the principle model. The design pattern is adopted as a distance model. For example, when the specified number of times is specified as two, two distance models close to the principle model are generated.

  FIG. 20 shows the principle model by ● and the distance model by ○. In this way, a plurality of distance models are generated in the vicinity of the existing sampling, and a response surface approximation formula is created for the characteristics of the design space to which sampling based on the distance model is added.

  Here, FIG. 21 shows an example in which the difference between the response curved surface of the existing sampling only and the response curved surface of the sixth embodiment appears remarkably. When creating a response surface approximation formula for an existing sampling, if the differential value at each sampling is not known, the point can only be connected. Therefore, as shown in FIG. 21, when existing samplings are arranged with a certain characteristic value, there is a possibility of creating a horizontal straight line.

  On the other hand, if a plurality of samplings are generated in the vicinity of each sampling, it is possible to find an element corresponding to the differential value in each sampling. Therefore, even if existing samplings are lined up with a certain characteristic value, the differential value of each sampling is different, so it is possible to connect with a curve, and create a response surface that is close to the actual characteristic (ActualPhenomenon) Can do.

  As described above, in the sixth embodiment, sampling is classified by hierarchical clustering, and clusters that satisfy the threshold are selected (region selection means). Next, a new sampling is generated by the distance model generation method using the existing sampling as a principle model in the selected region, and a response surface approximation formula is created for the region including this new sampling to obtain the optimum value. It was decided to extract. Therefore, by creating a response surface approximation formula for each region, it is possible to improve the accuracy of the response surface approximation formula without excessive computational effort, and it is possible to extract a highly accurate optimum value.

  Next, Example 7 will be described. The purpose of the seventh embodiment is to generate new sampling in a focused area. FIG. 22 is a flowchart showing the concept of the seventh embodiment. Steps S1 to S3 are the same as those in the first embodiment, and a description thereof will be omitted.

  In step S61, a cluster is selected. This cluster may be a cluster focused by the designer.

  In step S62, the maximum Euclidean distance in the cluster is extracted. In other words, since the Euclidean distance of the limiting element constituting the sampling is adopted as an index indicating the similarity, it is synonymous with extracting the similarity that can be determined to be similar.

In step S63, a random number model is generated.
In step S64, it is determined whether or not the Euclidean distance between the random number model and the existing sampling that constitutes the selected cluster is within the maximum Euclidean distance. If it is within the maximum Euclidean distance, the process proceeds to step S65. Repeat generation.
In step S65, the characteristic value of the generated random number model is calculated and used as a new sampling.

  FIG. 23 is a diagram showing an image of the new sampling generation process. Classify existing samplings into clusters by hierarchical clustering. Of the plurality of clusters, attention is focused on Cluster A with thick arrows in FIG.

  The maximum Euclidean distance of ClusterA is extracted to generate a random model of the design pattern. Then, the Euclidean distance between each random number model and the sampling constituting Cluster A is calculated, and it is determined whether or not this Euclidean distance is within the maximum Euclidean distance. Among the generated random number models, a model within the maximum Euclidean distance is adopted as a new model, and a characteristic value of this model is calculated and adopted as a new sampling.

  As a basic model generation method, for example, the distance model generation method described in the fifth embodiment is used. However, in the distance model generation method, only the model closest to the principle model is used, whereas in Example 7, the principle model is an existing sampling that constitutes a cluster, and the Euclidean distance from the existing sampling is the maximum Euclidean distance. The difference is that all models within the distance are used.

  In the random number model, when the Euclidean distance from each existing sampling is less than a predetermined value, it is assumed that a restriction rule (see formula (4.5) in the second embodiment) is applied that is determined not to be the same model. . However, the setting Euclidean distance 0.01 in equation (4.5) is a factor that controls the evolution rate of the cluster, and is thus set as appropriate according to the intention of the designer. For example, by setting the set Euclidean distance to be smaller each time the hierarchy is lowered, sampling corresponding to the hierarchy can be obtained relatively, and the speed at which this hierarchy is directed to the lower layer can be controlled.

  As shown in FIG. 23, it can be said that Cluster A composed of four samplings is a higher-order cluster of a plurality of samplings having a shorter Euclidean distance (high similarity). That is, by generating a new model within the maximum Euclidean distance of the selected cluster, it is possible to generate a sampling that forms a lower cluster.

  As described above, in the seventh embodiment, sampling is arranged based on the Euclidean distance between the limiting elements, and a cluster in an arbitrary range is selected from the arranged samplings. Then, by generating new sampling within the selected cluster, it becomes possible to grasp the selected cluster by further hierarchization, and it is possible to efficiently generate a new model similar to the characteristics of the focused cluster. it can.

  Next, Example 8 will be described. The eighth embodiment aims to generate new sampling in a design space that is completely different from the design space in which existing sampling exists. FIG. 24 is a flowchart showing the concept of the eighth embodiment. Steps S1 to S3 are the same as those in the first embodiment, and a description thereof will be omitted.

  In step S71, the maximum Euclidean distance of the highest cluster is extracted. In other words, since the Euclidean distance of the limiting element constituting the sampling is adopted as an index representing the similarity, it is synonymous with extracting the similarity that can be determined not to be similar to the existing sampling.

In step S72, a random number model is generated.
In step S73, it is determined whether or not the Euclidean distance between the random number model and the existing sampling is equal to or greater than the maximum Euclidean distance. If the Euclidean distance is equal to or greater than the maximum Euclidean distance, the process proceeds to step S74.
In step S74, the characteristics of the generated random number model are calculated and adopted as new sampling.

  FIG. 25 is a diagram showing an image of the new sampling generation process. Classify existing samplings into clusters by hierarchical clustering. At this time, the maximum Euclidean distance of the highest cluster in the design space where the existing sampling exists is extracted, and a random model of the design pattern is generated.

  Then, the Euclidean distance between each random number model and the sampling constituting the uppermost cluster is calculated, and it is determined whether this Euclidean distance is equal to or greater than the maximum Euclidean distance. Among the generated random number models, a model having the maximum Euclidean distance or more is adopted as a new model, and the characteristic value of this model is calculated and adopted as a new sampling. Since the basic model generation method is the same as the method described in the seventh embodiment, the description thereof is omitted.

  As shown in FIG. 25, it can be said that the uppermost cluster composed of the existing samplings is a cluster in parallel (or the same hierarchy) with a plurality of samplings having a longer Euclidean distance (small similarity). That is, by generating a new model that is greater than or equal to the maximum Euclidean distance of the topmost cluster, it is possible to generate a sampling having a new design pattern in a design space that cannot be obtained by existing sampling. From this, a new concept that exceeds the existing concept is generated.

  As described above, in the eighth embodiment, sampling is arranged based on the Euclidean distance between limiting elements, and the highest cluster is selected from the arranged samplings. By generating a new sampling outside the highest cluster, it becomes possible to generate a new concept that has never existed before, and it is possible to provide useful information at the concept design stage and the basic design stage.

(Other examples)
As described above, in the first to eighth embodiments, the method for efficiently generating new sampling according to the purpose has been described. However, the present invention is not limited to the above-described embodiments, and can be applied in various situations. For example, in the first to fourth embodiments, a new sampling is generated using the (boundary) local model creation method. However, a new sampling may be generated by appropriately combining with the distance model generation method described in the fifth embodiment. good. Conversely, a new sampling may be generated in the fifth to eighth embodiments using the (boundary) local model creation method.

  In each embodiment, the hierarchical clustering is used as the classification means. However, the classification is not limited to the hierarchical clustering, and the classification may be performed by other classification means. For example, the centroid of the design pattern constituting each sampling may be calculated and arranged according to the distance between the centroids. Moreover, you may arrange | position in a horizontal line according to the Euclidean distance of each design pattern.

1 is a system diagram illustrating a multidimensional information processing system according to a first embodiment. 3 is a flowchart showing the flow of a technical concept of Example 1. FIG. 3 is a conceptual diagram illustrating a concept of a hierarchical response surface methodology according to the first embodiment. 3 is a diagram illustrating a cluster generation method in hierarchical clustering according to Embodiment 1. FIG. FIG. 3 is a tree diagram formed by hierarchical clustering according to the first embodiment. It is the schematic showing the relationship between a cluster and the characteristic value when the sampling of Example 1 is arrange | positioned on a two-dimensional plane. It is a schematic explanatory drawing showing the distance model production | generation process of Example 1. FIG. 10 is a flowchart showing the flow of a technical concept of Example 2. It is a figure showing the relationship between the design space of Example 2, and a characteristic. FIG. 10 is a schematic explanatory diagram illustrating a local model creation process according to the second embodiment. 10 is a flowchart showing the flow of a technical concept of Example 3. It is a figure showing the relationship between the design space of Example 3, and a threshold value. 10 is a flowchart showing the flow of a technical concept of Example 4. FIG. 10 is a schematic explanatory diagram illustrating a boundary local model creation process according to a fourth embodiment. 10 is a flowchart illustrating a local model creation process according to the fourth embodiment. 10 is a flowchart showing the flow of a technical concept of Example 5. FIG. 10 is a schematic explanatory diagram illustrating a relationship between a cluster connection point generated by hierarchical clustering of Example 5 and a response surface approximation formula. FIG. 10 is a schematic explanatory diagram illustrating a distance model generation method according to the fifth embodiment. 10 is a flowchart showing the flow of a technical concept of Example 6. FIG. 10 is a schematic explanatory diagram illustrating an approximate expression for each region according to a sixth embodiment. It is a schematic explanatory drawing showing the relationship between the response curved surface of Example 6, and the response curved surface of only a principle model. 10 is a flowchart showing the flow of a technical concept of Example 7. It is the schematic explanatory drawing which expressed the technical concept of Example 7 using the tree diagram by hierarchical clustering. 10 is a flowchart showing the flow of a technical concept of Example 8. It is the schematic explanatory drawing which expressed the technical concept of Example 8 using the tree diagram by hierarchical clustering.

Explanation of symbols

1 arithmetic processing unit 2 display unit 3 keyboard

Claims (33)

When there is a set of samplings consisting of a combination of multiple limiting elements and characteristics representing the input-output relationship for the system defined by these limiting elements,
Limiting element model generating means for generating a new limiting element model that differs by a set Euclidean distance with reference to the limiting elements constituting the sampling;
Sampling generation means for generating a new sampling composed of a combination with the characteristics defined by the new limiting element model;
A sampling generation device comprising: The sampling generator according to claim 1,
Placing means for placing the sampling based on a Euclidean distance between the limiting elements;
Range selection means for selecting an arbitrary range from the arranged sampling;
Provided,
The sampling generation device, wherein the limiting element model generation unit generates a new limiting element model within the selected range. The sampling generator according to claim 2, wherein
The arrangement means is means for hierarchically arranging the sampling into a plurality of clusters based on the Euclidean distance between the limiting elements,
The sampling generation apparatus according to claim 1, wherein the range selection means is means for selecting an arbitrary cluster from the plurality of clusters. The sampling generator according to claim 2 or 3,
An approximate expression generating means for generating an approximate expression for the sampling characteristics;
An optimum value extracting means for extracting an optimum value based on the approximate expression;
A sampling generator characterized by comprising: The sampling generator according to claim 1,
Classification means for hierarchically classifying the set including the new sampling into a plurality of clusters based on the Euclidean distance of the limiting element;
Range selection means for selecting an arbitrary cluster from the plurality of clusters;
An approximate expression generating means for generating an approximate expression for the characteristics of the selected cluster;
An optimum value extracting means for extracting an optimum value based on the approximate expression;
A sampling generator characterized by comprising: The sampling generator according to claim 1,
Classification means for hierarchically classifying the set including the new sampling into a plurality of clusters hierarchically based on the Euclidean distance of the limiting element;
Hierarchy selection means for selecting a cluster of any hierarchy from the plurality of clusters;
An approximate expression generating means for generating an approximate expression for the characteristics of the cluster of the selected hierarchy;
An optimum value extracting means for extracting an optimum value based on the approximate expression;
A sampling generator characterized by comprising: The sampling generator according to claim 1,
Classification means for hierarchically classifying the set into a plurality of clusters based on the Euclidean distance of the limiting element;
An approximate expression generating means for generating an approximate expression for the sampling characteristics;
Provided,
The limiting element model generation means is a means for generating a new limiting element model within a Euclidean distance between sampling limiting elements located at the boundary of the classified cluster,
The classifying means is means for classifying a new set obtained by adding the new sampling to the set.
The sampling generation device according to claim 1, wherein the approximate expression generation means is means for generating an approximate expression for the sampling characteristics constituting the new set. The sampling generator according to claim 1,
Placing means for placing the sampling based on a Euclidean distance between the limiting elements;
Range selection means for selecting an arbitrary range from the arranged sampling;
Provided,
The sampling generator is characterized in that the sampling generator generates a new sampling outside the selected range. The sampling generator according to claim 8,
The arrangement means is means for hierarchically classifying and arranging the set including the new sampling into a plurality of clusters hierarchically based on the Euclidean distance of the limiting element,
The sampling generation apparatus, wherein the range selection means is means for selecting an arbitrary cluster from the plurality of clusters. The sampling generator according to claim 1,
First characteristic target setting means for setting a first target of the characteristic;
First target attainment set extraction means for extracting sampling having characteristics satisfying the first target among characteristics of the set;
A step of generating a new limiting element model based on the set Euclidean distance for the limiting element corresponding to the sampling extracted by the first target reaching set extracting means, and the generated new limiting element model First sampling generation step execution means for executing a step of generating a new sampling composed of a combination with the characteristic,
Second target setting means for setting the second target in a more optimal orientation with respect to the first target;
Second target reaching set extraction means for extracting sampling having characteristics satisfying the second target among characteristics of the set including new sampling generated by the first sampling generation step execution means;
A step of generating a new limiting element model based on the set Euclidean distance for the limiting element corresponding to the sampling extracted by the second target reaching set extracting means, and the generated new limiting element model Second sampling generation step execution means for executing a step of generating a new sampling composed of a combination with the above-mentioned characteristics;
Repeating means for repeating the first sampling generation step execution means and the second sampling generation step execution means for a set number of times;
A sampling generation device comprising: The sampling generator according to claim 1,
Characteristic target setting means for setting a target of the characteristic;
A goal reaching set extraction means for extracting a sampling having characteristics satisfying the target among the characteristics of the set;
A target unachieved set extraction means for extracting a sampling having characteristics that do not satisfy the target among the characteristics of the set;
Euclidean distance setting means for setting a set Euclidean distance so as to go to the sampling restriction element extracted by the target unachieved set extraction means, with reference to the sampling restriction element extracted by the target reaching set extraction means;
Provided,
The sampling generation apparatus according to claim 1, wherein the limiting element model generation means is a means for generating a new limiting element model based on the set Euclidean distance set by the Euclidean distance setting means. When there is a set of samplings consisting of a combination of multiple limiting elements and characteristics representing the input-output relationship for the system defined by these limiting elements,
A limiting element model generation processing unit that generates a new limiting element model that differs by a set Euclidean distance on the basis of the limiting elements constituting the sampling;
A sampling generation processing unit for generating a new sampling composed of a combination with the characteristics defined by the new limiting element model;
A medium on which a sampling generation program is recorded. In the medium on which the sampling generation program according to claim 12 is recorded,
An arrangement processing unit that arranges the sampling based on the Euclidean distance between the limiting elements;
A range selection processing unit for selecting an arbitrary range from the arranged sampling;
Provided,
The medium on which the sampling generation program is recorded, wherein the limiting element model generation command unit generates a new limiting element model within the selected range. In the medium on which the sampling generation program according to claim 13 is recorded,
The arrangement processing unit is a processing unit that classifies and arranges the sampling hierarchically into a plurality of clusters based on the Euclidean distance between the limiting elements,
The medium on which a sampling generation program is recorded, wherein the range selection processing unit is a processing unit that selects an arbitrary cluster from the plurality of clusters. A medium in which the sampling generation program according to any one of claims 12 to 14 is recorded,
An approximate expression generation processing unit for generating an approximate expression for the sampling characteristics;
An optimum value extraction processing unit for extracting an optimum value based on the approximate expression;
A medium on which a sampling generation program is recorded. In the medium on which the sampling generation program according to claim 12 is recorded,
A classification processing unit that hierarchically classifies the set including the new sampling into a plurality of clusters based on the Euclidean distance of the limiting element;
A range selection processing unit for selecting an arbitrary cluster from the plurality of clusters;
An approximate expression generation processing unit for generating an approximate expression for the characteristics of the selected cluster;
An optimum value extraction processing unit for extracting an optimum value based on the approximate expression;
A medium on which a sampling generation program is recorded. In the medium on which the sampling generation program according to claim 12 is recorded,
A classification processing unit that hierarchically classifies the set including the new sampling into a plurality of clusters hierarchically based on the Euclidean distance of the limiting element;
A hierarchy selection processing unit for selecting a cluster of any hierarchy from the plurality of clusters;
An approximate expression generation processing unit for generating an approximate expression for the characteristics of the cluster of the selected hierarchy;
An optimum value extraction processing unit for extracting an optimum value based on the approximate expression;
A medium on which a sampling generation program is recorded. The sampling generator according to claim 12,
A classification processing unit that hierarchically classifies the set into a plurality of clusters based on the Euclidean distance of the limiting element;
An approximate expression generation processing unit for generating an approximate expression for the sampling characteristics;
Provided,
The limiting element model generation processing unit is a processing unit that generates a new limiting element model within a Euclidean distance between sampling limiting elements located at a boundary of the classified cluster.
The classification processing unit is a processing unit that classifies a new set obtained by adding the new sampling to the set.
The medium on which the sampling generation program is recorded, wherein the approximate expression generation processing unit is a processing unit that generates an approximate expression for the sampling characteristics constituting the new set. In the medium on which the sampling generation program according to claim 12 is recorded,
An arrangement processing unit that arranges the sampling based on the Euclidean distance between the limiting elements;
A range selection processing unit for selecting an arbitrary range from the arranged sampling;
Provided,
The medium on which the sampling generation program is recorded, wherein the sampling generation processing unit generates new sampling outside the selected range. In the medium on which the sampling generation program according to claim 19 is recorded,
The arrangement processing unit is a processing unit that hierarchically classifies and sets the set including the new sampling into a plurality of clusters hierarchically based on the Euclidean distance of the limiting element,
The medium on which a sampling generation program is recorded, wherein the range selection processing unit is a processing unit that selects an arbitrary cluster from the plurality of clusters. In the medium on which the sampling generation program according to claim 12 is recorded,
A first characteristic target setting processing unit for setting a first target of the characteristic;
A first goal attainment set extraction processing unit for extracting sampling having characteristics satisfying the first goal among the characteristics of the set;
A step of generating a new limiting element model based on the set Euclidean distance for the limiting element corresponding to the sampling extracted by the first target reaching set extracting means, and the generated new limiting element model A first sampling generation step execution processing unit for executing a step of generating a new sampling composed of a combination with the characteristics,
A second target setting processor for setting the second target in a more optimal orientation with respect to the first target;
A second target reaching set extraction processing unit that extracts sampling having characteristics satisfying the second target among characteristics of the set including new sampling generated by the first sampling generation step execution processing unit;
A step of generating a new limiting element model based on the set Euclidean distance for the limiting element corresponding to the sampling extracted by the second target reaching set extraction processing unit, and the regulation by the generated new limiting element model A second sampling generation step execution processing unit for executing a step of generating a new sampling composed of a combination with the characteristics to be performed;
A repeat command unit that repeats the first sampling generation step execution processing unit and the second sampling generation step execution processing unit set times;
A medium on which a sampling generation program is recorded. In the medium on which the sampling generation program according to claim 12 is recorded,
A characteristic target setting processing unit for setting the target of the characteristic;
A target reaching set extraction processing unit that extracts sampling having characteristics satisfying the target among the characteristics of the set;
A target unachieved set extraction processing unit that extracts sampling having characteristics that do not satisfy the target among the characteristics of the set;
A Euclidean distance setting processing unit that sets a set Euclidean distance so as to go to the sampling limiting element extracted by the target unachieved set extraction processing unit on the basis of the sampling limiting element extracted by the target reaching set extraction processing unit When,
Provided,
The medium on which the sampling generation program is recorded, wherein the limiting element model generation processing unit is a processing unit that generates a new limiting element model based on the set Euclidean distance set by the Euclidean distance setting means. When there is a set of samplings consisting of a combination of multiple limiting elements and characteristics representing the input-output relationship for the system defined by these limiting elements,
A limiting element model generating step for generating a new limiting element model that differs by a set Euclidean distance with reference to the limiting elements constituting the sampling;
A sampling generation step for generating a new sampling composed of a combination with the characteristics defined by the new limiting element model;
A sampling generation method characterized by comprising: The sampling generation method according to claim 23,
Placing the sampling based on a Euclidean distance between the limiting elements;
A range selection step of selecting an arbitrary range from the arranged samplings;
Provided,
The sampling generation method, wherein the limiting element model generation step is a step of generating a new limiting element model within the selected range. The sampling generation method according to claim 24, wherein
The arranging step is a step of classifying and arranging the sampling hierarchically into a plurality of clusters based on the Euclidean distance between the limiting elements,
The sampling generation method, wherein the range selection step is a step of selecting an arbitrary cluster from the plurality of clusters. The sampling generation method according to any one of claims 23 to 25,
An approximate expression generating step for creating an approximate expression for the sampling characteristics;
An optimum value extracting step for extracting an optimum value based on the approximate expression;
A sampling generation method characterized by comprising: The sampling generation method according to claim 23,
A classification step of hierarchically classifying the set including the new sampling into a plurality of clusters based on the Euclidean distance of the limiting element;
A range selection step of selecting an arbitrary cluster from the plurality of clusters;
An approximate expression generating step for generating an approximate expression for the characteristics of the selected cluster;
An optimum value extracting step for extracting an optimum value based on the approximate expression;
A sampling generation method characterized by comprising: The sampling generation method according to claim 23,
A classification step of hierarchically classifying the set including the new sampling into a plurality of clusters hierarchically based on the Euclidean distance of the limiting element;
A hierarchy selection step of selecting a cluster of an arbitrary hierarchy from the plurality of clusters;
An approximate expression generating step for generating an approximate expression for the characteristics of the cluster of the selected hierarchy;
An optimum value extracting step for extracting an optimum value based on the approximate expression;
A sampling generation method characterized by comprising: The sampling generator according to claim 23,
A classification step of hierarchically classifying the set into a plurality of clusters based on the Euclidean distance of the limiting element;
An approximate expression generating step for creating an approximate expression for the sampling characteristics;
Provided,
The limiting element model generation step is a step of generating a new limiting element model within a Euclidean distance between sampling limiting elements located at a boundary of the classified cluster,
The classification step is a step of classifying a new set obtained by adding the new sampling to the set.
The approximate expression generation step is a step of generating an approximate expression for the sampling characteristics constituting the new set. The sampling generation method according to claim 23,
Placing the sampling based on a Euclidean distance between the limiting elements;
A range selection step of selecting an arbitrary range from the arranged samplings;
Provided,
In the sampling generation method, a new sampling is generated outside the selected range. The sampling generation method according to claim 30, wherein
The arrangement step is a step of hierarchically classifying and arranging the set including the new sampling into a plurality of clusters hierarchically based on the Euclidean distance of the limiting element,
The sampling generation method, wherein the range selection step is a step of selecting an arbitrary cluster from the plurality of clusters. The sampling generation method according to claim 23,
A first characteristic target setting step for setting a first target of the characteristic;
A first goal attainment set extraction step for extracting a sampling having characteristics satisfying the first goal among the characteristics of the set;
The step of generating a new limiting element model based on the set Euclidean distance for the limiting element corresponding to the sampling extracted by the first target reaching set extraction step, and the generated new limiting element model A first sampling generation step of performing a step of generating a new sampling composed of a combination with the characteristic;
A second target setting step for setting the second target in a more optimal orientation with respect to the first target;
A second target reaching set extraction step for extracting a sampling having characteristics satisfying the second target from the characteristics of the set including the new sampling generated by the first sampling generation step;
The step of generating a new limiting element model based on the set Euclidean distance for the limiting element corresponding to the sampling extracted by the second target reaching set extraction step, and the generated new limiting element model A second sampling generation step of performing a step of generating a new sampling composed of a combination with the characteristic;
Repeating the first sampling generation step and the second sampling generation step a set number of times;
A sampling generation method characterized by comprising: The sampling generation method according to claim 23,
A characteristic target setting step for setting a target of the characteristic;
A goal reaching set extraction step of extracting a sampling having characteristics satisfying the target among the characteristics of the set;
A target unachieved set extraction step for extracting a sampling having characteristics that do not satisfy the target among the characteristics of the set;
A Euclidean distance setting step for setting a set Euclidean distance so as to go to the sampling limiting element extracted by the target unachieved set extracting means with reference to the sampling limiting element extracted by the target reaching set extraction step;
Provided,
The sampling generation method, wherein the limiting element model generation step is a step of generating a new limiting element model based on the set Euclidean distance set by the Euclidean distance setting means.

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