Parameter search device and parameter search method

Abstract

To efficiently search for parameters that achieve the target performance while satisfying these constraints.SOLUTION: The parameter search device includes: a first calculation update unit that updates a candidate parameter vector for a target performance in a first update process; a second calculation update unit that updates a candidate parameter vector for a constraint condition using the candidate parameter vector for the target performance updated in the first update process as an input; and an iterative calculation control unit that repeatedly executes the second update process until a predetermined condition is satisfied, and repeatedly executes the first update process using the candidate parameter vector for the constraint condition updated in the second update process as an input to the first update process until the predetermined condition is satisfied.SELECTED DRAWING: Figure 5

Description

[Technical Field]

[0001] The present invention relates to a parameter search device and a parameter search method. [Background technology]

[0002] Conventionally, there are parameter search methods. For example, there is a technology related to an optimal search problem with equality or inequality constraints (see Patent Document 1). This technology discloses a method for safely and accurately finding an optimal point on the boundary of an equality or inequality constraint when the optimal point in the absence of constraints is outside the constraints.

[0003] There is also a technology related to an information processing device for efficiently and accurately performing optimization processing (see Patent Document 2). This technology discloses a method for searching for new constraint variables that satisfy constraint conditions and updating constraint thresholds.

[0004] Furthermore, parameter search methods that take constraint conditions into consideration are being studied (for example, Non-Patent Document 1). [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Japanese Patent Application Laid-Open No. 2010-250397 [Patent Document 2] Japanese Patent Publication No. 2022-144049 [Non-patent literature]

[0006] [Non-Patent Document 1] Seiji Tagawa and Takashi Miyanaga: Empirical Distribution and Differential Evolution Method for Optimization Problems with Individual Chance Constraints, IPSJ Technical Report, Vol. 2017-MPS-112 No. 14, February 2017 Summary of the Invention [Problem to be solved by the invention]

[0007] However, when performing parameter search using an iterative method while taking constraint conditions into consideration, it is difficult to search for parameters that achieve target performance within a range that satisfies the constraint conditions.

[0008] In consideration of the above, an object of the present invention is to efficiently search for parameters that achieve target performance while satisfying constraints. [Means for solving the problem]

[0009] In order to achieve the above object, a parameter search device of the present invention includes: a setting unit that sets a target performance, constraints, and candidate parameter vectors; a first calculation and update unit that takes the candidate parameter vector as an input, and performs a first update process for the target performance by calculating a first error vector with respect to the target performance and calculating parameters of the input candidate parameter vector so as to reduce the first error vector, thereby updating the candidate parameter vector with respect to the target performance; a second calculation and update unit that takes the candidate parameter vector with respect to the target performance updated in the first update process as an input, and performs a second update process for the constraints by calculating a second error vector with respect to the constraints and calculating parameters of the input candidate parameter vector so as to reduce the second error vector, thereby updating the candidate parameter vector with respect to the constraints; and an iterative calculation control unit that repeatedly executes the second update process until a predetermined condition is satisfied, and that repeatedly executes the first update process by using the candidate parameter vector with respect to the constraints updated in the second update process as an input until the predetermined condition is satisfied. As an example, the following describes a method of determining whether an error vector is larger than an allowable error using the norm of the error vector. [Effects of the Invention]

[0010] According to the present invention, it is possible to obtain an effect that it is possible to efficiently search for parameters that achieve target performance while satisfying constraint conditions. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 1 is a diagram showing the flow of parameter search in the conventional method. [Figure 2] Figure 2 shows an image of the conventional search approach. [Figure 3] FIG. 3 is a diagram showing the flow of parameter search in this method. [Figure 4] Figure 4 shows an image of the search approach using this method. [Figure 5] FIG. 5 is a block diagram showing the configuration of the parameter searching device. [Figure 6] FIG. 6 is a flowchart showing the search process in the parameter search device. [Figure 7] Figure 7 shows the results of a study using nonlinear FEM analysis. [Figure 8] FIG. 8 shows the load-displacement relationship of the forced displacement part. [Figure 9] Figure 9 is a table summarizing the conditions for each case considered. [Figure 10] Figure 10 is a table summarizing the results of each case. [Figure 11] Figure 11 shows the load-displacement relationship for Case 1, the history of the residual sum of squares of the error vector {Er1} with the target, and the history of fluctuations in the volume ratio. [Figure 12] Figure 12 shows the load-displacement relationship for Case 2, the history of the residual sum of squares of the error vector {Er1} with the target, and the history of fluctuations in the volume ratio. [Figure 13] Figure 13 shows the load-displacement relationship for Case 3, the history of the residual sum of squares of the error vector {Er1} with the target, and the history of fluctuations in the volume ratio. [Figure 14] Figure 14 shows the load-displacement relationship for Case 4, the history of the residual sum of squares of the error vector {Er1} with the target, and the history of fluctuations in the volume ratio. DETAILED DESCRIPTION OF THE INVENTION

[0012] Hereinafter, an embodiment of the present invention will be described with reference to the drawings.

[0013] First, an overview of the method according to this embodiment will be described. In parameter search, it is often necessary to perform a search that sets some kind of constraint while achieving the target performance. Possible solutions when constraints exist include a method of adjusting the search range of parameters so as to satisfy the constraints, or a method of adding the constraints directly to the target and adjusting the search weights. However, it is not easy to appropriately set the parameter range so as to satisfy the constraints, and similarly, it is not easy to find appropriate weights for the target performance and the constraints.

[0014] For comparison, the parameter search of the conventional method will be explained. Figure 1 shows the flow of parameter search in the conventional method. (1): Set the initial parameters. In setting the initial parameters, the target performance, constraints, and initial input parameter vector are set. (2): Search for and correct a parameter vector that satisfies the target performance. (2-1): Use the candidate parameter vector (input vector) to find the error vector {Er1} with the target (target performance). The error vector is repeatedly corrected until the norm of the error vector (Er1) becomes smaller than the allowable error. (2-2): Correct the current candidate parameter vector so as to reduce the error vector {Er1}.

[0015] Figure 2 shows an image of the search approach of conventional methods. (a) When the target is only the target performance, and (b) when the target is the target performance and constraints. The gradation represents the error from the target (target performance (+ constraints)), with darker areas meaning smaller errors. In conventional methods, as in the example of (a), the search is for the point with the smallest error. Furthermore, we want to search for a solution (the position of the black circle) that minimizes the error while satisfying the constraints. When the target is the target performance and constraints, as in (b), the solution that is searched for is the solution with the smallest error from the target (both the target performance and constraints). Even within the framework of conventional methods, if appropriate search weights can be assigned to the target target performance and constraints, it is possible to search for the parameters of the location of the solution we want to search for, but assigning appropriate weights is not easy.

[0016] Therefore, in order to realize a parameter search that takes into account constraints, the method according to this embodiment (hereinafter referred to as the present method) has been found to have a nested structure in which parameter search targeting constraints is performed within parameter search targeting target performance. This makes it possible to efficiently search for parameters that achieve target performance while satisfying constraints.

[0017] Figure 3 shows the flow of parameter search in this method. The differences from conventional methods are explained below. (2-3): Using the candidate parameter vector obtained in (2-2), calculate the error vector {Er2} with respect to the constraints. (2-4): Modify the current candidate parameter vector to reduce the error vector {Er2}. (2-5): Repeat steps (2-3) to (2-4) until the norm of the error vector {Er2} is less than the allowable error or until the number of convergences reaches a specified number (Loop 2 processing for constraints). Then, return to step (2-1). (2-6): Repeat steps (2-1) to (2-5) until the error vector {Er1} is less than the allowable error or until the number of convergences reaches a specified number (Loop 1 processing for target performance). The maximum number of convergences and the specified number of iterations for Loop 1 and Loop 2 can be specified separately. Any error correction method (such as Newton's method, modal iterative error correction method, nonlinear least squares method, or steepest descent method) may be used for error correction in the iterative calculation.

[0018] Figure 4 shows an image of the search approach used by this method. This method makes it possible to search for parameters that achieve the target performance within the range that satisfies the constraints by including a calculation process that searches for a solution that satisfies the constraints in each iteration of the convergence calculation that targets the main target performance. Note that none of the conventional techniques have a nested structure in which an iterative method is performed within another iterative method.

[0019] This method has the following features. It has a nested structure in which calculations are performed to search for parameters that satisfy constraint conditions within the loop of convergence calculations for parameter search that targets conventional target performance. In addition, by separately performing conventional parameter search and parameter search that satisfies constraint conditions, parameter search can be performed within the range that satisfies constraint conditions (note that it is assumed that parameter search that satisfies constraint conditions is easier). Furthermore, multiple constraint conditions can be handled simultaneously.

[0020] Fig. 5 is a block diagram showing the configuration of the parameter search device 100. As shown in Fig. 5, the parameter search device 100 includes a setting unit 110, a first calculation update unit 112, a second calculation update unit 114, and an iterative calculation control unit 116.

[0021] The parameter search device 100 is realized as a hardware configuration by a computer including a CPU (Central Processing Unit), a ROM (Read Only Memory) storing programs for implementing each processing routine, a RAM (Random Access Memory) for temporarily storing data, a memory as a storage means, a network interface, etc. Note that a GPGPU or accelerator may be used instead of the CPU depending on the suitability of each process, and an arithmetic unit appropriate for the process may be used as appropriate. In particular, the use of a GPGPU or accelerator is preferable for processes related to learning and inference.

[0022] The setting unit 110 sets the target performance, constraint conditions, and candidate parameter vectors.

[0023] The first calculation update unit 112 receives a candidate parameter vector as input and performs the following calculation and update as a first update process for the target performance. The first calculation update unit 112 calculates a first error vector with respect to the target performance. The first calculation update unit 112 calculates parameters of the input candidate parameter vector so as to reduce the first error vector, and updates the candidate parameter vector for the target performance (corresponding to (2-1) and (2-2) above).

[0024] The second calculation update unit 114 receives the candidate parameter vector for the target performance updated in the first update process as input and performs the following calculation and update as a second update process for the constraints. The second calculation update unit 114 calculates a second error vector with respect to the constraints. The second calculation update unit 114 calculates parameters of the input candidate parameter vector so as to reduce the second error vector, and updates the candidate parameter vector for the constraints (corresponding to (2-3) and (2-4) above).

[0025] The iterative calculation control unit 116 repeatedly executes the second update process until a predetermined condition is satisfied. The iterative calculation control unit 116 uses the candidate parameter vector for the constraint condition updated in the second update process as an input to the first update process and repeatedly executes the first update process until a predetermined condition is satisfied (corresponding to (2-5) and (2-6) above). Here, the predetermined condition for the first update process may be either an allowable error or the number of convergences determined for the first error vector. Furthermore, the predetermined condition for the second update process may be either an allowable error or the number of convergences determined for the second error vector. In this embodiment, the case of an allowable error is illustrated.

[0026] Next, the operation of the embodiment of the present invention will be described. Fig. 6 is a flowchart showing the search process in the parameter search device 100. The CPU, GPGPU, or accelerator arithmetic unit of the parameter search device 100 reads and executes programs and various data from the ROM, causing the arithmetic unit to perform processing as each part of the parameter search device.

[0027] In step S100, the setting unit 110 sets the target performance, constraint conditions, and candidate parameter vectors.

[0028] In step S102, the first calculation update unit 112 receives the candidate parameter vector as an input and calculates a first error vector from the target performance as a first update process for the target performance. Here, the initial input of the candidate parameter vector is the candidate parameter vector set in step S100, and in the repeated processes, the candidate parameter vector for the constraint condition updated in the second update process is used as an input.

[0029] In step S104, the iterative calculation control unit 116 determines whether the first error vector calculated in the previous step is smaller than the allowable error defined for the first error vector (for example, the norm of the first error vector {Er1}<the allowable error). If it is smaller than the allowable error, the process ends; if it is not smaller, the process proceeds to step S106.

[0030] In step S106, the first calculation update unit 112 receives the candidate parameter vector and the first error vector as input, and as a first update process, calculates the parameters of the input candidate parameter vector so as to reduce the first error vector, thereby updating the candidate parameter vector for the target performance.

[0031] In step S108, the second calculation update unit 114 receives as input the candidate parameter vector for the target performance updated in the first update process, and calculates a second error vector with respect to the constraint condition as a second update process for the constraint condition.

[0032] In step S110, the iterative calculation control unit 116 determines whether the second error vector calculated in the previous step is smaller than the allowable error determined for the second error vector (for example, the norm of the second error vector {Er2}<the allowable error). If it is smaller than the allowable error, the process proceeds to step S102; if it is not smaller, the process proceeds to step S1112.

[0033] In step S112, the first calculation update unit 112 receives the candidate parameter vector for the target performance and the second error vector as input, and calculates the parameters of the input candidate parameter vector so as to reduce the second error vector as the second update process, thereby updating the candidate parameter vector for the constraint condition. After this step, the process proceeds to step S108.

[0034] As described above, the parameter search device 100 according to the embodiment of the present invention can efficiently search for parameters that achieve target performance while satisfying constraint conditions.

[0035] [Example study] To confirm the effectiveness of the method of the present invention, a study was carried out using the nonlinear FEM analysis shown in Figure 7 as an example. The parameter to be searched is the plate thickness ratio of each plate element, and the target is the load-displacement relationship of the forced displacement part shown in Figure 8. The constraint condition was a volume ratio of 0.33 from the volume due to the initial plate thickness.

[0036] For comparison, parameter searches were carried out for the following four cases. Figure 9 is a table summarizing the conditions for each case considered. Case 1 is a parameter search with constraints using this method, and Case 2 is a parameter search using the conventional method with no constraints. Cases 3 and 4 are cases in which both load displacement and volume ratio were added to the targets in the calculation process of the conventional method, and the search weights were adjusted.

[0037] Figure 10 is a table summarizing the results of each case. Figures 11 to 14 show the load-displacement relationship obtained using the parameters with the smallest error, the history of the residual sum of squares of the error vector {Er1} with the target, and the history of fluctuations in the volume ratio.

[0038] Figure 11 confirms that parameter search using this method is able to find parameters that approach the target performance while satisfying the constraints. On the other hand, while the conventional method in Case 2 achieves the target performance, the volume ratio at the time of minimum error is not 0.33, and it can be confirmed that the constraints are not satisfied (Figure 12). Also, in Case 3, the weighting on the volume ratio search is too strong, so although the final volume ratio is 0.33, the load-displacement relationship cannot be reproduced (Figure 13). Conversely, in Case 4, the volume ratio is 0.464, which is significantly different from the target of 0.33 (Figure 14). From the above, it can be confirmed that this method is more effective than the conventional method.

[0039] The present invention is not limited to the above-described embodiment, and various modifications and applications are possible without departing from the spirit and scope of the present invention. [Explanation of symbols]

[0040] 100 Parameter search device 110 Setting section 112 Calculation update section 114 Calculation update section 116 Iterative calculation control section

Claims

1. a setting unit that sets a target performance, constraint conditions, and candidate parameter vectors; a first calculation and update unit that uses the candidate parameter vector as an input, calculates a first error vector with respect to the target performance as a first update process for the target performance, calculates parameters of the input candidate parameter vector so as to reduce the first error vector, and updates the candidate parameter vector for the target performance; a second calculation and update unit that uses the candidate parameter vector for the target performance updated in the first update process as an input, calculates a second error vector with respect to the constraint condition as a second update process for the constraint condition, calculates parameters of the input candidate parameter vector so as to reduce the second error vector, and updates the candidate parameter vector for the constraint condition; an iterative calculation control unit that repeatedly executes the second update process until a predetermined condition is satisfied, and repeatedly executes the first update process using the candidate parameter vector for the constraint condition updated in the second update process as an input to the first update process until the predetermined condition is satisfied; A parameter search device including:

2. 2. The parameter search device according to claim 1, wherein the predetermined condition for the first update process is either an allowable error or a number of convergence times defined for the first error vector, and the predetermined condition for the second update process is either an allowable error or a number of convergence times defined for the second error vector.

3. The computer Set the target performance, constraints, and candidate parameter vectors; using the candidate parameter vector as an input, as a first update process for the target performance, calculating a first error vector with respect to the target performance, and calculating parameters of the input candidate parameter vector so as to reduce the first error vector, thereby updating the candidate parameter vector for the target performance; using the candidate parameter vector for the target performance updated in the first update process as an input, calculating a second error vector with respect to the constraint as a second update process for the constraint, and calculating parameters of the input candidate parameter vector so as to reduce the second error vector, thereby updating the candidate parameter vector for the constraint; repeatedly executing the second update process until a predetermined condition is satisfied, and using the candidate parameter vector for the constraint condition updated in the second update process as an input to the first update process, repeatedly executing the first update process until a predetermined condition is satisfied. A parameter search method for performing processing.

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