A proxy optimization method for pressure vessel design under constraint weight expectation criterion

Abstract

The present invention proposes a pressure vessel design proxy optimization method under the constraint weight expectation criterion, adopts the maximum minimum Latin hypercube sampling method for initial test design; obtains the target response value of the total cost of the pressure vessel and the constraint response values ​​of the cylindrical length, shell thickness, hemispherical thickness and container volume, and establishes a DS database; establishes a Kriging proxy model based on the data in the DS database, obtains the predicted mean and predicted variance of the target response and the constraint; constructs a feasibility probability strategy and a maximization constraint weight expectation improvement criterion, and iteratively updates the DS database until the maximum number of iterations is reached or the threshold of the maximum constraint expectation improvement is met, thereby obtaining the minimum total cost target value and the corresponding optimal parameter combination. The present invention adjusts the global exploration and local search capabilities of the constraint weight expectation criterion, weakens the greedy characteristics of the constraint expectation improvement criterion, accelerates the optimization convergence and reduces the simulation cost.

Description

Technical Field

[0001] The invention relates to computer simulation and engineering optimization calculation, and in particular to a pressure vessel design proxy optimization method under the action of constraint weight expectation criterion. Background Art

[0002] With the emergence of marketing strategies such as customized products, the personalized needs of consumers have made product design and production have the characteristics of small batches and customization. Traditional physical test design can no longer meet the system design requirements of high product complexity and fast update speed. High-precision simulation models developed based on computer discipline modeling, numerical calculation and computer software and hardware technology are widely used in product and system optimization design, effectively improving the quality and reliability of traditional physical test design. In actual engineering design optimization problems, optimization efficiency is crucial. High-precision simulation modeling greatly reduces R&D costs, but modeling takes a lot of time and there is often no clear functional relationship in actual optimization problems, which brings great difficulties to engineering modeling and optimization.

[0003] The proxy optimization method is to establish a proxy model of the objective function and constraint function, drive new samples to fill the space through historical data, and continuously update the proxy model until the generated sample point sequence approaches the local or global optimal solution. The combination of the Kriging proxy model and the CEI point addition criterion realizes fast proxy optimization design under small sample conditions, which has been widely used in solving various engineering problems.

[0004] In the process of computer experimental modeling, it was found that the constrained expectation improved filling criterion has good global exploration ability and effectively improves the prediction accuracy and modeling efficiency of the Kriging model, but it is easy to fall into the trap of local optimal solution due to its greedy characteristics. Therefore, a new expectation filling criterion is urgently needed to be developed by using a weight function with distance characteristics. Summary of the invention

[0005] The purpose of the present invention is to propose a parallel agent optimization method for aviation reducers based on a mean improvement control strategy to solve the problems of expensive simulation time-consuming and low computing resource utilization in the design of aviation reducers.

[0006] The technical solution to achieve the purpose of the present invention is: a pressure vessel design proxy optimization method under the constraint weight expectation criterion, comprising the following steps:

[0007] Step 1: For the pressure vessel tooth cylindrical shell thickness, hemispherical thickness, inner radius and length of the cylindrical part of the vessel, the maximum and minimum Latin hypercube sampling method is used to perform initial test design to obtain the initialization design parameter sample;

[0008] Step 2, taking the minimum total cost of the pressure vessel as the optimization goal, taking the cylindrical length, shell thickness, hemispherical thickness and container volume of the container as constraints, constructing a pressure vessel design optimization model, using computer simulation software to implement functional evaluation, obtaining the target response value of the total cost of the pressure vessel and the constraint response values ​​of the cylindrical length, shell thickness, hemispherical thickness and container volume of the container, and saving the initialized design parameter sample and the obtained total cost target and the response values ​​of each constraint, and establishing a DS database;

[0009] Step 3: construct a Kriging proxy model based on the DS database data to obtain the predicted mean and predicted variance of the total cost target response and each constraint response;

[0010] Step 4: Determine whether there is a feasible solution for the sample in the DS database. If there is no feasible solution, construct a feasible probability strategy based on the predicted mean and predicted variance of the constraint to achieve sample filling. Otherwise, construct a maximum constraint expectation improvement criterion based on the target response and the predicted mean and predicted variance of the constraint to obtain the reference point, obtain a new test sample based on the maximum constraint weight expectation improvement criterion, and use computer software to realize simulation calculation, and place the new test sample data and its corresponding simulation output target value and response value in the DS database;

[0011] Step 5: Iterate steps 3-4 in a loop to update the DS database until the maximum number of iterations is reached or the threshold of the constraint expectation improvement criterion is met, thereby obtaining the minimum total cost target value and the corresponding optimal design parameter combination.

[0012] Furthermore, in step 2, the minimum total cost of the pressure vessel is taken as the optimization goal, and the pressure vessel design optimization model is constructed with the cylindrical length, shell thickness, hemispherical thickness and container volume of the container as constraints. Functional evaluation is achieved by computer simulation to obtain the target response value of the total cost of the pressure vessel and the constraint response values ​​of the cylindrical length, shell thickness, hemispherical thickness and container volume of the container, and the initialization design parameter sample and the target and constraint response values ​​obtained by simulation are saved to establish a DS database, in which the pressure vessel design optimization model is expressed as:

[0013] min y(x)

[0014] stg i (x)≤0,i=1,2,…,r

[0015] x∈[x l ,x r ]

[0016] Where y(x) represents the total cost of the pressure vessel; g i (x) represents the i-th pressure vessel design constraint; r = 4 represents the total number of constraints; x l ,xr denote the left and right boundary vectors of the design parameters respectively;

[0017] The simulation calculation is carried out in the finite element simulation software. First, Catia software is used for 3D modeling, and HyperMesh pre-processing software is used for meshing. Then, the finite element simulation software is used for analysis to obtain the target response value set y and the constraint response value set g. i , establish DS database.

[0018] Further, in step 3, a Kriging proxy model is established based on the data in the DS database to obtain the predicted mean and predicted variance of the target response and constraints. The specific method is as follows:

[0019] Construct a Kriging surrogate model for the total cost of a pressure vessel:

[0020]

[0021]

[0022] in, and They represent the predicted mean and predicted variance of the total cost target response of the pressure vessel respectively; 1 represents a unit vector with 1 as its element; is the estimated value of the undetermined trend term coefficient μ; y=[y1,y2,…,y m ] T is the target response vector of the total cost of the pressure vessel; R(x,x m )=R(x,x m |θ) is the Kriging kernel function selected for modeling; Variance The estimated value of; m is the number of samples in the DS database; r(x) = [R(x,x1), R(x,x2),…, R(x,x m )] T represents the design vector determined by the regression basis function; R is the correlation coefficient matrix, which is expressed as follows:

[0023]

[0024] Similarly, construct the Kriging proxy model for each constraint condition:

[0025]

[0026]

[0027] in, and Respectively represent the predicted mean and predicted variance of the i-th constraint; Rgi is the correlation coefficient matrix of the i-th constraint; is the constraint undetermined trend term coefficient The estimated value of ; obtained by generalized least squares estimation, is the estimated variance of the i-th constrained Gaussian process distribution.

[0028] Further, step 4 determines whether there is a feasible solution that satisfies the pressure vessel constraint conditions in the sample in the DS database. If there is no feasible solution, the maximum feasibility probability criterion is constructed according to the predicted mean and predicted variance of the constraint to achieve sample filling. Otherwise, the maximum constraint expectation improvement criterion is constructed according to the predicted mean and variance of the target and constraint to obtain the new test sample reference point, and the constraint weight expectation improvement criterion is constructed according to the obtained reference point and the Kriging proxy model to achieve spatial sample filling, and the computer simulation software is used to realize the simulation calculation, and the obtained filling sample data and its corresponding simulation target and each constraint response value are placed in the DS database. The specific method is as follows:

[0029] Step 41: The total cost target response vector y = [y1, y2, ..., y n ] T , calculate the current minimum total cost y of the pressure vessel min =min{y1,y2,…,y m};

[0030] Step 42: construct a maximization feasibility probability criterion based on the predicted mean and predicted variance of each constraint target, construct a maximization constraint expectation improvement criterion based on the total cost target response of the pressure vessel and the predicted mean and predicted variance of each constraint, obtain new sample reference points, and construct a constraint weight expectation improvement criterion based on the obtained reference points and the Kriging proxy model;

[0031] assumed The criterion for maximizing feasibility probability can be expressed as follows:

[0032]

[0033] Among them, x n+1 is the m+1th new design sample, Φ(·) is the cumulative probability density function; r is the number of constraints; Respectively represent the response mean and standard deviation of the i-th constraint;

[0034] Assuming that the total cost target of the pressure vessel and each constraint condition are independent of each other, the new sample reference point is obtained by maximizing the constraint expectation improvement criterion, which can be expressed as:

[0035]

[0036] Among them, xR is the new sample reference point, assuming The total cost target of pressure vessels is to improve the incremental Under these conditions, the criterion for maximizing EI points can be expressed by the following function:

[0037]

[0038] Among them, y min is the current optimal target value, and represents the predicted value and the predicted standard deviation. Φ(·) and φ(·) are the cumulative distribution function and the distribution probability density function; is the local search term, which represents the local search capability of the EI criterion; is the global exploration item of the EI criterion, representing the global exploration capability of the EI criterion;

[0039] According to the obtained reference points and the predicted mean and predicted variance provided by the Kriging model, two improved criteria for maximizing the constraint weight expectation can be obtained, which are expressed as follows:

[0040]

[0041] and

[0042]

[0043] in, and Represents the expected improvement criteria of the constraint right; represents the weighted expected improvement function, represents the pseudo-expected improvement function, PoF represents the probability of calculating the feasibility of the current test point; Kriging kernel function hyperparameters derived from Kriging modeling; d is the dimension of design variables; is the weight function; represents the kth dimension of the reference point;

[0044] Step 43: Determine whether there is a feasible solution that satisfies all constraints in the DS database. If there is no feasible solution, sample filling is implemented according to the maximization feasibility probability criterion. Otherwise, a reference point is obtained according to the maximization constraint expectation improvement criterion, and then a new sample is obtained according to any maximization constraint weight expectation improvement criterion to implement sample filling.

[0045] Step 44: Use a computer to perform simulation calculations, and place the (m+1)th filled sample data and its corresponding simulation output pressure vessel total cost target value and corresponding constraint response values ​​in the DS database, and update the DS database.

[0046] A pressure vessel design proxy optimization system under the constraint weight expectation criterion realizes the pressure vessel proxy optimization design based on the pressure vessel design proxy optimization method under the constraint weight expectation criterion.

[0047] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the pressure vessel design agent optimization method based on the constraint weight expectation criterion is used to achieve the optimal design of the pressure vessel.

[0048] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements an optimized design of a pressure vessel based on a pressure vessel design proxy optimization method under the constraint weight expectation criterion.

[0049] Compared with the prior art, the present invention has the following significant advantages: 1) The proposed proxy optimization method for pressure vessel design under the constraint weight expectation filling criterion can be used for expensive optimization and black box problems, and has certain advantages in feasibility, modeling efficiency and robustness of solutions; 2) The two constructed constraint weight expectation filling criteria can both efficiently perform spatial exploration of reference points and new test parameters, and the selected new parameter sample points are all better than the current optimal values, thereby realizing rapid proxy optimization of pressure vessel design problems and facilitating rapid solution of expensive constraint optimization problems; 3) The two constructed weight expectation filling criteria realize the adjustment of the Kriging model and the global optimization of the pressure vessel design problem, so that it can improve the model prediction accuracy and Kriging modeling efficiency when solving multi-parameter black box optimization problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 Flowchart of the improvement criteria expected for the constraints of the present invention.

[0051] Figure 2 It is a comparison chart of the optimization results of the test problem of the present invention under the action of three filling criteria.

[0052] Figure 3 This is a comparison chart of the approximate optimal solution results of the test problem of the present invention.

[0053] Figure 4 A simplified schematic diagram of a pressure vessel constructed for the present invention. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0055] The design proxy optimization method of pressure vessels under the constraint weight expectation criterion of the present invention first adopts the maximum and minimum Latin hypercube sampling technology (latin hypercube sampling, LHS) for space filling, and uses computer simulation to obtain response data; secondly, using the sample data in the DS database, the Kriging model is selected for alternative estimation to reduce the simulation calculation burden; then, the prediction uncertainty information of the Kriging model is fully utilized, and the weight expectation improvement criterion is constructed according to the functional relationship between the distance function and the improvement increment, so that it has the characteristics of adaptive adjustment according to the reference point distance and then jumping out of the local optimal solution to achieve global optimization; finally, the termination condition is reached, and the optimal target value and the best design parameters of the expensive constrained optimization problem are obtained.

[0056] It is worth noting that if there is no feasible solution in the initial DS database, the maximization feasibility probability criterion is used to fill the space until the feasible solution conditions are met and then the constrained weight expectation improvement criterion is switched to maximize; the weight in the constrained weight expectation improvement criterion is related to the distance and is the control function of the new test sample with respect to the reference point; in the optimization process, the Kriging proxy model is used to replace the time-consuming simulation model, which can greatly reduce the computational cost.

[0057] like Figure 1 As shown, the pressure vessel design proxy optimization method under the constraint weight expected filling criterion of the present invention specifically includes the following steps:

[0058] Step 1: Determine the thickness T of the cylindrical shell of the pressure vessel s , hemisphere thickness T h The maximum and minimum LHS method was used to carry out the initial test design for the four parameters, namely, the inner radius R and the length L of the cylindrical part of the container, and 5×4+1=21 initialization parameter samples were obtained;

[0059] The LHS method is a method of approximating random sampling from a multivariate parameter distribution. It belongs to the stratified sampling technique and is often used in computer experiments or Monte Carlo integration. It is not limited by the number of levels and factors, has high flexibility and is easy to implement. It is most widely used in computer experimental design. In the implementation of the LHS method, it is assumed that n sample points need to be drawn, and the sample point x∈[0,1] d Sampling satisfies: (1) Each sample point is evenly distributed in a small interval; (2) When all sample points are projected onto any dimension, there is only one sample point in each of the n subintervals on the dimension. Divide the d-dimensional design space into n subspaces evenly along each dimension of the design variable: The n subspaces of all design variables are combined into dn subspaces, and one sample is randomly drawn in each d-dimensional subspace.

[0060] For the maximum minimum LHS method, for each extracted sample point, the minimum distance of the remaining previous sample points is selected as the characteristic distance of the sample, and the sample distance is maximized as much as possible. All the extracted sample points fill the entire sample space instead of being close together. Suppose the real sample x∈[x l ,x r ], then use the maximum and minimum extraction of all sample points x∈[0,1] d , so the following transformation is required

[0061] x=x l +(x r -x l )x

[0062] Step 2: Use computer simulation software to implement functional evaluation, obtain the target response value of the total cost of the pressure vessel and the constraint response values ​​of the cylindrical length, shell thickness, hemispherical thickness and vessel volume of the vessel, save the initialization design parameter sample and the obtained total cost target and the response value of each constraint, and establish a DS database;

[0063] The pressure vessel design optimization model is expressed as:

[0064] min y(x)

[0065] stg i (x)≤0,i=1,2,…,r

[0066] x∈[x l ,x r ]

[0067] Where y(x) represents the total cost of the pressure vessel; g i (x) represents the i-th pressure vessel design constraint; r = 4 represents the total number of constraints; x l ,x r denote the left and right boundary vectors of the design parameters respectively;

[0068] The simulation calculation is carried out in the finite element simulation software. First, Catia software is used for 3D modeling, and HyperMesh pre-processing software is used for meshing. Then, the finite element simulation software is used for analysis to obtain the target response value set y and the constraint response value set g. i , establish DS database.

[0069] Step 3: Establish a Kriging proxy model based on the data in the DS database to obtain the predicted mean and predicted variance of the target response and constraints. The specific method is as follows:

[0070] Construct a Kriging surrogate model for the total cost of a pressure vessel:

[0071]

[0072]

[0073] in, and They represent the predicted mean and predicted variance of the total cost target response of the pressure vessel respectively; 1 represents a unit vector with 1 as its element; is the estimated value of the undetermined trend term coefficient μ; y=[y1,y2,…,y m ] T is the target response vector of the total cost of the pressure vessel; R(x,x m )=R(x,x m |θ) is the Kriging kernel function selected for modeling; Variance The estimated value of; m is the number of samples in the DS database; r(x) = [R(x,x1), R(x,x2),…, R(x,x m )] T represents the design vector determined by the regression basis function; R is the correlation coefficient matrix, which is expressed as follows:

[0074]

[0075] Similarly, the Kriging proxy model of each constraint condition can be obtained:

[0076]

[0077]

[0078] in, and They represent the predicted mean and predicted variance of the i-th constraint respectively; is the correlation coefficient matrix of the i-th constraint; is the constraint undetermined trend term coefficient The estimated value of ; obtained by generalized least squares estimation, is the estimated variance of the i-th constrained Gaussian process distribution.

[0079] Step 4: Determine whether there is a feasible solution that meets the pressure vessel constraint conditions in the sample in the DS database. If there is no feasible solution, construct the maximum feasibility probability criterion according to the predicted mean and predicted variance of each constrained Kriging model to achieve sample filling. Otherwise, construct the maximum constraint expectation improvement criterion according to the predicted mean and variance of the target Kriging model and each constrained Kriging model to obtain the new test sample reference point, and construct the constraint weight expectation improvement criterion according to the obtained reference point and the Kriging proxy model to achieve spatial sample filling, and use computer simulation software to realize simulation calculation, and place the obtained filling sample data and its corresponding simulation target and each constraint response value in the DS database. The specific method is as follows:

[0080] Step 41: The total cost target response vector y = [y1, y2, ..., y n ] T , calculate the current minimum total cost y of the pressure vessel min =min{y1,y2,…,y m};

[0081] Step 42: construct a maximization feasibility probability criterion based on the predicted mean and predicted variance of each constraint target, construct a maximization constraint expectation improvement criterion based on the total cost target response of the pressure vessel and the predicted mean and predicted variance of each constraint, obtain a new sample reference point, and then construct a constraint weight expectation improvement criterion;

[0082] assumed The criterion for maximizing feasibility probability can be expressed as follows:

[0083]

[0084] Where Φ(·) is the cumulative probability density function; r is the number of constraints; Respectively represent the response mean and standard deviation of the i-th constraint;

[0085] Assuming that the total cost target of the pressure vessel and each constraint condition are independent of each other, the new sample reference point is obtained by maximizing the constraint expectation improvement criterion, which can be expressed as:

[0086]

[0087] Among them, x R is the new sample reference point, assuming The total cost target of pressure vessels is to improve the incremental Under these conditions, the criterion for maximizing EI points can be expressed by the following function:

[0088]

[0089] Among them, ymin is the current optimal target value, and represents the predicted value and the predicted standard deviation. Φ(·) and φ(·) are the cumulative distribution function and the distribution probability density function; is the local search term, which represents the local search capability of the EI criterion; It is the global exploration item of the EI criterion, representing the global exploration capability of the EI criterion.

[0090] According to the obtained reference points and the predicted mean and predicted variance provided by the Kriging model, two improved criteria for maximizing the constraint weight expectation can be obtained, which are expressed as follows:

[0091]

[0092] and

[0093]

[0094] in, and Represents the expected improvement criteria of the constraint right; represents the weighted expected improvement function, represents the pseudo-expected improvement function, PoF represents the probability of calculating the feasibility of the current test point; Kriging kernel function hyperparameters derived from Kriging modeling; d is the dimension of design variables; is the weight function; Represents the kth dimension of the reference point.

[0095] Step 43: Determine whether there is a feasible solution that satisfies all constraints in the DS database. If there is no feasible solution, sample filling is implemented according to the maximization feasibility probability criterion. Otherwise, a reference point is obtained according to the maximization constraint expectation improvement criterion, and then a new sample is obtained according to any maximization constraint weight expectation improvement criterion to implement sample filling.

[0096] Step 44: Use a computer to perform simulation calculations, and place the (m+1)th filled sample data and its corresponding simulation output pressure vessel total cost target value and corresponding constraint response values ​​in the DS database, and update the DS database.

[0097] Step 5: The termination condition can be set according to the computing resources or according to the threshold of the maximum constraint expected improvement criterion. If it is set according to the computing resources in the project, let T max It represents the maximum number of iterations set in the optimization process. The DS database is updated by iterative steps 3-4 until the maximum number of iterations is reached. Based on this, the minimum target value of the total cost of the pressure vessel and the corresponding optimal parameter combination x are obtained. *If the termination condition is set according to the threshold of the maximum constraint expectation improvement criterion, it can be expressed as:

[0098] CEI max ≤10 -5 ε,

[0099] Among them, 10 -5 ε is the set improvement threshold; CEI max is the maximum value of the constrained expected improvement criterion; ε, (ε∈[1,5]) is an integer.

[0100] It is worth noting that the proxy model referred to in the present invention is the Kriging model, and the proposed optimization strategy is also applicable to other proxy models and prediction problems under the Bayesian framework; the evolutionary method for maximizing the constrained expected improvement criterion to obtain new space filling sample processes selects the particle swarm method, and in addition, methods such as grid search, differential evolution method and greedy wolf method can all be used to solve this sub-optimization problem; the modeling process of the present invention selects the Kriging kernel function as the Gaussian kernel function, and it can also extend this method to other Kriging kernel functions to achieve distance adjustment; the application field of the present invention is the expensive constrained optimization problem in engineering, and it is also applicable to the expensive unconstrained optimization problem without considering the constraints.

[0101] Example

[0102] In order to verify the effectiveness of the scheme of the present invention, the following experiment was carried out.

[0103] In this embodiment, Figure 4 The pressure vessel design case shown in the figure is tested, and the pressure vessel design agent optimization method under the constraint weight expected filling criterion is specifically comprised of the following steps:

[0104] Step 1: According to Figure 4 The design diagram of the pressure vessel shown in the figure adopts the maximum and minimum LHS sampling technology to measure the thickness T of the cylindrical shell of the pressure vessel. s , hemisphere thickness T h The maximum and minimum LHS method was used to carry out the initial test design for the four parameters, namely, the inner radius R and the length L of the cylindrical part of the container, and 5×4+1=21 initialization parameter samples were obtained;

[0105] Step 2: Use computer simulation software to perform a functional evaluation of the pressure vessel design problem to obtain the total cost y of the vessel c (x) and the constraint response values ​​of the cylindrical length, shell thickness, hemispherical thickness and container volume, and save the initialization parameter sample and the obtained target and constraint response values ​​to establish a sample database DS;

[0106] Step 3: Obtain the predicted mean and predicted variance of the total cost of the pressure vessel, as well as the predicted uncertainty information of each constraint condition;

[0107] Step 4: Determine whether there is a feasible solution that meets the pressure vessel constraint conditions among the 21 samples in the DS database. If there is no feasible solution, the PoF criterion is maximized to achieve sample filling. Otherwise, the reference point of the new test sample is obtained based on the CEI criterion. According to the obtained reference point and the Kriging proxy model, the constraint weight expectation improvement criterion is constructed to achieve spatial sample filling. The computer finite element simulation software is used to realize the simulation calculation, and the obtained filling sample data and its corresponding simulation target and each constraint response value are placed in the DS database;

[0108] Step 5: Set the total number of simulation tests T according to the computing resources max =100, when T≥T max When it is satisfied, the method stops; otherwise, the above steps are repeated until the termination condition is reached and the optimal parameter combination is output.

[0109] Select the worst result (maxY) and average the results and standard deviation (σ Y ) is used as the measurement index, and the data of 30 repeated tests are statistically analyzed. The specific results are shown in Table 1.

[0110] Table 1 Comparison of design optimization results of pressure vessels with three filling strategies

[0111]

[0112] Comparing the results in Table 1, we can see that the approximate solutions obtained by the three criteria are all close to the optimal values, which shows the effectiveness of the two newly proposed point-adding criteria, and the proxy optimization methods under the action of the two proposed criteria have achieved ideal optimization results. The CPEI strategy is the best. This shows that the proposed proxy optimization method can solve practical engineering problems well.

[0113] In order to better illustrate the effectiveness of the weighted expectation filling criterion, the classic test cases of G4 and G7 containing 5 and 10 parameters and CS and SRD containing 11 and 7 parameters are selected for verification, and the results are compared with the classic CEI criterion to verify the effectiveness, efficiency and robustness of the proposed proxy optimization method. The test case is expressed as follows:

[0114]

[0115] st:g1(x)=85.334407+0.0056858x2x5+0.0006262x1x4-0.0022053x3x5-92≤0;

[0116] g2(x)=-85.334407-0.0056858x2x5-0.0006262x1x4+0.0022053x3x5≤0;

[0117]

[0118]

[0119] g5(x)=9.300961+0.0047026x3x5+0.0012547x1x3+0.0019085x3x4-25≤0;

[0120] g6(x)=-9.300961-0.0047026x3x5-0.0012547x1x3-0.0019085x3x4+20≤0,

[0121] 78≤x1≤102,33≤x2≤45,27≤x i ≤45(i=3,4,5)

[0122]

[0123] s.t:g1(x)=-105+4x1+5x2-3x7+9x8≤0;

[0124] g2(x)=10x1-8x2-17x7+2x8≤0;

[0125] g3(x)=-8x1+2x2+5x9-2x 10 -12≤0;

[0126]

[0127]

[0128]

[0129]

[0130] g8(x)=-3x1+6x2+12(x9-8) 2 -7x 10 ≤0,-10≤x i ≤0(i=1,2,…,10)

[0131] CSI:min f(x)=1.98+4.9x1+6.67x2+6.98x3+4.01x4+1.78x5+0.00001x6+2.73x7;

[0132] s.t.g1(x)=1.16-0.317x2x4-0.00931x2x 10 -0.484x3x9+0.01343x6x 10 -1≤0,

[0133] g2(x)=0.261-0.0159x1x2-0.188x1x8-0.87570x5x 10 +0.08045x6x9+0.00139x8x 11 +0.00001575x 10 x 11 -0.32≤0,

[0134] g3(x)=0.214+0.00817x5-0.131x1x8-0.0704x1x9+0.03099x2x6-0.018x2x7+0.0208x3x8+0.121x3x9-0.00364x5x6+0.0007715x5x 10 -0.0005354x6x 10 +0.00121x8x 11 +0.00184x9x 10 -0.018x2 2 -0.32≤0,

[0135] g4(x)=0.74-0.61x2-0.163x3x8+0.001232x3x 10 -0.166x7x9+0.227x2 2 -0.32≤0,

[0136] g5(x)=28.98+3.818x3-4.2x1x2+0.0207x5x 10 +6.63x6x9-7.77x7x8+0.32x9x 10 -32≤0,

[0137] g6(x)=33.86+2.95x3+0.1792x 10 -5.057x1x2-11x2x8-0.0215x5x 10 -9.98x7x8+22x8x9-32≤0,

[0138] g7(x)=46.36-9.9x2-12.9x1x8+0.1107x3x 10 -32≤0,

[0139] g8(x)=4.72-0.5x4-0.19x2x3-0.0122x4x 10 +0.009325x6x 10 +0.000191x 11 2 -4≤0,

[0140] g9(x)=10.58-0.674x1x2-1.95x2x8+0.02054x3x 10 -0.0198x4x 10 +0.028x6x 10 -9.9≤0,

[0141] g 10 (x)=16.45-0.489x3x7-0.843x5x6+0.0432x9x 10 -0.0556x9x 11 -0.000786x 11 2 -15.7≤0,

[0142] 0.5≤x1,x3,x4≤1.5,0.45≤x2≤1.35,0.875≤x5≤2.625,0.4≤x6≤1.2,0.4≤x7≤1.2

[0143]

[0144]

[0145]

[0146]

[0147] g8(x)=5x2≤x1;g9(x)=x1≤12x2;g 10 (x)=1.5x6+1.9≤x4;

[0148] g 11 (x)=1.1x7+1.9≤x5,

[0149] 2.6≤x1≤3.6,0.7≤x2≤0.8,17≤x3≤28,7.3≤x4,x5≤8.3,

[0150] The convergence effects of the proxy optimization methods under the CEI, CWEI and CPEI filling criteria of the four test cases are compared. In order to eliminate the influence of the randomness of the initial test design on the optimization results, the average value of the optimization results under 30 groups of initial test designs versus the number of iterations is used to evaluate the optimization ability and convergence of each method. Figure 2 shown.

[0151] Depend on Figure 2 It is known that the four examples can converge to the approximate optimal solution with the increase of the number of iterations under the three criteria, which shows the effectiveness of the proxy optimization method under the two new weight expectation filling criteria. For the G7, CSI and SRD examples, when reaching the same accuracy, the CWEI criterion has fewer iterations than the CEI criterion, which shows that the optimization method under the CWEI criterion is an effective method to speed up the convergence speed. For the CPEI criterion, although its convergence speed is slower than that of the classic CEI criterion and CWEI criterion, its approximate optimal solution has better accuracy. For the G4 example, although the convergence speed of the CPEI and CWEI criteria is slower than that of the CEI criterion, the overall gap is not very large, and it can converge to the approximate optimal solution very well. In general, the proxy optimization methods under the CWEI and CPEI criteria have excellent performance in the accuracy of optimization results and optimization efficiency.

[0152] Each case is simulated in T max = 100 times, a final optimal value will be output. In order to further compare the optimization robustness and effectiveness of the three criteria, the statistical data of each case was repeated 30 times for statistical analysis. The results are shown in Table 2:

[0153] Table 2 Comparison of proxy optimization results under different filling criteria

[0154]

[0155] As shown in Table 2, for the G4 and SRD examples, the maximum value, average value and standard deviation of the CPEI criterion are better than those of the CEI criterion, indicating that the optimization method under the CPEI criterion can better explore the optimal solution area and the criterion is least affected by the randomness of the initial experimental design; while the CWEI criterion is better than the CEI criterion in terms of standard deviation. Although the maximum value and average value are not better than the CEI criterion, its results are close to the known optimal value, indicating that the criterion is effective. For the CSI example, the results of the CWEI criterion are better, and the CPEI criterion also has a good performance. For the G7 example, although the results of the CEI criterion are better, the average values ​​of the CWEI and CPEI criteria are not much different from those of the CEI criterion, indicating that the optimization methods under the two criteria also have good accuracy. In general, the two newly proposed point-adding criteria have good effectiveness and optimization robustness.

[0156] The proxy optimization method under the three filling criteria is optimized for four examples, repeated 30 times, and the obtained approximate optimal values ​​are statistically analyzed and box plots are drawn. Figure 3 As shown:

[0157] Depend on Figure 3 It can be seen that for the G4 example, the results of the CWEI and CPEI criteria are more concentrated than those of the classic CEI criterion, and the box plots are also flatter, indicating that the two criteria are less affected by the randomness of the experiment; among them, the result of the CPEI criterion is the best. For the G7 and CSI examples, the results of the CWEI and CPEI criteria are similar to those of the classic CEI criterion, while the box plot of the CWEI criterion is flatter. For the SRD example, the box plots of the results of the three criteria are similar in flatness, but the mean of the results of the CPEI criterion is better. In general, the proxy optimization methods under the constraint weight expectation improvement criterion can obtain good approximate optimal solutions with good robustness.

[0158] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0159] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A pressure vessel design proxy optimization method under the constraint weight expectation criterion, characterized in that: The steps include: Step 1: For the thickness of the cylindrical shell of the pressure vessel, the thickness of the hemisphere, the inner radius and the length of the cylindrical part of the vessel, the maximum and minimum Latin hypercube sampling method is used to perform initial test design to obtain the initialization design parameter sample; Step 2, taking the minimum total cost of the pressure vessel as the optimization goal, taking the cylindrical length, shell thickness, hemispherical thickness and container volume of the container as constraints, constructing a pressure vessel design optimization model, using computer simulation software to implement functional evaluation, obtaining the target response value of the total cost of the pressure vessel and the constraint response values ​​of the cylindrical length, shell thickness, hemispherical thickness and container volume of the container, and saving the initialized design parameter sample and the obtained total cost target and the response values ​​of each constraint, and establishing a DS database; Step 3: construct a Kriging proxy model based on the DS database data to obtain the predicted mean and predicted variance of the total cost target response and each constraint response; Step 4: Determine whether there is a feasible solution for the sample in the DS database. If there is no feasible solution, construct a feasible probability strategy based on the predicted mean and predicted variance of the constraint to achieve sample filling. Otherwise, construct a maximum constraint expectation improvement criterion based on the target response and the predicted mean and predicted variance of the constraint to obtain the reference point, obtain a new test sample based on the maximum constraint weight expectation improvement criterion, and use computer software to realize simulation calculation, and place the new test sample data and its corresponding simulation output target value and response value in the DS database; Step 5, iterate steps 3-4 to update the DS database until the maximum number of iterations is reached or the threshold of the constraint expectation improvement criterion is met, thereby obtaining the minimum total cost target value and the corresponding optimal design parameter combination; Step 2: Taking the minimum total cost of the pressure vessel as the optimization goal, taking the cylindrical length, shell thickness, hemispherical thickness and vessel volume of the vessel as constraints, constructing a pressure vessel design optimization model, using computer simulation to achieve functional evaluation, obtaining the target response value of the total cost of the pressure vessel and the constraint response values ​​of the cylindrical length, shell thickness, hemispherical thickness and vessel volume of the vessel, and saving the initialization design parameter sample and the target and constraint response values ​​obtained by simulation, and establishing a DS database, where the pressure vessel design optimization model is expressed as: min y(x) s.t.g i (x)≤0,i=1,2,…,r x∈[x l ,x r ] Where y(x) represents the total cost of the pressure vessel; g i (x) represents the i-th pressure vessel design constraint; r = 4 represents the total number of constraints; x l ,x r denote the left and right boundary vectors of the design parameters respectively; The simulation calculation is carried out in the finite element simulation software. First, Catia software is used for 3D modeling, and HyperMesh pre-processing software is used for meshing. Then, the finite element simulation software is used for analysis to obtain the target response value set y and the constraint response value set g. i , establish DS database; Step 3: Establish a Kriging proxy model based on the data in the DS database to obtain the predicted mean and predicted variance of the target response and constraints. The specific method is as follows: Construct a Kriging surrogate model for the total cost of a pressure vessel: in, and They represent the predicted mean and predicted variance of the total cost target response of the pressure vessel respectively; 1 represents a unit vector with 1 as its element; is the estimated value of the undetermined trend term coefficient μ; y=[y1,y2,…,y m ] T is the target response vector of the total cost of the pressure vessel; R(x,x m )=R(x,x m |θ) is the Kriging kernel function selected for modeling; Variance The estimated value of; m is the number of samples in the DS database; r(x) = [R(x,x1), R(x,x2),…, R(x,x m )] T represents the design vector determined by the regression basis function; R is the correlation coefficient matrix, which is expressed as follows: Similarly, construct the Kriging proxy model for each constraint condition: in, and They represent the predicted mean and predicted variance of the i-th constraint respectively; is the correlation coefficient matrix of the i-th constraint; is the constraint undetermined trend term coefficient The estimated value of ; obtained by generalized least squares estimation, is the estimated variance of the i-th constrained Gaussian process distribution; Step 4: Determine whether there is a feasible solution that satisfies the pressure vessel constraint conditions in the samples in the DS database. If there is no feasible solution, construct the maximum feasibility probability criterion according to the predicted mean and predicted variance of the constraint to achieve sample filling. Otherwise, construct the maximum constraint expectation improvement criterion according to the predicted mean and predicted variance of the target and constraint to obtain the new test sample reference point, and construct the constraint weight expectation improvement criterion according to the obtained reference point and the Kriging proxy model to achieve spatial sample filling. Use computer simulation software to realize simulation calculation, and place the obtained filling sample data and its corresponding simulation target and each constraint response value in the DS database. The specific method is as follows: Step 41: The total cost target response vector y = [y1, y2, ..., y n ] T , calculate the current minimum total cost y of the pressure vessel min =min{y1,y2,…,y m }; Step 42: construct a maximization feasibility probability criterion based on the predicted mean and predicted variance of each constraint target, construct a maximization constraint expectation improvement criterion based on the total cost target response of the pressure vessel and the predicted mean and predicted variance of each constraint, obtain new sample reference points, and construct a constraint weight expectation improvement criterion based on the obtained reference points and the Kriging proxy model; assumed The criterion for maximizing feasibility probability is expressed as follows: Among them, x n+1 is the m+1th new design sample, Φ(·) is the cumulative probability density function; r is the number of constraints; Respectively represent the response mean and standard deviation of the i-th constraint; Assuming that the total cost target of the pressure vessel and each constraint condition are independent of each other, the new sample reference point is obtained by maximizing the constraint expectation improvement criterion, which is expressed as: Among them, x R is the new sample reference point, assuming The total cost target of pressure vessels is to improve the incremental Under these conditions, the criterion for maximizing EI points is expressed by the following function: Among them, y min is the current optimal target value, and represents the predicted value and predicted standard deviation, Φ(·) and φ(·) are the cumulative distribution function and the distribution probability density function; is the local search term, which represents the local search capability of the EI criterion; is the global exploration item of the EI criterion, representing the global exploration capability of the EI criterion; According to the obtained reference points and Kriging model, two improvement criteria for maximizing the constraint weight expectation are constructed, which are expressed as follows: and in, and Represents the expected improvement criteria of the constraint right; represents the weighted expected improvement function, represents the pseudo-expected improvement function, PoF represents the probability of calculating the feasibility of the current test point; Kriging kernel function hyperparameters derived from Kriging modeling; d is the dimension of design variables; is the weight function; represents the kth dimension of the reference point; Step 43: Determine whether there is a feasible solution that satisfies all constraints in the DS database. If there is no feasible solution, sample filling is implemented according to the maximization feasibility probability criterion. Otherwise, a reference point is obtained according to the maximization constraint expectation improvement criterion, and a new sample is obtained according to any maximization constraint weight expectation improvement criterion to implement sample filling. Step 44: Use a computer to perform simulation calculations, and place the (m+1)th filled sample data and its corresponding simulation output pressure vessel total cost target value and corresponding constraint response values ​​in the DS database, and update the DS database.

2. A pressure vessel design agent optimization system under the constraint weight expectation criterion, characterized in that: Based on the pressure vessel design proxy optimization method under the constraint weight expectation criterion described in claim 1, the pressure vessel proxy optimization design is realized.

3. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the pressure vessel design agent optimization method based on the constraint weight expectation criterion described in claim 1 is used to achieve pressure vessel optimization design.

4. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the pressure vessel design agent optimization method under the constraint weight expectation criterion of claim 1 is used to achieve the optimal design of the pressure vessel.

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