Complex equipment discrete variable optimization method and device based on grey relational degree

Abstract

The invention discloses a grey relational degree-based complex equipment discrete variable optimization method and device. The method specifically comprises the following steps of: firstly, determining a multi-state structure dynamics optimization problem and setting optimizer parameters; then constructing a discrete design variable table and a three-level design variable table, constructing a test table with minimum orthogonality, calculating target functions and constraint values in different states, and processing tests violating constraints by adopting an elimination strategy and a penalty function; secondly, calculating grey correlation degree coefficients and weights of the objective function in different states, further obtaining grey correlation degree for preferential selection, and verifying and determining an optimal combination by means of mean analysis; and finally, moving the three-level design table for multiple times and reducing a design variable search space to finally obtain stable optimal solutions in different states. According to the method, equipment in a multi-target, variable discrete, complex and changeable working scene is optimized, and it is guaranteed that the optimized product can keep good performance under the complex actual working condition.

Description

Technical Field

[0001] The invention relates to the technical field of multi-objective optimization design, in particular to a method and a device for optimizing discrete variables of complex equipment based on grey correlation. Background Art

[0002] In the field of complex equipment dynamics analysis and optimization design, improving dynamics performance is a key factor in improving the competitiveness of complex equipment. Designing the dynamic parameters of equipment through optimization methods to achieve performance improvement has become an important research direction in current engineering technology.

[0003] The Grey-Taguchi robust optimization method arranges test plans through orthogonal tables, simulates various interference factors of product quality fluctuations, and uses the signal-to-noise ratio as an indicator to measure the robustness of product quality. Through statistical analysis of various test plans, it finds the design method with the strongest anti-interference ability, the best adjustability, the most stable and reliable performance, which can effectively enhance the robustness of design parameters. It is particularly suitable for structural optimization design with discrete design variables, and is therefore considered to be an important means to solve complex engineering design problems with multiple objectives and discrete variables. However, with the increase in the number of design variables and the number of discrete levels, it is difficult for the orthogonal test design table used in the Taguchi method to directly determine the optimal design combination, and the optimal value of each indicator is often subjective.

[0004] In order to accommodate more design variables and improve the optimization effect, the use of continuous orthogonal array iterative selection of design variables has become an effective solution. However, this also requires a reasonable optimization strategy. In actual application, complex equipment often faces changes in load conditions and working scenarios. Current product design and optimization are mostly only carried out for typical working conditions. As a result, the optimized products may not be able to maintain stable performance under a variety of actual working conditions.

[0005] Therefore, it is an urgent problem to establish a discrete variable optimization method that can accommodate complex changes in working conditions and achieve robust design and optimization of the dynamic performance of complex equipment. Summary of the invention

[0006] The purpose of the present invention is to provide a method and device for optimizing complex equipment discrete variables, which can optimize complex equipment under multi-objective, discrete variables and complex and changeable working scenarios, and ensure that the optimized products can still maintain good performance when facing diverse actual working conditions.

[0007] The technical solution to achieve the purpose of the present invention is: a complex equipment discrete variable optimization method based on grey correlation, comprising the following steps:

[0008] Step 1: Define the multi-state structural dynamics optimization problem;

[0009] Step 2: Set optimizer parameters;

[0010] Step 3: construct a discrete design variable table;

[0011] Step 4: construct a three-level design variable table;

[0012] Step 5: construct a three-level orthogonal test table, use the cross product array to calculate each group of tests, and obtain the target response value and constraint response value of each noise factor design point;

[0013] Step 6: Use elimination strategy and penalty function to handle constraints;

[0014] Step 7, calculate the grey correlation coefficient through the objective function value of each group of experiments;

[0015] Step 8: Calculate the weight of each correlation coefficient;

[0016] Step 9, calculate the grey correlation degree of each group of test objective function values, and take the design variables corresponding to the group of tests with the largest grey correlation degree as the grey optimal design variables;

[0017] Step 10: Obtain the mean values ​​of the grey correlation corresponding to the three levels of each design variable through mean analysis, and select the group with the largest mean value of the grey correlation of each design variable as the design variable with the optimal mean value;

[0018] Step 11, determine the optimal design variables for this round;

[0019] Step 12: Determine whether the optimization satisfies the stopping criteria;

[0020] Step 13: Determine whether the preset maximum number of cycles has been reached.

[0021] Compared with the prior art, the present invention has the following significant advantages: (1) It solves the problem of dynamic optimization design of complex equipment with changeable working scenes, introduces signal factors, and constructs an objective function that meets diverse actual working conditions through multiple signal factors, thereby ensuring that the optimized product can still maintain good performance when facing diverse actual working conditions; (2) It adopts a dynamic iterative minimum orthogonal test scheme, which can accommodate more design variables and solve the problem of limited variable dimension in the original test design table. The iterative optimization scheme integrates the update strategy combining mean analysis and grey correlation degree, which is suitable for iteratively selecting the design variable level in a continuous orthogonal array and guiding the design variable to the optimal point; (3) For the multi-objective discrete variable optimization problem with constraints, the elimination strategy and penalty function method are used to construct a constraint processing method, and the grey correlation analysis method is combined to objectively deal with the conflict of multiple objectives, thereby realizing the joint optimization of multiple objectives under the premise of meeting strict constraints. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 The figure is a flow chart of a method for optimizing discrete variables of complex equipment based on grey correlation according to the present invention.

[0023] Figure 2 It is a schematic diagram of the principle of dividing the three-level design variable table in the present invention.

[0024] Figure 3 Schematic diagram of the process for selecting the optimal design variables in the present invention.

[0025] Figure 4 FIG. 4 is a flow chart of determining the stopping criteria in the present invention.

[0026] Figure 5 The present invention is a structural block diagram of a complex equipment discrete variable optimization device based on grey correlation.

[0027] Figure 6 It is a structural block diagram of the optimization solution module in the present invention.

[0028] Figure 7 It is a structural block diagram of the parameter initialization module in the present invention.

[0029] Figure 8 It is a structural block diagram of the orthogonal design table module in the present invention.

[0030] Fig. 9 It is a structural block diagram of the grey correlation analysis module in the present invention.

[0031] Fig.10 It is a structural block diagram of the mean analysis module in the present invention.

[0032] Fig.11It is a structural block diagram of the optimal design variable judgment module in the present invention.

[0033] Fig.12 It is a structural block diagram of the stop judgment module in the present invention.

[0034] Fig.13 It is a structural block diagram of the output module in the present invention.

[0035] Fig.14 It is a structural block diagram of the module hardware device in the present invention.

[0036] Fig.15 It is a curve chart of multi-objective optimization iteration in an embodiment of the present invention.

[0037] Fig.16 It is a multi-objective Pareto solution distribution diagram and an optimized position change diagram in an embodiment of the present invention. DETAILED DESCRIPTION

[0038] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0039] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0040] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0041] Example 1

[0042] This embodiment provides a discrete variable optimization method based on grey relational analysis (Discrete Variable Optimization Grey Relational Analysis, DVOGRA), which introduces signal factors in the process of constructing the objective function, introduces noise factors in the design variables, constructs an orthogonal test table through discrete variables to evaluate the objective function and constraints, and constructs the optimal design optimization search strategy of grey relational analysis and mean analysis for iterative optimization. Figure 1 As shown, the discrete variable optimization method of complex equipment based on grey correlation in this embodiment includes the following steps:

[0043] Step 1: Define the multi-state structural dynamics optimization problem as follows:

[0044] The multi-state structural dynamics optimization problem is defined as shown in formula (1):

[0045]

[0046] In the formula, n signal factors M=(m1,m2,…m n ), different signal factors represent the objective function vector F(x) under different states, x is the design variable; N is the total number of design variables; for each design variable x n There is an upper boundary x nmax and the lower boundary x nmin ; m is the number of objective functions f(x) under a certain state; g p (x) is the pth constraint function; P is the total number of constraints.

[0047] Step 2, set the optimizer parameters, including the maximum number of cycles, i.e., the number of grid divisions t, the initial grid size s, and the maximum number of moves;

[0048] If robust optimization design is performed, the noise factors are set and sensitivity analysis is performed on the noise factors to determine the noise factor combinations N1 and N2 under the most unfavorable characteristics and standard conditions.

[0049] Step 3: Construct a discrete design variable table, as follows:

[0050] Constructing a discrete design variable table is also called grid division, that is, discretizing the design variables according to the initial grid size, and dividing the design variable space into s discrete variables with equal spacing. The discretization formula is:

[0051]

[0052] In the formula, d is the discretization step size, x ni is the i-th discrete variable of the n-th design variable.

[0053] Step 4: Construct a three-level design variable table, as follows:

[0054] For each design variable, in the discrete design variable table, specify or randomly select a discrete variable as the intermediate level value, that is, the second level value, the previous value of the discrete variable as the first level value, and the next value as the third level value; if the selected discrete variable is the maximum boundary value, it is used as the third level value, the previous value of the discrete variable as the second level value, and the second value as the first level value; if the selected discrete variable is the minimum boundary value, it is used as the first level value, the next value of the discrete variable as the second level value, and the second value as the first level value, to construct a three-level design variable table.

[0055] like Figure 2 As shown in the figure, it is the setting process of a certain design variable level, where the number of design variables in the discrete design variable table is four, and each has five discrete values. If the initial design is arbitrarily set to A3B2C4D1, the initial values ​​of variables A, B, and C are assigned to the second level, and the initial value of variable D is assigned to the first level; Figure 2 Determine the other levels of design variables as shown in the three-level design variable table.

[0056] Step 5: For M (M = m i ,i=1,2,…,n) signal factors, in the mth i Under the signal factor, call or construct an N-factor three-level orthogonal test table with α trials and calculate n×α objective function response values ​​and constraint response values; if there is a noise factor, the noise factor has two levels of standard characteristics N1 and the most unfavorable characteristics N2. Construct a cross product array and calculate 2n×α target response values ​​and constraint response values ​​under each noise factor characteristic.

[0057] There are n signal factors M (M = m i , i=1,2,…,n), as shown in the first row of Table 1; taking three levels and four design variables (such as A, B, C and D) as an example, the minimum orthogonal design table required is L9(3 4 ), the number of single tests α = 9, the minimum orthogonal design table constructed is L9(3 4 ) as shown in the 5 columns on the left of Table 1; and assuming that there are two levels of noise factor characteristics, the standard characteristic N1 and the most unfavorable characteristic N2, the test calculation is performed on the α=i group to obtain the target response value and the constrained response value under each noise factor characteristic. The F in Table 1 ijk and g ijk They represent the target response value and constraint value under the i-th trial of the j-th noise factor under the k-th signal factor, respectively.

[0058] Table 1 Cross product array of n signal factors and two horizontal noise factors

[0059]

[0060] Step 6: Use the elimination strategy and penalty function to handle constraints, as follows:

[0061] Under the elimination strategy method, the trial numbers with defaults are marked and excluded in the subsequent process of selecting the optimal design variables;

[0062] Under the penalty function method, if there are constraints, they should be processed according to the penalty function, as shown in formula (3):

[0063]

[0064] In the formula, F new (x) is the new objective function vector, M(x) represents the penalty function vector, if g p If (x) violates the constraint, it is multiplied by the penalty coefficient c plus the original objective function vector. The penalty coefficient c is one order of magnitude higher than the original objective function, that is, c = 10×F(x).

[0065] Step 7, calculate the grey correlation coefficient through the objective function value of each group of experiments;

[0066] Step 8: Calculate the weights, and obtain the weights of each correlation coefficient by using weight calculation methods such as AHP method, entropy weight method, and principal hierarchy analysis method; when the dynamic target responses are equally important, the weights are all set to 1;

[0067] Step 9: Calculate the grey correlation of the objective function value of each group of experiments, and take the design variables corresponding to the group of experiments with the largest grey correlation as the grey optimal design variables, as follows:

[0068] Calculate the grey correlation of the objective function value of each group of experiments, and take the design variables corresponding to the group of experiments with the largest grey correlation as candidate optimal design variables, recorded as grey optimal design variables

[0069] The calculation formula of grey relational degree is:

[0070]

[0071] Step 10. Since the orthogonal table is not a full design, a non-optimal design combination may be obtained. It is necessary to perform mean analysis and re-determine the optimal design combination. The mean of the gray correlation degree corresponding to the three levels of each design variable is obtained through mean analysis. The group with the largest mean of gray correlation degree of each design variable is selected as the design variable with the optimal mean, which is recorded as the mean optimal

[0072] Step 11: Determine the optimal design variables for this round, such as Figure 3As shown, the details are as follows:

[0073] Determine the optimal grey design variables and mean optimal design variables Are they the same set of design variables? If so, this set of design variables is the optimal design variable; if not, further calculate the mean optimal design variable Corresponding objective function value and constraint value, if a breach occurs, select the gray optimal design variable As the optimal design variable; if there is no breach of contract, the optimal design variable is the one with the smallest binary norm of the multi-objective function vector.

[0074] Step 12: Determine whether the optimization meets the stopping criteria, such as Figure 4 As shown, the details are as follows:

[0075] Determine whether the maximum number of moves has been reached. If so, the optimization ends. If not, determine whether the optimal design variables obtained in this round of optimization are consistent with the optimal design variables obtained in the previous round of optimization. If they are consistent, proceed to step 13. If not, specify the design variables of this round as intermediate design variables and return to step 4, repeating steps 4 to 12.

[0076] Step 13: Determine whether the preset maximum number of cycles has been reached. Figure 4 As shown, the details are as follows:

[0077] Determine whether the preset maximum number of cycles has been reached. If so, the optimization ends. If not, the adjacent discrete values ​​of the optimal design variable of this round are used as new upper and lower boundaries. If the optimal design variable of this round contains the lower boundary of the design boundary, the lower boundary remains unchanged, and the second discrete value after the optimal design variable of this round is selected as the upper boundary. If the optimal design variable of this round contains the upper boundary of the design boundary, the upper boundary remains unchanged, and the second discrete value before the optimal design variable of this round is selected as the lower boundary. Return to step 3 and repeat steps 3 to 12.

[0078] Example 2

[0079] This embodiment illustrates the calculation process of the gray correlation coefficient in DVOGRA, which mainly includes the following steps:

[0080] Step 7.1, construct the original objective function matrix F, that is, the objective function values ​​corresponding to n tests, forming the n×m original objective function matrix F:

[0081]

[0082] Step 7.2: Data normalization: convert the data into the Wang Xiao index according to the Wang Xiao normalization method. The calculation formula is:

[0083]

[0084] In the formula, is the normalized data, F * That is the expected small objective function matrix, F (j) Represents the j-th column of the original objective function matrix F;

[0085] Step 7.3, set the reference sequence F0 to all 1s:

[0086] F0=[1 1 … 1] (6)

[0087] Step 7.4, calculate the difference matrix D, that is, the i-th row of the minimization objective function matrix The difference with F0 is taken as the i-th row of the difference matrix D i , and thus form the difference matrix D:

[0088]

[0089] Step 7.5: Find the maximum value D in the difference matrix D min With the minimum value D min , the formula is:

[0090] D min =max(max(D)) (8)

[0091] D min =min(min(D)) (9)

[0092] Step 7.6, calculate the grey correlation coefficient matrix γ (j) , use the grey correlation coefficient matrix formula composed of the difference matrix D and its maximum value M and minimum value m to calculate, the formula is:

[0093]

[0094] In the formula, ξ is the resolution coefficient, which is generally taken as ξ=0.5.

[0095] Example 3

[0096] This embodiment illustrates that when calculating the grey relational degree in DVOGRA, the entropy weight method is used to calculate the weight ω j The process mainly includes the following steps:

[0097] Step 8.1, set the grey correlation coefficient matrix γ to have n rows, each row has m values, as shown in formula (11):

[0098]

[0099] Step 8.2: Determine the geometric projection P of each response ij, calculate the proportion P of the i-th record under the j-th index ij , the calculation formula is:

[0100]

[0101] Step 8.3: Calculate the entropy value E of the jth indicator j , the calculation formula is:

[0102]

[0103] Step 8.4: Calculate the weight ω of the jth indicator j , the calculation formula is:

[0104]

[0105] Example 4

[0106] Since the experiment using the orthogonal table is not a full design, a non-optimal design combination may be obtained, and a mean analysis is required to re-determine the optimal design combination. This embodiment illustrates the calculation process of the mean analysis in DVOGRA, which mainly includes the following steps:

[0107] Step 10.1: Use the grey correlation degree r calculated from the orthogonal test design table i According to the different levels of each design variable, the L9(3 2 ) Taking the orthogonal experiment design table and the calculated grey correlation degree as an example, as shown in Table 2.

[0108] Table 2 Orthogonal test design table and grey correlation calculation results diagram

[0109]

[0110] The grey relational degree r in Table 2 i The extraction of different levels of each design variable is listed in Table 3:

[0111] Table 3 Schematic diagram of screening and sorting results according to different levels of design variables

[0112]

[0113] Step 10.2: Calculate the grey correlation degree r at different levels of each design variable i The average value is calculated as:

[0114]

[0115] The mean values ​​of grey correlation degree at different levels of the design variables in Table 3 are calculated as shown in Table 4:

[0116] Table 4 Schematic diagram of grey correlation degree mean calculation results

[0117]

[0118] Step 10.3: Select the level corresponding to the maximum mean value of the grey correlation degree of each design variable as the optimal design variable for the mean value.

[0119] Example 5

[0120] This embodiment provides a multi-objective engineering example, taking a multi-objective structural dynamics problem with a single signal factor (only one state), two variables [x1, x2] (no noise factor) and two dynamic dynamic response objective functions [f1, f2] as an example, and using a complex equipment discrete variable optimization method based on grey correlation provided by the present invention to perform optimization, verifying the effectiveness of the optimization method of the present invention. The specific steps are as follows:

[0121] Step 1: Define the multi-state structural dynamics optimization problem as follows:

[0122]

[0123] Where x1,x2∈[0.1,10].

[0124] Step 2: Set the optimizer parameters, set the number of grid divisions to 3, the maximum number of moves to 30, and the initial grid size s=9.

[0125] Step 3: Construct a discrete design variable table. According to the initial grid size, the design variables are discretized according to the discretization formula: The design variable space is equally spaced into 9 discrete variables. The first round of discrete design variable table is listed in Table 5:

[0126] Table 5 Discrete design variable table

[0127]

[0128] Step 4: Construct a three-level design variable table. For each design variable, in the discrete design variable table, specify x1=10, x2=10 as the starting intermediate level values. However, since x1=10, x2=10 are the maximum boundary values, the constructed three-level design variable table is as listed in Table 6:

[0129] Table 6 Three-level design variables

[0130]

[0131] Step 5: Construct a 2-factor 3-level orthogonal test table with 9 tests, as listed in Table 7:

[0132] Table 7L9(32 )Orthogonal test table

[0133]

[0134] Evaluate the objective function value [f1(x),f2(x),…,f m (x)] and constraint values, as listed in Table 8:

[0135] Table 8L9(3 2 )Orthogonal test table

[0136]

[0137] Step 6: Process constraints. Use elimination strategy to process constraints. If there are no experiments that violate constraints in this round of evaluation data, go to step 7.

[0138] Step 7: Calculate the grey correlation coefficient by the objective function value of each group of tests. The calculation results are listed in Table 9:

[0139] Table 9 Grey correlation coefficient calculation results

[0140]

[0141] Step 8: Calculate the weights. In this embodiment, the dynamic target responses f1 and f2 are considered to be equally important, and the weights are both set to 1, that is, ω1=1, ω2=1.

[0142] Step 9: Calculate the grey correlation degree of each group of test objective function values. The calculation formula of the grey correlation degree is shown in formula (15). The calculation results are listed in Table 10:

[0143] Table 10 Grey correlation calculation results

[0144]

[0145] The design variables corresponding to the group of experiments with the largest grey correlation degree are taken as candidate optimal design variables, which is the group with experiment number 1, recorded as the grey optimal

[0146] Step 10: Mean analysis. The mean values ​​of the grey correlation degrees corresponding to the three levels of each design variable are obtained through mean analysis, as listed in Table 11. The group with the largest mean value of the grey correlation degree of each design variable, i.e., the first level values ​​of x1 and x2, are selected as candidate optimal design variables, which are recorded as the mean optimal

[0147] Table 11 Mean analysis calculation results

[0148]

[0149] Step 11: Determine the optimal design variables of this round. If the gray optimal and mean optimal are the same set of design variables, then this set of design variables is the optimal design variables.

[0150] Step 12: Determine whether the maximum number of moves is reached. This round of optimization is the first round of optimization. If the maximum number of moves is not reached, no comparison is required. Specify the design variables of this round as intermediate design variables and return to step 4, repeating steps 4 to 12.

[0151] Step 13. After the sixth movement process, the optimal design variables are [2.575 3.8125] for two consecutive times. Perform the first re-gridding, update the upper and lower boundaries of x1 to [1.3375 3.8125], and update the upper and lower boundaries of x2 to [2.575 5.05]. Return to step 3 and repeat steps 3 to 12.

[0152] Finally, after 13 moves, the number of grid divisions reached the maximum, and the optimization stopped. The optimization results are listed in Table 12:

[0153] Table 12 Optimization results of the example

[0154]

[0155] The iteration curve is as follows Fig.15 As shown in Figure 2, from the Pareto solution distribution diagram and the optimized position change diagram, we can see that DVOGRA can effectively optimize the design variables to obtain the Pareto solution, such as Fig.16 shown.

[0156] Example 6

[0157] This embodiment provides a multi-state and multi-objective engineering example, and performs a multi-state robust optimization design on a frame collision problem with multiple objectives and discrete design parameters constructed by the dynamic model of the frame frontal collision and side collision, thereby verifying the effectiveness of the proposed method. The specific steps are as follows:

[0158] Step 1. Define the optimization problem. When a car collides, the impact degree of the vehicle can be characterized by peak deceleration to protect the safety of the occupants. However, the deceleration decreases with the increase of absorbed energy, but it will cause the mass of the frame structure to increase. In addition, the maximum lateral intrusion may destroy the integrity of the battery compartment, causing battery breakdown and spontaneous combustion. Therefore, maximizing energy absorption f1(x), minimizing mass f2(x) and minimizing instantaneous maximum intrusion f3(x) are taken as the three goals of vehicle crashworthiness design. The number of people on the car as a dynamic factor also has a certain functional relationship with the corresponding indicators generated when the car collides. Therefore, the number of people on the car is set as the signal factor M = (m1, m2), with one person on the car M = m1 and a full load on the car M = m2.

[0159] Through the sensitivity relationship between the structural parameters and the three objective functions, and taking into account the symmetry of the frame structure, six frame steel plate thicknesses are selected as design variables x = [x1, x2, x3, x4, x5, x6], and these thicknesses are all discrete variables in actual products. Therefore, the optimization problem can be expressed in mathematical form as follows:

[0160] Findx=[x1,x2,x3,x4,x5,x6]

[0161]

[0162] In the formula, F1 is the objective function under the condition of one person riding in the vehicle, and F2 is the objective function under the condition of full load. In order to simplify the calculation process of this embodiment, no relevant constraint function is set in the optimization problem. For the setting and implementation of constraints, please refer to Example 5.

[0163] Step 2, set the optimizer parameters, set the number of mesh divisions to 3, the maximum number of moves to 30, and the initial mesh size s to 20. The accuracy of the design variable x is related to the number of mesh updates t. For example, the thickness of the frame steel plate as the design variable x1 is designed to have a boundary of [2.0, 4.0] mm, the initial value of the design variable x1 is x1 = 2.5 mm, the tolerance accuracy of the steel plate after rolling is 0.001 mm, and the number of mesh updates in the engineering design is t = 3 times, which can meet the design requirements of processing accuracy.

[0164] Considering the influence of the uncertainty of the elastic modulus of the material, their fluctuations are selected as noise factors. The noise factor is set to 2 levels, namely the normal elastic modulus of the material N1 and the lowest lower limit N2.

[0165] Step 3: Construct a discrete design variable table, and discretize it according to the discretization formula (2). Divide the design variable space into 20 discrete variables with equal intervals. Take x1 as an example, as shown in Table 13:

[0166] Table 13 Discrete design variable table

[0167]

[0168] Step 4: Construct a three-level design variable table, as shown in Table 14:

[0169] Table 14 Three-level design variable table

[0170]

[0171] Step 5: Call the 6-factor 3-level orthogonal test table of 27 tests and calculate. Some calculation results are listed in Table 15:

[0172] Table 15 Orthogonal test table calculation results

[0173]

[0174] Step 6: Processing constraints. In this embodiment, there are no constraints in the optimization problem, so go directly to step 7.

[0175] Step 7 to step 9, calculate the grey relational coefficient by the objective function value of each group of experiments, and use the AHP method to calculate the weight coefficients of 0.4, 0.3, and 0.3. Then calculate the grey relational degree according to formula (15). The calculation results are listed in Table 16:

[0176] Table 16 Grey correlation calculation results

[0177]

[0178] The design variables corresponding to the group of experiments with the largest grey correlation degree are taken as the candidate optimal design variable level combination, which is the group with experiment number 27 in this case. Recorded as gray optimal.

[0179] Step 10: Mean analysis. The calculation results are listed in Table 17:

[0180] Table 17 Mean analysis calculation results

[0181]

[0182] Select the group with the largest mean value of grey correlation for each design variable, that is, the combination of design variable levels with the optimal mean value. Recorded as the optimal mean.

[0183] Step 11: Determine the optimal design variables for this round. The gray optimal and mean optimal are not the same set of design variables. Then we further calculate the objective function value corresponding to the optimal mean. The calculation results are listed in Table 18. Since there are no constraints in the optimization problem, we directly determine the second norm of the objective function vector. The gray optimal calculation result is The optimal calculation result of the mean is visible So the optimal design variable is the one with the best mean.

[0184] Table 18 Mean optimal calculation results

[0185]

[0186] Steps 12-13, determine the stopping criteria, and finally the maximum number of mesh divisions is reached after 16 optimization moves. The results of the optimization design variables are listed in Table 19:

[0187] Table 19 Comparison of design variable results before and after optimization

[0188]

[0189] The optimized response value results are listed in Table 20:

[0190] Table 20 Response value optimization results table

[0191]

[0192] From the perspective of design variables, the optimized design variables are all moved to the boundary values. From the perspective of optimized response, the response output is increased by 7.1% compared with the starting point, indicating that the method of the present invention can effectively handle robust optimization problems under multiple states.

[0193] Example 7

[0194] This embodiment provides a complex equipment discrete variable optimization device based on grey correlation. Figure 5 As shown, it includes an optimization solution module, a parameter initialization module, an orthogonal design table module, a grey correlation analysis module, a mean analysis module, an optimal design variable judgment module, a stop judgment module, and an output processing module;

[0195] like Figure 6 As shown, the optimization solution module drives the following units to perform optimization problem setting and calculation steps: an objective function setting unit, which sets the objective function; a constraint condition setting unit, which sets the constraint condition; an objective function calculation unit, which calculates the objective function; a constraint condition calculation unit, which calculates the constraint value; a constraint condition processing unit, which uses two methods to eliminate the strategy and the penalty function to process the constraint condition;

[0196] like Figure 7As shown, the parameter initialization module drives the following units to perform parameter initialization steps: an optimization parameter setting unit to set the number of grid updates, the maximum number of moves, and the initial grid size s; a noise factor setting unit to set the noise factor; a signal factor setting unit to set the signal factor; an optimization starting point setting unit to set the starting point of the optimization system;

[0197] like Figure 8 As shown, the orthogonal design table module drives the following units to perform variable discretization and objective function evaluation: a discrete variable design table construction unit to construct a discrete design variable table; a three-level design variable table construction unit to construct a three-level design variable table; an orthogonal test table construction unit to construct an orthogonal test table; an optimization evaluation unit to evaluate the objective function and constraint value of each group of tests in the orthogonal test table;

[0198] like Fig. 9 As shown, the grey correlation analysis module drives the following units to perform the grey correlation degree calculation step: a data normalization unit converts the data into a small index according to the small normalization method; a grey correlation coefficient calculation unit calculates the grey correlation coefficient matrix γ (j) ; Weight calculation unit, using weight calculation method to calculate the weight of grey correlation coefficient; optimal design variable selection unit, selecting a group with the largest mean grey correlation of each design variable as the candidate optimal design variable, recorded as grey optimal design variable;

[0199] like Fig.10 As shown, the mean analysis module drives the following units to perform mean analysis steps: the data screening and sorting unit calculates the grey correlation degree r obtained from the orthogonal test design table i Screen and sort according to different levels of each design variable; mean calculation unit, calculate the grey correlation degree r at different levels of each design variable i The average value of the optimal design variable selection unit, select the level corresponding to the maximum mean value of the grey correlation degree of each design variable as the optimal level, recorded as the mean optimal design variable;

[0200] like Fig.11 As shown, the optimal design variable judgment module drives the following units to execute the optimal design variable judgment step: the design variable judgment unit judges whether the gray optimal and the mean optimal are the same set of design variables; the constraint judgment unit judges whether the constraint value corresponding to the mean optimal is in violation of the contract; the objective function judgment unit judges whether the objective function obtained by the mean optimal calculation and the objective function obtained by the gray optimal calculation have the smallest two-norm; the feedback unit feeds back the judgment result to the corresponding module;

[0201] like Fig.12As shown, the stop judgment module drives the following units to execute the step of whether the optimization system stops: the design variable judgment unit judges whether the design variables of this round are the same set of design variables as those of the previous round; the grid number judgment unit judges whether the grid division times reaches the maximum value; the boundary update unit uses the adjacent discrete values ​​of the optimal design variables of this round as new upper and lower boundaries; the feedback unit feeds back the judgment result to the corresponding module;

[0202] like Fig.13 As shown, the output processing module drives the following units to perform processing and output optimization results: a result processing unit: processes the results of the optimization solution; and a result output unit: outputs the final optimization result.

[0203] As a specific example, Fig.14 As shown, the module may include at least one processor, such as a CPU (Central Processing Unit), at least one user interface or output interface, a memory and at least one communication bus;

[0204] Optionally, the processor may include a parameter initialization module, wherein the parameter initialization module may set initialization parameters and subsequent parameter update rules through a user interface. The processor may also include an optimization solution module, which solves the optimization model by calling a calculator and a solver program in a memory. The processor may also include an output module, wherein the output module outputs the solution result through an output interface.

[0205] Alternatively, the user interface may include a display, a keyboard or a pointing device such as a mouse, a trackball, a touch pad or a touch-sensitive display screen.

[0206] Optionally, the memory may include a high-speed RAM, and may also include a non-volatile memory, such as at least one disk storage.

[0207] The communication bus is used to realize the connection and communication between the above components.

[0208] As a specific example, the memory may store a solver, a calculator, and a software program, so that the optimization solution module of the processor can call the solver and the calculator from the memory to perform optimization solution; the parameter initialization module, the stop judgment module, and the output module can implement their basic services through the software program. In some embodiments, the memory stores the following elements, executable modules or data structures, or their subsets, or their extended sets:

[0209] Optionally, the software program includes an operating system and an application program, wherein the operating system includes various system programs for implementing various basic services and processing hardware-based tasks; and the application program includes various application programs for implementing various application services. Specifically, the application program may include the application program of the complex equipment discrete variable optimization method based on grey correlation degree of the present application, and the application program may run under the operating system.

[0210] Optionally, the memory may further include a cache unit, which may be used to store cache data and optimization results generated during the optimization process.

[0211] The above is only a preferred embodiment of the present invention. The modules or units involved in the embodiments of the present application can be implemented by software or hardware. The modules or units described can also be set in a processor. For example, they can be described as: a processor includes an optimization solution module, a parameter initialization module, an orthogonal design table module, a gray correlation analysis module, a mean analysis module, an optimal design variable judgment module, a stop judgment module, and an output processing module. Among them, the names of these modules do not constitute a limitation on the module itself under certain circumstances. For example, the parameter initialization module can also be described as a "module configured to initialize user parameters and update parameters."

[0212] On the other hand, the present application also provides a computer-readable storage medium, which may be a computer-readable storage medium included in the device described in the above embodiment; or a computer-readable storage medium that exists independently and is not assembled in a terminal. The computer-readable storage medium stores one or more programs, and the programs are used by one or more processors to execute the discrete variable optimization method based on gray correlation described in the present application. The above description is only a preferred embodiment of the present application and an explanation of the technical principles used.

[0213] Those skilled in the art should understand that the scope of the invention involved in this application is not limited to the technical solutions formed by a specific combination of the above-mentioned technical features, but should also cover other technical solutions formed by any combination of the above-mentioned technical features or their equivalent features without departing from the inventive concept. For example, the above-mentioned features are replaced with the technical features with similar functions disclosed in this application but not limited thereto, and the technical solutions formed. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A complex equipment discrete variable optimization method based on grey relational degree, characterized in that: The following steps are involved: Step 1: Define the multi-state structural dynamics optimization problem; Step 2: Set optimizer parameters; Step 3: construct a discrete design variable table; Step 4: construct a three-level design variable table; Step 5: construct a three-level orthogonal test table, use the cross product array to calculate each group of tests, and obtain the target response value and constraint response value of each noise factor design point; Step 6: Use elimination strategy and penalty function to handle constraints; Step 7, calculate the grey correlation coefficient through the objective function value of each group of experiments; Step 8: Calculate the weight of each correlation coefficient; Step 9, calculate the grey correlation degree of each group of test objective function values, and take the design variables corresponding to the group of tests with the largest grey correlation degree as the grey optimal design variables; Step 10: Obtain the mean values ​​of the grey correlation corresponding to the three levels of each design variable through mean analysis, and select the group with the largest mean value of the grey correlation of each design variable as the design variable with the optimal mean value; Step 11, determine whether the round is the optimal design variable; Step 12: Determine whether the optimization satisfies the stopping criteria; Step 13: Determine whether the preset maximum number of cycles has been reached.

2. The complex equipment discrete variable optimization method based on grey relational degree according to claim 1 is characterized in that: The definition of the multi-state structural dynamics optimization problem described in step 1 is as follows: The multi-state structural dynamics optimization problem is defined as shown in formula (1): In the formula, n signal factors M=(m1,m2,…m n ), different signal factors represent the objective function vector F(x) under different states, x is the design variable; N is the total number of design variables; for each design variable x n There is an upper boundary x nmax and the lower boundary x nmin ; m is the number of objective functions f(x) under a certain state; g p (x) is the pth constraint function; P is the total number of constraints.

3. The complex equipment discrete variable optimization method based on grey relational degree according to claim 2 is characterized in that: The optimizer parameters set in step 2 include the maximum number of cycles, i.e., the number of grid divisions t, the initial grid size s, and the maximum number of moves; If robust optimization design is performed, the noise factors are set and sensitivity analysis is performed on the noise factors to determine the noise factor combinations N1 and N2 under the most unfavorable characteristics and standard conditions.

4. The complex equipment discrete variable optimization method based on grey relational degree according to claim 3 is characterized in that: The construction of the discrete design variable table described in step 3 is as follows: Constructing a discrete design variable table is also called grid division, that is, discretizing the design variables according to the initial grid size, and dividing the design variable space into s discrete variables with equal spacing. The discretization formula is: In the formula, d is the discretization step size, x ni is the i-th discrete variable of the n-th design variable; The three-level design variable table described in step 4 is constructed as follows: For each design variable, in the discrete design variable table, specify or randomly select a discrete variable as the intermediate level value, that is, the second level value, the previous value of the discrete variable is used as the first level value, and the next value is used as the third level value; if the selected discrete variable is the maximum boundary value, then it is used as the third level value, the previous value of the discrete variable is used as the second level value, and the second value is used as the first level value; if the selected discrete variable is the minimum boundary value, then it is used as the first level value, the next value of the discrete variable is used as the second level value, and the second value is used as the first level value, to construct a three-level design variable table.

5. The complex equipment discrete variable optimization method based on grey relational degree according to claim 4 is characterized in that: In step 5, a three-level orthogonal test table is constructed, and a cross product array is constructed to calculate each group of tests to obtain the target response value and the constrained response value of each noise factor design point, as follows: For M signal factors, M = m i ,i=1,2,…,n, in the mth i Under the signal factor, call or construct an N-factor three-level orthogonal test table with α tests, and calculate n×α objective function response values ​​and constraint response values; If there is a noise factor, the noise factor has two levels: standard characteristic N1 and most unfavorable characteristic N2. A cross product array is constructed to calculate 2n×α target response values ​​and constrained response values ​​under each noise factor characteristic.

6. The complex equipment discrete variable optimization method based on grey relational degree according to claim 5 is characterized in that: Step 6 describes two methods of using elimination strategy and penalty function to handle constraints, as follows: Under the elimination strategy method, the trial numbers with defaults are marked and excluded in the subsequent process of selecting the optimal design variables; Under the penalty function method, if there are constraints, they should be processed according to the penalty function, as shown in formula (3): In the formula, F new (x) is the new objective function vector, M(x) represents the penalty function vector, if g p If (x) violates the constraint, it is multiplied by the penalty coefficient c plus the original objective function vector. The penalty coefficient c is one order of magnitude higher than the original objective function, that is, c = 10×F(x).

7. The complex equipment discrete variable optimization method based on grey relational degree according to claim 6 is characterized in that: The grey correlation coefficient is calculated by the objective function value of each group of experiments as described in step 7, as follows: Step 7.1, construct the original objective function matrix F, that is, the m objective function values ​​corresponding to the n tests, forming the n×m original objective function matrix F: Step 7.2: Data normalization: convert the data into the Wang Xiao index according to the Wang Xiao normalization method. The calculation formula is: In the formula, is the normalized data, F * That is the expected small objective function matrix, F (j) Represents the j-th column of the original objective function matrix F; Step 7.3, set the reference sequence F0 to all 1s: F0＝[1 1…1] (6) Step 7.4, calculate the difference matrix D, that is, the i-th row of the minimization objective function matrix The difference with F0 is taken as the i-th row of the difference matrix D i , and thus form the difference matrix D: Step 7.5: Find the maximum value D in the difference matrix D min With the minimum value D min , the formula is: D min =max(max(D)) (8) D min =min(min(D)) (9) Step 7.6, calculate the grey correlation coefficient matrix γ (j) , use the grey correlation coefficient matrix formula composed of the difference matrix D and its maximum value M and minimum value m to calculate, the formula is: Where ξ is the resolution coefficient, ξ=0.5; The weight of calculating each correlation coefficient described in step 8 is as follows: The entropy weight method is used to calculate the weight of each correlation coefficient. When the dynamic target response is equally important, the weight is set to 1; Use the entropy weight method to calculate the weight ω j The specific process is as follows: Step 8.1, set the grey correlation coefficient matrix γ to have n rows, each row has m values, as shown in formula (11): Step 8.2: Determine the geometric projection P of each response ij , calculate the proportion P of the i-th record under the j-th index ij , the calculation formula is: Step 8.3: Calculate the entropy value E of the jth indicator j , the calculation formula is: Step 8.4: Calculate the weight ω of the jth indicator j , the calculation formula is:

8. The complex equipment discrete variable optimization method based on grey relational degree according to claim 9 is characterized in that: The grey correlation degree of each group of test objective function values ​​is calculated in step 9, and the design variables corresponding to the group of tests with the largest grey correlation degree are taken as the grey optimal design variables, as follows: Calculate the grey correlation of the objective function value of each group of experiments, and take the design variables corresponding to the group of experiments with the largest grey correlation as candidate optimal design variables, recorded as grey optimal design variables The calculation formula of grey relational degree is: The grey correlation means corresponding to the three levels of each design variable are obtained through mean analysis as described in step 10, and the group with the largest grey correlation mean of each design variable is selected as the mean optimal design variable, as follows: Step 10.1: Use the grey correlation degree r calculated from the orthogonal test design table i Filter and sort by different levels of each design variable; Step 10.2: Calculate the grey correlation degree r at different levels of each design variable i The average value is calculated as: Step 10.3: Select the level corresponding to the maximum mean value of the grey correlation degree of each design variable as the optimal design variable for the mean value.

9. The complex equipment discrete variable optimization method based on grey relational degree according to claim 8 is characterized in that: The determination of whether the wheel is the optimal design variable in step 11 is as follows: Determine the optimal grey design variables and mean optimal design variables Are they the same set of design variables? If so, this set of design variables is the optimal design variable; if not, further calculate the mean optimal design variable Corresponding objective function value and constraint value, if a breach occurs, select the gray optimal design variable As the optimal design variable; if there is no breach of contract, the vector with the smallest bi-norm of the multi-objective function is taken as the optimal design variable; The determination of whether the optimization satisfies the stopping criteria described in step 12 is as follows: Determine whether the maximum number of moves is reached. If so, the optimization ends. If not, determine whether the optimal design variables obtained in this round of optimization are consistent with the optimal design variables obtained in the previous round of optimization. If they are consistent, proceed to step 13. If not, specify the design variables in this round as intermediate design variables and return to step 4, and repeat steps 4 to 12. The determination of whether the preset maximum number of cycles is reached in step 13 is as follows: Determine whether the preset maximum number of cycles has been reached. If so, the optimization ends. If not, the adjacent discrete values ​​of the optimal design variable of this round are used as new upper and lower boundaries. If the optimal design variable of this round contains the lower boundary of the design boundary, the lower boundary remains unchanged, and the second discrete value after the optimal design variable of this round is selected as the upper boundary. If the optimal design variable of this round contains the upper boundary of the design boundary, the upper boundary remains unchanged, and the second discrete value before the optimal design variable of this round is selected as the lower boundary. Return to step 3 and repeat steps 3 to 12.

10. A complex equipment discrete variable optimization device based on grey correlation, characterized in that: The device is used to implement the complex equipment discrete variable optimization method based on grey correlation as described in any one of claims 1 to 9, and the device includes an optimization solution module, a parameter initialization module, an orthogonal design table module, a grey correlation analysis module, a mean analysis module, an optimal design variable judgment module, a stop judgment module, and an output processing module; The optimization solution module drives the following units to perform optimization problem setting and calculation steps: an objective function setting unit to set the objective function; a constraint condition setting unit to set the constraint condition; The objective function calculation unit calculates the objective function; the constraint condition calculation unit calculates the constraint value; the constraint condition processing unit uses two methods to eliminate the strategy and the penalty function to process the constraint condition; The parameter initialization module drives the following units to perform the parameter initialization step: an optimization parameter setting unit to set the number of grid updates, the maximum number of moves, and the initial grid size s; A noise factor setting unit is used to set the noise factor; The signal factor setting unit is used to set the signal factor; the optimization starting point setting unit is used to set the starting point of the optimization system; The orthogonal design table module drives the following units to perform variable discretization and objective function evaluation: a discrete variable design table construction unit to construct a discrete design variable table; a three-level design variable table construction unit to construct a three-level design variable table; an orthogonal test table construction unit to construct an orthogonal test table; an optimization evaluation unit to evaluate the objective function and constraint value of each group of tests in the orthogonal test table; The grey correlation analysis module drives the following units to perform the grey correlation degree calculation step: a data normalization unit converts the data into a small index according to the small normalization method index; a grey correlation coefficient calculation unit calculates the grey correlation coefficient matrix γ (j) ; Weight calculation unit, using weight calculation method to calculate the weight of grey correlation coefficient; The optimal design variable selection unit selects the group with the largest mean value of grey correlation degree of each design variable as the candidate optimal design variable, which is recorded as the grey optimal design variable; The mean analysis module drives the following units to perform mean analysis steps: the data screening and sorting unit calculates the grey correlation degree r obtained from the orthogonal test design table. i Filter and sort by different levels of each design variable; Mean Calculation unit, calculate the grey correlation degree r of each design variable at different levels i The average value of the optimal design variable selection unit, select the level corresponding to the maximum mean value of the grey correlation degree of each design variable as the optimal level, recorded as the mean optimal design variable; The optimal design variable judgment module drives the following units to execute the optimal design variable judgment step: a design variable judgment unit to judge whether the gray optimal and the mean optimal are the same set of design variables; a constraint judgment unit to judge whether the constraint value corresponding to the mean optimal is in violation of the contract; an objective function judgment unit to judge whether the objective function calculated by the mean optimal and the objective function calculated by the gray optimal have the smallest two-norm; a feedback unit to feed back the judgment result to the corresponding module; The stop judgment module drives the following units to execute the step of whether the optimization system should be stopped: a design variable judgment unit judges whether the design variables of this round are the same set of design variables as those of the previous round; A grid number judgment unit, for judging whether the grid division times reaches a maximum value; The boundary updating unit takes the adjacent discrete values ​​of the optimal design variables of this round as new upper and lower boundaries; A feedback unit feeds back the judgment result to the corresponding module; The output processing module drives the following units to perform processing and output optimization results: Result processing unit: processes the results of the optimization solution; Result output unit, outputs the final optimization result.

Images