JP4956779B2 - Optimization support device, optimization support program, optimization support display device, and optimization support method - Google Patents

Description

  The present invention relates to an optimization support apparatus using a computer.

Conventionally, a technique described in Patent Document 1 has been disclosed as a system that supports optimization. In this publication, an interface is provided between the analysis calculation unit and the modeling unit, and the design parameters of the structure are automatically changed and remodeled from the analysis results, and the optimal model that satisfies the design specifications is output after iterative calculation. To help with optimization.
Japanese Patent Laid-Open No. 3-224063.

  However, although the above-described conventional technique is modified so as to satisfy the design specification after the iterative calculation, no reference is made to a technique for generating a reference initial shape. In other words, a reasonable shape cannot be generated easily and quickly at the initial design stage, and optimization processing is executed from an appropriately set shape. There has been a problem that the calculation time is increased and the calculation time is increased.

  The present invention has been made based on the above problems, and an object of the present invention is to provide an optimization support apparatus that can suppress useless calculation and can reduce calculation time.

In order to achieve the above object, in the optimization support apparatus of the present invention, a system having characteristics corresponding to a plurality of limiting elements, and a plurality of samplings that are combinations of the limiting elements and the characteristics of the system are generated. Sampling generating means, hierarchical clustering means for hierarchically clustering the sampling based on similarity of the characteristics, and correlation between the variation of the limiting element and the fluctuation of the characteristics in each clustered cluster From the comparison result of the comparison element that compares the high restriction element between the same hierarchy and / or between different hierarchies, and the comparison means, the restriction element that is common among the clusters among the restriction elements with high correlation. Extraction means for extracting, target characteristic setting means for setting target characteristics, and extracted common limiting elements as a reference Second sampling generating means for generating sampling, and whether or not the sampling characteristic generated by the second sampling generating means is the optimal sampling satisfying the target characteristic, and if it is determined to be optimal, the sampling is optimal And sampling evaluation means for outputting as sampling.

  Therefore, by extracting common limiting elements from a small number of samplings, it is possible to generate a rational shape at the initial design stage, and by generating sampling based on this rational shape, an efficient solution can be obtained. A space can be searched, and optimization can be achieved with a small number of operations.

  Hereinafter, the best mode for realizing the optimization support apparatus of the present invention will be described based on an embodiment shown in the drawings.

[Technical concept of Example 1]
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.

  Such a layered system structure related to a specific event can be applied to almost all events such as economy, culture, design, and biology. It is accepted as a classification method that is easy to catch.

  For example, in an automobile suspension, the abstract system is a suspension, the individual system is a multilink or torsion beam, the concrete system is a specific multilink 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. Here, the top layer system is called an “abstract system”, the middle layer system is called a “formal system”, and the bottom layer system is called a “concrete system”.

  In this embodiment, in order to enable understanding of the entire system, a “trend system” is introduced as a system in which a trend or range is limited between an abstract system and a formal system, and between a concrete system and a formal system. By deciding (systems classified by Cluster), it became possible to consider the understanding of the whole system, the understanding of characteristics between systems, the further understanding of events, the possibility of creating a new system, and so on. FIG. 1 shows these relationships.

  It was stated that the three-layer system structure is classified based on some commonality. 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. Such a feature is related to the commonality described above, and can be defined as a “common concept” of the system for realizing the phenomenon.

  In a certain formal system, various phenomena that occur as a result of changing various parameters of a concrete system are governed by a common concept peculiar to that formal system, and this concept realizes the tendency of various phenomena. It is thought that there is. And the specific tendency of each phenomenon shown by the concrete system is realized by taking a specific form derived from it based on a common concept.

  Here, the common concept is the value of specific parameters that can best explain the tendency of various complex phenomena, the combination of specific parameters, the relationship between specific parameters, the tendency of specific parameters, the value of specific parameters. Any of the ranges, or some combination of these. On the other hand, based on the common concept, the value of a specific parameter other than the common concept, the combination of specific parameters, the relationship between specific parameters, the tendency of specific parameters, the range of specific parameter values, or Some combinations of these can be defined as unique forms.

  Note that the common concept may exist between different systems that exist to realize a certain phenomenon. That is, various systems that exist in the formal system hierarchy exist in order to realize a specific phenomenon, and therefore there is a common concept (that is, in an abstract system) at the upper level of the formal system. The trend of the phenomenon is realized. And the phenomenon peculiar phenomenon is realized by adding the peculiar form of the formal system or the concrete system to the common concept.

  The first embodiment is configured based on the concept as described above in order to understand complicated phenomena. FIG. 2 shows a common concept extraction concept of the embodiment. In FIG. 2, common concept 0 is a concept that prescribes all phenomena, common concept 1 is a concept that prescribes phenomena only in the hatched area, and common concept 2 prescribes phenomena only in the hatched area. It is a concept. Common concept 0 includes common concepts 1 and 2, and when each common concept is overlapped with another common concept, a region is further defined.

  The abstract system and the format system may be set as appropriate while paying attention only to the upper limit relationship between all layers. Therefore, the abstract system is not limited to the upper layer. Moreover, the order which connects between the abstract system, the formal system, and the concrete system which were set suitably is defined as a tendency system.

  FIG. 3 shows the optimization support concept of the first embodiment. For example, after categorization into systems of each hierarchy (formal system, trend system, concrete system, etc.) by hierarchization, for example, a new sampling is generated using a common concept existing in the existing trend system, and the optimum is determined from this sampling. Providing a system is the main purpose of the first embodiment.

[Optimization support flow]
In the first embodiment, after extracting a common concept that defines a complex phenomenon, a parameter that constitutes the common concept and other parameters are changed in various ways to extract a structure that matches a phenomenon desired by the designer. To extract this common concept, it is necessary to prepare several combinations (hereinafter referred to as sampling) of phenomena (hereinafter referred to as characteristics) and parameters (hereinafter referred to as limiting elements) taken by a system that realizes the phenomenon. Then, by classifying these characteristics into some and comparing the limiting elements, a common concept that best explains all phenomena is extracted.

  Next, the restriction elements constituting the common concept are changed after following the tendency of the restriction elements of the common concept. In addition, the restriction elements other than the common concept are changed by changing the restriction elements constituting the common concept, and then changing the other restriction elements based on the changed common concept. Here, the designer determines a desired characteristic or a range of the characteristic in advance, and determines whether a response is applicable to the determined condition.

  From here, a structure that realizes a certain characteristic or a structure that realizes a response within a certain range is extracted.

From the above, in Example 1, as shown in FIG.
Step [1] Site for preparing sampling (first sampling generating means)
Step [2] Parts for classifying characteristics (hierarchical clustering means)
Step [3] A part for comparing the limiting elements and extracting the common concept (comparison means and extraction means)
Step [4] Parts for setting target characteristics (target characteristic setting means)
Step [5] Generation of sampling based on common concept (second sampling generation means)
Step [6] Site for judging whether sampling is possible in step [5] (sampling evaluation means)
It consists of 6 steps. In this way, since sampling can be efficiently generated using the common concept, it is possible to predict what kind of response will be obtained as a result because it is efficient and has no omissions.

(Preparation for sampling)
In the stage of sampling preparation in step [1], it is sufficient to prepare sampling of the target phenomenon that has been grasped so far. However, if there is a bias in the sampling to be compared, the common concept extracted as a result is biased to a certain characteristic, so it cannot often be said that all phenomena can be explained. Therefore, it is necessary to prepare sampling in which characteristics are not biased. When preparing for sampling, prepare all combinations of limiting elements, or combinations of limiting elements using an orthogonal table, and investigate the response of the characteristics to avoid sampling bias. That's fine.

  Here, an example of an orthogonal table is shown in FIG. An orthogonal table is a table created so that all the levels of other limiting elements are combined evenly when focusing on a specific level of an allocated limiting element. Therefore, the maximum value and minimum value of each limiting element that constitutes the limiting element are set, and the maximum and minimum values are divided into several according to the number of levels of the selected orthogonal table, and assigned to the orthogonal table. That's fine.

  If you have a simulator that simulates a system defined by multiple limiting elements and reproduces the characteristics that represent the relationship between input and output, link it with the simulator to work efficiently. It is desirable. The simulator may be in the same arithmetic device, or may be connected to another device with a cable or the like.

(Classification of characteristics)
Hierarchical clustering is used in the part for classifying the characteristics of step [2]. Clustering is an object of gathering groups that are similar to each other to create a community (hereinafter referred to as a cluster) in order to efficiently organize a meaningful system from a group of people with different characteristics. It is a general term for the method of classifying. Among these, hierarchical clustering is a method of generating hierarchies so that groups are nested. In the first embodiment, clustering is performed based on “similarity of characteristic tendency” as “similar”.

  Hierarchical clustering was adopted in the first embodiment because, as described in [Technical concept of the first embodiment], the system originally targeted by us is based on a hierarchical classification (i.e., most understood). This is because it is not possible to know in advance how many hierarchies and clusters exist in the trend system for understanding the relationship between the systems of each hierarchy. 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. The hierarchical clustering method is described below.

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

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

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

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, but here, the Ward's Method is taken up. 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 (3.4). Here, the element is a value included in the individual x _i .

At this time, if the center of gravity M (G) with respect to the cluster G is set as shown in formula (3.5), each component is expressed by formula (3.6).

Here, if the sum of squares E (G) of the difference between the center of gravity and the individual in the cluster G is defined as in the equation (3.7), the difference in distance between the two different clusters G _i and G _j is expressed by the equation ( It can be expressed as 3.8). Therefore, the coupling rule for the cluster of (II) of AHC selects G _q and G _r that minimize ΔE, as represented by the equation (3.9).

ここで、G'＝G_q∈G_rのとき

以上のように，AHCの（III）の再計算は、個体間の類似度を参照することなく、クラスター間の類似度のみを用いて再計算がなされる。図５に以上のアルゴリズムに基づくクラスターの生成方法を、図６に階層的クラスタリングの例を示す。 On the other hand, the recalculation of the similarity d (G ′, G _i ) of AHC (III) can be expressed using d (G _q , G _i ) and d (G _r , G _i ) before combining. If d (G _i , G _j ) = ΔE (G _i , G _j ) is defined, the initial cluster G _i = {x _i } can be expressed as shown in Expression (3.10).

Where G '= G _q ∈ G _r

As described above, the recalculation of (III) of AHC is performed by using only the similarity between clusters without referring to the similarity between individuals. FIG. 5 shows a cluster generation method based on the above algorithm, and FIG. 6 shows an example of hierarchical clustering.

Here, the cluster generation method is summarized as follows based on FIG.
(A) Sampling is clustered to generate clusters p, qr. In FIG. 5, 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. 5, cluster p and cluster q are combined to generate a new cluster t.
(D) Calculate the center of gravity of the combined cluster t.
(E) Combine clusters with small similarity (close distance).
(F) Repeat (C) to (E) until there is one cluster.
In the step (A), not the cluster but the point information before clustering may be used, and there is no particular limitation.

[Extraction of common concepts]
In the part that compares the restriction elements and extracts the common concept shown in Step [3], after extracting the causal relationship between the restriction elements existing in each classified hierarchy and the characteristics, it is common to all the hierarchy. Find causality. The common causality found here is called the common concept.

(Extraction of the causal relationship between the characteristics and the relationship between the restriction elements that exist for each classified hierarchy)
Extract the physical causal relationship between the limiting elements and phenomena that exist for each classified phenomenon hierarchy. The feature that the phenomenon shows can only be said in a complete way that various limiting elements are involved. However, in other words, the phenomenon is realized through various forms of relationships while changing the relationship between the limiting elements. If this is a network of limiting elements leading to the realization of the phenomenon, this network can be considered as a causal relationship. Here, this network is called a “causal network”.

  When one path is considered, the formation of this path may be influenced by other limiting factors, and this influence may also be influenced by other limiting factors. When finding a route with such characteristics, rather than judging the route from pure connections after eliminating the influence of other restrictive elements, the route is based on the relationship of the restrictive elements that have the influence of other restrictive elements. It is better to judge.

  In other words, when a route is determined from a pure connection that eliminates the influence of other limiting elements, a determination is made based on the magnitude of the numerical value of the degree of influence between certain limiting elements or between a certain limiting element and a phenomenon. It will be. Therefore, it is difficult to say that the physical relationship between the cut-off restriction element and the path is cut off, and the whole represents a causal network without knowing whether the cut-off is correct. On the other hand, when judging a route that has the influence of other limiting factors, truncation based on the existing concept is not performed, so a causal network that can explain all the physical connections describing the phenomenon itself This is because it is considered to form.

  However, since it tends to be complicated, it is necessary to provide a numerical index in the path between the limiting elements. Here, Pearson's product-moment correlation coefficient is taken up as a measure for measuring the strength of the connection between two limiting elements that have the influence of other limiting elements. In order to extract the causal network from the limiting element to the phenomenon, each limiting element and the phenomenon are considered in the same dimension. Each limiting element and phenomenon placed in the same dimension will be called the fulcrum of the path that makes up the causal network.

The number of data one fulcrum with n, 1 single fulcrum x, average x fulcrum x ^-, the other fulcrum y, the mean of the fulcrum y y ^- if that, the are two fulcrums x, between y A correlation coefficient r (xy) representing the strength of connection is expressed by equation (5.2).

  By applying the formula (5.2) between all the fulcrums, all the causal networks up to the phenomenon can be extracted together with the strength of connection including the influence of other limiting factors (see Fig. 7). . By applying this to a phenomenon cluster of all layers, it becomes possible to grasp a phenomenon process that is gradually hierarchized from a complicated phenomenon to a simple phenomenon together with a change in the causal network.

(Extraction of common concepts)
Complex phenomena have a hierarchical structure in which they are gradually divided into simple phenomena based on physical characteristics. Therefore, it is considered that the causal network changes along the hierarchy accordingly. The factors that determine a single phenomenon in a hierarchy and the factors that determine its complexity are: a causal network that is common to single phenomena in all hierarchies, the target phenomenon, and its upper and lower hierarchies. It can be defined as a heterogeneous causal network that exists between these phenomena.

  In the case of hierarchization accompanied by feature differentiation of complex phenomena using hierarchical clustering, the lowest layer is a cluster composed of one sample. Since it becomes a hierarchy which emphasizes the complexity of a phenomenon as it goes to the lowest layer, there is a feature that commonality fades. On the other hand, the cluster is composed of more samples as it goes to the top layer, but since the number of clusters included in the hierarchy is reduced, there is a feature that there is a lot of commonness including noise.

  Therefore, it can be considered that there is a most suitable hierarchy for extracting a common concept from this relationship. Here, the hierarchy which can extract a common concept is specified, and the method of extracting a common concept from here is described.

First, the hierarchy suitable for the extraction of the common concept is specified. Here, the sensitivity S and SN ratio η of the correlation coefficient of a certain path p are used. The hierarchy of interest i, when the number of clusters included in the layer n, the correlation coefficient in the path p in the m-th cluster included in the layer and r _ipm, the correlation coefficient superposed r _ip ^- in the formula ( It is expressed as 5.3).

If one of the common causal networks in this hierarchy is the path p, the sensitivity S of the correlation coefficient can be expressed as in equations (5.3) to (5.4).
(5.4)

Further, the total variation S _t of the correlation coefficient in the path p for each cluster included in the layer i is expressed by equation (5.5).

Further, the correlation coefficient variation S _β of the path p is expressed by Expression (5.6), where Euclidean distance d _im for dividing each cluster and average Euclidean distance are di ⁻ .

Therefore, the error variance V _e in the path p can be expressed by Equation (5.7).

Therefore, the SN ratio η of the correlation coefficient in the path p of each cluster included in the hierarchy i can be expressed by Expression (5.8).

  Since the common concept is a common causal network that can explain all phenomena, the sensitivity S expressed by equation (5.4) is large and the SN ratio η expressed by equation (5.8) is large in all common paths. The hierarchy is suitable for extracting common concepts. However, the hierarchy of common concept extraction must be examined in a hierarchy that is less than or equal to the maximum Euclidean distance that causes a branch when searching from the top layer to the bottom layer of the tree diagram.

  In the hierarchy suitable for common concept extraction obtained as described above, the common causal network that becomes the common concept corresponds to the path p having a high correlation coefficient sensitivity expressed by the equation (5.4). FIG. 8 shows an example of a network display method and a common concept display method common to these networks. A line representing a strong causal relationship common to each cluster corresponds to a common concept.

  In addition, as shown here, the notation method of the limiting element is that each limiting element is arranged on the circumference, and the causal network is described by connecting the limiting elements with a straight line. Good. In addition to the method of changing the line type as a means for expressing the causal relationship, a method of coloring a line, a method of expressing by a line thickness, or the like can be considered. The common concept of FIG. 8, that is, the common network is naturally included in the network of individual clusters of FIG. Further, it is only necessary that the limiting element having a strong causal relationship is expressed so as to be visible, and may be described in a three-dimensional shape.

(Setting of characteristic value or range)
In the setting of the characteristic value or range shown in step [4], the designer previously determines the characteristic value to be satisfied by the structure derived using the common concept or the characteristic range to be satisfied. Here, the characteristic may be one or more. In this case, the optimum structure is extracted for the set characteristic. In the latter case, the structure is extracted in a form having a certain range with respect to a range of characteristics or a combination thereof. In this case, the design space in which the structure exists is extracted. After that, optimization for deriving the structure having the optimum characteristics is performed. However, here, it can be appropriately set according to the purpose of the designer, and can be applied to other than optimization.

(Sampling based on common concepts)
In the generation of sampling based on the common concept shown in step [5], it is a part for which sampling of the structure based on the common concept is sought. First, the restriction elements constituting the common concept are changed. Here, the restriction element is changed after following the causal relationship of the common concept such as the value or range of the restriction element of the extracted common concept, the tendency of the relationship between the restriction elements, and the like. This compensates for the nature (trend) of the resulting system characteristics.

  Next, the restriction elements other than the common concept are changed. Here, any changes may be made to the limiting elements other than the common concept. Calculation is performed based on the combination of the common concept obtained here and other limiting elements, and the characteristics of this structure are obtained. That is, sampling is performed. Here, it is efficient to generate a distance model based on the changed limiting element. Further, the restriction elements other than the common concept may be changed by a general model generation method such as an orthogonal table or a random number. As described above, the limiting elements other than the common concept may try to derive a new limiting element by increasing or decreasing the number of limiting elements.

(Distance model generation method)
The extracted common concept is represented by a combination of limit element values representing a causal relationship with a characteristic, a combination of ranges, a tendency of a relationship between the limit elements, and a combination thereof. If the common concept is a combination based only on the value of the limiting element, this cannot be changed. Further, when the common concept is expressed in the range of the limiting element, model generation may be performed using, for example, an orthogonal table or a random number within this range.

  On the other hand, in the case of a common concept with other expressions, it is necessary to change the limiting element following the common concept. Here, a distance model generation method is proposed to generate a model that follows the common concept efficiently.

  The distance model generation method is a method for newly generating a model similar to the limiting elements constituting the common concept. This method uses a measure between individuals used in a clustering grouping algorithm. In the clustering grouping algorithm, the distance between individuals is used as a measure for the degree of similarity (dissimilarity) between individuals. Various types of scales have been proposed. Here, the Euclidean distance, which makes it easy to imagine the similarity between individuals and is easy to handle, is taken up.

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, if the model generated by uniform random numbers is d _rand , the model expressed by the limiting elements constituting the common concept is x _c , and the model that does not satisfy the threshold is x _o , the newly generated model and these distances are It is expressed by (4.2).

Next, a restriction rule that does not employ a model extremely similar to the model x _c of the restriction element constituting the common concept is applied. For example, when the Euclidean distance is 0.01 or less and you want to recognize that two individuals are almost the same, the newly generated model x _rand must comply with the restriction law of Equation (4.3) for the common conceptual model x _c. adopt. 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 common concept models, the formula (4.3) is calculated using other common concept models and the generated model in order to prevent the generation of the same model.

In the following, a model generation algorithm will be described. An image of model generation is shown in FIG.
(i) Prepare a model of the limiting elements that make up the common concept.
(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 common conceptual model is stored.
(iii) Again, generate a model using random numbers based on the common concept, 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 common conceptual model is stored.
(iv) Thereafter, the above (i) to (iii) are repeated.

(Judgment of structure availability)
In determining whether the structure shown in step [6] is acceptable, it is determined whether or not the value matches the characteristic value set in step [4], that is, whether or not the target optimum value is reached. Here, when the value is the optimum value, the structure is adopted. When the value is not the optimum value, the step [5] is repeated again.

(Concrete example)
Hereinafter, an example applied to a specific mode based on the first embodiment will be described. Here, we will discuss the beam problem of optimizing a light-weight structure with a small amount of tip displacement by providing a plurality of beams from the wall surface. FIG. 9 shows an example of a beam structure. Here, the characteristic to be handled is the amount of displacement in the load direction of the tip P5 when a load acts on the tip P5, and the limiting element is the thickness of the beam provided between the nodes P1 to P9. .

(Preparation for sampling)
For the beam structure provided between the nodes P1 to P9 shown in FIG. 10, the thickness including presence or absence is appropriately selected from the combinations shown in FIG. Therefore, the limiting elements are beams B1 to B29 provided between the nodes, and the values of the limiting elements are set between 0 and a certain thickness (range). Here, for the thickness, select an evenly assigned value using an orthogonal table, etc., perform mechanism calculation according to the uniformly extracted combination among all the combinations of these limiting elements, and the load acts on the tip P5 The amount of displacement is calculated, and sampling is prepared. FIG. 12 is a schematic view showing a distance model of the limiting element, and FIG. 13 shows characteristics showing the relationship between all the displacement amounts and weights of the sampling.

(Classification of characteristics)
The sampling prepared in the above (preparation for sampling) is classified according to characteristics, that is, the relationship between weight and displacement. FIG. 14 shows a tree diagram of characteristics obtained as a result of classification. FIG. 15 shows the characteristics of groups (hereinafter referred to as clusters) in a certain classified hierarchy.

(Extraction of common concepts)
From the classification result obtained in the above (classification of characteristics), the hierarchy from which the common concept is extracted is specified according to the method for extracting the common concept. A causal network between the restriction elements of each cluster existing in the identified hierarchy is extracted according to the above-described common concept extraction method. The causal network between the limiting elements obtained as a result is expressed using limiting element notation means.

  FIG. 16 shows some examples of the causal network between the limiting elements. In this notation method, the limiting element that has the greatest influence on the characteristics of the characteristics indicated by the cluster is indicated by a solid line, and the dotted line indicates the limiting element that has the next highest influence. Here, the common concept is a causal network of common limiting elements existing in all clusters. Therefore, the extraction of the common concept is equivalent to finding the common causal network by comparing the notation of the restriction elements of the clusters obtained here. FIG. 17 shows the notation of the common concept obtained.

  The common concept obtained here is an element that determines the relationship of the displacement of the tip P5 of the beam thickness. That is, in order to realize the desired weight and displacement, it is possible to guarantee at least by designing with an emphasis on the relationship (trend) of the beam, which is a common concept.

(Set characteristic value)
The relationship between the target weight and the amount of displacement was set as shown in FIG. As described in the extraction of the common concept, the characteristics shown in FIG. 18 have a range similar to the characteristics of the cluster 2 shown in FIG. Therefore, the relationship of the limiting elements constituting the common concept for achieving the characteristic tendency shown in FIG. 18 may follow the relationship of providing a thin beam between thick beams as shown in cluster 2 of FIG. It will be.

(Change of common concept and other restriction elements and extraction of system characteristics)
FIG. 19 shows an example of a distance model based on the common concept. Here, a solid line indicates the relationship between beam thicknesses, which is a common concept, and a dotted line is a distance model generated using the distance model generation method.

(Judgment of structure availability)
A beam structure that matches the value of FIG. 18 set in the setting of the value of the characteristic was extracted from the distance model. The extracted structure is shown in FIG. As described above, optimization can be efficiently performed by generating only the sampling based on the common concept, compared with the case of performing the optimization calculation based on the relationship between the thicknesses of all the beams. According to this method, the optimum value can be calculated with a calculation time of 1/3 or less of the conventional calculation time.

  As described above, in the first embodiment, the following effects can be obtained.

  (1) A system having characteristics corresponding to a plurality of limiting elements, first sampling generating means for generating a plurality of samplings that are combinations of the limiting elements and the characteristics of the system, and the similarity of the sampling to the characteristics From the result of the comparison by the hierarchical clustering means for hierarchically clustering based on the above, the comparison means for comparing the restriction elements of each clustered cluster between the same hierarchy and / or between different hierarchies, and the comparison means, Out of the limiting elements, an extracting unit that extracts a limiting element that is common among the clusters, a target characteristic setting unit that sets a target characteristic, and a second sampling that generates sampling based on the extracted common limiting element And the characteristics of the sampling generated by the second sampling generating means are the target Determine the optimal sampling or not to satisfy the sex, when it is determined that the optimum has and a sampling evaluating means for outputting as the optimum sampling the sampling.

  Therefore, by extracting common limiting elements from a small number of samplings, it is possible to generate a rational shape at the initial design stage, and by generating sampling based on this rational shape, an efficient solution can be obtained. A space can be searched, and optimization can be achieved with a small number of operations.

  (2) We decided to change the common restriction elements within the common range. As a result, the tendency and characteristics of the new sampling can follow the tendency and characteristics of the existing sampling, and the existing characteristics can be compensated for while being a new sampling. Note that when a new sampling is generated, the same effect can be obtained even if the tendency of the common limiting element is maintained and changed.

  (3) The values of limiting elements other than the extracted common limiting elements are arbitrarily changed to generate new sampling. Specifically, sampling that follows the common concept is generated by generating a distance model.

  Therefore, new sampling that follows the common concept can be easily generated.

  Note that all of the above-described actions may be provided in a state described in a program or the like that can be read by the arithmetic device. Specifically, a sampling generation command unit that outputs a command for generating a plurality of samplings, which is a combination of the limiting element and the characteristic of a system having characteristics corresponding to a plurality of limiting elements, and the sampling similar to the characteristic Hierarchical clustering command unit for outputting a command for hierarchical clustering based on degree, and a comparison command unit for outputting a command for comparing the restriction elements of each clustered cluster between the same hierarchies and / or between different hierarchies From the result of comparison by the comparison means, an extraction unit that extracts a restriction element that is common among the clusters among the restriction elements, and a target characteristic setting unit that requests setting of the target characteristic are extracted and shared A second sampling generator for outputting a command to generate sampling with reference to the limiting element; and the second sample A sampling evaluation unit that determines whether or not the sampling characteristic generated by the generation unit is an optimal sampling that satisfies the target characteristic, and outputs the sampling as an optimal sampling when it is determined to be optimal. By using the medium on which the optimization support program is recorded, it is possible to improve distribution.

  Further, when executing the optimization support, as a display means for the designer, sampling that is a combination of the limiting element and the characteristic of the system having characteristics corresponding to a plurality of limiting elements is used. A hierarchical clustering display means for displaying the result of hierarchical clustering based on the above, a comparison display means for displaying the restriction elements of each clustered cluster in a comparable manner between the same hierarchy and / or between different hierarchies, From the result of comparison by the comparison display means, an extraction result display means for displaying a result of extracting a restriction element common among the clusters among the restriction elements, a target characteristic setting display means capable of inputting a target characteristic, Optimal sampling in which the sampling characteristics generated based on the extracted common limiting elements satisfy the target characteristics And providing an optimization support display device characterized by comprising a sampling evaluation result display means for displaying the sampling as an optimal sampling when it is determined to be optimal. The ease can be further improved.

The technical ideas that can be grasped from the above embodiments will be listed below.
(4) When there is a set of characteristics indicating the relationship between input and output for a system defined by a plurality of limiting elements, the set is classified based on the tendency of the characteristics, and the limiting elements corresponding to the classified characteristics The restriction element for a given classification is compared with the restriction element for the other classification. In other words, by comparing the characteristics classified based on the tendency between the limiting elements that define this characteristic, it becomes possible to grasp the limiting elements that define the tendency, and to understand the technical meaning of the classification. it can.

  (5) We decided to extract common concepts based on the limiting elements common to each category. Therefore, a common concept can be extracted from a complex phenomenon.

  (6) We used a hierarchical clustering method that clustered hierarchically based on trends. In other words, considering the fact that our target system is based on hierarchical classification, the most understandable system can be obtained by hierarchical clustering. Further, considering that the number of layers existing in the system is not known in advance, it is not necessary to set a threshold or the like in advance, and a result that is not bound by an existing concept can be obtained.

  (7) We decided to extract common concepts based on the limiting elements common to each level. Therefore, it is possible to extract a common concept that defines between hierarchies.

  (8) We decided to extract common concepts based on restrictive elements common to only certain hierarchies. Therefore, a common concept that defines a certain hierarchy can be extracted.

  (9) When sampling the system, it was decided to sample without limitation on the combination of limiting elements. Therefore, the limiting elements can be compared without causing a bias in the characteristics. Moreover, a common concept can be extracted without causing a bias in characteristics.

  (10) When performing sampling, an orthogonal table is used. Therefore, when focusing on the specific level of an assigned limiting element, all the levels of other limiting elements are created so that they are combined evenly. it can. Moreover, a common concept can be extracted without causing a bias in characteristics.

  (11) The characteristics are classified based on the similarity according to the distance in the Euclidean space. Therefore, it becomes possible to express a multidimensional restriction element in an orthogonal coordinate system based on the similarity, and it is possible to easily compare in a form that can be understood by humans.

  (12) The classification is based on the similarity based on the distance between the center of gravity of a certain classification and each characteristic. Therefore, it becomes possible to observe complex phenomena on a scale of distance, and to compare in a form that can be understood by humans.

  (13) The limiting element notation means arranges limiting elements on a two-dimensional plane. Therefore, it is possible to easily compare in a form that can be understood by humans.

  (14) The limiting element notation means arranges each limiting element on a polygon. Therefore, when connecting between the limiting elements with a causal network, it becomes possible to connect with a straight line, and the causal network can be easily understood.

  (15) The restriction element notation means expresses all restriction elements. Therefore, since the truncation based on the existing concept is not performed, the physical connection describing the phenomenon itself can be accurately described.

  (16) The limiting element notation means arranges the limiting element and the characteristic in the same dimension, and configures a causal network representing the connection between the limiting element and the characteristic. Therefore, the physical connection between the limiting element and the characteristic can be expressed in a form that can be understood by humans.

  (17) When limiting elements and characteristics on the causal network are defined as fulcrums, a correlation coefficient representing the strength of the connection between each fulcrum is calculated between all fulcrums, and a causal network with a large correlation coefficient is extracted. It was decided to. Therefore, it is possible to grasp a phenomenon process that is gradually hierarchized from a complicated phenomenon to a simple phenomenon together with a change in the causal network.

  (18) The error variance representing the size of the variance area of the causal network is calculated, and the common concept is extracted in a hierarchy having a large correlation coefficient and a small error variance. Therefore, a numerical index can be provided in the path between the limiting elements, and even if all the limiting elements are compared, a causal network can be easily formed without complication.

  Although not specifically shown in the first embodiment, it is industrially effective to use an information processing technique based on the logical configuration as a program medium that can be processed by a computer or the like. The program medium may be a medium such as a CD or a DVD, or may be configured to store the program in a server or the like and download the program as appropriate. Also, a device written in advance in a Flash memory or ROM may be provided.

It is a figure showing the concept which introduce | transduces the tendency system which added the limitation of a tendency or a range between the abstract system of Example 1, and a format system, and between a concrete system and a format system. It is a conceptual diagram showing the relationship between the cluster of Example 1, and a common concept. It is a figure showing the optimization assistance flow of Example 1. FIG. It is a figure showing the example of the direct table which prepares the sampling of Example 1. FIG. FIG. 6 is a diagram illustrating a specific example of clustering according to the first exemplary embodiment. 3 is a diagram illustrating a specific example of hierarchical clustering according to Embodiment 1. FIG. It is a figure showing the causal network of Example 1. FIG. An example is shown in the common concept display method common to the causal network of the first embodiment. It is the schematic showing the image of the distance model production | generation of Example 1. FIG. It is a figure which shows the structure of the beam in a specific example. It is a figure showing the beam (restriction element) in a specific example with the relationship with a node. It is sampling showing the relationship between the beam and the thickness of a beam in a specific example. It is a figure showing the characteristic of all the sampling created according to the orthogonal table | surface with the thickness of the beam in a specific example. It is a figure showing the dendrogram of the characteristic obtained as a result of the clustering in a specific example. It is a figure showing the characteristic of the cluster in a classified hierarchy. It is a figure showing some examples of the causal network of the limiting element in a certain cluster in a specific example. It is a figure showing the common concept in the common causal network in a specific example. It is a figure showing the target characteristic of a specific example. It is a figure showing the distance model on the basis of the common concept of a specific example. It is a figure showing the optimal beam structure of a specific example.

Explanation of symbols

p, q, r cluster
t cluster (cluster p + cluster q)

Claims (6)

A system having characteristics corresponding to a plurality of limiting elements;
First sampling generating means for generating a plurality of samplings that are combinations of the limiting element and the characteristic of the system;
Hierarchical clustering means for hierarchically clustering the sampling based on the similarity of the characteristics;
Comparing means for comparing limiting elements having a high correlation between the variation of the limiting element and the variation of the characteristics in each clustered cluster between the same hierarchy and / or between different hierarchies;
From the result of comparison by the comparison means, an extraction means for extracting a restriction element that is common among the clusters, among the restriction elements having a high correlation , and
Target characteristic setting means for setting the target characteristic;
Second sampling generating means for generating sampling based on the extracted common limiting element;
Sampling evaluation means for determining whether or not the sampling characteristic generated by the second sampling generation means is optimal sampling that satisfies the target characteristic, and when determining that the sampling is optimal, sampling evaluation means for outputting the sampling as optimal sampling;
An optimization support apparatus characterized by comprising: The optimization support apparatus according to claim 1,
The second sampling generating means changes the common limiting element within a common range. The optimization support apparatus according to claim 1 or 2,
The optimization support apparatus characterized in that the second sampling generation means changes the common limiting factor while maintaining the tendency. When there is a system with characteristics corresponding to multiple limiting elements ,
Computer
And Lusa sampling onset producing unit is generating multiple combinations at which sampling of the characteristics and the limiting element,
And hierarchically Kurasutaringusu Ru hierarchical manner clustering unit based on the sampling of the similarity of the characteristics,
In each cluster is the cluster, a comparator the variation of the limiting element and a correlation between high limiting element and variations in the properties, you compare between the same inter-layer and / or different layers,
From the result of comparison in the comparison unit , an extraction unit that extracts a restriction factor that is common between the clusters, among the restriction factors having a high correlation , and
And the target characteristic setting unit Ru set Teisu of target characteristics,
A second sampling generator which Ru generates sampling the extracted common restriction element as a reference,
A sampling evaluation unit that determines whether the sampling characteristic generated by the second sampling generation unit is an optimal sampling that satisfies the target characteristic, and outputs the sampling as an optimal sampling when it is determined to be optimal;
Optimization support program for causing to function as. A hierarchical clustering display means for displaying a result of hierarchically clustering sampling, which is a combination of the limiting element and the characteristic of a system having characteristics corresponding to a plurality of limiting elements, based on the similarity of the characteristics;
Comparison display means for displaying a restriction element having a high correlation between the fluctuation of the restriction element and the fluctuation of the characteristic in each clustered cluster so as to be comparable between the same hierarchy and / or between different hierarchies;
From the result of comparison by the comparison display means, an extraction result display means for displaying a result of extracting a restriction element common among the clusters among the restriction elements having a high correlation , and
A target characteristic setting display means capable of inputting a target characteristic;
Sampling evaluation result display means for determining whether or not the sampling characteristic generated based on the extracted common limiting element is the optimal sampling satisfying the target characteristic, and displaying the sampling as the optimal sampling when it is determined to be optimal When,
An optimization support display device characterized by comprising: When there is a system with characteristics corresponding to multiple limiting elements ,
Computer
A step be multiple generating sampling is a combination of the characteristics and the limiting element,
Clustering the sampling hierarchically based on the similarity of the characteristics;
Comparing the limiting elements having a high correlation between the variation of the limiting element and the variation of the characteristics in each clustered cluster between the same hierarchy and / or between different hierarchies;
From the result of comparison by the comparison means, a step of extracting a restriction element that is common among the clusters among restriction elements having a high correlation ; and
Setting target characteristics;
A step that occur sampling the extracted common restriction element as a reference,
Determining whether or not the sampling characteristic generated based on the extracted common limiting element is the optimal sampling that satisfies the target characteristic, and outputting the sampling as the optimal sampling when it is determined optimal;
The optimization support method characterized by performing .

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