Parameter output method, machine learning method, parameter output program, and storage medium storing the parameter output program.

Abstract

Provided is a parameter output method and the like for improving user convenience related to orthogonal arrays. 【Solution means】The method obtains a first reference value r and a second reference value s from among two or more positive integers, selects a pair of a first integer q and a second integer n that satisfy both formula (A) and formula (B), selects the first integer q as a candidate value for the number of levels, and based on the selected first integer q, the second integer n that forms a pair with the first integer q, formula (C), and formula (D), determines and outputs candidate values for each of the number of samples M and the number of factors N, and based on each of the output candidate values, generates a matrix of M rows and N columns or N rows and M columns composed of M-dimensional and N vectors of the q-level system, and selects and outputs a matrix that holds as an orthogonal array as a non-mixed orthogonal array L M (q N ) for selection and output. q≧r…(A) (q n -1) / (q-1)≧s…(B) M=q n …(C) N=(q n -1) / (q-1)…(D)

Description

Technical Field

[0001] The present disclosure relates to a parameter output method, a machine learning method, a parameter output program, and a computer-readable storage medium storing the parameter output program.

Background Art

[0002] Patent Document 1 discloses, as an example of a parameter output method, an analysis method using a computer. This analysis method includes acquiring a first parameter set and estimating a second parameter set.

[0003] Here, the first parameter set includes at least one of parameters related to a certain product and parameters related to the operation of the product. The second parameter set estimates a second parameter set related to the performance of the product from the first parameter set using parameter optimization.

[0004] Furthermore, the analysis method according to Patent Document 1 includes generating a factor effect diagram based on the second parameter set and outputting a multi-level orthogonal table including the factor effect diagram via an output interface.

[0005] According to Patent Document 1, a robust design solution can be calculated in fewer times or a shorter time.

Prior Art Documents

Patent Documents

[0006]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0007] Generally, the number of factors required to construct an orthogonal array is known to vary depending on the number of levels in the orthogonal array. Similarly, the sample size of the orthogonal array is also known to vary depending on the number of factors and levels. Since the number of levels in an orthogonal array fluctuates according to user needs, the values ​​of the number of factors and levels required to construct the orthogonal array will vary accordingly.

[0008] On the other hand, the selection of orthogonal arrays has traditionally been based on existing technical books and libraries, and a system for systematically outputting the number of factors and samples has not been known until now. If such a system can be built, user convenience can be improved compared to the past.

[0009] This disclosure has been made in view of the above, and its purpose is to improve user convenience related to orthogonal arrays. [Means for solving the problem]

[0010] A first aspect of this disclosure relates to a parameter output method for outputting a set of parameters that characterize an orthogonal array by using a computer comprising a storage unit for storing a program and an arithmetic unit for executing the program stored in the storage unit.

[0011] Furthermore, according to the first embodiment, if the number of samples in the orthogonal array is M, the number of factors in the orthogonal array is N, a first criterion value indicating the selection criteria for the number of levels in the orthogonal array is r, a second criterion value indicating the selection criteria for the number of factors N is s, and two integers are the first integer q and the second integer n, then the parameter output method is as follows: the calculation unit obtains the first criterion value r and the second criterion value s from among 2 or more positive integers, the calculation unit selects a pair of the first integer q and the second integer n that satisfies both equation (A) and equation (B), the calculation unit selects the first integer q as a candidate value for the number of levels, and determines and outputs candidate values ​​for the number of samples M and the number of factors N based on the selected first integer q, the second integer n that forms the pair with the first integer q, and equations (C) and (D).

[0012]

number

[0013]

number

[0014] Based on the findings obtained through diligent research by the inventors of this application, it is possible to systematically output candidate values ​​for the sample size M and the number of factors N by using the above formulas (A) to (D).

[0015] In other words, according to the first embodiment, by having the calculation unit acquire the first reference value r and the second reference value s, respectively, it becomes possible to systematically output candidate values ​​for the number of samples M and the number of factors N. This allows for the orthogonal array L M (q N This can improve user convenience related to ).

[0016] Furthermore, according to a second aspect of this disclosure, the calculation unit generates an M x N or N x M matrix composed of M-dimensional and N vectors in a q-level system based on the output candidate values ​​for the number of samples M and the candidate values ​​for the number of factors N, the calculation unit determines whether the matrix is ​​valid as an orthogonal array, and the calculation unit determines which matrix has the smallest first integer q among the matrices that are valid as orthogonal arrays to be a non-mixed orthogonal array L M (q N Alternatively, you could select and output it as follows:

[0017] Furthermore, according to the second aspect of this disclosure, in addition to outputting the sample size M and factor size N of the orthogonal array, a non-mixed orthogonal array L based on those parameters is also provided. M (q N ) is output. As a result, the orthogonal array L M (q N This can improve user convenience related to ).

[0018] Also, according to the third aspect of the present disclosure, among the pairs of the first integer q and the second integer n that satisfy both the formula (A) and the formula (B), the operation unit selects the matrix in which the first integer q is the smallest and which holds as the orthogonal array, as the orthogonal array L M (q N ) and outputs it.

[0019] According to the third aspect, when the first integer q is the smallest, the first integer q will be closest to the first reference value r. Thereby, the first reference value r can be regarded as the user-desired value of the number of levels, and the user convenience related to the orthogonal array L M (q N ) can be improved.

[0020] Further, the fourth aspect of the present disclosure relates to a machine learning method using the parameter output method. In this machine learning method, the operation unit obtains the non-mixed orthogonal array L M (q N ), the operation unit regards the non-mixed orthogonal array L M (q N ) as N components and M types of multi-component variables, and configures training data input to the non-linear machine learning model with numerical data associated with each value of the M types of multi-component variables, and the operation unit learns the non-linear machine learning model based on the training data.

[0021] Generally, when using the non-mixed orthogonal array L[[ID=​​​​​​​​​​​​​​Alternatively, a mixed-system orthogonal array may be used. However, the mixed-system orthogonal array only guarantees the effect of suppressing the concentration of interactions when used in conjunction with a linear model; its effect is not necessarily guaranteed when used in conjunction with a nonlinear model, as in the fourth embodiment described above.

[0023] Furthermore, for objects that can be represented with a small number of levels (objects for which a linear model is sufficient), there may be advantages to using mixed orthogonal arrays. However, for broader, more general objects, such as those involving a huge number of factors or nonlinearity, mixed orthogonal arrays are used in conjunction with nonlinear models to ensure generalization performance, and non-mixed orthogonal arrays are superior to non-mixed orthogonal arrays. M (q N This is inconvenient compared to [another option].

[0024] In contrast, according to the fourth embodiment, the non-mixed orthogonal array L M (q N A nonlinear machine learning model is trained using training data based on ). By training a nonlinear model, the effects of interactions can be suppressed without using mixed orthogonal arrays. This allows for the training of non-mixed orthogonal arrays L M (q N By using this method, it is possible to achieve both the ability to handle a vast number of factors and ensure generalization performance with the smallest possible number of samples, and the suppression of interaction effects by using a nonlinear machine learning model.

[0025] Furthermore, a fifth aspect of this disclosure relates to a parameter output program that outputs a set of parameters characterizing an orthogonal array by using a computer comprising a storage unit for storing a program and an arithmetic unit for executing the program stored in the storage unit.

[0026] Furthermore, according to the fifth embodiment, if the number of samples in the orthogonal array is M, the number of factors in the orthogonal array is N, a first criterion value indicating the selection criteria for the number of levels in the orthogonal array is r, a second criterion value indicating the selection criteria for the number of factors N is s, and two integers are the first integer q and the second integer n, then the parameter output program causes the computer to execute the following processes: the calculation unit obtains the first criterion value r and the second criterion value s from among 2 or more positive integers; the calculation unit selects a pair of the first integer q and the second integer n that satisfies both equation (A) and equation (B); and the calculation unit selects the first integer q as a candidate value for the number of levels, and determines and outputs candidate values ​​for the number of samples M and the number of factors N based on the selected first integer q, the second integer n that forms the pair with the first integer q, and equations (C) and (D).

[0027]

number

[0028]

number

[0029] Based on the findings obtained through diligent research by the inventors of this application, it is possible to systematically output candidate values ​​for the sample size M and the number of factors N by using the above formulas (A) to (D).

[0030] In other words, according to the fifth embodiment, by having the calculation unit acquire the first reference value r and the second reference value s, respectively, it becomes possible to systematically output candidate values ​​for the number of samples M and the number of factors N. This allows for the orthogonal array L M (q N This can improve user convenience related to ).

[0031] Furthermore, a sixth aspect of this disclosure relates to a computer-readable storage medium that stores the parameter output program. [Effects of the Invention]

[0032] As explained above, this disclosure makes it possible to improve user convenience related to orthogonal arrays. [Brief explanation of the drawing]

[0033] [Figure 1] Figure 1 is a diagram illustrating the hardware configuration of the output device. [Figure 2] Figure 2 illustrates the software configuration of the output device. [Figure 3] Figure 3 is a flowchart illustrating the steps for the output method. [Figure 4] Figure 4 is a block diagram illustrating the input and output of an output device. [Figure 5] Figure 5 is a flowchart illustrating the processes involved in the selection process. [Figure 6] Figure 6 is a flowchart illustrating the processes performed in the candidate value output process. [Figure 7] Figure 7 is a flowchart illustrating the processes performed in the orthogonal array generation process. [Figure 8A] Figure 8A is an example of a display screen in the orthogonal array generation process. [Figure 8B] Figure 8B is an example of a display screen in the orthogonal array generation process. [Figure 9] Figure 9 is a table showing a specific example of the orthogonal array generation process. [Figure 10A] Figure 10A is an example of a partial excerpt of the non-mixed orthogonal array L2401(7400). [Figure 10B] Figure 10B is an example of a partial excerpt of the non-mixed orthogonal array L2401(7400). [Figure 11] Figure 11 is a flowchart illustrating the processes performed in a machine learning process. [Figure 12A] Figure 12A is a diagram illustrating the generalization performance. [Figure 12B]Figure 12B is a diagram illustrating the generalization performance. [Modes for carrying out the invention]

[0034] The embodiments of this disclosure will be described below with reference to the drawings. Note that the following description is illustrative.

[0035] <1.Device configuration> Figure 1 is a diagram illustrating the hardware configuration of the output device (specifically, computer 1 which constitutes the output device) as a parameter output device and machine learning device, and Figure 2 is a diagram illustrating its software configuration.

[0036] As illustrated in Figure 1, computer 1 includes a CPU (Central Processing Unit) 3 as a processor, a ROM (Read Only Memory) 5 for storing boot programs and the like, a RAM (Random Access Memory) 7a that functions as main memory, and a storage device 7b as secondary storage. Note that the storage device 7b may be an SSD (Solid State Drive) or an HDD (Hard Disk Drive).

[0037] Of these elements, the CPU 3 executes various programs. The CPU 3 constitutes the arithmetic unit in this embodiment. The RAM 7a and storage 7b temporarily or continuously store the programs executed by the CPU 3. The RAM 7a and storage 7b constitute the storage unit 7 in this embodiment.

[0038] Computer 1 also includes a display 9, graphics memory (Video RAM: VRAM) 11 for storing image data displayed on the display 9, and a keyboard 13a and mouse 13b as human-machine interfaces.

[0039] The display 9 can display a screen Sc based on the calculation results of the CPU 3, and constitutes the display unit in this embodiment. The display 9 is electrically connected to the CPU 3 via an I / O interface or the like.

[0040] The keyboard 13a and mouse 13b each accept at least one of user input and / or operation (hereinafter collectively referred to as "operation input"). The keyboard 13a and mouse 13b constitute the reception unit 13 in this embodiment. The reception unit 13 is electrically connected to the CPU 3 wirelessly or via a wired connection through an I / O interface or the like.

[0041] Furthermore, the computer 1 according to this embodiment can send and receive data with other external devices via a communication unit 15 configured as a communication interface. The computer 1 is connected to external devices via the communication unit 15.

[0042] Furthermore, as illustrated in Figure 2, the program memory of storage 7b stores the output program 20, an OS (Operating System) (not shown), and an application program (also not shown).

[0043] The output program 20 includes a parameter output program 21 and a machine learning program 23. The parameter output program 21 and the machine learning program 23 are pre-stored in a computer-readable storage medium 18, as illustrated in Figure 1. This storage medium 18 is a tangible storage medium, such as a disk medium.

[0044] The parameter output program 21 is a program that causes the computer 1 to execute the parameter output method according to this embodiment. The parameter output program 21 causes the computer 1, which acts as an output device, to execute each process that constitutes the parameter output method.

[0045] The machine learning program 23 is a program that causes computer 1 to execute the machine learning method according to this embodiment. The machine learning program 23 causes computer 1, which acts as an output device, to execute each process that constitutes the machine learning method.

[0046] The parameter output program 21 and the machine learning program 23 are launched in response to commands input from the keyboard 13a, mouse 13b, etc., respectively. At that time, each program is loaded from storage 7b into RAM 7a and executed by CPU 3.

[0047] Note that the classifications of parameter output program 21 and machine learning program 23 are merely convenient groupings corresponding to the processes executed by computer 1.

[0048] Furthermore, it is not necessary for the computer 1 running the parameter output program 21 and the computer 1 running the machine learning program 23 to be the same computer. Two or more computers 1 may be used. In addition, each process constituting the parameter output program 21 may be divided and executed by two or more computers 1, or each process constituting the machine learning program 23 may be divided and executed by two or more computers 1.

[0049] On the other hand, as shown in Figure 2, the data memory of storage 7b temporarily or continuously stores the parameter set 31 and orthogonal array data 33, the training data 35 and machine learning model data 37, and the orthogonal array database 39.

[0050] Here, the parameter set 31 and orthogonal array data 33 are generated by the parameter output program 21. The training data 35 and machine learning model data 37 are generated by the machine learning program 23. The orthogonal array database 39 is pre-stored in storage 7b.

[0051] In addition, various data generated by the parameter output program 21 and the machine learning program 23, as well as the execution results of the application program, are continuously stored in the storage 7b or temporarily stored in the RAM 7a as needed.

[0052] <2. Outline of Output Method> Figure 3 is a flowchart illustrating the procedure for parameter output. Figure 4 is a block diagram illustrating the input and output of computer 1 as an output device.

[0053] The output method generally includes a parameter output method and a machine learning method. However, the machine learning method is not essential in this disclosure.

[0054] The parameter output method is configured to output a set of parameters that characterize the orthogonal array by using computer 1. As shown in Figure 3, the parameter output method according to this embodiment includes a variable acquisition process (step S1), a selection process (step S2), a candidate value output process (step S3), and an orthogonal array generation process (step S4). In the candidate value output process, a parameter set 31 representing the set of parameters is output. In the orthogonal array generation process, orthogonal array data 33 representing the orthogonal array is output.

[0055] Here, the orthogonal array characterized by the parameter set 31 according to this embodiment is an orthogonal array of intensity 2 and non-mixed systems. In this case, if the number of samples (number of experiments) of the orthogonal array is M, the number of factors of this orthogonal array is N, and the number of levels of this orthogonal array is q, then the orthogonal array according to this embodiment is L M (q N It can be written as ) or OA(M,N,q,2). Here, the exponent λ(=M / q 2 The notation regarding ) has been omitted.

[0056] The machine learning method is a method that uses the parameter output method described above. The machine learning method according to this embodiment includes a machine learning process (step S5), as shown in Figure 3.

[0057] The output program 20 is configured to cause the CPU 3 of computer 1 to execute these control processes. Specifically, the CPU 3 executes the four steps (steps S1 to S4) via the parameter output program 21 and executes step S5 via the machine learning program 23.

[0058] The CPU 3 executes the output program 20, thereby configuring the output device by the computer 1. This output device functions as both a parameter output device and a machine learning device.

[0059] Computer 1 as a parameter output device includes a variable acquisition means 1A that performs step S1, a selection means 1B that performs step S2, a candidate value output means 1C that performs step S3, and an orthogonal array generation means 1D that performs step S4. Computer 1 as a machine learning device includes a first machine learning means 1E and a second machine learning means 1F that perform step S5.

[0060] <3. Details of output method> (3-1. Variable acquisition process) First, in step S1, the variable acquisition process is executed by the variable acquisition means 1A. In this variable acquisition process, the CPU 3 acquires a first criterion value r and a second criterion value s from among positive integers of 2 or more. The first criterion value r is a positive integer of 2 or more that indicates the selection criterion for the number of levels q of the orthogonal array. The first criterion value r is a positive integer of 2 or more that indicates the selection criterion for the number of factors N.

[0061] Specifically, the CPU 3 acquires the first and second reference values ​​r and s by receiving input of the first and second reference values ​​r and s via the reception unit 13, or by reading the first and second reference values ​​r and s from the storage unit 7. When reading from the storage unit 7, the first and second reference values ​​r and s may be acquired via an electronic file in CSV format.

[0062] Once the acquisition of the first and second reference values ​​r and s is complete, the CPU 3 proceeds the control process from step S1 to step S2 in Figure 3. In step S2, the selection means 1B executes the selection process.

[0063] (3-2. Selection Process) Figure 5 is a flowchart illustrating the processes performed in the selection process. The flowchart in Figure 5 illustrates the process performed in step S2 of Figure 3.

[0064] Here, if the two integers are the first integer q and the second integer n, then in the selection process according to this embodiment, the CPU3 selects a pair of the first integer q and the second integer n that satisfies both equations (A) and (B) shown below.

[0065]

number

[0066] Specifically, in the selection process (step S2), CPU3 first executes step S21 in Figure 5. In step S21, CPU3 selects a first integer q that satisfies equation (A) based on the first reference value r. Hereafter, the first integer q is a positive integer greater than or equal to 2. The first integer q represents a candidate value for the number of levels and can be called the "category size index".

[0067] For example, during the first execution of the selection process (step S2), CPU3 selects the smallest first integer q that satisfies equation (A) above. In this case, as indicated in parentheses in step S21, "first integer q = first reference value r".

[0068] In the subsequent step S22, the CPU3 selects a second integer n that satisfies equation (B) based on the second reference value s and the value of the first integer q selected in step S21. The second integer n is a positive integer greater than or equal to 2. The second integer n is an index that characterizes the size of the sample size M and the number of factors N, and can be called the "sample size index".

[0069] In the subsequent step S23, the CPU 3 temporarily or continuously stores the pair of first integer q and second integer n selected in steps S21 and S22 in the storage unit 7.

[0070] As an example, the CPU 3 according to this embodiment fixes the value of a first integer q selected based on a first reference value r, and then selects one or more values ​​for a second integer n that satisfy equation (B) for that first integer q. The CPU 3 stores the pairs of the first integer q and one or more second integer n in the storage unit 7.

[0071] As an example, consider the case where (r,s)=(2,2). In this case, among the pairs of first integers q and second integers n selected based on (A) and (B) above, the pair in which the first integer q and the second integer n are each smallest is (q,n)=(2,2).

[0072] Here, if the first integer q is a positive integer greater than or equal to 2, the left side of equation (B) will have a positive correlation with the second integer n. Therefore, for any n greater than or equal to 2, such as (q,n)=(2,3), (2,4), etc., we can generate pairs with the first integer q (=2).

[0073] Similarly, when the second integer n is a positive integer greater than or equal to 2, the left-hand side of equation (B) has a positive correlation with the first integer q. Therefore, for any q greater than or equal to 2, such as (q,n)=(3,2), (4,2), etc., a pair with the second integer n (=2) can be generated.

[0074] The left-hand side of equation (B) has a positive correlation with respect to both the first integer q and the second integer n. On the other hand, the right-hand side of equation (B) is fixed to the second reference value s. Therefore, pairs of first integers q and second integers n that satisfy equations (A) and (B) are constructed from any combination of a first integer q greater than or equal to 2 and a second integer n greater than or equal to 2.

[0075] As a first alternative example, consider the case where (r,s) = (2,3). In this case, among the pairs of first integers q and second integers n selected based on (A) and (B) above, the pair in which the first integer q and the second integer n are each smallest is (q,n) = (2,2).

[0076] In the first alternative example, pairs of first integers q and second integers n that satisfy equations (A) and (B) are composed of any combination of a first integer q greater than or equal to 2 and a second integer n greater than or equal to 2, such as (q,n) = (3,2), (2,3), etc.

[0077] As a second alternative example, consider the case where (r,s)=(3,3). In this case, among the pairs of first integers q and second integers n selected based on (A) and (B) above, the pair in which the first integer q and the second integer n are each smallest is (q,n)=(3,2).

[0078] In the second alternative example, pairs of first integers q and second integers n that satisfy equations (A) and (B) are constructed from any combination of a first integer q greater than or equal to 3 and a second integer n greater than or equal to 2, such as (q,n) = (4,2), (5,2), (3,3), etc.

[0079] Once the processing in step S23 is complete, the CPU3 advances the control process from step S2 to step S3 in Figure 3. In step S3, the candidate value output means 1C executes the candidate value output process.

[0080] (3-3. Candidate Value Output Process) Figure 6 is a flowchart illustrating the process performed in the candidate value output process. The flowchart in Figure 6 illustrates the process performed in step S3 of Figure 3.

[0081] In the candidate value output process according to this embodiment, the CPU 3 selects a first integer q as a candidate value for the number of levels. The CPU 3 also determines and outputs candidate values ​​for the number of samples M and the number of factors N, respectively, based on the selected first integer q, a second integer n that forms a pair with the first integer q, and equations (C) and (D).

[0082]

number

[0083] Specifically, in the selection process (step S3), CPU3 first executes step S31 in Figure 6. In step S31, CPU3 selects a value for the first integer q as a candidate value for the number of levels. In the subsequent step S32, CPU3 calculates a candidate value for the number of samples M that satisfies the above formula (C) based on the values ​​of the first integer q and the second integer n.

[0084] In the subsequent step S33, the CPU3 calculates candidate values ​​for the number of factors N that satisfy equation (D) based on the values ​​of the first integer q and the second integer n.

[0085] In the subsequent step S34, the CPU 3 temporarily or continuously stores the candidate values ​​for the number of levels q, the number of samples M, and the number of factors N, which were selected and calculated in steps S31 and S32, in the storage unit 7 as a parameter set 31 that characterizes the orthogonal array.

[0086] If multiple second integers n are assigned to a single first integer q, the CPU 3 calculates candidate values ​​for both the sample size M and the number of factors N based on each of the multiple second integers n. Multiple candidate values ​​for both the sample size M and the number of factors N will be calculated. In this case, the CPU 3 temporarily or continuously stores these multiple candidate values ​​in the memory unit 7.

[0087] Once the processing in step S34 is complete, the CPU 3 advances the control process from step S3 to step S4 in Figure 3. In step S4, the orthogonal array generation means 1D executes the orthogonal array generation process.

[0088] (3-4. Orthogonal Array Generation Process) Figure 7 is a flowchart illustrating the processes performed in the orthogonal array generation process. Figures 8A and 8B illustrate the display screen Sc in the orthogonal array generation process. The flowchart in Figure 7 illustrates the process performed in step S4 of Figure 3.

[0089] In the orthogonal array generation process according to this embodiment, the CPU3 generates an M x N or N x M matrix composed of M-dimensional and N column vectors of the q-level system based on the output candidate values ​​for sample number M and candidate values ​​for factor number N (see step S42).

[0090] Furthermore, in the orthogonal array generation process, CPU3 determines whether the generated matrix is ​​valid as an orthogonal array, and assigns matrices that are valid as orthogonal arrays to non-mixed orthogonal arrays L M (q N Select and output (see steps S43 to S44).

[0091] More specifically, in the orthogonal array generation process, CPU3 generates the matrix L of the non-mixed system from among the pairs of first integer q and second integer n that satisfy both equation (A) and equation (B), such that the first integer q is minimized and the matrix is ​​valid as an orthogonal array. M (q N Select and output.

[0092] Specifically, in the orthogonal array generation process (step S4), the CPU3 first executes step S41 in Figure 6. In this step S41, it reads the parameter set 31 output in the candidate value output process (step S3).

[0093] In the following step S42, the CPU3 generates an M x N or N x M matrix based on the candidate values ​​for the number of levels q, the candidate values ​​for the number of samples M, and the candidate values ​​for the number of factors N. The following explanation will use an M x N matrix as an example. This matrix is ​​composed of M-dimensional and N vectors in the q-level system. Each component of the matrix stores q possible variables.

[0094] In the subsequent step S43, the CPU3 determines whether the matrix generated in step S43 is a valid orthogonal array. As mentioned above, in this embodiment, an orthogonal array of strength 2 is generated, so the CPU3 determines whether any two columns out of the M rows and N columns contain q combinations of variables the same number of times across all M rows.

[0095] For example, if q=2, CPU3 determines whether the combinations of "0" and "0", "0" and "1", "1" and "0", and "1" and "1" appear the same number of times.

[0096] If the determination in step S43 is YES, that is, if the matrix generated in step S42 is valid as an orthogonal array, the CPU3 proceeds to step S44. In step S44, the CPU3 converts the matrix determined to be valid as an orthogonal array into a non-mixed orthogonal array L M (q N ) was selected, and its orthogonal array L M (q N The values ​​of the components in each row and column of the output are output as orthogonal array data 33. The orthogonal array data 33 is, for example, electronic data in CSV format.

[0097] Here, as mentioned above, for each level q, multiple candidate values ​​will be calculated for both the sample size M and the number of factors N. CPU3 may perform steps S42 and S43 for each candidate value, or it may perform the orthogonal array L where the value of the number of factors N is close to the second criterion value s. M (q N You may select and output only the following:

[0098] In step S45, following step S44, the CPU 3 displays an orthogonal array L on the display 9, which serves as the display unit. M (q N The selection result of step S44 is displayed. Step S45 may be executed before step S44.

[0099] When the processes in steps S42 and S43 are performed for each candidate value, an orthogonal array L corresponding to each candidate value is generated, as illustrated in the display screen Sc of Figure 8A. M (q N ) can be displayed. Orthogonal array L where the number of factors N is close to the second reference value s. M (q N If only ) is selected, a specific orthogonal array L will be selected, as illustrated in the display screen Sc of Figure 8B. M (q N ) can be displayed.

[0100] On the other hand, if the determination in step S43 is NO, that is, if the matrix generated in step S42 does not form an orthogonal array, the CPU3 proceeds to step S45 of the control process.

[0101] In step S45, CPU3 updates the value of the first integer q by adding "+1" to it ("first integer q = first integer q + 1"). For example, during the first execution of the orthogonal array generation process (step S4), CPU3 updates "first integer q = first reference value r" to "first integer q = first reference value r + 1".

[0102] Once the processing in step S45 is complete, the CPU3 returns the control process to step S22 in Figure 5. Thereafter, based on the updated value of the first integer q, the selection of the second integer n, the candidate value output process (step S3), and the orthogonal array generation process (step S4) are repeatedly executed.

[0103] Returning to step S44, once the processing of that step is complete, the CPU 3 advances the control process from step S4 to step S5 in Figure 3. In step S5, the first machine learning means 1E and the second machine learning means 1F execute the machine learning process.

[0104] [Examples of orthogonal array generation processes] Figure 9 is a table illustrating a specific example of the orthogonal array generation process. The vertical axis of the table in Figure 9 represents the first integer q as a category size index. The horizontal axis of the same table represents the second integer n as a sample size index.

[0105] The inventors of this application have identified the non-mixed orthogonal array L illustrated in Figure 9. M (q N ) has been confirmed to be fully realized. Figures 10A and 10B show the orthogonal array L for non-mixed systems. 2401 (7 400 The present inventors have provided an example of the matrix shown in Figures 10A and 10B, which is an orthogonal array L. 2401 (7 400 It has been confirmed to function as such.

[0106] (3-5. Machine Learning Process) Figure 11 is a flowchart illustrating the processes performed in a machine learning process. The flowchart in Figure 11 illustrates the process performed in step S5 of Figure 3.

[0107] In the first half of the machine learning process (steps S51 to S53), training data 35 is generated by the first machine learning means 1E. In this first half, the CPU 3 generates a non-mixed orthogonal array L M (q N) obtain the non-mixed orthogonal array L M (q N The variable ) is considered to have N components and M possible multicomponent variables, and the numerical data associated with each of the M possible values ​​of the multicomponent variables constitutes the training data 35 that is input to the nonlinear machine learning model. As an example, the numerical data constituting the training data 35 may have a positive or negative correlation with each of the M possible values ​​of the multicomponent variables.

[0108] In the latter part of the machine learning process (steps S54 to S55), machine learning model data 37 is generated by the second machine learning means 1F. In this latter part, the CPU 3 learns a nonlinear machine learning model Ma based on the training data 35.

[0109] Specifically, in step S51, the CPU 3 first reads the orthogonal array data 33. The CPU 3 then reads the non-mixed orthogonal array L via the orthogonal array data 33. M (q N ) obtain.

[0110] In the following step S52, the CPU3 generates a non-mixed orthogonal array L M (q N Based on this, training data 35 is generated to be input into a nonlinear machine learning model.

[0111] For more details, CPU3 is a non-mixed orthogonal array L M (q N We consider ) as a multicomponent variable with N components and M possibilities. The M possibilities for the multicomponent variable correspond to M possibilities for sample data. Each of the M possibilities for sample data corresponds to a discrete variable with N factors and q levels.

[0112] The CPU3 then assigns numerical data to each factor of the M-type sample data, associated with the discrete variables corresponding to each factor. This assignment constructs the training data 35 that is input into the nonlinear machine learning model. This training data 35 is a data set with M samples and N factors, representing the explanatory variables to be input into a given machine learning model.

[0113] For example, if the nth factor represents the plate thickness of a vehicle component, then each of the M sample data sets will have its nth factor (nth column) assigned one of q plate thickness values.

[0114] In the subsequent step S53, the CPU3 assigns a value for the target variable corresponding to each sample data in the training data 35. The value of the target variable corresponding to each sample data may be obtained by various numerical calculations such as the response surface method, or by simulations and experiments using equipment other than a computer, such as collision experiments or chemical experiments. Note that step S53 is not mandatory.

[0115] The explanatory variables (training data 35) generated in step S52 and the target variable assigned in step S53 are used to construct the training data used for machine learning of the machine learning model Ma.

[0116] In the following step S54, the CPU3 learns a nonlinear machine learning model Ma based on the training data 35. This machine learning model Ma is, for example, a surrogate model. For example, the machine learning model Ma includes nonlinear terms, including the direct product of the factors.

[0117] The nonlinear machine learning model Ma includes a machine learning model that models the performance of an automobile. This machine learning model may be a model of heat transfer paths including power units and air conditioning equipment, a predictive model of the NV performance of an automobile such as vibration transmission paths in an automobile, a manufacturing method model in materials development, or an experimental design model based on CFD.

[0118] <4. Regarding generalization performance> Figures 12A and 12B are diagrams used to explain generalization performance. Specifically, both Figures 12A and 12B have "number of factors N=3". Figure 12A illustrates the breakdown of an orthogonal array of a non-mixed system with "number of samples M=4" and "number of levels q=2". Figure 12B illustrates the breakdown of a Latin hypersquare method or D-optimal design with "number of samples M=3" and "number of levels q=2".

[0119] In the example shown in Figure 12A, using the 3D coordinates (factors) of the boundary and interior of the regular tetrahedron AFHC as explanatory variables corresponds to interpolation, while using the 3D coordinates (factors) outside the regular paper tetrahedron AFHC as explanatory variables corresponds to extrapolation. Hereafter, the 3D space corresponding to interpolation will be referred to as the interpolation region, and the 3D space corresponding to extrapolation will be referred to as the extrapolation region.

[0120] For example, the areas around the four vertices B, D, E, and G will be located in the extrapolated region. Here, the distance between each of the four vertices located in the extrapolated region and the interpolated region (the distance to the centroid of the regular tetrahedron AFHC) will be equidistant and the shortest distance for all four vertices.

[0121] Therefore, no particular vertex among the four vertices B, D, E, and G is disadvantaged during extrapolation, and the extrapolated regions around each vertex do not become unbalanced. The four vertices B, D, E, and G represent homogeneous sampling. Using non-mixed orthogonal arrays contributes to improving generalization performance in machine learning.

[0122] In the example shown in Figure 12B, using the 3D coordinates (factors) within and around the boundary of the equilateral triangle DBE as explanatory variables corresponds to interpolation, while using the 3D coordinates (factors) outside the equilateral triangle DBE as explanatory variables corresponds to extrapolation. Similar to Figure 12A, the 3D space corresponding to interpolation is called the interpolation region, and the 3D space corresponding to extrapolation is called the extrapolation region.

[0123] As shown in Figure 12B, the areas surrounding the five vertices A, C, F, G, and H are located within the extrapolation region. Here, the distance between each vertex located in the extrapolation region and the interpolation region (distance to the centroid of equilateral triangle DBE) is non-uniform. This imbalance in the extrapolation region is detrimental to improving generalization performance.

[0124] For example, vertex G and the nearest equilateral triangle FCH from vertex G (i.e., the equilateral triangle that intersects the centroid at the shortest distance when a perpendicular is drawn from vertex G) are both extrapolation regions. In this case, the area around vertex G is unfavorable for extrapolation because it is further away from the interpolation region than equilateral triangle FCH.

[0125] Similarly, vertex F and the equilateral triangle EBG closest to vertex F also form an extrapolation region, except for side EB. In this case, the area around vertex F is further from the extrapolation region than equilateral triangle EBG, making it unfavorable for extrapolation.

[0126] The same applies to the remaining vertices A, C, and H.

[0127] Thus, when the sample size M is reduced using the Latin hypercube method or D-optimal design, it becomes unfavorable for extrapolation, which is detrimental to improving generalization performance in machine learning compared to using non-mixed orthogonal arrays.

[0128] On the other hand, using non-mixed orthogonal arrays can be detrimental when considering the effects of interactions. However, as mentioned above, by training a nonlinear machine learning model Ma, the effects of interactions can be suppressed without using mixed orthogonal arrays.

[0129] <5. Significance of the Output Method> Based on the findings obtained through diligent research by the inventors of this application, it is possible to systematically output candidate values ​​for the sample size M and the number of factors N by using the above formulas (A) to (D).

[0130] In other words, according to the above embodiment, by having the CPU3 acquire the first reference value r and the second reference value s, it becomes possible to systematically output candidate values ​​for the number of samples M and the number of factors N. This allows for the orthogonal array L M (q N This can improve user convenience related to ).

[0131] Furthermore, as illustrated in Figures 9, 10A, and 10B, the orthogonal array L M (q N Not only the sample size M and the number of factors N, but also the non-mixed orthogonal array L based on those parameters. M (q N ) is output. As a result, the orthogonal array L M (q N This can improve user convenience related to ).

[0132] Furthermore, when the first integer q is minimized, that first integer q will be nearest to the first reference value r. This allows the first reference value r to be considered as the user's desired value for the number of levels, and the orthogonal array L M (q N This can improve user convenience related to ).

[0133] In general, non-mixed orthogonal arrays L M (q N When using ), interactions may be concentrated on specific factors. Non-mixed orthogonal array L M (q N When machine learning a linear model using training data 35 based on ), attention must be paid to certain factors where interactions may be concentrated.

[0134] To suppress the effects of interactions, an orthogonal array L for non-mixed systems is used. M (q N Alternatively, one could consider using a mixed-system orthogonal array. However, a mixed-system orthogonal array only guarantees the suppression of interaction concentration when used in conjunction with a linear model; its effect is not necessarily guaranteed when used in conjunction with a nonlinear model.

[0135] Furthermore, for objects that can be represented with a small number of levels (objects for which a linear model is sufficient), there may be advantages to using mixed orthogonal arrays. However, for broader, more general objects, such as those involving a huge number of factors or nonlinearity, mixed orthogonal arrays are used in conjunction with nonlinear models to ensure generalization performance, and non-mixed orthogonal arrays are superior to non-mixed orthogonal arrays. M (q N This is inconvenient compared to [another option].

[0136] In contrast, according to the above embodiment, as illustrated in Figure 11, the non-mixed orthogonal array L M (q N A nonlinear machine learning model Ma is trained using training data 35 based on ). By training a nonlinear machine learning model Ma, the effects of interactions can be suppressed without using a mixed orthogonal array. This allows for the training of a non-mixed orthogonal array L M (q N By using this method, it is possible to achieve both the ability to handle a vast number of factors with the smallest possible sample size and ensure generalization performance, and the suppression of interaction effects by using a nonlinear machine learning model Ma.

[0137] Other embodiments In the above embodiment, a parameter output method was illustrated based on Figures 5 to 7, but this disclosure is not limited to such illustrations. For example, before executing step S21 in Figure 5, it may be determined whether the first reference value r is prime factorizable, and if the determination is YES, the first reference value r may be prime factorized. In that case, processing from step S21 onwards may be performed for each of the prime factors, and finally a mixed system orthogonal array may be output. For example, if "first reference value r=6" is input, a two-level system orthogonal array and a three-level system orthogonal array may be generated, and their tensor product may be output as the final result of the orthogonal array. When performing the tensor product, the CPU 3 may read an existing orthogonal array from the orthogonal array database 39 illustrated in Figure 2 and calculate the tensor product of the read orthogonal array.

[0138] It is not essential to execute step S5 immediately after the completion of step S4. The orthogonal array generated in step S4 may be stored in the storage 7b, an external server, etc., and then step S5 may be executed based on the stored orthogonal array.

[0139] Also, regarding the screen for displaying the orthogonal array L M (q N ), it is not limited to the display screen Sc on the display 9 of the computer 1. The orthogonal array L M (q N ) etc. may be displayed on a screen prepared separately from the computer 1. That is, the "display unit" in the present disclosure does not necessarily have to be a part of the computer 1.

[0140] Also, different computers 1 may be used for the parameter output method and the machine learning method. Also, different computers 1 may be used among the processes constituting the parameter output method.

[0141] Also, the computer 1 in the present disclosure includes parallel computers such as supercomputers and PC clusters. Each computer 1 may include a plurality of CPUs 3, and it is not essential to execute all the processes on the same CPU 3.

[0142] Also, regarding the screen for displaying various visualized information, it is not limited to the display screen Sc on the display 9 of the computer 1. A directed graph structure Gs etc. may be displayed on a screen prepared separately from the computer 1. That is, the "display unit" in the present disclosure only needs to be connected to the CPU 3, and it does not necessarily have to be a part of the computer 1.

[0143] 《Industrial Applicability》 As described above, the present disclosure is generally useful for applications of orthogonal arrays, including the generation of training data for evaluating the performance of automobiles, and has industrial applicability.

Explanation of Signs

[0144] 1. Computer (output device, parameter output device, machine learning device) 3 CPU (arithmetic unit) 7 Memory section 7a RAM 7b Storage 9. Display (Display Unit) 13 Reception Department 13a Keyboard 13b Mouse 18 Storage medium 20 Output Program 21 Parameter Output Program 23 Machine Learning Programs 31 Parameter Set S1 Variable acquisition process S2 Selection Process S3 Candidate Value Output Process S4 Orthogonal Array Generation Process S5 Machine Learning Process

Claims

1. A parameter output method for outputting a set of parameters characterizing an orthogonal array by using a computer comprising a storage unit for storing a program and an arithmetic unit for executing the program stored in the storage unit, Let M be the number of samples in the orthogonal array, N be the number of factors in the orthogonal array, let r be the first criterion value indicating the selection criteria for the number of levels in the orthogonal array, let s be the second criterion value indicating the selection criteria for the number of factors N, and let the two integers be the first integer q and the second integer n. The calculation unit obtains the first reference value r and the second reference value s from among two or more positive integers. The calculation unit selects a pair of the first integer q and the second integer n that satisfies both equation (A) and equation (B), The calculation unit selects the first integer q as a candidate value for the number of levels, and determines and outputs candidate values ​​for the number of samples M and the number of factors N based on the selected first integer q, the second integer n that forms the pair with the first integer q, and equations (C) and (D). [Math 1] [Math 2] Parameter output method.

2. In the parameter output method described in claim 1, The calculation unit generates an M x N or N x M matrix composed of M-dimensional and N vectors of the q-level system based on the output candidate values ​​for the number of samples M and the candidate values ​​for the number of factors N. The calculation unit determines whether the matrix is ​​valid as the orthogonal array, The calculation unit transforms the matrix that forms the orthogonal array into a non-mixed orthogonal array L Ｍ (q Ｎ Select and output as follows: Parameter output method.

3. In the parameter output method described in claim 2, The calculation unit determines the matrix that satisfies both equation (A) and equation (B) among the pairs of first integer q and second integer n such that the first integer q is minimized and the matrix is ​​valid as an orthogonal array L of the non-mixed system. Ｍ (q Ｎ Select and output as follows: Parameter output method.

4. A machine learning method using the parameter output method described in claim 2 or 3, The calculation unit determines the non-mixed orthogonal array L Ｍ (q Ｎ ) obtain, The calculation unit determines the non-mixed orthogonal array L Ｍ (q Ｎ ) is considered as an N-component, M-way multi-component variable, and the numerical data associated with each of the M values ​​of the multi-component variable is used to construct the training data to be input into the nonlinear machine learning model. The calculation unit learns the nonlinear machine learning model based on the training data. Machine learning methods.

5. A parameter output program that outputs a set of parameters characterizing an orthogonal array by using a computer comprising a storage unit for storing a program and an arithmetic unit for executing the program stored in the storage unit, Let M be the number of samples in the orthogonal array, N be the number of factors in the orthogonal array, let r be the first criterion value indicating the selection criteria for the number of levels in the orthogonal array, let s be the second criterion value indicating the selection criteria for the number of factors N, and let the two integers be the first integer q and the second integer n. To the aforementioned computer, The calculation unit performs a process of obtaining the first reference value r and the second reference value s from among two or more positive integers, The calculation unit performs a process of selecting a pair of the first integer q and the second integer n that satisfies both equation (A) and equation (B), The calculation unit performs a process of selecting the first integer q as a candidate value for the number of levels, and determining and outputting candidate values ​​for the number of samples M and the number of factors N based on the selected first integer q, the second integer n that forms the pair with the first integer q, and equations (C) and (D). Parameter output program. [Math 3] [Math 4]

6. The system stores the parameter output program described in claim 5. A computer-readable storage medium.

Images