Feasible solution search device and feasible solution search method

Abstract

To provide a feasible solution search device and a feasible solution search method with which it is possible to search for a feasible solution capable of establishing multi-performance, in designing a rear suspension system of a vehicle.SOLUTION: A feasible solution search method includes the steps of: setting design specifications and performance values through confirmation of performance and specifications to be satisfied; filling a design space according to design of experiments; generating a regression model in a prediction model of response values by using machine learning; performing optimization on the basis of constraint conditions; determining design specification values of a rear suspension system; generating displacement vector candidates from initial individual generation in the optimization; performing approximate calculation allowing continuous evaluation of the maximum value of the amount of deviation from a plurality of response constraint ranges by using the KS function, selecting an individual at a distance farthest from an existing solution in a feasible region; and dividing a population into a plurality of partial populations to execute the optimization.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present invention relates to a feasible solution search device and a feasible solution search method, and more particularly to an improvement that enables the determination of design specifications that achieve multi-performance when designing a rear suspension system for a vehicle. [Background technology]

[0002] When designing a vehicle's rear suspension system, it is important to consider the feasibility of multiple performances and clarify the range of nonlinear characteristics and specifications that will satisfy the performance targets. In other words, it is important to consider the probability of a design method that can optimize multiple mutually different performances (multiple performances) or multiple conflicting performances. Up until now, methods have been proposed for optimizing multiple performances simultaneously using computer simulations.

[0003] For example, Patent Document 1 discloses a multi-performance optimization design system. Specifically, Patent Document 1 proposes BAL (Bayesian Active Learning) as a method for searching for design variables that satisfy constraints for multiple responses. BAL is a method for actively searching for feasible solutions by performing sequential sampling using a Gaussian process regression model and an acquisition function. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Publication No. 2022-12511 Summary of the Invention [Problem to be solved by the invention]

[0005] Incidentally, research into the aforementioned BAL, which applies Bayesian optimization (a method of probabilistically modeling an objective function and then using Bayesian statistical methods to sequentially search for an optimal solution and update the model), has been reported to date. In this BAL, an acquisition function (a function expressed from the mean and variance obtained by Gaussian process regression in Bayesian optimization) is defined using the posterior distribution of GP (Gaussian Process: a machine learning method that outputs the distribution of predicted values ​​of an objective variable as a normal distribution in response to input explanatory variables) and additional sampling positions are determined by finding a solution to the optimization problem that maximizes this acquisition function.

[0006] However, the search for a feasible solution using the BAL can only be performed based on a relatively small number of explanatory variables and constraint functions. The reason for this is that the amount of calculations required for GP training increases at a rate that is three times the increase rate of the number of training data, making it difficult to apply the method when the amount of training data is large. In other words, the data-driven set-based design method is only useful when the cost of evaluating the constraint function per time is high and the number of function evaluations is limited.

[0007] The present invention has been made in view of the above points, and its object is to provide a feasible solution searching apparatus and a feasible solution searching method that can search for a feasible solution that can achieve multiple performances when designing a vehicle rear suspension system. [Means for solving the problem]

[0008] The solution of the present invention for achieving the above object is a feasible solution search device that designs a vehicle rear suspension system using DEBAS and a set-based design method using DEBAS. The feasible solution search device includes a setting unit that sets design specifications and performance values ​​by confirming performance and specifications to be satisfied, a design space filling unit that fills a design space using a design of experiments, a regression model creation unit that creates a regression model with a response value prediction model using machine learning, an optimization unit that performs optimization based on constraints, a design specification value determination unit that determines design specification values ​​for the rear suspension system, a mutation vector candidate generation unit that generates initial individuals and generates mutation vector candidates in the optimization unit, an approximation calculation unit that performs approximate calculations using a KS function to continuously evaluate the maximum deviation of multiple responses from constraint ranges, an individual selection unit that selects an individual that is farthest from an existing established solution within a feasible region, and an optimization execution unit that divides a population into multiple subpopulations and performs optimization.

[0009] This specification makes it possible to search for a feasible solution that can achieve multiple performances when designing a vehicle rear suspension system.

[0010] Furthermore, the design space filling unit fills the design space with a Sobol quasi-random number sequence as the experimental design method.

[0011] This allows for optimization of the design space filling process.

[0012] As a means for achieving the above object, the technical concept of the present invention also encompasses a feasible solution search method implemented by the feasible solution search device. Specifically, the feasible solution search method involves designing a vehicle rear suspension system using DEBAS and a set-based design method using the DEBAS. The feasible solution search method includes the steps of: determining design specifications and performance values ​​by confirming performance and specifications to be satisfied; filling a design space using a design of experiments; creating a regression model using a machine learning model with a response value prediction model; optimizing based on constraints; determining design specification values ​​for the rear suspension system; generating initial individuals and generating mutation vector candidates in the optimization; performing approximate calculations using a KS function to continuously evaluate the maximum deviation of multiple responses from their constraint ranges; selecting an individual farthest from an existing solution within a feasible region; and dividing a population into multiple subpopulations for optimization.

[0013] This specification also makes it possible to search for a feasible solution that can achieve multiple performances when designing a vehicle rear suspension system.

[0014] Furthermore, in the step of filling the design space by the experimental design method, the design space is filled with a Sobol quasi-random number sequence.

[0015] This allows for optimization of the design space filling process. [Effects of the Invention]

[0016] According to the present invention, when designing a rear suspension system for a vehicle, it is possible to search for a feasible solution that can achieve multiple performances. [Brief explanation of the drawings]

[0017] [Figure 1] 1 is a diagram illustrating an overview of a feasible solution search device according to an embodiment. [Figure 2]FIG. 2 is a functional block diagram of a CPU of the feasible solution search device according to the embodiment. [Figure 3] FIG. 10 is a flowchart illustrating the procedure of a design specification value determination process performed in the feasible solution search device according to the embodiment. [Figure 4] FIG. 10 is a flowchart illustrating the procedure of an optimization process according to an embodiment. [Figure 5] FIG. 10 is a diagram for comparing the results of a search for a feasible region according to the present invention with a conventional optimization method using the Rosenbrock function. [Figure 6] FIG. 10 is a diagram for comparing feasible solutions that satisfy constraints in the prior art and the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0018] This embodiment describes the application of the present invention as a feasible solution search device and feasible solution search method for clarifying the range of nonlinear characteristics and specifications that satisfy performance targets when designing a rear suspension system for a vehicle (e.g., an electric vehicle).

[0019] A vehicle's rear suspension system is composed of tires, suspension, suspension members (also called subframes), motors, and a differential. This rear suspension system plays many important roles, such as supporting the vehicle, regulating its movement, and mitigating the transmission of vibrations to the body. Therefore, from the early stages of development, the development of a rear suspension system must verify the feasibility of many performance aspects, such as achieving resonance placement (the placement and characteristics of various components that remove the resonance frequency from the normal operating range or prevent the resonance point from being located in the high-force region within the normal operating range) and limiting the maximum mount movement (the placement and characteristics of various components that keep the rubber mount's range of movement within the allowable limits). Therefore, an optimization method for finding a feasible solution to achieve multiple performance aspects is needed.

[0020] Differential evolution (DE) is one of the optimization methods that has been known so far. DE is an evolutionary computation algorithm suitable for real-valued function optimization problems, and can find globally optimal solutions without requiring differentiability or convexity.

[0021] Other well-known evolutionary computation algorithms include GA (Genetic Algorithm), PSO (Particle Swarm Optimization), and CMA-ES (Covariance Matrix Adaptation Evolution Strategy), but DE has the advantage of being a simple algorithm with few control parameters. In recent years, many methods have been proposed that improve DE, such as MPDE, ILS-DE, and self-adaptive differential evolution, which have improved the optimality and convergence of the search. However, these methods are specialized in searching for global optimal solutions and cannot be used to search for feasible solutions.

[0022] This embodiment has been developed in consideration of this point, and proposes DEBAS (Differential Evolution Based Adaptive Sampling), a method that can improve DE and search for feasible solutions, and a set-based design method that uses it, and applies it to the development of a rear suspension system.

[0023] -Configuration of a feasible solution search device- FIG. 1 is a block diagram showing an example of a specific configuration of a feasible solution search device 10 according to this embodiment.

[0024] The feasible solution search device 10 is configured to include a computer 30. The computer 30 has a CPU 32, a ROM 34, a RAM 36, and an input / output port 38. As an example, the computer 30 is preferably a model capable of performing advanced arithmetic processing at high speed, such as an engineering workstation or a supercomputer.

[0025] In the computer 30, the CPU 32, ROM 34, RAM 36, and input / output port 38 are connected to one another via various buses such as an address bus, a data bus, and a control bus. The input / output port 38 is connected to various input / output devices, such as a display 40, a mouse 42, a keyboard 44, a hard disk (HDD) 46, and a disk drive 50 that reads information from various disks (e.g., CD-ROM, DVD, etc.) 48.

[0026] Furthermore, a network 52 is connected to the input / output port 38, enabling information to be exchanged with various devices connected to the network 52. In this embodiment, a data server 56 to which a database (DB) 54 is connected is connected to the network 52, enabling information to be exchanged with the DB 54.

[0027] Data related to feasible solution search (multi-performance optimization design) and the like are stored in advance in the DB 54. Information may be registered in the DB 54 by the computer 30 or the data server 56, or by other devices connected to the network 52.

[0028] In this embodiment, it is described that the data for feasible solution search and the like are stored in DB 54 connected to the data server 56, but the information in DB 54 may also be stored in an external storage device such as HDD 46 built into the computer 30 or an external hard disk.

[0029] A feasible solution search program (multi-performance optimization design program) for feasible solution search is installed on the HDD 46 of the computer 30. In this embodiment, the CPU 32 executes the feasible solution search program to perform the feasible solution search. The CPU 32 also displays the processing results of the feasible solution search program on the display 40. There are several methods for installing the feasible solution search program of this embodiment into the computer 30. For example, the feasible solution search program can be stored on a CD-ROM or DVD together with a setup program, and the disk 48 can be inserted into the disk drive 50. The setup program can then be executed by the CPU 32 to install the feasible solution search program on the HDD 46. Alternatively, the feasible solution search program can be installed on the HDD 46 by communicating with another information processing device connected to the computer 30 via a public telephone line or a network 52.

[0030] 2 is a functional block diagram of the CPU 32 of the feasible solution search device 10. Various functions realized by the CPU 32 of the feasible solution search device 10 executing the feasible solution search program will be described below. The CPU 32 includes a design unit 61, a design space filling unit 62, a regression model creation unit 63, an optimization unit 64, a design specification value determination unit 65, a mutation vector candidate generation unit 66, an approximation calculation unit 67, an individual selection unit 68, and an optimization execution unit 69 as functional units realized by the feasible solution search program.

[0031] -Design specification value determination process- The functions of the above-mentioned functional units will be explained below together with the procedure of the design specification value determination process performed in the feasible solution search device 10.

[0032] FIG. 3 is a flowchart for explaining the procedure of the design specification value determination process performed in the feasible solution search device 10 according to this embodiment.

[0033] First, in step ST1, design specifications and performance values ​​are set. Here, when designing a rear suspension system, the specifications and performance that the rear suspension system must satisfy (for example, the performance to realize the above-mentioned resonance arrangement and the restriction of the maximum amount of mount movement) are confirmed. The processing in step ST1 is performed by the function of the design unit 61 (the function of the present invention that sets the design specifications and performance values ​​by confirming the performance and specifications that must be satisfied).

[0034] In step ST2, the design space is filled by using a Sobol quasi-random number sequence in a design of experiments (DOE). The processing in step ST2 is performed by the function of the design space filling unit 62 (the function of filling the design space by a design of experiments, as referred to in the present invention).

[0035] In step ST3, a regression model is created. A response value prediction model (machine learning: a model obtained by deep learning utilizing a neural network) is used as this regression model. The regression model here is a prediction model for the resonance frequency and the maximum amount of movement of the mount. The processing in step ST3 is performed by the function of the regression model creation unit 63 (a function of creating a regression model from a response value prediction model using machine learning, as referred to in the present invention).

[0036] In step ST4, optimization is performed based on the constraint conditions. The processing in step ST4 is performed by the function of the optimization unit 64 (the function of performing optimization based on the constraint conditions, as referred to in the present invention).

[0037] The details of the processing operation (optimization processing) in step ST4 will be explained below with reference to the flowchart in FIG.

[0038] As shown in Fig. 4, in this optimization process, first, in step ST11, initial individuals are generated. Here, the initial individuals are randomly placed in the search space. The space (design space) filled by the DOE may be larger than the search space.

[0039] Specifically, in generating these initial individuals, m individuals are randomly generated from n-dimensional real-valued vectors, and the population P = (x 1 ,x 2 ,…X m )∈R n×m The DE is then generated by processing steps ST12 to ST14 described later from the population P. new will be generated.

[0040] In step ST12, processes related to the generation and mutation of mutant vectors are performed. Specifically, a parent individual (basic vector) that serves as a reference for each individual of the current generation, called a target vector, is randomly selected from the population, and a mutant vector is generated by mutating the target vector using a difference vector from that individual.

[0041] More specifically, let x be the basis vector. b In this case, the x that constitutes the difference vector r1 ,x r2 The selection is made based on the ILS-DE. In the ILS-DE, the selection is made according to the evaluation function, which can be expected to improve the search accuracy. In the DEBAS, each vector x b ,x r1 ,x r2 are selected in the order of evaluation of the function in the following formula (1), and the vector with the smallest value is x b ,The second smallest vector is x r1 ,The vector with the largest value is x r2 and the mutation vector is generated using the following formula (2).

[0042]

number

[0043]

number

[0044]

number

[0045]

number

[0046] Then, using the above-mentioned formula (4), the individual that is the furthest from the existing feasible solution is adopted. This makes it possible to search for points that are farther away from the existing feasible solution, thereby expanding the feasible region. The processing in this step ST12 is performed by the function of the mutation vector candidate generation unit 66 (the function of the present invention that generates mutation vector candidates from the initial individual generation in the optimization unit).

[0047] Regarding the generation of mutation vector candidates, in conventional technology, mutation vectors were created using three random points, but in this embodiment, by using any three points in the evaluation order, it is possible to improve the accuracy of searching the feasible region.

[0048] In step ST13, processes related to generation and crossover of trial vectors are performed. Specifically, the mutant vectors are crossed with the individuals of the current generation to generate child individuals (trial vectors).

[0049] More specifically, the target vector x i By binomial crossover between and the mutation vector v, a new solution candidate, trial vector u∈R n is generated as shown in the above equation (3).

[0050] where Cr∈[0,1] is the crossover rate, R∈{1,…,n} is a randomly chosen index, and r i ~U(0,1) is a uniform random value. The probability of the number of elements that u inherits from v follows a binomial distribution. In binomial crossover, the subscript R ensures that at least one element of u is chosen as an element of v.

[0051] In step ST14, a survival selection process is performed. Specifically, the trial vector is compared with the evaluation value of the individual of the current generation, and if the trial vector is better than the individual of the current generation, it is updated to an individual of the next generation.

[0052] More specifically, the trial vector u generated in step ST13 is compared with the target vector x, and the better vector is selected as a new set P using the following equation (5): new are candidates for.

[0053]

number

[0054] In addition, Jn(·) is defined as follows:

[0055]

number

[0056]

number

[0057]

number

[0058]

number

[0059] The function that converts multiple constraints into a single cost function is defined as in equation (7). The maximum deviation of all constraints is approximated using the Kreisselmeier-Steinhauser (KS) function.

[0060] α>0 is a parameter that adjusts the approximation of the max operation using the KS function; the larger the value, the closer it gets to the max operation. h(·) is the Heaviside function, with h(0) = 0. The first term in the above equation (6) is a term that utilizes the feasible region, and returns 0 if the design variable is included in the feasible region. On the other hand, the second term in the above equation (6) is a term that performs a search, and returns a smaller value when searching for a point that is as far away as possible from a point included in a feasible region that has been found previously, even within the feasible region.

[0061] As a result, points farther away than the existing feasible region become the targets for optimization, making it possible to search for a wider range of feasible regions.

[0062] In this embodiment, the approximation calculation that can continuously evaluate the maximum value of the deviation amount from the constraint range of a plurality of responses employs the KS function to convert the minimization of the deviation amount from all constraints into one variable, thereby enabling continuous evaluation of the maximum value. The processing in step ST14 is performed by the function of the approximation calculation unit 67 (the function of the present invention that performs approximation calculation that can continuously evaluate the maximum value of the deviation amount from the constraint range of a plurality of responses using the KS function).

[0063] Furthermore, when comparing feasible regions, selecting individuals that are far from the existing region using the following two methods makes it possible to search for a wider range of feasible regions.

[0064] When n=1, a larger value is returned when searching for a point within the feasible region that is as far away as possible from a point included in the feasible region Q found previously, while when n=2, a larger value is returned when searching for a point that is far away from the center of gravity of a feasible solution found previously.

[0065] Furthermore, these n=1 and n=2 are applied to steps ST12 to ST14, and the two groups are divided into two and searched independently. Then, by appropriately replacing the individuals in each group for each generation, a wide-ranging and uniform search can be performed. This process is performed by the function of the individual selection unit 68 (the function of selecting the individual with the greatest distance from the existing valid solution within the feasible region, as referred to in this invention).

[0066] When dividing a population into multiple subpopulations and performing optimization, if the feasible region is sparse, dividing it into a subpopulation for which a region is being sought and a subpopulation that expands the range of the existing region enables a wider search range. Then, for each generation, the subpopulations are replaced using the evaluation values. This process is performed by the function of the optimization execution unit 69 (the function of dividing a population into multiple subpopulations and performing optimization, as defined in the present invention).

[0067] In step ST15, it is determined whether the optimization process has been completed. If the optimization process has not yet been completed and the determination in step ST15 is NO, the process returns to step ST12. On the other hand, if the optimization process has been completed and the determination in step ST15 is YES, the process proceeds to step ST5 (FIG. 3). In step ST5, design specification values ​​that can achieve multi-performance are determined based on the above-described process, and the design specification value determination process is thereby completed. The process in step ST5 is performed by the function of the design specification value determination unit 65 (the function of determining the design specification values ​​of the rear suspension system, as referred to in the present invention).

[0068] By using the above design specification value determination process, it is possible to confirm the feasibility of many performance aspects, such as resonance placement and restrictions on the maximum amount of mount movement, from the early stages of development of the tires, suspension, suspension members, motor, differential, and other components that make up a vehicle's rear suspension system. In other words, it is possible to achieve optimization of a feasible solution that satisfies multiple performance aspects.

[0069] Furthermore, by using DEBAS and a set-based design method using DEBAS, it is possible to find a global optimal solution without requiring differentiability or convexity.

[0070] -Verification of effectiveness- In order to confirm the usefulness of the present invention, a comparison was made between the conventional optimization method using the Rosenbrock function shown in the following formula (10) and the results of searching the feasible region according to the present invention.

[0071]

number

[0072] On the other hand, Figures 5(d), 5(e), and 5(f) show the search results for the feasible region according to the present invention. Figure 5(d) shows the results when the number of dimensions N is 10, the number of calculations is 10,000, and the constraint f(x)<600, as in Figure 5(a). Figure 5(e) shows the results when the number of dimensions N is 20, the number of calculations is 20,000, and the constraint f(x)<5,000, as in Figure 5(b). Figure 5(f) shows the results when the number of dimensions N is 30, the number of calculations is 30,000, and the constraint f(x)<10,000, as in Figure 5(c).

[0073] As is clear from these figures, according to the present invention, many feasible solutions that achieve multi-performance can be obtained.

[0074] In addition, when specifically applied as a process for deriving the specifications of the motor mount characteristics in a rear suspension system, verification was conducted to see whether the constraints were met for both random sampling (conventional technology) and DEBAS sampling (this invention).

[0075] FIG. 6 shows the results of this verification. FIGS. 6(a), 6(b), 6(c), and 6(d) show points satisfying the constraints in random sampling. In FIG. 6(a), the horizontal axis represents the motor rear mount characteristic MOr, and the vertical axis represents the motor front mount characteristic MOf. Points on FIG. 6(a) represent points satisfying the respective constraints. In FIG. 6(b), the horizontal axis represents the maximum front mount movement MEf, and the vertical axis represents the maximum rear mount movement MEr. Points on FIG. 6(b) represent points satisfying the respective constraints (e.g., less than 10 mm). In FIG. 6(c), the horizontal axis represents the pitch resonance arrangement P1, and the vertical axis represents the vertical resonance arrangement Z1. Points on FIG. 6(c) represent points satisfying the respective constraints. In FIG. 6(d), the horizontal axis represents the pitch resonance arrangement P1, and the vertical axis represents the maximum pitch angle Y1. Points on FIG. 6(d) represent points satisfying the respective constraints.

[0076] On the other hand, Figures 6(e), 6(f), 6(g), and 6(h) show points that satisfy the constraints in DEBAS sampling. In Figure 6(e), like Figure 6(a), the horizontal axis represents the motor rear mount characteristic MOr, and the vertical axis represents the motor front mount characteristic MOf. Points on Figure 6(e) are points that satisfy the respective constraints. In Figure 6(f), like Figure 6(b), the horizontal axis represents the maximum front mount movement MEf, and the vertical axis represents the maximum rear mount movement MEr. Points on Figure 6(f) are points that satisfy the respective constraints (e.g., less than 10 mm). In Figure 6(g), like Figure 6(c), the horizontal axis represents the pitch resonance location P1, and the vertical axis represents the upper / lower resonance location Z1. Points on Figure 6(g) are points that satisfy the respective constraints. In Figure 6(h), like Figure 6(d), the horizontal axis represents the pitch resonance location P1, and the vertical axis represents the maximum pitch angle Y1. Points on Figure 6(h) are points that satisfy the respective constraints.

[0077] As is clear from these figures, according to the present invention, many feasible solutions that achieve multi-performance can be obtained.

[0078] -Other embodiments- The present invention is not limited to the above-described embodiments, and all modifications and applications that fall within the scope of the claims and equivalents thereto are possible.

[0079] For example, in the above embodiment, in step ST2 of the flowchart in FIG. 3, the design space is filled by using a Sobol quasi-random number sequence in the design of experiments (DOE), but a method other than using a Sobol quasi-random number sequence may be adopted. [Industrial Applicability]

[0080] The present invention is applicable to a feasible solution searching device and a feasible solution searching method for designing a rear suspension system of a vehicle. [Explanation of symbols]

[0081] 10. Feasible solution search device 61 Design Department 62 Design space filling part 63 Regression Model Creation Department 64 Optimization Section 65 Design specification value determination section 66 Mutation vector candidate generation unit 67 Approximate calculation section 68 Individual Selection Section 69 Optimization execution unit

Claims

1. A feasible solution search device for designing a vehicle rear suspension system using DEBAS and a set-based design method using the DEBAS, comprising: a setting unit that sets design specifications and performance values ​​by confirming the performance and specifications that should be satisfied; a design space filling unit that fills a design space by an experimental design method; a regression model creation unit that creates a regression model using a prediction model of a response value using machine learning; an optimization unit that performs optimization based on constraint conditions; a design specification value determination unit that determines design specification values ​​of the rear suspension system; a mutation vector candidate generation unit that generates mutation vector candidates from initial individual generation in the optimization by the optimization unit; an approximation calculation unit that performs approximation calculations using a KS function to continuously evaluate the maximum deviation amount of a plurality of responses from a constraint range; an individual selection unit that selects an individual that is the furthest away from an existing established solution within the feasible region; and an optimization execution unit that divides a population into a plurality of subpopulations and executes optimization.

2. 2. The feasible solution search device according to claim 1, The feasible solution search device is characterized in that the design space filling unit fills the design space with a Sobol quasi-random number sequence as the experimental design method.

3. A feasible solution search method for designing a vehicle rear suspension system using DEBAS and a set-based design method using the DEBAS, comprising: a step of setting design specifications and performance values ​​by confirming the performance and specifications to be satisfied; filling the design space by design of experiments; creating a regression model using machine learning to predict response values; performing optimization based on constraints; determining design specification values ​​of the rear suspension system; generating mutation vector candidates from initial individual generation in the optimization; a step of performing an approximate calculation using a KS function to continuously evaluate the maximum deviation amount of a plurality of responses from a constraint range; selecting an individual from the feasible region that is the furthest away from an existing solution; and dividing the population into a plurality of subpopulations and performing optimization.

4. 4. The method for searching for a feasible solution according to claim 3, A feasible solution search method, characterized in that in the step of filling the design space by the experimental design method, the design space is filled with a Sobol quasi-random number sequence.

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