Information processing method, information processing device, and computer program

Abstract

This invention provides an information processing method that can shorten the computation time required to obtain results equivalent to those obtained by a Pareto front using only finite element method calculations in the optimization calculation of design parameters using a genetic algorithm with CAE analysis such as the finite element method. [Solution] An information processing method for optimizing design parameters that define an individual model representing a design object using a genetic algorithm, wherein the computer calculates the response value of the individual model in each generation using a first calculation method or a second calculation method which has a faster calculation speed than the first calculation method. When the computer is calculating the response value of the individual model using the second calculation method, it calculates an optimization progress index that indicates the progress of the design parameters, and determines whether the optimization of the design parameters has stalled based on the amount of change in the optimization progress index with respect to generational progress, and if it determines that the optimization has stalled, it calculates the response value of the individual model using the first calculation method.

Description

Technical Field

[0001] The present disclosure relates to an information processing method, an information processing apparatus, and a computer program.

Background Art

[0002] In product design, it is common to calculate the characteristics or behaviors of a simulation target model representing a design object such as a motor by CAE analysis such as the finite element method. For example, Patent Document 1 discloses a design method that enables easy and rapid design of a desired inductor even for a non-expert designer. Specifically, the design method according to Patent Document 1 is a method for designing a wound inductor using a computer, and includes a step of initializing variables describing the structure of the inductor, a step of calculating the characteristics of the inductor having the structure described by the variables based on pre-input attribute information of a core and a coil conductor by magnetic field analysis, a step of calculating an evaluation value using a predetermined evaluation function having at least the inductor characteristics as parameters, a step of determining whether the evaluation value satisfies a predetermined convergence condition, and if the convergence condition is satisfied, ending the process, and if the convergence condition is not satisfied, varying the value of the variable by a genetic algorithm, and repeating the analysis process and the optimization process until the convergence condition is satisfied.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] However, in the optimization calculation using the genetic algorithm, there is a problem that CAE analysis needs to be repeatedly calculated, requiring a large amount of calculation time.

[0005] The purpose of this disclosure is to provide an information processing method, an information processing device, and a computer program that can shorten the computation time required to obtain results equivalent to those obtained by a Pareto front using only finite element method calculations in the optimization calculation of design parameters using a genetic algorithm with CAE analysis such as the finite element method. [Means for solving the problem]

[0006] An information processing method according to one aspect of the present disclosure is an information processing method in which a computer optimizes design parameters that define individual models representing an object to be designed using a genetic algorithm, wherein the computer generates multiple new individual models for the current generation by genetic processing based on a predetermined number of design parameters of individual models inherited from the previous generation, and from the second generation onward, calculates the response values ​​of the multiple individual models newly generated in the current generation using a first calculation method or a second calculation method which has a faster calculation speed than the first calculation method, ranks the predetermined number of individual models inherited from the previous generation and the multiple individual models newly generated based on the calculated response values, and executes a process to select a predetermined number of top-ranked individual models to be inherited by the next generation based on the ranking result, and further, if the response values ​​of the individual models are calculated using the second calculation method, the computer calculates an optimization progress index that shows the progress of the optimization of the design parameters, determines whether the optimization of the design parameters is stagnating based on the amount of change in the optimization progress index with respect to generational progress, and if it determines that the optimization is stagnating, calculates the response values ​​of the individual models using the first calculation method.

[0007] An information processing method according to one aspect of this disclosure is an information processing method in which a computer optimizes design parameters that define individual models representing an object to be designed using a genetic algorithm, wherein the computer generates multiple new individual models for the current generation by genetic processing based on a predetermined number of design parameters of individual models inherited from the previous generation, and from the second generation onward, calculates the response values ​​of the multiple individual models newly generated in the current generation using a first calculation method or a second calculation method which has a faster calculation speed than the first calculation method, ranks the predetermined number of individual models inherited from the previous generation and the multiple individual models newly generated based on the calculated response values, and based on the ranking result, The computer performs a process to select a predetermined number of top-ranked individual models to be passed on to the next generation. The first calculation method is a method for calculating response values ​​using CAE analysis including the finite element method. The second calculation method is a method for calculating response values ​​using a machine learning model. Furthermore, when the response values ​​of individual models are calculated using the first calculation method, the computer retrains the machine learning model using the design parameters of multiple individual models and the response values ​​of multiple individual models calculated using the first calculation method as training data. The computer then calculates a coefficient of determination that shows the correlation between the response values ​​calculated using the first calculation method and the response values ​​calculated using the second calculation method, and changes the number of generations for which the response values ​​of individual models are calculated using the second calculation method according to the calculated coefficient of determination.

[0008] An information processing device according to one aspect of the present disclosure is an information processing device comprising a calculation unit that performs a process of optimizing design parameters defining individual models representing an object to be designed using a genetic algorithm, wherein the calculation unit generates multiple new individual models for the current generation by genetic processing based on a predetermined number of design parameters of individual models inherited from the previous generation, calculates response values ​​of the multiple individual models newly generated in the current generation from the second generation onward using a first calculation method or a second calculation method which has a faster calculation speed than the first calculation method, ranks the predetermined number of individual models inherited from the previous generation and the multiple individual models newly generated based on the calculated response values, and selects a predetermined number of top-ranked individual models to be inherited by the next generation based on the ranking result, and further calculates an optimization progress index indicating the progress of the optimization of the design parameters when the response values ​​of the individual models are calculated using the second calculation method, determines whether the optimization of the design parameters is stagnating based on the amount of change in the optimization progress index with respect to generational progress, and calculates the response values ​​of the individual models using the first calculation method when it is determined that the optimization is stagnating.

[0009] An information processing device according to one aspect of this disclosure is an information processing device comprising a calculation unit that performs a process to optimize design parameters defining individual models representing an object to be designed using a genetic algorithm, wherein the calculation unit generates multiple new individual models for the current generation by genetic processing based on a predetermined number of design parameters of individual models inherited from the previous generation, calculates the response values ​​of the multiple individual models newly generated in the current generation from the second generation onward using a first calculation method or a second calculation method which has a faster calculation speed than the first calculation method, ranks the predetermined number of individual models inherited from the previous generation and the multiple individual models newly generated based on the calculated response values, and based on the ranking result The system is configured to select a predetermined number of high-ranking individual models to be passed on to the next generation. The first calculation method is a method for calculating response values ​​using CAE analysis including the finite element method. The second calculation method is a method for calculating response values ​​using a machine learning model. Furthermore, when the response values ​​of individual models are calculated using the first calculation method, the calculation unit retrains the machine learning model using the design parameters of multiple individual models and the response values ​​of multiple individual models calculated using the first calculation method as training data. It then calculates a coefficient of determination that shows the correlation between the response values ​​calculated using the first calculation method and the response values ​​calculated using the second calculation method, and changes the number of generations for which the response values ​​of individual models are calculated using the second calculation method according to the calculated coefficient of determination.

[0010] A computer program according to one aspect of this disclosure is a computer program that causes a computer to perform information processing to optimize design parameters defining individual models representing an object to be designed using a genetic algorithm, wherein the computer generates multiple new individual models for the current generation by genetic processing based on a predetermined number of design parameters of individual models inherited from the previous generation, calculates the response values ​​of the multiple individual models newly generated in the current generation from the second generation onward using a first calculation method or a second calculation method which has a faster calculation speed than the first calculation method, ranks the predetermined number of individual models inherited from the previous generation and the multiple individual models newly generated based on the calculated response values, and executes a process to select a predetermined number of top-ranked individual models to be inherited by the next generation based on the ranking result, and further causes the computer to calculate an optimization progress index indicating the progress of the optimization of the design parameters if the response values ​​of the individual models are calculated using the second calculation method, determines whether the optimization of the design parameters is stagnating based on the amount of change in the optimization progress index with respect to generational progress, and if it is determined that the optimization is stagnating, executes a process to calculate the response values ​​of the individual models using the first calculation method.

[0011] A computer program according to one aspect of this disclosure is a computer program that causes a computer to perform information processing to optimize design parameters that define individual models representing an object to be designed using a genetic algorithm, wherein the computer generates multiple new individual models for the current generation by genetic processing based on a predetermined number of design parameters of individual models inherited from the previous generation, and from the second generation onward, calculates the response values ​​of the multiple individual models newly generated in the current generation using a first calculation method or a second calculation method which has a faster calculation speed than the first calculation method, and ranks the predetermined number of individual models inherited from the previous generation and the multiple individual models newly generated based on the calculated response values, and ranks Based on the results, the system is instructed to select a predetermined number of top-ranked individual models to be passed on to the next generation. The first calculation method is a method for calculating response values ​​using CAE analysis including the finite element method, and the second calculation method is a method for calculating response values ​​using a machine learning model. Furthermore, if the response values ​​of individual models are calculated by the first calculation method, the system is instructed to retrain the machine learning model using the design parameters of multiple individual models and the response values ​​of multiple individual models calculated by the first calculation method as training data. The system is then instructed to calculate the coefficient of determination, which shows the correlation between the response values ​​calculated by the first calculation method and the response values ​​calculated by the second calculation method, and to change the number of generations for which the response values ​​of individual models are calculated according to the calculated coefficient of determination. [Effects of the Invention]

[0012] According to this disclosure, in the optimization calculation of design parameters using a genetic algorithm with CAE analysis such as the finite element method, the computation time required to obtain results equivalent to those of a Pareto front calculated using only the finite element method can be reduced. [Brief explanation of the drawing]

[0013] [Figure 1] The top diagram shows a conceptual analysis of an optimization method without using a surrogate model, and the bottom diagram shows a conceptual analysis of an online optimization method using a surrogate model. [Figure 2]A flowchart showing the processing procedure of online optimization in FIG. 1. [Figure 3] It is a conceptual diagram showing the FEA calculation generation. [Figure 4] It is a conceptual diagram showing the SM calculation generation. [Figure 5] It is a graph showing the relationship between the FEA calculation generation and the hypervolume. [Figure 6] It is a block diagram showing a configuration example of the information processing apparatus according to Embodiment 1. [Figure 7] It is a flowchart showing the processing procedure related to the optimization calculation in Embodiment 1. [Figure 8] It is a flowchart showing the FEA generation transition determination processing procedure according to Embodiment 1. [Figure 9] It is a conceptual diagram showing the hypervolume. [Figure 10] It is a conceptual diagram showing a method for determining a reference point for hypervolume calculation. [Figure 11] It is a conceptual diagram showing a method for determining the stagnation of the optimization process. [Figure 12] It is a graph showing the transition of the FEA calculation generation and the subsequent HV. [[ID=三十二]] [Figure 13] It is a graph comparing and displaying the transition of the hypervolume according to the present Embodiment 1 and the transition of the hypervolume by GA optimization that performs the FEA calculation generation at a fixed cycle. [Figure 14] It is a flowchart showing the FEA generation transition determination processing procedure according to Embodiment 2. [Figure 15] It is a conceptual diagram showing the change in the position of the centroid according to the generation when the distribution of the solution population progresses in the direction of a good solution. [Figure 16] It is a conceptual diagram showing the change in the position of the centroid according to the generation when the distribution of the solution population stagnates. [Figure 17] It is a flowchart showing the FEA generation transition determination processing procedure according to Embodiment 3. [Figure 18] It is a flowchart showing the processing procedure related to the optimization calculation in Embodiment 4. [Figure 19]This flowchart shows the processing procedure for determining the number of SM calculation generations to run. [Modes for carrying out the invention]

[0014] An information processing method, information processing apparatus, and computer program according to the embodiments of this disclosure will be described below with reference to the drawings. First, a method of using a proxy model, particularly an online method, will be described, and then the details of this embodiment will be described.

[0015] (Method of using a proxy model) In motor design and other applications involving electromagnetic field analysis, optimization calculations using genetic algorithms (GA) are employed. Known computational methods such as finite element analysis (FEA) are used for electromagnetic field analysis in GA optimization calculations. Hereinafter, numerical analysis such as electromagnetic field analysis using FEA will be referred to as FEA calculation.

[0016] To address the computational time challenge of GA (Genetic Algorithm) optimization, a method has been proposed that replaces FEA calculations with surrogate models. Hereafter, the surrogate model will be referred to as a surrogate model or SM (Surrogate Model), and numerical calculations using surrogate models will be referred to as SM calculations.

[0017] A surrogate model is a model that can instantly predict the output for any given input value by training it using a neural network (NN) or similar method with multiple sets of inputs and outputs as training data. In the case of motor design, the "inputs" are design parameters such as the position (for example, the distance from the rotor center to the center of the permanent magnets) and shape (for a rectangular cross-section, the vertical and horizontal dimensions) of the permanent magnets that make up the motor rotor, and the "outputs" are response values ​​such as average torque, torque ripple, and losses. Predictions using a surrogate model can be calculated instantaneously compared to FEA calculations, which can reduce the computation time for GA optimization.

[0018] Methods for using surrogate models for GA optimization can be broadly classified into two types: offline methods and online methods. The offline method involves preparing a surrogate model before the optimization calculation and performing the optimization calculation using a machine learning model (SM) calculation with this surrogate model. To obtain a highly accurate solution in the offline optimization calculation, it is necessary to prepare training data across the entire design space and train the surrogate model using machine learning, and the computational cost of this is a problem.

[0019] The online method is a method that combines FEA calculation and SM calculation in the optimization calculation process. Note that the reference "Asahino, Sano, Tani, Yamada, "Performance Evaluation of Surrogate Model-Assisted Optimization for Multi-Objective, Multi-Constraint Optimization Problems," Proceedings of the Joint Workshop of the Institute of Electrical Engineers of Japan on Static and Rotating Machinery, SA-25-037, RM-25-037, 2025" mentions both the series method and the parallel method as online methods, but here we will focus on the series method and explain the online method as the series method from now on.

[0020] Figure 1 shows a conceptual diagram of an optimization method without a surrogate model (top) and a conceptual diagram of an online optimization method using a surrogate model (bottom). Figure 2 is a flowchart showing the processing steps of the online optimization in Figure 1. Figure 3 is a conceptual diagram showing the FEA calculation generation, and Figure 4 is a conceptual diagram showing the SM calculation generation.

[0021] In Figure 1, the upper figure shows the optimization calculation without using a surrogate model, and the lower figure shows the optimization calculation of the online method using a surrogate model. Gen.0, Gen.1, ...Gen.6 represent the 0th, 1st, ...6th generations in GA optimization.

[0022] The arrow labeled "FEA" indicates that the numerical analysis of that generation in GA optimization is being performed using FEA calculation. The arrow labeled "SM" indicates that the numerical analysis of that generation in GA optimization is being performed using SM calculation. Hereafter, generations in which numerical analysis of response values ​​is performed using FEA will be referred to as FEA calculation generations (see Figure 3), and generations in which numerical analysis of response values ​​is performed using surrogate models will be referred to as SM calculation generations (see Figure 4).

[0023] As shown in Figure 1 (below), in the online method, the 0th generation calculates a predetermined number of response values ​​using FEA, just like in a normal optimization calculation. Next, a surrogate model is created or retrained using a neural network (NN) or similar method, using the predetermined number of input (design parameter) and response value pairs obtained above as training data. In the subsequent first generation, the response value is calculated using the surrogate model created above, and the optimization calculation is then performed. The detailed procedure is as follows:

[0024] First, as shown in Figure 2, the computer generates N individual models (initial individuals) of the initial generation (0th generation) (step S11), calculates the response value of each individual model using FEA based on the design parameters of each generated individual model (step S12), aggregates the design parameters of the initial individuals and the response values ​​of the N initial individuals calculated in the above process into the GA engine (NSGA-II's GA engine) (step S13), and creates a surrogate model using the design parameters of each individual model and the response values ​​calculated in step S12 as training data (step S14). Then, the computer assigns 1 to the variable m (step S15). The variable m is a variable that indicates the number of times FEA calculations have been performed since the start of processing (number of FEA calculation generations).

[0025] Next, the computer determines whether the next generation is an FEA calculation generation or not (step S16). In the example shown in Figure 1, every three generations is determined to be an FEA calculation generation.

[0026] If it is determined that it is not an FEA calculation generation (step S16: NO), the computer generates N individuals (child individuals) in the current generation (step S17), calculates the response values ​​of the generated N individual models (child individuals) using SM (step S18), and aggregates the generated N design parameters and the response values ​​of the individual models into the GA engine (step S19). The computer also ranks the 2N individual models based on the response values ​​of the 2N individual models (step S20) and selects the top-ranked N individual models (step S21).

[0027] If it is determined that it is an FEA calculation generation (step S16: YES), the computer generates N individuals (child individuals) in the current generation (step S22), performs FEA calculation on the response values ​​of the generated N individual models (child individuals) (step S23), and aggregates the generated N design parameters and the response values ​​of the individual models into the GA engine (step S24). Then, the computer ranks the 2N individual models based on the response values ​​of the 2N individual models (step S25), selects the top-ranked N individual models (step S26), and retrains the surrogate model based on the design parameters and response values ​​obtained in the FEA calculation generation (step S27). Next, the computer increments the variable m by 1 (step S28).

[0028] After completing the process in step S21 or step S28, the computer determines whether the number of iterations of the FEA calculation has reached M (step S29). The constant "M" indicates the number of times the FEA calculation generation will be performed. If it is determined that the number of iterations has not reached M (step S29: NO), the computer returns to step S16; if it is determined that the number of iterations has reached M (step S29: YES), the process ends.

[0029] As explained above, the online method is a method of inserting SM calculation generations between FEA calculation generations. In Figure 1, an FEA calculation generation is performed once every three generations, resulting in a total of 3 × M generations of numerical calculations. By adjusting the cycle of FEA calculation generations, the accuracy of optimization and computation time can be controlled. The advantage of the online method is that it can increase the total number of generations while minimizing computational costs through the surrogate model.

[0030] Figure 5 is a graph showing the relationship between FEA calculation generations and hypervolume. Figure 5B is a magnified view of a portion of the graph shown in Figure 5A. In the graphs shown in Figures 5A and 5B, the vertical axis represents hypervolume, and the horizontal axis represents FEA calculation generations. Hypervolume is one of the indicators that show the progress of the optimization calculation. The dotted line graph shows the change in hypervolume (progress of optimization) in optimization calculations without using a surrogate model. The dashed line shows the results of optimization calculations with a cycle of 10 for the FEA calculation generation, the solid line shows the results with a cycle of 100, and the thick line shows the results with a cycle of 200. Each graph shows how the hypervolume converges to a steady state.

[0031] As can be seen from Figure 5, the hypervolume convergence value reached by the optimization calculation differs depending on the execution cycle (Cycle value) of the FEA calculation generation. Furthermore, the acceleration performance relative to the convergence value differs, and in this example, there is a technical challenge in that the selection of the execution cycle is arbitrary and the optimal execution cycle is not clear.

[0032] The information processing method, information processing apparatus, and computer program according to this embodiment, described below, solve the problems associated with online methods. This embodiment will now be described.

[0033] (Embodiment 1) Figure 6 is a block diagram showing an example configuration of the information processing device 1 according to Embodiment 1. The information processing device 1 is a computer that implements the information processing method according to Embodiment 1, and comprises an arithmetic unit 11, a display unit 12, an operation unit 13, and a storage unit 14. Each unit is connected by a bus. The information processing method according to Embodiment 1 is a method for optimizing design parameters that define a design target object such as a motor using a genetic algorithm such as NSGA-II. Hereinafter, in the genetic algorithm, a model that represents a design target object using design parameters will be called an individual model.

[0034] The information processing device 1 may be a standalone computer or a server connected to a network. Furthermore, the information processing device 1 may be a computer in an on-premises environment or a server or other computer in a cloud environment. The information processing device 1 may be configured with multiple computers for distributed processing, implemented with multiple virtual machines on a single server, or implemented using a cloud server.

[0035] The arithmetic unit 11 is a processor having arithmetic circuits such as a CPU (Central Processing Unit), multi-core CPU, GPU (Graphics Processing Unit), GPGPU (General-purpose computing on graphics processing units), TPU (Tensor Processing Unit), ASIC (Application Specific Integrated Circuit), FPGA (Field-Programmable Gate Array), and NPU (Neural Processing Unit), internal storage devices such as ROM (Read Only Memory) and RAM (Random Access Memory), I / O terminals, a timing unit, etc. The arithmetic unit 11 preferably has a configuration having multiple arithmetic cores. The arithmetic unit 11 implements the information processing method according to this embodiment 1 by executing a computer program (program product) 141 stored in the storage unit 14, which will be described later. Note that each functional unit of the information processing device 1 may be implemented in software, or some or all of them may be implemented in hardware.

[0036] The display unit 12 is, for example, a display device such as a liquid crystal panel or an organic EL (Electro-Luminescence) display.

[0037] The operation unit 13 is, for example, an input device such as a hardware keyboard, a pointing device, or a touch panel. The user of the information processing device 1 can input any information into the information processing device 1 using the operation unit 13. The operation unit 13 may be configured integrally with the display unit 12.

[0038] The memory unit 14 includes, for example, a main memory unit and an auxiliary memory unit. The main memory unit is a temporary storage area such as SRAM (Static Random Access Memory), DRAM (Dynamic Random Access Memory), or flash memory, and temporarily stores data necessary for the arithmetic unit 11 to perform arithmetic processing. The auxiliary memory unit is a storage device such as a hard disk or EEPROM (Electrically Erasable Programmable ROM). The memory unit 14 stores the computer program 141, CAE model 142, and surrogate model 143 executed by the arithmetic unit 11. The surrogate model 143 is created during the optimization process of design parameters related to the object being designed.

[0039] The CAE model 142 includes, for example, a 3D shape model such as 3D CAD data representing the shape of the object to be designed, and material properties of each part constituting the 3D shape model. Specifically, if the object to be designed is a motor, the CAE model 142 includes a 3D shape model such as 3D CAD data representing the shapes of multiple coils, a stator, and a rotor that constitute the motor, and data such as material properties, boundary conditions, and voltage conditions of each part constituting the 3D shape model. Material properties include magnetization properties, electrical properties, and mechanical properties. The various data defining the CAE model 142 include the design parameters to be optimized in this embodiment 1. The design parameters include dimensional parameters and topology parameters. By changing these design parameters, it is possible to generate CAE models 142 with various shapes and properties, i.e., individual models.

[0040] The calculation unit 11 calculates response values ​​related to the characteristics or behavior of the individual model by analyzing the CAE model 142 using a known calculation method (first calculation method) such as the finite element method or the boundary element method. In other words, it simulates the characteristics or behavior of the individual model. For example, the calculation unit 11 performs a magnetic field analysis on the CAE model 142 of a motor. The magnetic field analysis is performed using a known magnetic field analysis simulator such as the finite element method or the boundary element method. The finite element method is a method that divides the rotor and stator of a motor, which have complex shapes and electromagnetic characteristics, into small regions (elements) with simple shapes and electromagnetic characteristics, and predicts the behavior or characteristics of the entire motor by approximately calculating the characteristics of each simplified element. Hereinafter, in this embodiment 1, the calculation process of response values ​​using the CAE model 142 as the individual model will be appropriately referred to as FEA calculation.

[0041] The surrogate model 143 is a machine learning model that outputs response values ​​regarding the characteristics or behavior of an individual model when design parameters defining the individual model of the object being designed are input. The surrogate model 143 includes, for example, a neural network trained by machine learning. The surrogate model 143 has an input layer into which design parameters defining the individual model are input, an intermediate layer, and an output layer that outputs response values ​​regarding the characteristics or behavior of the individual model.

[0042] The calculation unit 11 calculates response values ​​related to the characteristics or behavior of the individual model using a calculation method (second calculation method) that utilizes the surrogate model 143. The calculation of response values ​​using the surrogate model 143 is performed more quickly than the FEA calculation. Hereinafter, in this embodiment 1, the calculation of response values ​​using the surrogate model 143 as the individual model will be referred to as the SM calculation as appropriate.

[0043] The surrogate model 143 is generated by performing machine learning using training data in a computer-based learning device. The training data includes numerous datasets that associate design parameters defining individual models representing the object under design with response values ​​related to the characteristics or behavior of the individual models. The method for creating the surrogate model 143 is as follows. The learning device inputs design parameters that define the individual model, recorded in the training data, into a pre-trained model whose weight coefficients have not yet been adjusted. The pre-trained model outputs a response value corresponding to the input design parameters. The learning device adjusts the parameters of the pre-trained model so that the error between the response value output by the pre-trained model and the response value associated with the input design parameters is minimized. For example, the weight coefficients are adjusted using backpropagation.

[0044] The learning device generates a surrogate model 143 by repeatedly performing the above process using multiple datasets included in the training data and adjusting the weight coefficients of the pre-trained model. The weight coefficients of the surrogate model 143 are stored in the storage unit 14 of the information processing device 1.

[0045] While a neural network was described as an example of surrogate model 143, other models such as SVR (Support Vector Regression), decision trees, and linear regression are also acceptable, and the method used is not restricted.

[0046] The auxiliary storage unit may be an external storage device connected to the information processing device 1. The computer program 141 and surrogate model 143 may be written to the storage unit 14 during the manufacturing stage of the information processing device 1, or the information processing device 1 may acquire them via communication from an external server and store them in the storage unit 14. The computer program 141 and surrogate model 143 may also be recorded in a readable manner on a recording medium 10 such as a magnetic disk, optical disk, or semiconductor memory, and a reader may read them from the recording medium 10 and store them in the storage unit 14.

[0047] <Information Processing Methods> This section explains optimization processing using a genetic algorithm. In motor design using magnetic field analysis, optimization calculations using GA (genetic algorithm) are frequently used. Optimization calculations, for example, calculate motor designs that improve the average torque of the motor and suppress torque ripple and losses. The design parameters of the individual model are, for example, values ​​that characterize the position (e.g., distance from the rotor center to the center of the permanent magnet) and shape (vertical and horizontal dimensions in the case of a rectangular cross-section) of the permanent magnets constituting the motor rotor, and the shape of the flux barrier. The response values ​​calculated by the CAE model 142 and surrogate model 143 of the individual model are, for example, the average torque and the iron loss value in the rotor.

[0048] Figure 7 is a flowchart showing the processing procedure for the optimization calculation in Embodiment 1. The calculation unit 11 in Embodiment 1 repeatedly performs SM calculations after FEA calculations, as described below, and monitors the progress of the design parameter optimization process (specifically, the progress of the hypervolume obtained for each SM calculation generation). When the design parameter optimization process is progressing, the calculation unit 11 repeatedly performs SM calculations and performs FEA calculations when the optimization process stalls, updating the surrogate model 143. By monitoring the progress of the optimization calculations in this way and performing FEA calculations at timely intervals, the design parameter optimization process of the design object can be advanced more efficiently than when FEA calculations are performed periodically.

[0049] <Initial Generation (FEA Calculation Generation)> The calculation unit 11 generates N individual models (initial individuals) of the initial generation (0th generation) (step S111). Specifically, the calculation unit 11 creates N design parameters that define each of the N individual models. Since each individual model is defined by the design parameters, more precisely, the calculation unit 11 generates N sets of design parameters. The design parameters for the initial generation (0th generation) are preferably generated using random numbers. The method for generating the design parameters for the initial individuals is not particularly limited.

[0050] Next, the calculation unit 11 performs FEA calculations on the response values of each individual model based on the design parameters of each generated individual model (step S112). The calculation unit 11 aggregates the design parameters of the initial individuals and the response values of the N initial individuals calculated in the above process to the GA engine (step S113). The GA engine is a calculation module that optimizes the design parameters of the individual model using a genetic algorithm.

[0051] Then, the calculation unit 11 creates a surrogate model 143 using the design parameters of each individual model and the response values calculated in step S112 as training data (step S114).

[0052] Next, the calculation unit 11 substitutes 1 for the variable m (step S115). The variable m is a variable indicating the number of times the FEA calculation generation has been performed since the start of the process. In this embodiment, when the FEA calculation generation is executed M times, the process is terminated. M is a constant. The specific value of M may be set by the user or may be a fixed value.

[0053] Also, the calculation unit 11 sets the initial value of the FEA generation flag to false (step S116). The FEA generation flag is a flag indicating whether the next generation is the FEA calculation generation (true) or the SM calculation generation (false). The value of the FEA generation flag is determined by the FEA generation transition determination process described later.

[0054] After finishing the process of step S115, the calculation unit 11 determines the true or false of the FEA generation flag (step S117).

[0055] <SM calculation generation> If the FEA generation flag is false, that is, if it is determined that the next generation will be the SM calculation generation (step S117: false), the calculation unit 11 generates N individuals (offspring individuals) in the current generation (step S118). Specifically, the calculation unit 11 generates N new individual models for the current generation through genetic processing such as crossover and mutation, based on the design parameters of the N individual models inherited from the previous generation. Crossover is an operation that generates an individual model with new design parameters by combining the design parameters of multiple individual models inherited from the previous generation. Mutation is an operation that generates an individual model with new design parameters by randomly changing some of the design parameters of multiple individual models inherited from the previous generation. The calculation unit 11 may generate new individual models by both crossover and mutation operations.

[0056] Next, the calculation unit 11 performs SM calculation on the response values ​​of the N individual models (child models) generated in step S118 using the surrogate model 143 (step S119). Then, the calculation unit 11 aggregates the generated N design parameters and the response values ​​of the individual models into the GA engine (step S120). The response values ​​of the N individual models inherited from the previous generation have already been calculated and are used as is.

[0057] Then, the calculation unit 11 ranks the 2N individual models based on their response values ​​(step S121) and selects the top-ranked N individual models (step S122). For example, the arithmetic unit 11 classifies the 2N individual models into groups or individuals in order from those closest to the Pareto front using a non-superiority sort in the NSGA-II algorithm, and assigns a rank to each classified group or individual.

[0058] The Pareto front is a curve or surface formed by a set of non-dominated solutions (Pareto solutions) in a multi-objective optimization problem, where no response value can be further improved. When optimizing multiple objectives simultaneously, there is no single best solution because choosing one solution will deteriorate other objectives. For example, increasing the average torque of a motor and reducing torque ripple and losses are in a trade-off relationship. Therefore, multiple solutions (Pareto solutions) that are non-dominated with respect to each other, where improving any one response value will deteriorate other response values, can be obtained. Plotting these Pareto solutions in the objective space and connecting them continuously forms the Pareto front.

[0059] The smaller the population or individual rank number, the higher the rank (higher evaluation), that is, the closer the population or individual is to the Pareto front. As the rank number increases, the rank becomes lower (lower evaluation). For example, when performing a motor design to improve the average torque of a motor as the design object and suppress torque ripple and losses, the larger the average torque and the smaller the torque ripple and losses, the closer it is to the Pareto front and the smaller the rank number. Note that there may be multiple individuals belonging to a certain rank number, or there may be only one. Also, the number of individuals belonging to each rank varies depending on the rank. Among the 2N individual models, the N individual models that are far from the Pareto front and have large rank numbers are eliminated, and the N individual models that are close to the Pareto front and have small rank numbers are carried over to the next generation. When selecting individuals in order from those with small rank numbers, if the number of selected individuals exceeds N, by performing congestion sorting, some individuals with high congestion are selected so that the number of selected individuals becomes N.

[0060] After finishing the processing of step S122, the arithmetic unit 11 executes FEA generation transition determination processing (step S123). The details of the FEA generation transition determination processing will be described later.

[0061] <FEA calculation generation> If the FEA generation flag is true, that is, if it is determined that the next generation will be the FEA calculation generation (step S117: true), the calculation unit 11 generates N individuals in the current generation (step S124). Then, the calculation unit 11 performs FEA calculation on the response values ​​of the N individual models (child individuals) generated in step S124 using the CAE model 142 (step S125), and aggregates the generated N design parameters and the response values ​​of the individual models into the GA engine (step S126).

[0062] Then, the calculation unit 11 ranks the 2N individual models based on their response values ​​(step S127) and selects the top-ranked N individual models (step S128).

[0063] Next, the calculation unit 11 uses the design parameters of the N individual models (child individuals) generated in step S124 and the response values ​​calculated in step S125 as training data to retrain the surrogate model 143 (step S129). Then, the calculation unit 11 increments the variable m by 1 and sets the FEA generation flag to false (step S130).

[0064] After completing the processing in step S123 or step S130, the calculation unit 11 determines whether the number of times the FEA calculation has been performed is M (step S131). If it determines that the number of times the FEA calculation has been performed has reached M (step S131: YES), the calculation unit 11 terminates processing. If it determines that the number of times the FEA calculation has been performed has not reached M (step S131: NO), the calculation unit 11 returns to step S117.

[0065] Figure 8 is a flowchart showing the FEA generation transition determination process procedure according to Embodiment 1. In the FEA generation transition determination process, the calculation unit 11 initializes the FEA generation flag to "false" (step S151). Then, the calculation unit 11 calculates the hypervolume (HV_FEA) for the most recent FEA calculation generation (step S152). The calculation unit 11 also calculates the hypervolume (HV_SM) for the SM calculation generations after the most recent FEA calculation generation (step S153). Specifically, the calculation unit 11 adds the solution distribution of individuals calculated in the SM calculation generations (referred to as generation i) after the most recent FEA calculation generation to the solution distribution that constitutes the Pareto front of the most recent FEA calculation generation to create a Pareto front and calculate the hypervolume. The hypervolume is appropriately denoted as HV(i). "(i)" means the generation number of the subsequent SM calculation generations, with the most recent FEA calculation generation as the base (0).

[0066] Figure 9 is a conceptual diagram showing the hypervolume when there are two objective functions, and Figure 10 is a conceptual diagram showing the method for determining reference points for calculating the hypervolume. The vertical and horizontal axes of the graphs in Figures 9 and 10 represent response values ​​1 and 2. Response values ​​1 and 2 are, for example, average torque and torque ripple. The black circles plot the solution distribution calculated in a given generation, i.e., the calculated response values. The curve represents the Pareto front, and the white circles represent the reference points for calculating the hypervolume. The region enclosed by these reference points and the Pareto front (hatched region) is the hypervolume. Figure 9 shows the hypervolume in two dimensions, but generally, the hypervolume is the area or volume (hypervolume) of the region enclosed by a specific reference point and the Pareto front in a multidimensional space. If the hypervolume increases as the generations of the genetic algorithm progress, it can be evaluated that the optimization of the setting parameters is progressing.

[0067] The hypervolume will have different values ​​depending on how the reference points are chosen. It is desirable to update the reference points with each FEA calculation generation so that they accurately represent the progress of the optimization process. For example, as shown in Figure 10, the calculation unit 11 can determine the width based on the maximum and minimum values ​​of the Pareto solution, and then determine the reference points by considering a margin of twice that width. There are no particular limitations on how the margin is determined.

[0068] In other words, the calculation unit 11 determines a reference point that is located beyond the width (distribution range) of the solution distribution, on the non-optimized side of the response value, relative to the Pareto front related to the solution distribution obtained by the most recent FEA calculation. For example, the reference point can be a coordinate position located 2 to 3 times the width (distribution range) of the solution distribution, relative to the Pareto front.

[0069] More specifically, the calculation unit 11 identifies the maximum value of the first response value (for example, the average torque) (the far right of the Pareto front in Figure 10). The calculation unit 11 subtracts α times the width of the solution distribution in the direction of the first response value from the optimal value and uses this value as the X-coordinate value of the reference point (the value in the axis direction of the first response value). Similarly, the calculation unit 11 identifies the minimum value of the second response value (e.g., torque ripple) (the lowest point of the Pareto front in Figure 10). The calculation unit 11 adds α times the width of the solution distribution in the direction of the second response value to the optimal value and uses this value as the Y coordinate value of the reference point (the value in the direction of the second response value).

[0070] Following step S153, the arithmetic unit 11 compares the hypervolume of the most recent FEA calculation generation (HV_FEA) with the hypervolume of subsequent SM calculation generations (HV_SM) to determine whether the increase in the hypervolume of the SM calculation generation has stagnated. If it is determined that it has stagnated, it sets the FEA generation flag to true (step S154) and returns that value (true) as the return value. If it is determined that it has not stagnated, the FEA generation flag remains false, as initialized in step S151, and the arithmetic unit 11 returns that value (false) as the return value. The specific method for determining stagnation will now be explained.

[0071] Figure 11 is a conceptual diagram showing a method for determining stagnation in the optimization process. The asterisks indicate the hypervolume of the FEA calculation generation, i.e., the hypervolume calculated in step S152. The black circles indicate the hypervolume of the SM generation, i.e., the hypervolume calculated in step S153. If the calculation unit 11 does not find an improvement of HV_FEA×T(%) in the hypervolume HV(i) calculated in step S153 within P surrogate model generations, it stops continuing the SM generation and executes the next generation as the FEA calculation generation. In other words, the calculation unit 11 sets the FEA generation flag to "true".

[0072] By changing the truth value of the FEA generation flag in this way, it is possible to execute FEA calculation generations at the appropriate timing and advance the optimization calculation.

[0073] Figure 12 is a graph showing the change in hypervolume due to GA optimization according to this embodiment 1. In the graph shown in Figure 12, the vertical axis represents hypervolume and the horizontal axis represents the generation. In Figure 12, the X marks indicate FEA calculation generations, and the curve portion without X marks indicates SM calculation generations. It can be seen that the FEA calculation generation is performed when the change in hypervolume becomes small and flat. In the FEA calculation generation, the surrogate model 143 is updated, the hypervolume increases again, and it can be seen that the stagnation state of the optimization process can be overcome. By monitoring the progress of the optimization process and performing FEA calculation generations at the appropriate timing, the optimization of design parameters can be advanced efficiently.

[0074] According to the information processing method, etc., of Embodiment 1 configured in this way, the Pareto front can be advanced further with the same number of FEA calculations as the conventional optimization calculation method. However, although the surrogate model 143 is inserted during the FEA calculation, the SM calculation time is extremely small, so the overhead is small. Furthermore, this effect can be obtained with a more appropriate number of surrogate model 143 insertions compared to when the FEA calculation period is fixed.

[0075] In other words, the calculation unit 11 monitors the progress of the design parameter optimization process and, when a stagnation in the optimization process is detected, performs an FEA calculation to update the surrogate model 143, thereby advancing the optimization process.

[0076] Figure 13 is a graph comparing the hypervolume progression according to Embodiment 1 with the hypervolume progression resulting from GA optimization using FEA calculation generations at regular intervals. Figure 13 is a graph similar to Figure 5B, with the addition of a graph showing the optimization calculation results of this embodiment. Figure 13 includes three additional graphs with T(%) values ​​of 1%, 0.5%, and 0.1% for evaluating the hypervolume growth rate. In all graphs, it is clear that a larger hypervolume is reached more quickly. In other words, it can be seen that the optimization calculation is performed more effectively compared to when FEA calculation generations are performed at regular intervals.

[0077] Furthermore, by updating the reference point for calculating hypervolume with each FEA calculation generation, it is possible to more accurately determine whether the optimization process of design parameters is progressing or stagnating.

[0078] In this embodiment 1, a motor was described as the simulation target and magnetic field analysis was described as the simulation method using CAE model 142. However, the simulation target and simulation content are not particularly limited. For example, the information processing method according to this embodiment can be applied to the optimization of the magnetic circuit of a solenoid valve or the magnetic circuit of a plastic magnet. Furthermore, the simulation method may be thermal analysis, electric field analysis, structural analysis, fluid analysis, etc., or it may be an analysis process that combines multiple analysis processes, such as magnetic field analysis and structural analysis.

[0079] Furthermore, while examples of the first computation method include FEA calculation using CAE model 142 and an example of the second computation method include calculation using machine learning model surrogate model 143, the content of the first and second computation methods is not particularly limited. As long as the computational precision of the second computation method is lower than that of the first computation method, and the computational speed of the second computation method is faster than that of the first computation method, the content of the first and second computation methods is not particularly limited. For example, any model such as CAE model 142, SVR (Support Vector Regression), decision tree, linear regression, or neural network can be used as the first and second computation methods.

[0080] (Variation 1) The calculation unit 11 may be configured to normalize the response values ​​of each individual model in the most recent generation when performing the FEA generation determination process. For example, the calculation unit 11 converts the range of possible numerical values ​​for the response values ​​to a predetermined range, such as 0 to 1.0. The reason for normalizing the response values ​​is as follows.

[0081] For example, if the first response value (objective function 1) is 1.0e -2 The order of magnitude is such that the second response value 2 (objective function 2) is 1.0e +3 In the case of this order of magnitude, there will be an absolute difference of about five orders of magnitude between the two. In this case, as will be described later, when evaluating the progress of the optimization process using hypervolume, there is a possibility of overlooking a slight Pareto progression in the first response value. For this reason, the calculation unit 11 normalizes all response values ​​so that they have the same numerical range. By normalizing the response values, it is possible to more accurately determine the progress or stagnation of the response values.

[0082] Depending on the content and numerical range of the response values ​​of the individual model, it may be possible to configure the system to monitor changes in hypervolume without performing normalization.

[0083] (Modification 2) The calculation unit 11 may be configured to calculate a low-dimensional hypervolume when calculating the hypervolume in the FEA generation determination process.

[0084] When there are two or three response values, the hypervolume is the area in two-dimensional space or the volume in three-dimensional space, and the computational load is small. However, when there are many response values ​​in the optimization process, the hypervolume becomes a high-dimensional hypervolume, and the computational load is large. Therefore, the calculation unit 11 may evaluate the hypervolume in a simplified manner as follows. For example, when the number of response values ​​is 4 or more, the hypervolume needs to be calculated, and the computational load of the hypervolume becomes large. Therefore, when the number of response values ​​defining the individual model is 4 or more, a combination of two response values ​​selected from the 4 or more response values ​​is set. When the number of response values ​​increases further to 6, it becomes necessary to calculate a 6-dimensional hypervolume, which significantly increases the computational load of the hypervolume calculation. With 6 response values, 6C2 = 6 × 5 ÷ 2 = 15 combinations of response values ​​are obtained. The calculation unit 11 calculates a 2-dimensional hypervolume for each of these combinations of response values.

[0085] By reducing the dimensionality of the hypervolume, the monitoring burden of the design parameter optimization process can be reduced.

[0086] In the above explanation, we described an example of calculating hypervolume for all combinations of two response values ​​selected from multiple response values. However, it is not necessary to calculate hypervolume for all combinations; the system may be configured to calculate hypervolume for any subset of combinations.

[0087] Furthermore, while we have explained an example of calculating the hypervolume for a combination of two response values ​​selected from multiple response values, it is also possible to calculate the hypervolume for a combination of three response values. If there are three, the hypervolume will be a three-dimensional volume, so the computational load will be small.

[0088] (Embodiment 2) The information processing device 1 according to Embodiment 2 differs from that of Embodiment 1 in its FEA generation transition determination process. The other configurations and processes of the information processing device 1 are the same as those of the information processing device 1 according to Embodiment 1, so the same reference numerals are used for the same parts, and detailed explanations are omitted. The information processing device 1 according to Embodiment 2 efficiently optimizes design parameters by monitoring the distribution of the solution ensemble, which is a set of response values, and performing FEA calculation generations in accordance with the movement of the centroid (statistic) of the solution ensemble.

[0089] Figure 14 is a flowchart showing the FEA generation transition determination process procedure according to Embodiment 2. In the FEA generation transition determination process, the calculation unit 11 initializes the FEA generation flag to "false" (step S251). The calculation unit 11 then calculates the centroid of the solution group (G_FEA) in the most recent FEA calculation generation (step S252). The calculation unit 11 also calculates the centroid of the solution group (G_SM) in the SM calculation generations after the FEA calculation generation (step S253). Specifically, the calculation unit 11 adds the solution group of individuals calculated in the SM calculation generations (let's call them generation i) after the most recent FEA calculation generation to the solution group of the most recent FEA calculation generation and calculates the centroid of that solution group.

[0090] The arithmetic unit 11 then compares the centroid of the solution group of the most recent FEA calculation generation (G_FEA) with the centroid of the solution group of subsequent SM calculation generations (G_SM) to determine whether the centroid of the solution group of the SM calculation generation has stagnated. If it is determined that it has stagnated, it sets the FEA generation flag to true (step S254) and returns its value (true) as the return value. If it is determined that it has not stagnated, the FEA generation flag remains false, as initialized in step S251, and the arithmetic unit 11 returns its value (false) as the return value. For example, the calculation unit 11 determines whether there is stagnation by determining whether the distance between centroids is less than a predetermined distance over P generations. The centroid of the solution group or the distance between centroids is an example of an optimization progress index that shows the progress of the optimization of the design parameters. The distance between centroids is, for example, the statistical distance between the centroid of the solution group of the 0th generation or the most recent FEA calculation generation and the centroid of the solution group of the current generation. The method for calculating the distance between centroids is just one example, and is not particularly limited as long as it is a distance that can represent the progress of the optimization of the design parameters.

[0091] Figure 15 is a conceptual diagram showing the generational change in the centroid's position when the distribution of the solution ensemble progresses towards better solutions. The asterisks in Figure 15 indicate the centroid of the solution ensemble of response values. Figure 15 shows the progression of the scatter plot of solutions when a surrogate model 143, updated by adding the FEA results created in a certain FEA calculation generation to the training data, functions effectively in subsequent surrogate model generations.

[0092] Here, we assume that a multi-objective optimization process is being performed to maximize the first response value (Obj.1) and minimize the second response value (Obj.2). In Figure 15, the upper left figure shows the solution distribution of the response values ​​for the Kth generation, which is the FEA calculation generation. The horizontal axis represents the first response value, and the vertical axis represents the second response value. The other scatter plots show the solution distribution of the response values ​​in the SM calculation generations (K+1, K+2, ~K+5) that follow the FEA calculation generation. If the surrogate model 143 is functioning effectively, the centroid of the solution set of response values ​​shifts towards better solutions as the generations progress (K+1, K+2, ... K+5).

[0093] Figure 16 is a conceptual diagram showing the generational change in the centroid's position when the distribution of the solution population is stagnant. Figure 16 shows the progression of the scatter plot of solutions when a surrogate model 143, updated after a certain FEA calculation generation, ceases to function effectively in subsequent surrogate model generations. Similar to Figure 15, the upper left figure represents the Kth generation, which is the FEA calculation generation, and shows the solution distribution of the response values. The horizontal axis represents the first response value, and the vertical axis represents the second response value. The other scatter plots show the solution distribution of response values ​​in the SM calculation generations (K+1, K+2, ~K+5) following the FEA calculation generation.

[0094] There are two possible reasons why surrogate model 143 ceases to function as a model. The first reason is that, as shown in Figure 15, after several generations using the surrogate model 143 (for example, the K+5th generation), the optimization of the design parameters has progressed sufficiently, and the surrogate model 143 can no longer function adequately, resulting in no change in the solution distribution even if generations are advanced. Since optimization will not progress by continuing to use this surrogate model 143, it is necessary to update the surrogate model 143 by calculating the next generation as an FEA calculation generation. In such cases, the centroid of the solution ensemble remains in almost the same location. The second reason is that the updated surrogate model 143 has poor prediction accuracy and outputs almost the same response value regardless of the input variable. Figure 16 illustrates this situation, showing that the accuracy of the surrogate model 143 in Obj.1 has deteriorated, and it is now only returning values ​​between 20 and 30. Since such a surrogate model 143 does not function as a model, it is necessary to update the surrogate model 143 by calculating the next generation as an FEA calculation generation.

[0095] According to the information processing method of Embodiment 2 configured as described above, the calculation unit 11 monitors the change in the centroid position of the solution distribution obtained in the SM calculation model generation after the FEA calculation generation, and determines the timing of the FEA calculation generation. That is, the calculation unit 11 calculates the distance between centroids for each generation, starting from the centroid position of the solution distribution obtained as a result of the FEA calculation generation, and when the distance between centroids falls below a certain value over P generations, it determines that the solution distribution has stagnated, and the next generation executes the FEA calculation generation. Therefore, by monitoring the distribution of the solution ensemble, which is a set of response values, and performing FEA calculation generations in accordance with the movement of the centroid of the solution ensemble, the optimization of design parameters can be efficiently advanced. Thus, the computation time required for optimizing the design parameters of the object under design can be reduced.

[0096] In Embodiment 2, when calculating the centroid of the solution ensemble related to the response values ​​in each generation, the response values ​​may be normalized, and the centroid of the solution ensemble related to the normalized response values ​​may be calculated.

[0097] (Embodiment 3) The information processing device 1 according to Embodiment 3 differs from that of Embodiment 1 in its FEA generation transition determination process. The other configurations and processes of the information processing device 1 are the same as those of the information processing device 1 according to Embodiment 1, so the same reference numerals are used for the same parts, and detailed explanations are omitted. The information processing device 1 according to Embodiment 3 monitors the distribution of a set of design parameters of individual models for each generation (hereinafter referred to as the design parameter set), and efficiently advances design parameter optimization by performing FEA calculation generations in accordance with the movement of the centroid (statistic) of the design parameter set.

[0098] The information processing method according to Embodiment 3 replaces the solution distribution (distribution of response values) according to Embodiment 2 with the distribution of design parameters. That is, if the optimization progress stagnates in the SM calculation generation that follows the FEA calculation generation (i.e., the solution distribution stagnates), then it is assumed that the progress of the design parameter group calculated by the optimization engine toward a good solution also stagnates. The calculation unit 11 then calculates the distance between the centroids of the design parameters of the subsequent SM calculation generation and the centroids of the design parameters of the FEA calculation generation, starting from the centroid position of the design parameters of the FEA calculation generation. When the distance between the centroids falls below a certain value over P generations, it determines that the design parameters have stagnated, and the next generation will execute the FEA calculation generation.

[0099] Figure 17 is a flowchart showing the FEA generation transition determination process procedure according to Embodiment 3. In the FEA generation transition determination process, the calculation unit 11 initializes the FEA generation flag to "false" (step S351). The calculation unit 11 then calculates the centroid (G_FEA) of the design parameter set in the most recent FEA calculation generation (step S352). The calculation unit 11 also calculates the centroid (G_SM) of the design parameter set in the SM calculation generations after the FEA calculation generation (step S353). Specifically, the calculation unit 11 adds the design parameter set of individuals calculated in the SM calculation generations (let's call it generation i) after the most recent FEA calculation generation to the design parameter set of the most recent FEA calculation generation and calculates the centroid of that design parameter set.

[0100] The calculation unit 11 then compares the centroid of the design parameter set of the most recent FEA calculation generation (G_FEA) with the centroid of the design parameter set of the SM calculation generation after the FEA calculation (G_SM) to determine whether the centroid of the design parameter set of the SM calculation generation has stagnated. If it is determined that it has stagnated, it sets the FEA generation flag to true (step S354) and returns its value (true) as the return value. If it is determined that it has not stagnated, the FEA generation flag remains false, as initialized in step S351, and the calculation unit 11 returns its value (false) as the return value. For example, the calculation unit 11 determines whether there is stagnation by determining whether the distance between the centroids of the design parameter set is less than a predetermined distance over P generations. The centroid of the solution set or the distance between centroids is an example of an optimization progress index that shows the progress of the optimization of the design parameters. The distance between centroids is, for example, the statistical distance between the centroid of the design parameter set of the 0th generation or the most recent FEA calculation generation and the centroid of the design parameter set of the current generation. The method for calculating the distance between centroids is just one example, and is not particularly limited as long as it is a distance that can represent the progress of the optimization of the design parameters.

[0101] When the optimization process stalls, the distance between the centroids of the set parameters stops changing significantly. In this case, the surrogate model 143 is no longer functioning effectively as a model, so the calculation unit 11 performs an FEA calculation generation to update the surrogate model 143. By updating the surrogate model 143, the distance between the centroids of the design parameters begins to change again. In other words, the optimization process begins to progress.

[0102] According to the information processing method, etc., of Embodiment 3 configured in this manner, the distribution of the design parameter set, which is a collection of design parameters, is monitored, and FEA calculation generations are performed in accordance with the movement of the centroid of the design parameter set, thereby enabling efficient optimization of the design parameters. As a result, the computation time required for optimizing the design parameters of the object to be designed can be reduced.

[0103] In Embodiment 3, when calculating the centroid of the solution set relating to the design parameters in each generation, the design parameters may be normalized, and the centroid of the solution set relating to the normalized design parameters may be calculated. Since the design parameters can be current phase, current value, voltage value, and other numerical values ​​of various dimensions, normalizing them allows for a more accurate evaluation of the shift in the centroid position of the set of design parameters.

[0104] By normalizing the design parameters, it becomes possible to more accurately determine when the optimization process for those parameters has stalled, and to proceed with the optimization of the design parameters more efficiently.

[0105] (Embodiment 4) The information processing device 1 according to Embodiment 4 differs from that of Embodiment 1 in that it controls the number of SM calculation generations performed according to the accuracy of the surrogate model 143. The other configurations and processes of the information processing device 1 are the same as those of the information processing device 1 according to Embodiment 1, so the same reference numerals are used for the same parts, and detailed explanations are omitted.

[0106] When the surrogate model 143 is generated, a correlation between the ground truth and the predicted value is obtained. The response value calculated by the FEA calculation is the ground truth, and the response value calculated by the surrogate model 143 is the predicted value. The calculation unit 11 can calculate the coefficient of determination (COD), which indicates the magnitude of the correlation between the ground truth and the predicted value. The coefficient of determination generally has a value between 0.0 and 1.0. The closer the coefficient of determination is to 1, the higher the prediction accuracy of the surrogate model 143. A coefficient of determination of 1 means that the predicted value by the surrogate model 143 is equal to the ground truth.

[0107] The more training data available for creating the surrogate model 143, the more accurate the surrogate model 143 can be generated, and the closer the coefficient of determination becomes to 1.0. In the method of this embodiment, as the number of FEA calculation generations increases, the amount of training data available for creating the surrogate model 143 increases, so the coefficient of determination approaches 1.0.

[0108] In the information processing method according to Embodiment 4, the coefficient of determination is used to control the number of SM calculation generations performed after the FEA calculation generation. Specifically, when the surrogate model 143 is updated in the FEA calculation generation, the arithmetic unit 11 calculates the coefficient of determination based on the response value calculated by FEA and the response value calculated by SM using the updated surrogate model 143. The arithmetic unit 11 then determines the number of SM calculation generations to be performed according to the coefficient of determination. The closer the coefficient of determination is to 1, the greater the number of SM calculation generations performed by the arithmetic unit 11.

[0109] There are multiple types of response values, which are the objective function, and the coefficient of determination is calculated for each type of response value. For example, if the response values ​​include average torque, torque ripple, and loss, the calculation unit 11 calculates the coefficient of determination for average torque, torque ripple, and loss. Based on the value of each coefficient of determination, the calculation unit 11 determines the number of SM calculation generations to be performed. The closer each coefficient of determination is to 1, the more SM calculation generations the calculation unit 11 will perform.

[0110] Hereinafter, S is the variable indicating the number of SM calculation generations performed, X is the threshold for determining the magnitude of the coefficient of determination, P is the number of SM calculation generations performed when the coefficient of determination is greater than X, and Q is the number of SM calculation generations performed when the coefficient of determination is less than or equal to X. The values ​​of variables X, P, and Q are, for example, X=0.95, P=1000, and Q=50. Variable X is a value close to 1. Variable P is a value greater than variable Q. The values ​​of variables X, P, and Q are specified by the user. Specifically, the calculation unit 11 may receive the values ​​of variables X, P, and Q at the operation unit 13.

[0111] Figure 18 is a flowchart showing the processing procedure for the optimization calculation in Embodiment 4. The calculation unit 11 performs the same processing as steps S111 to S114 related to the generation of initial individuals and the creation of the surrogate model 143 (steps S411 to S414). Next, the calculation unit 11 sets the number of SM calculation generations S to be Q (step S415). The number Q is, for example, 50 times.

[0112] The calculation unit 11 assigns 1 to the variable m (step S416). The variable m is a variable that indicates the number of times the FEA calculation generation has been calculated since the start of processing.

[0113] Next, the arithmetic unit 11 executes the SM calculation generation process S times (steps S417 to S421). This process is the same as steps S118 to S122 in Embodiment 1.

[0114] The arithmetic unit 11, which has performed the SM calculation generation S times, executes processing related to the FEA calculation generation (steps S422 to S427). This processing is the same as steps S124 to S129 of Embodiment 1.

[0115] Next, the calculation unit 11 determines the number of times S to perform the next SM calculation generation (step S428). Figure 19 is a flowchart showing the processing procedure for determining the number of SM calculation generations. The calculation unit 11 sets the number of SM calculation generations S to Q (step S451). Next, it calculates the coefficient of determination based on the response value calculated by FEA and the response value calculated by SM using the updated surrogate model 143 (step S452). The calculation unit 11 calculates the coefficient of determination for each type of response value.

[0116] If the coefficient of determination of all objective functions, which are response values, exceeds X, the calculation unit 11 sets the number of SM calculation generation runs S to P (step S453) and ends the process related to determining the number of SM calculation generation runs. The number P is, for example, 1000 times.

[0117] Figure 19 shows an example where the number of SM calculation generation runs S is a step function that changes discontinuously with respect to the number of decisions at X. However, the calculation unit 11 may be configured to continuously change the number of SM calculation generation runs S according to the coefficient of determination. The number of SM calculation generation runs S is an increasing function with respect to the coefficient of determination. For example, the number of SM calculation generation runs S may be a sigmoid function with respect to the coefficient of determination.

[0118] Through the above process, the arithmetic unit 11 determines that if the coefficient of determination of all objective functions, which are response values, exceeds X, then the P generation becomes the SM calculation generation, and if the coefficient of determination is less than or equal to X, then the Q generation becomes the SM calculation generation.

[0119] After completing step S428, which determines the number of SM calculation generations to be performed, the arithmetic unit 11 increments the variable m by 1 (step S429) and determines whether the number of FEA calculations has been performed M times (step S430). If it is determined that the number of FEA calculations has reached M times (step S430: YES), the arithmetic unit 11 finishes processing. If it is determined that the number of FEA calculations has not reached M times (step S430: NO), the arithmetic unit 11 proceeds to processing S SM calculation generations.

[0120] According to the information processing method, etc., of Embodiment 4 configured in this way, the design parameter optimization can be efficiently advanced by checking the accuracy of the surrogate model 143 and controlling the number of SM calculation generations. Therefore, the computation time required for optimizing the design parameters of the object to be designed can be shortened.

[0121] Furthermore, this fourth embodiment can be combined with any one of embodiments 1 to 3. For example, the calculation unit 11 executes SM calculation generations only for the P generation or Q generation using the method according to this fourth embodiment, and then executes one of the FEA generation transition determination processes from embodiments 1 to 3 in subsequent SM calculation generations. By configuring it in this way, the FEA generation transition determination process can be reduced.

[0122] The embodiments disclosed herein should be considered in all respects to be illustrative and not restrictive. The technical features described in each embodiment can be combined with each other, and the scope of the present invention is intended to include all modifications within the claims and equivalents thereof. The sequences shown in each embodiment are not limiting, and within the bounds of consistency, the order of each processing step may be changed, and multiple processes may be executed in parallel. The processing entity for each process is not limiting, and within the bounds of consistency, the processing of each device may be executed by other devices.

[0123] The matters described in each embodiment can be combined with each other. Furthermore, the independent and dependent claims described in the claims can be combined with each other in any combination, regardless of the form of reference. In addition, the claims use a form in which claims referencing two or more other claims (multi-claim form), but are not limited to this. A form in which multi-claims referencing at least one multi-claim (multi-multi-claim) may also be used. [Explanation of Symbols]

[0124] 1: Information Processing Device 10: Recording media 11: Arithmetic section 12:Display section 13:Operation section 14: Storage section 141: Computer Programs 142: CAE Model 143: Surrogate Model

Claims

1. An information processing method in which a computer optimizes design parameters that define an individual model representing an object to be designed, using a genetic algorithm, The aforementioned computer, By performing genetic processing based on a predetermined number of individual model design parameters inherited from the previous generation, multiple new individual models for the current generation are generated. From the second generation onward, the response values ​​of multiple individual models newly generated in the current generation are calculated using either the first calculation method or a second calculation method which has a faster calculation speed than the first calculation method. A predetermined number of individual models inherited from the previous generation and several newly generated individual models are ranked based on the calculated response values. Based on the ranking results, a predetermined number of top-ranked individual models will be selected to be passed on to the next generation. Execute the process, Furthermore, the aforementioned computer, When calculating the response values ​​of individual models using the second calculation method, an optimization progress index is calculated that shows the progress of the optimization of the design parameters. Based on the change in the optimization progress index with respect to generational progression, it is determined whether or not the optimization of design parameters has stalled. If optimization is deemed to be stalled, the response value of the individual model is calculated using the first calculation method. Information processing methods.

2. The aforementioned computer, In the generation following the generation in which the response values ​​of the individual model were calculated using the first calculation method, the response values ​​of the individual model are calculated using the second calculation method. The response values ​​of the individual model are calculated using the second calculation method until it is determined that the optimization of the design parameters has stalled. The information processing method according to claim 1.

3. The aforementioned optimization progress indicator is, Includes hypervolume based on response value calculated by the second calculation method. The information processing method according to claim 1.

4. The aforementioned computer, Hypervolume is calculated based on two or three response values ​​selected from multiple response values. The information processing method according to claim 3.

5. The aforementioned computer, Hypervolume is calculated based on multiple pairs of response values. If the hypervolume growth rate calculated for each of the multiple combinations is below a predetermined value, it is determined that the optimization of the response value has stalled. The information processing method according to claim 3.

6. The aforementioned computer, The distribution range of the Pareto front is identified based on the response values ​​of the most recent generation calculated using the first calculation method. From the Pareto front, a point separated from the response value beyond the width of the distribution range is determined as a reference point, Based on the determined reference point and the response value calculated using the second calculation method, the hypervolume for each generation is calculated. The information processing method according to claim 3.

7. The aforementioned computer, The response value calculated using the first or second calculation method is normalized. Calculate hypervolume based on normalized response values. The information processing method according to claim 3.

8. The aforementioned optimization progress indicator is, Includes statistics on the distribution of response values ​​of multiple individual models calculated using the second calculation method. The information processing method according to claim 1.

9. The optimization progress indicator is, Includes statistics on the distribution of normalized response values ​​of multiple individual models calculated using the second calculation method. The information processing method according to claim 1.

10. The aforementioned optimization progress indicator is, Includes statistics on the distribution of design parameters of the individual models that make up each generation. The information processing method according to claim 1.

11. The aforementioned optimization progress indicator is, Includes statistics on the distribution of normalized design parameters of the individual models that make up each generation. The information processing method according to claim 1.

12. The first calculation method is a method for calculating response values ​​using CAE analysis including the finite element method. The second computation method is a method that uses a machine learning model to calculate the response value. The information processing method according to claim 1.

13. The aforementioned computer, When the response values ​​of individual models are calculated using the first calculation method, the machine learning model is retrained using the design parameters of multiple individual models and the response values ​​of multiple individual models calculated using the first calculation method as training data. The information processing method according to claim 12.

14. An information processing method in which a computer optimizes design parameters that define an individual model representing an object to be designed, using a genetic algorithm, The aforementioned computer, By performing genetic processing based on a predetermined number of individual model design parameters inherited from the previous generation, multiple new individual models for the current generation are generated. From the second generation onward, the response values ​​of multiple individual models newly generated in the current generation are calculated using either the first calculation method or a second calculation method which has a faster calculation speed than the first calculation method. A predetermined number of individual models inherited from the previous generation and several newly generated individual models are ranked based on the calculated response values. Based on the ranking results, a predetermined number of top-ranked individual models will be selected to be passed on to the next generation. Execute the process, The first calculation method is a method for calculating response values ​​using CAE analysis including the finite element method. The second calculation method is a method that calculates response values ​​using a machine learning model. Furthermore, the aforementioned computer, When the response values ​​of the individual models are calculated using the first calculation method, the machine learning model is retrained using the design parameters of multiple individual models and the response values ​​of multiple individual models calculated using the first calculation method as training data. The coefficient of determination, which shows the correlation between the response value calculated using the first calculation method and the response value calculated using the second calculation method, is calculated. Based on the calculated coefficient of determination, the number of generations for calculating the response values ​​of the individual model in the second calculation method is changed. Information processing methods.

15. An information processing device comprising a calculation unit that performs a process to optimize design parameters that define an individual model representing an object to be designed, using a genetic algorithm, The aforementioned arithmetic unit, By performing genetic processing based on a predetermined number of individual model design parameters inherited from the previous generation, multiple new individual models for the current generation are generated. From the second generation onward, the response values ​​of multiple individual models newly generated in the current generation are calculated using either the first calculation method or a second calculation method which has a faster calculation speed than the first calculation method. A predetermined number of individual models inherited from the previous generation and several newly generated individual models are ranked based on the calculated response values. Based on the ranking results, a predetermined number of top-ranked individual models are selected to be passed on to the next generation. Furthermore, the calculation unit, When calculating the response values ​​of individual models using the second calculation method, an optimization progress index is calculated that shows the progress of the optimization of the design parameters. Based on the change in the optimization progress index with respect to generational progression, it is determined whether or not the optimization of design parameters has stalled. If optimization is deemed to be stalled, the response value of the individual model is calculated using the first calculation method. Information processing device.

16. An information processing device comprising a calculation unit that performs a process to optimize design parameters that define an individual model representing an object to be designed, using a genetic algorithm, The aforementioned arithmetic unit, By performing genetic processing based on a predetermined number of individual model design parameters inherited from the previous generation, multiple new individual models for the current generation are generated. From the second generation onward, the response values ​​of multiple individual models newly generated in the current generation are calculated using either the first calculation method or a second calculation method which has a faster calculation speed than the first calculation method. A predetermined number of individual models inherited from the previous generation and several newly generated individual models are ranked based on the calculated response values. Based on the ranking results, a predetermined number of top-ranked individual models are selected to be passed on to the next generation. The first calculation method is a method for calculating response values ​​using CAE analysis including the finite element method. The second calculation method is a method that calculates response values ​​using a machine learning model. Furthermore, the calculation unit, When the response values ​​of the individual models are calculated using the first calculation method, the machine learning model is retrained using the design parameters of multiple individual models and the response values ​​of multiple individual models calculated using the first calculation method as training data. The coefficient of determination, which shows the correlation between the response value calculated using the first calculation method and the response value calculated using the second calculation method, is calculated. Based on the calculated coefficient of determination, the number of generations for calculating the response values ​​of the individual model in the second calculation method is changed. Information processing device.

17. A computer program that causes a computer to perform information processing to optimize design parameters that define an individual model representing the object to be designed, using a genetic algorithm, To the aforementioned computer, By performing genetic processing based on a predetermined number of individual model design parameters inherited from the previous generation, multiple new individual models for the current generation are generated. From the second generation onward, the response values ​​of multiple individual models newly generated in the current generation are calculated using either the first calculation method or a second calculation method which has a faster calculation speed than the first calculation method. A predetermined number of individual models inherited from the previous generation and several newly generated individual models are ranked based on the calculated response values. Based on the ranking results, a predetermined number of top-ranked individual models will be selected to be passed on to the next generation. Execute the process, Furthermore, the computer, When calculating the response values ​​of individual models using the second calculation method, an optimization progress index is calculated that shows the progress of the optimization of the design parameters. Based on the change in the optimization progress index with respect to generational progression, it is determined whether or not the optimization of design parameters has stalled. If optimization is deemed to be stalled, the response value of the individual model is calculated using the first calculation method. A computer program designed to execute a process.

18. A computer program that causes a computer to perform information processing to optimize design parameters that define an individual model representing an object to be designed, using a genetic algorithm. To the aforementioned computer, By performing genetic processing based on a predetermined number of individual model design parameters inherited from the previous generation, multiple new individual models for the current generation are generated. From the second generation onward, the response values ​​of multiple individual models newly generated in the current generation are calculated using either the first calculation method or a second calculation method which has a faster calculation speed than the first calculation method. A predetermined number of individual models inherited from the previous generation and several newly generated individual models are ranked based on the calculated response values. Based on the ranking results, a predetermined number of top-ranked individual models will be selected to be passed on to the next generation. Execute the process, The first calculation method is a method for calculating response values ​​using CAE analysis including the finite element method. The second calculation method is a method that calculates response values ​​using a machine learning model. Furthermore, the computer, When the response values ​​of the individual models are calculated using the first calculation method, the machine learning model is retrained using the design parameters of multiple individual models and the response values ​​of multiple individual models calculated using the first calculation method as training data. The coefficient of determination, which shows the correlation between the response value calculated using the first calculation method and the response value calculated using the second calculation method, is calculated. Based on the calculated coefficient of determination, the number of generations for calculating the response values ​​of the individual model in the second calculation method is changed. A computer program designed to execute a process.

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