JP7589592B2 - DESIGN SUPPORT METHOD, DESIGN SUPPORT PROGRAM, AND COMPUTER-READABLE STORAGE MEDIUM CONTAINING THE DESIGN SUPPORT PROGRAM - Google Patents

Description

The technology disclosed herein relates to a design support method, a design support program, and a computer-readable storage medium that stores the design support program.

For example, Patent Document 1 discloses a design support method for a structure having multiple parts. Specifically, the design support method for a structure disclosed in Patent Document 1 is configured to set a linear combination of design variables that quantify the specifications of each part as a response variable, and to identify a model that indicates the performance index of the structure by performing multiple regression analysis on the response variable.

JP 2020-71725 A

Incidentally, when formulating the performance of a structure using design variables such as those disclosed in Patent Document 1, in order to take into account more complex phenomena such as the mutual influence of parts on each other, it is possible to consider the terms expressed in more general functional forms, such as interaction terms in which design variables are multiplied together, and terms expressed by trigonometric functions with design variables as arguments, as performance factors and carry out the formulation.

However, because there are an infinite number of such performance factors, the calculations required to formulate the model become complicated and the time required for the calculations can become enormous. This is inconvenient for smoothly providing design support using the model.

The technology disclosed here has been developed in light of these issues, and its purpose is to formulate the performance of a structure simply and quickly.

The first aspect of the present disclosure relates to a design support method that uses a computer equipped with a calculation unit that executes a program and a storage unit that reads data to formulate the performance of a structure composed of multiple parts using design variables that quantify the specifications of each part.

According to a first aspect of the present disclosure, the design support method includes a read step in which the storage unit reads in a set of performance factors each having one or more of the design variables as arguments; an extraction step in which the calculation unit applies multiple types of extraction methods to the set of performance factors to extract performance factors that contribute to the performance of the structure for each extraction method; a ranking setting step in which the calculation unit sets a selection ranking for the performance factors based on the extraction results obtained for each extraction method; and a formulation step in which the calculation unit selects the performance factors from the set of performance factors according to the selection ranking, and formulates the performance of the structure by combining the selected performance factors.

Here, "performance factors" include factors used in polynomial approximation of design variables, such as linear terms of design variables, quadratic terms of design variables, etc., as well as factors that realize non-polynomial approximation, such as trigonometric functions with design variables as arguments.

According to the first aspect, the design support method applies multiple types of extraction methods to a set of performance factors to set a selection order for the performance factors. This selection order can be said to indicate the importance of the performance factors. When setting the selection order, by using multiple extraction methods individually rather than using only a specific extraction method, the selection order can be set more appropriately. Performance factors with a relatively high selection order are actively incorporated into a model formula that describes the performance, while performance factors with a relatively low selection order are passively incorporated into the model formula, thereby making it possible to faithfully describe the performance of the structure while suppressing the number of terms used in formulation. This makes it possible to formulate the performance of the structure simply and quickly.

Furthermore, according to a second aspect of the present disclosure, the performance factor may include a linear term consisting of the design variables themselves and a nonlinear term consisting of the multiplication of the design variables.

According to the second aspect, the performance factor includes a nonlinear term that is the product of the design variables. This allows the model to include interactions related to the connections between parts. This is effective when modeling dynamic phenomena such as the crash performance of a structure.

According to a third aspect of the present disclosure, the design support method may further include a pre-narrowing step in which the calculation unit sets the set of performance factors prior to the extraction step, and in the pre-narrowing step, the set of performance factors is set by performing a genetic operation on a tree structure in which the design variables are terminal nodes and multiplication operators are non-terminal nodes, and in the pre-narrowing step, the genetic operation is performed so that the number of levels in the tree structure is equal to or less than a predetermined maximum depth.

According to the third aspect, prior to selecting the performance factors based on the selection order, the performance factors are narrowed down using a tree structure. Here, by excluding the coefficients of the design variables from the terminal node, the narrowing down can be performed more quickly. At that time, by setting the number of levels of the tree structure in advance, the narrowing down can be performed in a way that is appropriate for the structure to be supported. This allows for more efficient formulation.

According to a fourth aspect of the present disclosure, the design support method may include a model reconstruction step in which the calculation unit excludes from the performance of the structure the nonlinear terms consisting of design variables that do not appear as linear terms in the performance of the structure, among the design variables that constitute the performance factor.

According to the fourth aspect, among the design variables constituting the nonlinear terms, those that do not appear in the model as first-order linear terms (for example, design variables that do not appear in the model as first-order terms (main effects) but appear in the model only as interaction terms) are excluded from the model. By performing this process, the number of performance factors to be considered can be reduced, thereby reducing the amount of calculations.

According to a fifth aspect of the present disclosure, the calculation unit may determine the extraction frequency for each of the performance factors based on the extraction results obtained for each of the extraction methods, and the calculation unit may set the selection order based on the level of the extraction frequency.

According to the fifth aspect, a performance factor that is extracted frequently, for example, a performance factor that is extracted by all extraction methods, is set to a high selection priority, while a performance factor that is extracted infrequently, for example, a performance factor that is extracted by only one of the extraction methods, is set to a low selection priority. By setting in this way, the selection priority can be set more appropriately, and the performance of the structure can be formulated more faithfully.

According to a sixth aspect of the present disclosure, the performance of the structure may be formulated by a linear combination of the performance factors, and the calculation unit may perform a multiple regression analysis for each of the multiple types of extraction methods with the performance factors as explanatory variables and the performance of the structure as a target variable, and the calculation unit may determine the extraction frequency based on the coefficients of the explanatory variables calculated by the multiple regression analysis.

According to the sixth aspect, the calculation unit determines the extraction frequency based on the magnitude of the coefficient multiplied by each performance factor. In this case, for example, a performance factor whose coefficient is calculated to be zero in a specific extraction method can be determined as not being extracted at least in that extraction method. By setting in this manner, the extraction frequency can be clearly determined, which is advantageous in formulating the performance of a structure simply and quickly.

Furthermore, according to a seventh aspect of the present disclosure, the multiple types of extraction methods may include regression analysis with sparsity.

According to the seventh aspect, when a regression analysis with sparsity is performed, coefficients with low contribution are set to zero. This allows the extraction frequency to be clearly determined, which is advantageous in formulating the performance of a structure simply and quickly.

According to an eighth aspect of the present disclosure, the multiple types of extraction methods may include stepwise regression analysis.

According to the eighth aspect, the coefficients of performance factors that were not selected when the stepwise method was performed can be considered to be zero. This allows the extraction frequency to be clearly determined, which is advantageous in formulating the performance of a structure simply and quickly.

According to a ninth aspect of the present disclosure, the design support method includes an index calculation step for calculating an evaluation index that characterizes the accuracy of the formulation in the formulation step, and a verification step for verifying the accuracy of the formulation in the formulation step based on the evaluation index calculated by the index calculation step, the storage unit reads a plurality of sample data corresponding to the set of performance factors, the calculation unit divides the plurality of sample data into learning data and verification data according to a predetermined division pattern, the calculation unit executes the extraction step, the ranking step, and the formulation step based on the learning data, while executing the index calculation step based on the remaining verification data, the calculation unit changes the division pattern multiple times, and repeatedly executes the extraction step, the ranking step, the formulation step, and the index calculation step for each changed division pattern, and then executes the verification step, and in the verification step, the calculation unit selects any one of the performances of the structure formulated for each division pattern based on the evaluation index calculated for each division pattern.

According to the ninth aspect, the design support method performs k-fold cross-validation when formulating based on the selection ranking. In other words, formulation is performed based on k types of learning data, and an evaluation index is calculated based on the remaining validation data for each formulation. Then, by selecting the model with the best evaluation index from among the k types of models obtained by each division pattern, a more robust formulation can be performed. This is effective in achieving both a simple and fast formulation of the performance of the structure and robustness of the model formula.

Furthermore, according to a tenth aspect of the present disclosure, the structure may be an automobile body, and the design variables may be the plate thicknesses of each of the plurality of parts.

An automobile body is made up of many parts. In this case, it is thought that many performance factors need to be considered. The present disclosure is effective in a technical field in which many performance factors can be considered, but it is not easy to secure sample data beyond that, in that it can actively narrow down important performance factors from among the many performance factors.

An eleventh aspect of the present disclosure relates to a design support program that, when executed by a computer having a calculation unit that executes a program and a storage unit that reads data, formulates the performance of a structure composed of multiple parts using design variables that quantify the specifications of each part.

According to an eleventh aspect of the present disclosure, the design support program causes the computer to execute a read step in which the storage unit reads a set of performance factors with one or more of the design variables as arguments, an extraction step in which the calculation unit applies multiple types of extraction methods to the set of performance factors to extract performance factors that contribute to the performance of the structure for each extraction method, a ranking step in which the calculation unit sets a selection ranking of the performance factors based on the extraction results obtained for each extraction method, and a formulation step in which the calculation unit selects the performance factors from the set of performance factors according to the selection ranking and formulates the performance of the structure by combining the selected performance factors.

According to the eleventh aspect, the performance of a structure can be formulated simply and quickly.

A twelfth aspect of the present disclosure relates to a computer-readable storage medium. This storage medium stores the design support program according to the eleventh aspect.

As described above, the present disclosure makes it possible to formulate the performance of a structure simply and quickly.

FIG. 1 is a diagram illustrating an example of a hardware configuration of a design support apparatus. FIG. 2 is a diagram illustrating an example of a software configuration of the design support apparatus. FIG. 3 is a flowchart illustrating the procedure of the design support method. FIG. 4 is a flowchart illustrating a specific procedure of the preliminary narrowing down phase. FIG. 5 is a diagram for explaining the relationship between a tree structure used in the preliminary narrowing down phase and a model formula corresponding to the tree structure. FIG. 6 is a diagram for explaining the one-point crossover method in the pre-narrowing phase. FIG. 7 is a flowchart illustrating a specific procedure of the performance factor extraction phase. FIG. 8 is a diagram for explaining the procedure for acquiring the performance factors according to the selection order. FIG. 9 is a diagram for explaining the k-fold intersection method. FIG. 10 is a diagram showing a specific example of the performance factor extraction phase. FIG. 11 is a diagram illustrating the influence of the interaction terms on the crash performance value. FIG. 12 is a diagram for explaining the model reconstruction step.

Embodiments of the present disclosure will be described below with reference to the drawings. Note that the following description is merely an example.

<Device Configuration>
Fig. 1 is a diagram illustrating an example of a hardware configuration of a design support apparatus (specifically, a computer 1 constituting the design support apparatus) according to the present disclosure. Fig. 2 is a diagram illustrating an example of a software configuration of the design support apparatus.

As shown in FIG. 1, the computer 1 includes a central processing unit (CPU) 3 that controls the entire computer 1, a read only memory (ROM) 5 that stores a boot program and the like, a random access memory (RAM) 7 that functions as a main memory, and a hard disk drive (HDD) 9 as a secondary storage device. Note that instead of the HDD 9, a solid state drive (SSD) or the like can also be used as the secondary storage device.

Of these elements, CPU 3 executes various programs. CPU 3 functions as a calculation unit in this embodiment. RAM 7 temporarily stores programs executed by CPU 3 and various data, while HDD 9 continuously stores programs, data, etc. RAM 7 can also read data from HDD 9 as necessary. RAM 7 functions as a storage unit in this embodiment.

The computer 1 also includes a display unit 11 consisting of a liquid crystal display, an organic EL display, a CRT display, or the like, a graphics memory (Video RAM: VRAM) 13 that stores image data to be displayed on the display unit 11, and a keyboard 15 and a mouse 17 as man-machine interfaces. The display unit 11 can display the results of calculations performed by the CPU 3. Furthermore, the computer 1 according to this embodiment can send and receive data to and from external devices via a communications interface 21.

As described below, the design support device according to the present disclosure may be configured with multiple computers 1. In that case, the CPU 3 and RAM 7 of each computer 1 can be regarded as the calculation unit and storage unit according to the present disclosure, respectively.

As shown in FIG. 2, the program memory of the HDD 9 stores an operating system (OS) 19, a pre-narrowing program 29A, a performance factor extraction program 29B, a design knowledge extraction program 29C, etc.

Of these elements, the pre-narrowing program 29A, the performance factor extraction program 29B, and the design knowledge extraction program 29C constitute the design support program 29 in this embodiment.

The design support program 29 is a program configured to cause the computer 1 to execute the design support method according to this embodiment, and can cause the computer 1 to execute each step constituting the design support method. The design support program 29 is pre-stored in the computer-readable storage medium 18 (see FIG. 1).

In the program memory of the HDD 9, the pre-narrowing program 29A, the performance factor extraction program 29B, and the design knowledge extraction program 29C are each started in response to commands input from the keyboard 15, the mouse 17, etc. At that time, the pre-narrowing program 29A, etc. are loaded from the HDD 9 to the RAM 7 and executed by the CPU 3. The CPU 3 executes the pre-narrowing program 29A, etc., causing the computer 1 to function as a design support device.

On the other hand, multiple sample data 49 are stored in the data memory of the HDD 9. Each sample data 49 is defined as multivariate data consisting of multiple independent variables. Each sample data 49 is loaded from the HDD 9 to the RAM 7 as necessary and used in calculations by the CPU 3.

Here, each sample data 49 indicates the specifications of a structure to be analyzed and the performance value realized in the structure. This structure is composed of multiple parts. Each sample data 49 also stores multiple design variables x _i (i=1, 2, ..., N) in which the specifications of each part are quantified, and a response y (also called performance value y or objective variable y) output when the specifications are input. Each sample data 49 may be generated in step S12, step S21, etc. described later, or may be generated in advance and read from the outside and stored.

For example, when designing a car body by model-based development, the structure corresponds to the car body, and the multiple parts correspond to car body components such as B-pillars, side sills, front tunnels, roof rails, front frames, side frames, rear side frames, cross members, floor panels, front panels, rear panels, engine covers, bonnets, rear fenders, roofs, doors, lift gates, rear end panels, rear wheel house outers, rear end members, rear pillar outers, rear pillar inners, rear pillar reinforcements, upper reinforcements, and rear roof rails. In this case, as design variables x _i corresponding to each part, the plate thickness, shape, joint strength, weight, material, and the like of the corresponding part can be used. In this case, as the response y, the collision performance value of the car body (performance index indicating the resistance to deformation during a collision), the torsional rigidity of the car body (performance index indicating the resistance to torsional deformation), the driving stability, the NVH performance, and the like can be used.

In addition, various data generated by executing the pre-narrowing program 29A, the performance factor extraction program 29B, and the design knowledge extraction program 29C, as well as the execution results of the application program 39, are stored in the data memory of the HDD 9 or temporarily stored in the RAM 7 as the main memory, as necessary.

The specific methodology of the design support method is explained in detail below.

<Methodology>
Fig. 3 is a flow chart illustrating the procedure of a design support method. The flow illustrated in Fig. 3 is a design support method in which the performance of a structure composed of a plurality of parts is formulated by using design variables in which the specifications of each part are quantified, by using a computer 1.

The design support method is basically implemented by sequentially executing a pre-narrowing phase S1 as a pre-narrowing step, a performance factor extraction phase S2 consisting of a reading step, an extraction step, a ranking step, a formulation step, an index calculation step, and a verification step described below, and a design knowledge extraction phase S3 consisting of a model reconstruction step. Note that the pre-narrowing phase S1 and the design knowledge extraction phase S3 are not essential.

Of these phases S1 to S3, the pre-narrowing phase S1 is implemented by the CPU 3 executing the above-mentioned pre-narrowing program 29A. Similarly, the performance factor extraction phase S2 is implemented by the CPU 3 executing the performance factor extraction program 29B, and the design knowledge extraction phase S3 is implemented by the CPU 3 executing the design knowledge extraction program 29C.

Below, we explain each phase of the design support method in order.

(Pre-narrowing phase S1)
Fig. 4 is a flow chart illustrating a specific procedure of the pre-narrowing phase S1. Fig. 5 is a diagram for explaining the relationship between a tree structure T1 used in the pre-narrowing phase S1 and a response y corresponding to the tree structure T1. Fig. 6 is a diagram for explaining the one-point crossover method in the pre-narrowing phase S1.

In this embodiment, the performance of the structure is formulated by a linear combination of performance factors X _j (j=1, 2, ..., M). Here, the performance factor X _j is generated by using one or more of the design variables x _i as arguments. Then, a linear combination of the term β _j ·X _j obtained by multiplying each performance factor X _j by the contribution β _j as the amount of work is calculated, and the response y is formulated as shown in the lower part of FIG. 5. In the example shown in FIG. 5, the response y is formulated by an intercept and a linear combination of four performance factors X ₁ to X _4. Each performance factor X _j is formed by using one or more of the design variables x _i as arguments. Here, the performance factor X _j includes a term obtained by multiplying one or more of the design variables x _i , a trigonometric function with the design variable x _i as an argument, an n-th root of the design variable x _i , a logarithm of the design variable x _i , an exponential function with the design variable x _i as an argument, and the like.

Here, in order to formulate the response y, it is necessary to extract the performance factors _Xj that contribute to the performance of the structure and to calculate the contribution _βj by which each performance factor _Xj should be multiplied. In particular, when nonlinear terms such as interactions, which will be described later, are taken into consideration, when there are many design variables _xi , it is considered that there are countless variations in the performance factors _Xj .

The inventors of the present application have conceived of performing a process (pre-narrowing phase S1) of narrowing down combinations of performance factors _Xj in advance, prior to the performance factor extraction phase S2 for determining the performance factors _Xj and the contribution degrees _βj .

That is, the pre-narrowing phase S1 according to this embodiment is a process executed prior to the performance factor extraction phase S2, and is a process for the CPU 3 to set a set of performance factors _Xj (candidate list).

Specifically, in this embodiment, the CPU 3 executes genetic programming (GP) to formulate a response y from N design variables x _i . As is well known, GP is a function extension of a genetic algorithm (GA) so that it can be expressed in a tree structure. In a commonly known GP, the performance factor X _j and the contribution β _j to be multiplied therewith are set at the terminal nodes, respectively, so that both are determined simultaneously.

In contrast, in the pre-narrowing phase S1 according to this embodiment, a set of M performance factors _Xj is determined by GP, and the contribution _βj to be multiplied by each performance factor _Xj is determined in the subsequent performance factor extraction phase S2. That is, the tree structure used in the pre-narrowing phase S1 is described by only N design variables _xi as shown in Fig. 5. In the example shown in Fig. 5, four performance factors _x1 , _x3 , _x1.x2 , ^{and x32} _are determined based on three design variables _x1 , _x2 , _{and x3} .

Specifically, first, in step S11, the maximum depth is set. This maximum depth is a parameter that is referenced when performing the one-point crossover method in step S17 described below.

In the next step S12, an initial set (initial population) of combinations of performance factors _Xj is generated widely across the entire design space as an initial generation based on N design variables _xj . The number of individuals in the initial generation can be determined according to the number of design variables _xj , and can be set to, for example, 1 to 4 times the number of design variables _xj .

In the next step S13, the list set (a set of combinations of performance factors _Xj ) is evaluated based on the randomly generated initial set. For example, when step S13 is executed for the first time, an L-th order polynomial approximation of the design variable _xj is performed based on the maximum depth L. In this case, each term constituting the L-th order polynomial corresponds to a set of performance factors _Xj . Then, a multiple regression analysis is performed with reference to sample data 49, and the contribution degree _βj obtained as the coefficient of each term is determined. After that, the initial set is evaluated by evaluating the mean square error for the determined polynomial.

In the next step S14, it is determined whether the mean squared error calculated in step S13 has converged. If it has converged (step S14: YES), the process proceeds to step S15, where a candidate list, which is the set of lists at the time of convergence, is output.

On the other hand, if convergence has not been achieved in step S14 (step S14: NO), the process proceeds to step S16, where an excellent list set is selected. Here, several parent individuals from the current generation that have high fitness and are distant from each other are selected. Then, in the following step S17, one-point crossover, which is equivalent to genetic recombination, is performed.

Specifically, in steps S17 and S18, a set of performance factors _Xj is set by executing a genetic operation on a tree structure having design variables _xj as terminal nodes and multiplication operators as non-terminal nodes.

Specifically, in step S17, as shown in Fig. 6, one-point crossover is performed between the first list set L1 and the second list set L2 to generate new list sets L1', L2'. At this time, as can be seen from Fig. 6, one-point crossover is performed with each element of the combination of the performance factor _Xj as the rearrangement target, without using the contribution degree _βj as the terminal node. In the illustrated example, the fourth performance factor N1 (= _x32 ) in the first list set L1 and the fourth performance factor N1 (= _x22 ⁾ in the second list set are the rearrangement targets ^.

Here, the genetic operation is performed so that the number of layers of the tree structure is equal to or less than the predetermined depth (maximum depth) set in step S11. For example, if the maximum depth is set to 2 and the multiplication operator is set as a non-terminal node as described above, the performance factor _Xj includes a first-order linear term consisting of the design variable _xj itself and a second-order nonlinear term obtained by multiplying the design variables _xj together. In this case, the latter nonlinear term includes a term _xj2 obtained by ^squaring a specific design variable _xj and a so-called interaction term _xj.xj obtained by multiplying different _design variables _xj and _xj together.

In step S18, which follows step S17, a sudden mutation is performed that probabilistically changes the genetic information to give diversity to the individual, generating offspring individuals. Steps S13 to S18 are then repeated, and when convergence is reached to the optimal solution or a predetermined number of evolutionary generations is reached, the process proceeds from step S14 to step S15, and the calculation ends. Here, the predetermined number of evolutionary generations can be determined according to the number of design variables, etc., but can be, for example, 100 to 500 generations.

Although not shown in detail, k-fold cross-validation may be performed in the pre-narrowing phase S1. In this case, the sample data 49 referenced in the multiple regression analysis may be divided into training data and validation data.

Note that a sequential approximation optimization method may be used to address problems such as increased calculation time and over-learning that accompany an increase in the number of design variables. The sequential approximation optimization method is a method in which an approximation equation is found from a relatively small number of sample points and the response value of the objective function using a response surface, and an optimal solution is searched for using this, and the optimal solution and several sample points are added. The sequential approximation optimization method reduces the amount of calculation per CAE, making it possible to improve the efficiency of optimization calculations.

When the control process proceeds to step S15, it ends the flow shown in FIG. 4 and proceeds from the pre-narrowing phase S1 in FIG. 3 to the performance factor extraction phase S2.

(Performance factor extraction phase S2)
7 is a flow chart illustrating a specific procedure of the performance factor extraction phase S2. FIG. 8 is a diagram for explaining the procedure of acquiring the performance factor _Xj according to the selection order.
FIG. 9 is a diagram showing a specific example of the performance factor extraction phase S2.

First, in step S21, which is a reading step, the RAM 7, which serves as a storage unit, reads in a set of performance factors _Xj . In step S21, the CPU 3 assigns the values of the design variables _xj corresponding to each sample to the performance factors _Xj , and associates the assignment results with the response y to generate a large number of sample data Dt corresponding to the set of performance factors _Xj .

In the next step S22, the RAM 7 reads multiple pieces of sample data Dt, and the CPU 3 divides the multiple pieces of sample data Dt into learning data Ds and verification data Dv according to predetermined division patterns P1 to P9.

Specifically, in step S22, the CPU 3 divides the multiple sample data Dt into k data blocks to perform k-fold cross-validation. Then, as shown in FIG. 9, of each of the k divided data blocks, one data block is set as validation data Dv, and the remaining (k-1) data blocks are set as learning data Ds. In other words, there are a total of k different settings for validation data Dv and learning data Ds. Hereinafter, the k different settings are referred to as split patterns P1 to Pk.

The CPU 3 executes step S23 as an extraction step, step S24 as a ranking setting step, step S25 as a formulation step, and step S26 based on the learning data Ds, while executing step S27 as an index calculation step based on the remaining validation data Dt.

Next, in step S23 as an extraction step, the CPU 3 applies a plurality of types of extraction methods to a set (list set) of performance factors _Xj , thereby extracting performance factors _Xj that contribute to the performance of the structure for each extraction method.

As described above, the response y indicating the performance of the structure is formulated by a linear combination of one or more performance factors _Xj . The CPU 3 executes a multiple regression analysis by individually applying a plurality of types of extraction methods to the linear combination, with each performance factor _Xj as an explanatory variable and the response y represented by the linear combination as a response variable.

In step S23, a regression analysis is performed using the values of the performance factors _Xj when multiple pieces of learning data Ds are input, and the value of the response y as the objective variable is output, thereby calculating the contribution degree _βj , which is a coefficient to be multiplied by the performance factor _Xj . The value of the contribution degree _βj may vary depending on the extraction method applied.

Here, the extraction method applied in step S23 includes a regression analysis method having sparsity and a stepwise regression analysis method. Furthermore, as the former regression analysis method, for example, a lasso regression with L1 regularization (Lasso), an elastic net regression in which a ridge term is added to the L1 regularization, and an adaptive lasso regression in which a weight is added to the L1 regularization can be used. Note that all of these methods use a regularization parameter λ. The magnitude of the regularization parameter λ can be determined using a k-fold cross-validation method. In this case, in step S23, apart from the division of the sample data described in step S22, the learning data Ds is further divided into a plurality of data blocks in order to perform cross-validation for determining the regularization parameter λ. In this case, apart from the loop related to cross-validation executed in steps S22 to S28, a loop related to cross-validation is executed for each of the division patterns P1 to Pk in step S23. Here, in the cross-validation for determining the regularization parameter λ, an evaluation index without a penalty term, such as deviance, is used. Therefore, many of the contribution degrees β _j have non-zero values, and a wide range of options can be left when narrowing down the options using the selection probabilities described below.

Furthermore, when a regression analysis method having sparsity, such as Lasso regression, is used, a significant value (non-zero value) is obtained for the contribution degree βj that contributes greatly to the objective variable, while a value of zero is obtained for the contribution degree βj that does not contribute relatively. This makes it possible to further narrow down (extract ₎ the set of performance factors _Xj narrowed down in the pre-narrowing phase S1 based on the magnitude of the contribution degree _βj .

In addition, when the stepwise regression analysis method is applied in step S23, the performance factors _Xj that contribute to the performance of the structure are extracted from the set of performance factors _Xj by using the information criteria AIC, BIC, etc. expressed by the following formula.

Here, n is the number of samples, the variable with a hat symbol attached to σ ² is the mean square error (MSE) based on the estimator, and the variable with a hat symbol attached to df is the degree of freedom of the estimated model. AIC and BIC are used as evaluation indexes of the model. The smaller the value of this evaluation index, the better the model accuracy. Using this, in the stepwise method, each element of the set of performance factors X _j is added to the linear combination one by one, or removed from the linear combination, and the AIC or BIC obtained at that time is determined, making it possible to further narrow down (extract) the set of performance variables X _j narrowed down in the pre-narrowing phase S1. In addition, the method for selecting and discarding performance factors in the stepwise method can be an increase method, a decrease method, or an increase/decrease method, and any of these methods may be used. In the specific example described below, the increase method is configured to be used.

Next, in step S24 as a ranking setting step, the CPU 3 sets the selection ranking of the performance factors _Xj based on the extraction results of the performance factors _Xj obtained by the extraction method. In detail, the CPU 3 judges the extraction frequency for each performance factor ^Xj based on the extraction results of the performance factors _Xj obtained by the extraction method, and sets the selection ranking based on the high or low of the extraction frequency.

For example, as illustrated in the upper table of FIG. 8, if the performance factor X ₁ =x ₁ is extracted (≠0) in all of the three methods A to C, the extraction frequency of the performance factor can be determined to be high. On the other hand, if the performance factor X ₃ =x ₃ in the third column is not extracted (0) in any of the methods A to C, the extraction frequency of the performance factor can be determined to be low. In the example illustrated in FIG. 8, the CPU 3 sets the selection order of the performance factor X ₁ =x ₁ in the first column to the first with an extraction probability (selection) of 100%, the selection order of the performance factor X ₄ =x ₄ in the fourth column to the second with a selection probability of 66%, the selection order of the performance factor X ₂ =x ₂ in the second column to the third with a selection probability of 33%, and the selection order of the performance factor X ₃ =x ₂ in the third column to the fourth with a selection probability of 0%. The selection order thus set may be temporarily stored in the RAM 7 or may be continuously stored in the HDD 9.

The frequency of occurrence can be determined based on the coefficients (contribution degrees β ^j ) of the performance factors X _j calculated in step S23. As described above, when a regression analysis with sparsity or a stepwise regression analysis is used in the multiple regression analysis, coefficients with low contribution degrees become zero. Therefore, when the contribution degree β _j is zero, it can be considered that the performance factor X _j has not been extracted, and when the contribution degree β _j is nonzero, it can be considered that the performance factor X _j has been extracted.

Here, when a more general method is used for multiple regression analysis, a coefficient with a low contribution degree does not necessarily become zero. In that case, if the value of the contribution degree β _j exceeds a predetermined threshold, it can be determined that the performance factor X _j has been extracted, and if the value is equal to or less than the threshold, it can be determined that the performance factor X _j has not been extracted. The threshold value to be referred to in that case can be, for example, a value set in advance. This threshold value may be prepared for each contribution degree β _j , or may be a common value between the contribution degrees β _j when standardization is performed on the performance factor X _j .

Next, in step S25 as a formulation step, the CPU 3 selects a performance factor _Xj from the set of performance factors _Xj in accordance with the selection order calculated in step S24. The CPU 3 also formulates the performance of the structure by combining the performance factors _Xj thus selected.

Specifically, in step S25, the response y is formulated as a response variable by linearly combining the performance factors _Xj in descending order of selection rank. In the example shown in Fig. 8, the performance factor _X1 = _x1 , which has the first selection rank, is incorporated first. In this case, the response _{y is a one-variable function of x1 that} combines the intercept _β0 and the linear term _β1 x1 (first loop).

Then, in step S26 following step S25, the CPU 3 executes a multiple regression analysis on the objective variable formulated in step S25. In the first loop in Fig. 8, a multiple regression analysis using the learning data Ds is executed on the one-variable function formulated using _x1 . In the example shown in Fig. 8, a multiple regression analysis is executed on the one-variable function of _x1 , and an intercept _β0 and a coefficient _β1 of _x1 are calculated. This completes the formulation of the response y in the first loop.

Next, in step S27 as an index calculation step, the CPU 3 calculates an evaluation index CV _l (l=1, 2, ..., l) that characterizes the accuracy of the formulation executed in step S25 (more specifically, the accuracy of the model obtained by the formulation). The CPU 3 determines whether or not to continue the import of the performance factor X _j based on the evaluation index CV _l thus calculated. This determination can be made, for example, by inputting the verification data Dv set in step S22 for the response y formulated in step S26 and calculating a predetermined evaluation index CV _l based on the output.

Specifically, in this embodiment, in addition to the above-mentioned AIC and BIC, a relaxed Cp criterion Cp _mit as shown in the following formula can also be used as the evaluation index CV ₁ .

In addition, in this embodiment, the coefficient of determination with adjusted degrees of freedom ^R2 and the root mean square error RMSE can be used as the evaluation index _CV1 .

In the above equation, the norm with the subscript "2" indicates the _L2 norm.

For example, when AIC is used as the evaluation index _CV1 , in step S27, the calculated AIC is compared with a predetermined threshold value, and if the AIC is below the threshold value, the process proceeds to step S28, whereas if the AIC is equal to or greater than the threshold value, the process returns to step S25.

Here, the configuration may be such that any one of the multiple evaluation indexes _CV1 is selected in advance, or the configuration may be such that multiple evaluation indexes are calculated in parallel, and whether or not to proceed to step S28 is determined by a majority vote.

Next, when returning from step S27 to step S25, the CPU 3 selects a performance factor _Xj that is lower in rank than the previously selected performance factor _Xj , and linearly combines it with the response y to update the response y. In the example shown in FIG. 8, the performance factor _X4 = _x4 , which is second in the selection rank, is incorporated second. In this case, the response y becomes a two-variable function that combines the intercept _β0 , the linear term _β1 · _x1 , and the linear term _β4 · _x4 (second loop). After that, the CPU 3 advances the control process to step S26, and updates the value of the contribution _βj . In the example shown in FIG. 8, a multiple regression analysis is performed on the two-variable function of the _x1 and _x4 , and the intercept _β0 , the coefficient _β1 of _x1 , and the coefficient _β4 of _x4 are calculated. This completes the formulation of the response y in the second loop. After that, the CPU 3 advances to the control process S27, and executes a judgment based on the evaluation index _CV1 .

The CPU 3 repeats steps S25 to S27 to sequentially incorporate the performance factors _Xj and update the objective variables. When the judgment related to the evaluation index _CVl is satisfied for the updated objective variables (for example, when the AIC is less than the threshold), the CPU 3 completes the formulation of the response y in the current division pattern _Pl (l=1, 2, ..., k) and advances the control process from step S27 to step S28. At that time, the CPU 3 temporarily stores in the RAM 7 the function form of the formulated response y and the value of the evaluation index _CVl referred to at that time, or stores them continuously in the HDD 9.

In step S28, the CPU 3 judges whether the end condition of the cross-validation is satisfied. Specifically, in this step, the CPU 3 judges whether the response y is formulated in all k division patterns _P1 . If the judgment is YES, the process proceeds to step S29, whereas if the judgment is NO, the division pattern _P1 is changed and the process returns to step S22.

In this manner, in this embodiment, the CPU 3 changes the division pattern _P1 k times, repeatedly executing steps S23 to S28 for each changed division pattern P, and then advances the control process to step S29.

Next, in step S29, the CPU 3 verifies the accuracy of the formulation performed in step S25 based on the evaluation index CV _l calculated for each division pattern. In detail, in this step S29, the CPU 3 selects one of the k responses y formulated for each division pattern P _l based on the evaluation index CV _l calculated for each division pattern P _l . More specifically, the CPU 3 compares the k evaluation indexes CV _l with each other and selects the division pattern P l corresponding to the smallest evaluation index CV _{l ,} and further the contribution degree β _j , performance factor X _j, and response y. The CPU 3 outputs the contribution degree β _j, etc. corresponding to the selected division pattern P _l as the final result.

Upon completing step S29, the control process ends the flow shown in FIG. 7 and proceeds from performance factor extraction phase S2 in FIG. 3 to design knowledge extraction phase S3.

(Design knowledge extraction phase S3)
FIG. 12 is a diagram for explaining the model reconstruction step.

In the design knowledge extraction phase S3, the CPU 3 executes a model reconstruction step. Specifically, in this model reconstruction step, the CPU 3 removes from the response y a nonlinear term consisting of the design variable x _{i that does not appear in the response y as a linear term, among the design variables x i that} constitute the performance factor X _j .

For example, as shown in the upper part of Fig. 12, five performance factors _x1 , _x3 , _x5 , _x1 · _x3 , and _x2 · _x4 are extracted by the performance factor extraction phase S2, and one intercept _β0 and contributions _β1 to _β5 to be multiplied by each performance factor are obtained. In this case, the first three of the five performance factors correspond to linear terms, i.e., main effects, and the remaining two correspond to nonlinear terms, particularly interaction terms. Here, _x1 to _x5 are all standardized.

In this case, focusing on the design variables _x1 to _x4 , among the five performance factors _Xj , _x1 and _x3 appear in the response y as both main effects and interaction terms, whereas _x1 and _x4 do not appear in the response y as main effects, but only as interaction terms (f1 = _{x2 x4} ).

Here, consider the case where only _x1 and _x3 are changed and _x2 , _x4 , and _x5 are fixed. In this case, when a design variable such as _x1 appears in both the main effect and the interaction term, the magnitude of the response y changes linearly overall due to the influence of the main effect, but as shown in the left diagram in Figure 12, the slope is considered to increase or decrease depending on the magnitude of _x3 . This can be interpreted as the influence of the interaction acting between _x1 and _x3 . In this case, when an interaction term exists, the main effect is not determined, and it can be seen that the slope of the main effect changes depending on the value of the other design variable _x3 that forms the interaction.

On the other hand, if we consider the case where only _x2 and _x4 are changed and _x1 , _x3 , and _x5 are fixed, when there is no main effect such as design variable _x4 and only interaction term f1 exists, the magnitude of response y will completely depend on the value of design variable _x2 that appears in interaction term f1.

For example, when the structure is regarded as a car body and the design variables are regarded as the plate thicknesses of the car body components, the above-mentioned tendency can be interpreted in engineering terms as follows: when it appears in both the main effect and the interaction term, such as design variable _x1 , the plate thickness of the part corresponding to design variable _x1 affects the performance represented by response y, but the degree of influence on the performance changes depending on the balance of the plate thickness with another part corresponding to design variable _x3 .

On the other hand, when only an interaction term appears, such as in the case of design variable _x4 , it can be interpreted that the plate thickness of the part corresponding to design variable _x1 does not affect the performance, but affects the performance only depending on the plate thickness of another part corresponding to design variable _x2 .

However, when considering vehicle body structure, it is difficult to imagine a structure that affects performance solely through its dependency on other parts, and even if such a structure did exist, its overall impact would likely be relatively low compared to those with a main effect.

Therefore, in the model reconstruction step, performance factors with no corresponding main effects, such as the interaction term f1 shown in FIG. 12, are deleted, and the model obtained by the above formulation is reconstructed. Although detailed illustration is omitted here, in this model reconstruction step, the CPU 3 executes the multiple regression analysis again, and updates the contribution rate by which each performance factor should be multiplied. Note that the timing for performing the multiple regression analysis may be after the performance factor extraction phase S2 has been completed once, as shown in FIG. 3, or may be during the performance factor extraction phase S2.

In the latter case, when extracting the performance factor _Xj based on the selection probability as exemplified in step S25, it may be configured so that after first preferentially extracting the design factor _Xj appearing as the main effect, a nonlinear term including the design variable _xj constituting the design factor _Xj (the design factor _Xj appearing as the main effect) is incorporated.

--Specific examples of pre-narrowing phase S1 and performance factor extraction phase S2--
FIG. 9 is a diagram showing a specific example of the performance factor extraction phase S2. FIG. 10 is a diagram showing the influence of the interaction term on the crash performance value. The inventors of the present application verified the validity of the pre-narrowing phase S1 and the performance factor extraction phase S2 by numerical calculation. When verifying the validity, the difference between the true coefficient value (contribution degree) of the artificially generated nonlinear function and the contribution degree β _j calculated by the two phases is compared. The artificially created true function is composed of a total of 20 performance factors X _j (j = 1, 2, ..., 20), and is composed of 15 linear terms (main effects), 4 interaction terms as nonlinear terms, and 1 as a nonlinear term, and 50 samples are generated using the nonlinear function. In addition, noise is given to the objective variable value of the sample data, and 4 dummy performance factors (dummy factors) that do not affect the output are added. The result of applying the pre-narrowing phase S1 and the performance factor extraction phase S2 to the generated sample data corresponds to the first column from the right in FIG. 10. The second column from the right in FIG. 10 shows the results of applying the conventional method, and the third column from the right corresponds to the true count values.

In addition, in the first column from the left, "X_i (i = 1, 2, ..., 20)" corresponds to the design variable x _i . In addition, the coefficient value (contribution degree β _j ) is shown in a graph in each cell. As shown in FIG. 10, the value of the contribution degree β _j obtained when the method according to the present invention is applied is closer to the true count value than the conventional method. It can also be seen that the nonlinear terms that exert an interaction effect also have close values, except for X_8 * X_8. It is considered that X_8 * X_8 is compensated by calculating the contribution degree β _j of the linear term X_8 to be larger.

In particular, in the conventional method, although the value of the coefficient of determination ^R2 is approximately 96%, unlike the method according to the present invention, the coefficient values of the nonlinear terms are all set to zero. In the conventional method, it is not possible to incorporate the interaction term into the response y.

As described above, the interaction term is considered to indicate the dependency between parts. For example, in the case where the response y is the crash performance value of the vehicle body (particularly the crash performance value in a full-overlap frontal collision) and the plate thickness of the vehicle body component is considered as the design variable x _i , consider the cases where only the plate thickness of part A is increased, only the plate thickness of part B is increased, and both the plate thicknesses of parts A and B are increased, as shown in FIG.

As shown in graph V1 in FIG. 11, if only the plate thickness of part A is increased, the collision performance value deteriorates, and if only the plate thickness of part B is increased, the collision performance value improves. When the plate thicknesses of both parts A and B are increased, if there is no interaction term between the design variable corresponding to part A and the design variable corresponding to part B, the collision performance value will be the sum of the amount of change when only the plate thickness of part A is increased and when only the plate thickness of part B is increased (see graph V3 in FIG. 11).

On the other hand, if an interaction term exists between the design variables corresponding to parts A and B when the plate thicknesses of both parts A and B are increased, the collision performance value will differ from the sum of the changes in the case where only the plate thickness of part A is increased and the case where only the plate thickness of part B is increased, as shown in graph V4 in FIG. 11. The occurrence of such a difference means that an interaction term exists. In the example shown in FIG. 11, parts A and B are parts that can transmit loads to each other, such as a B-pillar and a side sill or roof rail. The magnitude of the load transmission at that time, in other words, the strength of the connection between the parts, can be characterized by the magnitude of the coefficient of the interaction term. The effect of the balance of plate thickness between parts on the collision performance value varies depending on the magnitude of the coefficient of the interaction term. This shows that the balance of plate thickness can greatly vary the transmission path of energy.

<Formulation of structural performance>
As described with reference to FIG. 8, the design support method according to this embodiment applies a plurality of types of extraction methods to a set of performance factors _Xj , thereby setting the selection order of the performance factors _Xj . This selection order can be said to indicate the importance of the performance factors _Xj . When setting the selection order, by using a plurality of extraction methods, rather than using only a specific extraction method, the selection order can be set more appropriately. Then, the performance factors _Xj with a relatively high selection order are actively incorporated into the model formula y describing the performance of the structure, while the performance factors _Xj with a relatively low selection order are passively incorporated into the model formula y, thereby making it possible to faithfully describe the performance of the structure while suppressing the number of terms used in formulation. This makes it possible to formulate the performance of the structure simply and quickly.

As shown in Fig. 5, the performance factor _Xj includes a nonlinear term, particularly an interaction term _{xj xk} , which is obtained by multiplying the design variables _xi together. This allows the model to include interactions related to the connections between parts. This is effective when modeling dynamic phenomena such as the crash performance of a structure.

As shown in Fig. 4, the design support method according to the third aspect of the present embodiment narrows down the performance factors _{Xj using the tree structure T1 before selecting the performance factors Xj based} on the selection order. Here, as shown in Fig. 6, the narrowing down can be performed more quickly by excluding the coefficient of the design variable _xj from the terminal node. At that time, by setting the number of layers of the tree structure T1 in advance, the narrowing down can be performed in a manner suitable for the structure to be supported. This allows more efficient formulation.

12, among the design variables x _i constituting the nonlinear terms, those that do not appear in the model formula as first-order linear terms but appear in the model only as interaction terms are excluded from the model formula. By carrying out this process, the number of performance _{factors X j to} be considered can be reduced, and therefore the amount of calculation can be reduced.

8, the selection order is set high for a frequently extracted performance factor X _j , for example, a performance factor extracted by all extraction methods, while the selection order is set low for a less frequently extracted performance factor, for example, a performance factor extracted by only one of the extraction methods. By setting in this way, the selection order can be set more appropriately, and the performance of the structure can be formulated more faithfully.

In this case, by determining the extraction frequency based on the magnitude of the coefficient _βj multiplied by each performance factor _Xj , the extraction frequency can be determined clearly, which is advantageous in formulating the performance of the structure simply and quickly. In this case, by using a regression analysis and a stepwise regression analysis having sparsity, the magnitude of the coefficient _βj can be determined even more clearly.

As explained with reference to Figure 9, a more robust formulation can be achieved by using k-fold cross-validation for formulation. This is effective in achieving both a simple and fast formulation of the structure's performance and robustness of the model formula.

Other Embodiments
In the above embodiment, a computer having one CPU 3 is exemplified as an example of the computer 1, but the present disclosure is not limited to this example. The computer 1 includes parallel computers such as supercomputers and PC clusters in addition to personal computers. For example, only steps that require a calculation time, such as the pre-narrowing phase S1 and the performance factor extraction phase S2 in FIG. 3, may be executed by a parallel computer, and the remaining steps, such as the design knowledge extraction phase S3, may be executed by a personal computer.

In other words, the "computing unit" in this disclosure may be configured by combining a computing unit in a specific computer with a computing unit in another computer. In that case, "computer 1" refers to a computing system consisting of multiple computers. The same applies to the memory unit.

As explained above, the present disclosure is useful in supporting the design of structures consisting of multiple parts, such as the body of an automobile, and has industrial applicability.

1 Computer 3 CPU (calculation unit)
7 RAM (storage unit)
Ds Learning data Dv Verification data Pl Split pattern S1 Pre-narrowing phase (pre-narrowing step)
S2 Performance factor extraction phase S21 Reading step S23 Extraction step S24 Rank setting step S25 Formulation step S27 Index calculation step S29 Verification step S3 Design knowledge extraction phase (model reconstruction step)
T1 Tree structure x _i Design variable X _j Performance factor

Claims (12)

A design support method for formulating the performance of a structure made up of a plurality of parts using design variables in which the specifications of each part are quantified, by using a computer having a calculation unit that executes a program and a storage unit that reads data, comprising:
a reading step in which the storage unit reads a set of performance factors having one or more of the design variables as arguments;
an extraction step in which the calculation unit applies a plurality of types of extraction methods to the set of performance factors to extract performance factors that contribute to the performance of the structure for each of the extraction methods;
a ranking setting step in which the calculation unit sets a selection ranking of the performance factors based on the extraction results obtained by the extraction methods;
a formulation step in which the calculation unit selects a performance factor from the set of performance factors in accordance with the selection priority, and formulates the performance of the structure by combining the selected performance factors. 2. The design support method according to claim 1,
A design support method, characterized in that the performance factors include linear terms consisting of the design variables themselves and non-linear terms consisting of the multiplication of the design variables. 3. The design support method according to claim 2,
a pre-narrowing step in which the calculation unit sets a set of the performance factors prior to the extraction step;
In the pre-narrowing step, a genetic operation is performed on a tree structure having the design variables as terminal nodes and multiplication operators as non-terminal nodes to set the set of performance factors;
A design support method, comprising: performing the genetic operation in the pre-narrowing step so that the number of levels in the tree structure is equal to or less than a predetermined maximum depth. The design support method according to claim 2 or 3,
A design support method comprising a model reconstruction step in which the calculation unit excludes, from the performance of the structure, nonlinear terms consisting of design variables that do not appear as linear terms in the performance of the structure, among the design variables that constitute the performance factor. 5. The design support method according to claim 1,
The calculation unit determines an extraction frequency for each of the performance factors based on the extraction results obtained for each of the extraction methods,
The design support method according to the present invention, wherein the calculation unit sets the selection priority based on the extraction frequency. 6. The design support method according to claim 5,
The performance of the structure is formulated by a linear combination of the performance factors;
the calculation unit executes a multiple regression analysis using the performance factors as explanatory variables and the performance of the structure as a response variable for each of the plurality of types of extraction methods;
The design support method according to the present invention, wherein the calculation unit determines the extraction frequency based on the coefficients of the explanatory variables calculated by the multiple regression analysis. 7. The design support method according to claim 6,
The design support method, wherein the plurality of types of extraction methods includes a regression analysis having sparsity. The design support method according to claim 6 or 7,
The design support method, wherein the plurality of types of extraction methods includes stepwise regression analysis. A design support method according to any one of claims 6 to 8,
an index calculation step of calculating an evaluation index that characterizes the accuracy of the formulation in the formulation step;
a verification step of verifying the accuracy of the formulation in the formulation step based on the evaluation index calculated in the index calculation step;
The storage unit reads a plurality of sample data each corresponding to a set of the performance factors;
The calculation unit divides the plurality of sample data into training data and validation data according to a predetermined division pattern;
the calculation unit executes the extraction step, the ranking step, and the formulation step based on the learning data, and executes the index calculation step based on the remaining verification data;
the calculation unit executes the extraction step, the rank setting step, the formulation step, and the index calculation step repeatedly for each changed division pattern while changing the division pattern a plurality of times, and then executes the verification step;
A design support method characterized in that, in the verification step, the calculation unit selects one of the performances of the structure formulated for each division pattern based on the evaluation index calculated for each division pattern. A design support method according to any one of claims 1 to 9,
the structure is a vehicle body,
A design support method, characterized in that the design variable is a plate thickness of each of the plurality of components. A design support program for formulating the performance of a structure composed of a plurality of parts using design variables in which the specifications of each part are quantified, by causing a computer having a calculation unit for executing the program and a storage unit for reading data to execute the program,
The computer includes:
a reading step in which the storage unit reads a set of performance factors having one or more of the design variables as arguments;
an extraction step in which the calculation unit applies a plurality of types of extraction methods to the set of performance factors to extract performance factors that contribute to the performance of the structure for each of the extraction methods;
a ranking setting step in which the calculation unit sets a selection ranking of the performance factors based on the extraction results obtained by the extraction methods;
the calculation unit selects the performance factors from the set of performance factors in accordance with the selection priority, and formulates the performance of the structure by combining the selected performance factors. A computer-readable storage medium storing the design support program according to claim 11.

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