A Variable Credibility Constraint Optimization Method and System Based on Surrogate Model

Abstract

The present invention discloses a variable credibility constraint optimization method and system based on a surrogate model. The method includes: taking the design parameters of the structure to be optimized as variables, establishing constraints and an objective function; randomly generating initial design parameters and substituting them into finite element models with different precisions to obtain response values with different precisions, using the initial design parameters and their corresponding response values as initial sample points to form a sample point library, and thus establishing a variable credibility surrogate model; searching for the minimum value of the target supplementary point criterion to determine the target candidate supplementary points and the corresponding finite element model precision, searching for the minimum value of the constraint supplementary point criterion to determine the constraint candidate supplementary points, and selecting the corresponding finite element model precision; selecting update points from the target and constraint candidate supplementary points, and adding the update points including the response values to the sample point library; satisfying the stopping criterion, and selecting the design parameters corresponding to the optimal response value from the sample point library as the optimal design parameters. The present invention makes full use of model information with different precisions and has high optimization efficiency.

Description

Technical Field

[0001] The present invention belongs to the cross - field of optimization algorithm design and structural design, and more specifically, relates to a variable - credibility constraint optimization method and system based on a surrogate model. Background Art

[0002] In engineering optimization design that relies on time - consuming numerical simulations, the optimization method based on a surrogate model has been widely used due to its high efficiency. Generally, a high - precision numerical simulation model can obtain relatively accurate numerical simulation results, but it requires a high time cost. A low - precision numerical simulation model can obtain simulation results at a relatively low time cost, but the difference between the simulated value and the true value is large.

[0003] In the optimization method based on a surrogate model, the most common way is to use a single - precision surrogate model to approximate the time - consuming simulation model, and design the optimization criterion according to the predicted value of the surrogate model and the uncertainty of the predicted value. For example, the efficient global optimization algorithm based on the constrained expected improvement criterion (CEI). In this algorithm, the Kriging surrogate model is used to approximately calculate the time - consuming objective simulation model and constraint simulation model, and then, according to the product of the probability of feasibility (PoF) of the predicted value and the expected improvement value (EI) of the current feasible optimal solution, the supplementary point is selected. Through iteration, the CEI criterion is maximized to gradually supplement points with high probability of feasibility and the maximum expected improvement value until the stopping criterion is met, and the obtained feasible optimal solution is output. Although this method has achieved high efficiency in many practical problems, when the optimal solution is located on the constraint boundary, due to the lack of explicit treatment of constraints, its optimization efficiency is reduced.

[0004] The algorithm MCSO based on self - detection of constraint accuracy uses a single - precision surrogate model to approximate the objective function and constraint function. Through the supplementary - point criterion of actively improving the accuracy of the constraint boundary, the algorithm efficiency has been effectively improved. In addition, by self - detecting the constraint accuracy to stop the supplementary points of the constraint boundary, the supplementary - point efficiency is further improved. Although this method has certain advantages compared with the classical single - precision constraint optimization algorithm, when different - precision models exist, it cannot make full use of the information provided by different - precision models to effectively reduce the time cost of optimization design.

[0005] Therefore, the existing surrogate - model optimization technologies have technical problems such as being unable to make full use of the information of different - precision models and having low optimization efficiency. Summary of the Invention

[0006] In view of the above - mentioned defects or improvement requirements of the existing technology, the present invention provides a variable - credibility constraint optimization method and system based on a surrogate model, thereby solving the technical problems that the existing surrogate - model optimization technologies are unable to make full use of the information of different - precision models and have low optimization efficiency.

[0007] To achieve the above object, according to one aspect of the present invention, a variable credibility constraint optimization method based on a surrogate model is provided, including the following steps:

[0008] (1) Taking the design parameters of the structure to be optimized as variables, constraining the structure to be optimized, establishing a constraint function, obtaining finite element models with different precisions by using different unit mesh densities, calculating the optimization objective through finite element models with different precisions, and establishing an objective function;

[0009] (2) Randomly generating initial design parameters within the range of the design parameter values, substituting the initial design parameters into finite element models with different precisions, obtaining response values with different precisions for the optimization objective, taking the initial design parameters and their corresponding response values as initial sample points, forming a sample point library, and thus establishing a variable credibility surrogate model;

[0010] (3) Combining the variable credibility lower confidence bound function of the objective function with the constraint function to establish an objective supplementary point criterion, combining the predicted mean and standard deviation of the surrogate model to establish a constraint supplementary point criterion, searching for the minimum value of the objective supplementary point criterion to determine the objective candidate supplementary point and the corresponding finite element model precision, searching for the minimum value of the constraint supplementary point criterion to determine the constraint candidate supplementary point, and selecting the corresponding finite element model precision;

[0011] (4) Selecting an update point from the objective candidate supplementary point and the constraint candidate supplementary point, calculating the response value of the update point by using the finite element model with the precision corresponding to the update point, and adding the update point including the response value to the sample point library;

[0012] (5) Judging whether the stopping criterion is satisfied. If not, establishing a new surrogate model through the updated sample point library, and then entering step (3). If satisfied, selecting the design parameter corresponding to the optimal response value from the sample point library as the optimal design parameter of the structure to be optimized.

[0013] Further, the update point in step (4) is selected in the following manner:

[0014] If there is no feasible solution in the current sample point library, select the constraint candidate supplementary point as the update point;

[0015] If there is a feasible solution in the current sample point library, select the update point based on the constraint boundary precision index value R: If R < 0.05, select the objective candidate supplementary point as the update point; otherwise, calculate the distance between the objective candidate supplementary point and the constraint candidate supplementary point to determine the update point: If the distance is less than the preset critical value γ and the finite element model precision of the update point is the same as that of the objective candidate supplementary point, select the objective candidate supplementary point as the update point; otherwise, select the objective candidate supplementary point and the constraint candidate supplementary point as the update point.

[0016] Further, the constraint boundary precision index value R is calculated in the following manner:

[0017] Randomly generate N test test points within the range of design parameter values, and count the number N test of the uncertain points on the constraint boundary where the feasible points become infeasible points or the infeasible points become feasible points after considering the prediction standard deviation of the variable-fidelity surrogate model among the N error test points, as well as the number N f of the predicted feasible points, and the constraint boundary accuracy index value

[0018] Furthermore, the target supplementary point criterion is as follows:

[0019]

[0020] Among them, different precision finite element models are divided into high-precision and low-precision finite element models. t represents the precision level. t = l represents the predicted value of the variable-fidelity surrogate model for the low-precision finite element model, and t = h represents the predicted value of the variable-fidelity surrogate model for the high-precision finite element model. mfplcb vf (x, t) is the target supplementary point criterion value of point x when the precision of the variable-fidelity surrogate model is t. is the high-precision active constraint prediction value of the variable-fidelity surrogate model of point x. The active constraint is the constraint function with the largest predicted value among all constraint functions. lcb vf (x, t) is the variable-fidelity confidence lower bound function of the objective function, and α is the penalty coefficient of the constraint violation degree in the target supplementary point criterion.

[0021] Furthermore, the variable-fidelity confidence lower bound function of the objective function is as follows:

[0022]

[0023] Among them, ω1 and ω2 are the local search weight coefficient and the global search weight coefficient respectively. is the predicted value of the variable-fidelity surrogate model for the high-precision finite element model at point x. CR(t) is the cost function. is the variable-fidelity prediction error function of the objective function.

[0024] Furthermore, the cost function is as follows:

[0025]

[0026] Among them, C h and C l are the calculation costs of the high-precision finite element model and the low-precision finite element model respectively.

[0027] The local search weight coefficient and the global search weight coefficient are calculated in the following way:

[0028]

[0029] Among them, CoV f and CoV rmse are respectively used to measure the fluctuation amplitude of the predicted value of the variable credibility surrogate model for the high-precision finite element model and the fluctuation amplitude of the predicted error function value of the variable credibility surrogate model for the high-precision finite element model.

[0030] Furthermore, the constraint supplementary point criterion is as follows:

[0031]

[0032] Among them, and are the predicted mean value and the standard deviation of the predicted value of the variable credibility surrogate model for the high-precision finite element model, w1 and w2 are the local and global factors in the constraint supplementary point criterion, and flag is the number of times the optimal response value appears in the current sample library.

[0033] Furthermore, the accuracy t of the surrogate model corresponding to the constraint candidate supplementary point cons is selected in the following manner:

[0034]

[0035] Among them, R is the constraint boundary accuracy index value. Assume that the constraint candidate supplementary point x cons is used for low-precision finite element model calculation, and assume that the predicted value of the variable credibility surrogate model at this point for the low-precision finite element model is the low-precision finite element model calculation value, and the surrogate model is updated and the constraint boundary accuracy measurement index is calculated accordingly Assume that the constraint candidate supplementary point x cons is used for high-precision finite element model calculation, and assume that the predicted value of the variable credibility surrogate model at this point for the high-precision finite element model is the high-precision finite element model calculation value, and the surrogate model is updated and the constraint boundary accuracy measurement index is calculated accordingly

[0036] According to another aspect of the present invention, a variable credibility constraint optimization system based on a surrogate model is provided, including:

[0037] A function establishment module, which uses the design parameters of the structure to be optimized as variables, constraints the structure to be optimized, establishes a constraint function, obtains different precision finite element models by using different element mesh densities, calculates the optimization objective through different precision finite element models, and establishes an objective function.

[0038] The model establishment module is used to randomly generate initial design parameters within the range of design parameter values, substitute the initial design parameters into finite element models with different precisions, obtain response values with different precisions as the optimization objectives, and use the initial design parameters and their corresponding response values as initial sample points to form a sample point library, thereby establishing a variable confidence proxy model;

[0039] The supplementary point search module is used to establish a target supplementary point criterion by combining the variable confidence lower bound function of the objective function and the constraint function, establish a constraint supplementary point criterion by combining the predicted mean and standard deviation of the proxy model, search for the minimum value of the target supplementary point criterion to determine the target candidate supplementary points and the corresponding finite element model precision, search for the minimum value of the constraint supplementary point criterion to determine the constraint candidate supplementary points, and select the corresponding finite element model precision;

[0040] The update module is used to select update points from the target candidate supplementary points and the constraint candidate supplementary points, calculate the response values of the update points using the finite element model with the precision corresponding to the update points, and add the update points including the response values to the sample point library;

[0041] The optimization module is used to determine whether the stopping criterion is met. If not, a new proxy model is established through the updated sample point library, and then the supplementary point search module is executed. If so, the design parameters corresponding to the optimal response value are selected from the sample point library as the optimal design parameters of the structure to be optimized.

[0042] According to another aspect of the present invention, there is provided an application of a variable confidence constraint optimization method based on a proxy model. The method is applied to the buckling optimization of a variable stiffness stiffened cylindrical shell. The panel thickness, panel width, web thickness, and web height of the small ribs, the panel thickness, panel width, web thickness, and web height of the large ribs, and the outer plate thickness of the cylindrical shell of the variable stiffness stiffened cylindrical shell are used as design parameters. Constraints are imposed on the strength, local stability, geometry, and weight of the variable stiffness stiffened cylindrical shell to establish constraint functions. The objective function is established with the maximum value of the minimum buckling pressure as the objective. The buckling optimization of the variable stiffness stiffened cylindrical shell is performed using a variable confidence constraint optimization method based on a proxy model to obtain the optimal design parameters of the variable stiffness stiffened cylindrical shell.

[0043] Generally speaking, compared with the prior art through the above technical solutions conceived by the present invention, the following beneficial effects can be achieved:

[0044] (1) In order to integrate the information provided by high-precision models and low-precision models, reduce the cost required for optimal design, and provide a reliable optimal design solution, the present invention proposes a variable-confidence constraint optimization method based on a surrogate model to solve time-consuming constraint optimization problems. When there are simulation models with different precisions, the method of the present invention can adaptively determine the supplementary points for optimization and the precision of the simulation model because different-precision finite element models and variable-confidence surrogate models are designed, and supplementary points are searched based on the objective supplementary point criterion and the constraint supplementary point criterion. The present invention makes full use of the information of different-precision models, can effectively reduce the optimization time cost, and efficiently obtain a feasible optimal solution.

[0045] (2) In the present invention, both the objective candidate supplementary points and the constraint candidate supplementary points are candidate points for updated points. The selection algorithm for determining updated points proposed by the present invention fully considers whether there is a feasible solution in the current sample library, and when there is a feasible solution, fully considers the index value based on constraint precision self-detection and the distance between the supplementary points determined according to the objective criterion and the constraint criterion, and can adaptively determine the supplementary points for optimization and efficiently obtain a feasible optimal solution.

[0046] (3) Because there are errors in the surrogate model, the surrogate model itself provides the confidence level of the surrogate model prediction value. After considering the prediction standard deviation, the change in feasibility indicates that these points are likely to be located on the boundary of the feasible region. Therefore, when calculating the constraint boundary precision index value, the number of relevant points is statistically considered after considering the surrogate model prediction standard deviation. The closer the constraint boundary precision index value is to 0, the higher the fitting precision of the constraint surrogate model to the constraint boundary.

[0047] (4) The weight coefficient in the variable-confidence lower confidence bound function of the objective function is determined by measuring the fluctuation range of the pre-estimated value of the variable-confidence surrogate model and the pre-estimated error function value at this time, and the size of the weight parameter can be adaptively adjusted according to the prediction information of the surrogate model.

[0048] (5) The constraint supplementary point criterion designed by the present invention innovatively proposes an ln(flag) term in the global factor, where flag is the number of occurrences of the optimal response value in the current sample library. This factor can adaptively adjust the balance between the global search and the local search for constraint point addition during the optimization process. If during the optimization process, the current feasible optimal solution falls into a certain local area; at this time, the constraint supplementary point criterion gradually increases the weight of the global factor to gradually explore a new feasible region, so that the optimization process can jump out of the current local area. During the optimization process, the constraint candidate supplementary points are determined by minimizing the constraint supplementary point criterion.

[0049] (6) and can respectively quantify the improvement in constraint boundary precision when the constraint update points are of low and high precision. Considering that the computing resources required for different precision levels are not necessarily the same, when determining the precision level of the constraint supplementary points, respectively and Divide by the computational cost of the corresponding precision to calculate the improvement of each low and high precision for the constraint boundary precision under unit computational resources. Based on this, the precision level of the constrained candidate supplementary points can be cleverly solved to maximize the computational resource utilization rate.

[0050] (7) The optimization method of the present invention can solve the buckling optimization design problem of variable stiffness stiffened cylindrical shells. Structures with equal stiffness can be designed through theoretical calculations without the need for finite element analysis, while variable stiffness structures require finite element analysis. Compared with equal stiffness structures, variable stiffness structures can obtain higher strength and stability and better mechanical properties under the same weight. When there are simulation models with different precisions, the optimization method proposed by the present invention can adaptively determine the supplementary points and simulation model precision for the buckling optimization of variable stiffness stiffened cylindrical shells, effectively reducing the optimization time cost and efficiently obtaining a feasible optimal solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 is a flowchart of a variable credibility constraint optimization method based on a surrogate model provided by an embodiment of the present invention;

[0052] FIG. 2(a) is a schematic structural diagram of a variable stiffness stiffened cylindrical shell provided by an embodiment of the present invention;

[0053] FIG. 2(b) is a detailed schematic diagram of a variable stiffness stiffened cylindrical shell provided by an embodiment of the present invention;

[0054] Figure 3 (a) in is a schematic diagram of circumferential load application provided by an embodiment of the present invention;

[0055] Figure 3 (b) in is a schematic diagram of longitudinal load application provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0056] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0057] As Figure 1 shown, a variable credibility constraint optimization method based on a surrogate model includes:

[0058] (1) Taking the design parameters of the structure to be optimized as variables, constraining the structure to be optimized, establishing a constraint function, obtaining finite element models with different precisions by using different element mesh densities, calculating the optimization objective through finite element models with different precisions, and establishing an objective function,

[0059] (2) Randomly generate initial design parameters within the range of design parameter values, substitute the initial design parameters into finite element models with different precisions, and obtain response values with different precisions for the optimization objective. Take the initial design parameters and their corresponding response values as initial sample points to form a sample point library, and thus establish a variable-fidelity surrogate model.

[0060] (3) Combine the variable-fidelity confidence lower bound function of the objective function with the constraint function to establish an objective complementary point criterion, and combine the predicted mean and standard deviation of the surrogate model to establish a constraint complementary point criterion. Search for the minimum value of the objective complementary point criterion to determine the objective candidate complementary points and the corresponding finite element model precision, search for the minimum value of the constraint complementary point criterion to determine the constraint candidate complementary points, and select the corresponding finite element model precision.

[0061] (4) Select update points from the objective candidate complementary points and the constraint candidate complementary points, calculate the response values of the update points using the finite element model with the precision corresponding to the update points, and add the update points containing the response values to the sample point library.

[0062] (5) Judge whether the stopping criterion is satisfied. If not, establish a new surrogate model through the updated sample point library, and then enter step (3). If satisfied, select the design parameters corresponding to the optimal response value from the sample point library as the optimal design parameters of the structure to be optimized.

[0063] When a variable-fidelity constraint optimization method based on a surrogate model is applied to the buckling optimization of a variable-stiffness stiffened cylindrical shell, it includes:

[0064] Take the panel thickness, panel width, web thickness, and web height of the small ribs, the panel thickness, panel width, web thickness, and web height of the large ribs, and the plate thickness of the outer plate of the variable-stiffness stiffened cylindrical shell as design parameters, constrain the strength, local stability, geometry, and weight of the variable-stiffness stiffened cylindrical shell, establish a constraint function, and establish an objective function with the maximum value of the minimum buckling pressure as the objective.

[0065] Min-P e (x)

[0066]

[0067]

[0068]

[0069] Among them, P e (x) is the minimum buckling pressure, which is directly calculated by the finite element method; P cr1The actual critical load for the local instability of a variable-stiffness stiffened cylindrical shell is approximately calculated using the theoretical calculation formula for the actual critical load of an equal-stiffness ring-stiffened cylindrical shell; P j = 3 Mpa is the calculated pressure; g1(x) - g3(x) are strength constraints, where σ1 is the circumferential stress at the mid-surface of the shell plate, σ2 is the longitudinal stress at the inner surface of the shell end, and σ f is the rib stress, and σ s = 550 MPa is the material yield limit; g4(x) is the local stability constraint, g5(x) - g8(x) are geometric constraints, and g9(x) is the weight constraint of the variable-stiffness stiffened cylindrical shell, where w represents the weight, with the unit of ton (t), and w0 = 95 t is the allowable weight of the structure; the structural Poisson's ratio is 0.3, the elastic modulus is 2.1×10 5 MPa, and the material density is 7.85×10 3 Kg / m 3 ; the radius of the cylindrical shell is 3500 mm, the rib spacing is 500 mm, and the total circumferential length is 12000 mm. When performing finite element analysis, the cost ratio of the high-precision model to the low-precision model is 5:1, and different precision finite element models are obtained by using different element mesh densities.

[0070] Initial sample points are obtained through Latin hypercube experimental design, and high-precision and low-precision response values are obtained based on the corresponding precision finite element models;

[0071] Using the information of the sample points in the current sample point library, a hierarchical Kriging surrogate model is established;

[0072] Based on the Kriging surrogate model, the particle swarm optimization algorithm is used to search for the minimum value of the designed target supplementary point criterion mfplcb(x) to determine the target candidate supplementary points and the corresponding model accuracy (x obj , t obj );

[0073] Based on the Kriging surrogate model, the particle swarm optimization algorithm is used to search for the minimum value of the designed constraint supplementary point criterion mfmlcb(x) to determine the constraint candidate supplementary points x cons ;

[0074] The "R-Believer" accuracy selection algorithm (Algorithm 1) is used to determine the model accuracy t of the constraint candidate supplementary points cons ;

[0075] The update point selection algorithm (Algorithm 2) is used to determine the position and accuracy level information of the update points (x new , t new );

[0076] The update points are evaluated using the corresponding precision model to obtain the target and constraint response values of the corresponding precision, and the sample point library is updated;

[0077] Iteratively determine the positions of supplementary points and the model accuracy until the stopping criterion (exhaustion of computing resources) is met, and output the feasible optimal solution in the high-precision sample point library.

[0078] The target supplementary point criterion mfplcb(x) for determining the target candidate supplementary points and the corresponding model accuracy is as follows:

[0079]

[0080] It is the estimated high-precision function value of the active constraint for this point. The active constraint is the constraint function with the largest estimated value among all constraint functions, and the calculation formula is: N c is the number of constraints. t = h represents using the high-precision model, and t = l represents using the low-precision model. lcb vf (x, t) is the variable confidence level confidence lower bound function of the objective function. α is the penalty coefficient for the degree of constraint violation in the target supplementary point criterion. In theory, the value of α should be infinite to ensure the feasibility of the updated points selected according to the objective function supplementary point criterion; in practice, α = 10 10 .

[0081] By using the particle swarm algorithm, search for the minimum point of this criterion to obtain the target candidate supplementary points and the corresponding model accuracy (x obj , t obj ).

[0082] Preferably, the variable confidence level confidence lower bound function lcb vf (x, t) is as follows:

[0083]

[0084] is the high-precision predicted response value at the design point; is the variable confidence level prediction error function of the objective function.

[0085] Preferably, the weight coefficients ω1 and ω2 in the variable confidence level confidence lower bound function lcb vf (x, t) are adaptively adjusted according to a weight coefficient calculation method based on the coefficient of variation according to the prediction information of the Kriging model. Specifically, use Latin hypercube sampling to randomly generate m weight = min(2000d, 20000) test points in the design space, where d is the problem dimension. Calculate the high-precision surrogate model predicted values and prediction errors of the test points based on the variable precision surrogate model, and calculate the mean and standard deviation of the predicted values and prediction errors respectively, denoted as μ f , μrmse , σ f , σ rmse . Calculate the coefficient of variation of the predicted value and the predicted variance respectively:

[0086]

[0087] CoV f and CoV rmse are respectively used to measure the fluctuation range of the predicted value of the high-precision surrogate model and the predicted error function value at this time. And calculate the weight coefficient accordingly:

[0088]

[0089] Preferably, the cost function is:

[0090]

[0091] C h and C l are the calculation costs of the high-precision finite element model and the low-precision finite element model respectively.

[0092] Preferably, the constraint complementary point criterion mfmlcb(x) for determining the constraint candidate complementary point is:

[0093]

[0094] Where and are the predicted mean value and the predicted value standard deviation of the variable-fidelity surrogate model for the high-precision finite element model, w1 and w2 are the local and global factors in the constraint complementary point criterion, and flag is the number of times the optimal response value appears in the current sample library. w1 = 1 and w2 = 2 are the local and global coefficients in the constraint complementary point criterion. In this method, the term ln(flag) is innovatively proposed in the global factor, where flag is the number of times the optimal response value appears in the current sample library. This factor can adaptively adjust the balance between the global search and the local search for constraint point addition during the optimization process. If during the optimization process, the current feasible optimal solution falls into a certain local area; at this time, the constraint complementary point criterion gradually increases the weight of the global factor to gradually explore a new feasible region, so that the optimization process can jump out of the current local area. During the optimization process, the constraint candidate complementary point x cons is determined by minimizing the constraint complementary point criterion.

[0095] Preferably, the method for self-detecting the constraint boundary accuracy of the constraint surrogate model: Randomly generate N in the design space testDetection points are used, and the number N of the uncertain points of the constraint boundary feasibility that change from feasible points to infeasible points or from infeasible points to feasible points is counted after considering the Kriging prediction standard deviation (the predicted value of the feasible point constraint surrogate model plus 1.96 times the prediction standard deviation, and the predicted value of the infeasible point constraint surrogate model minus 1.96 times the prediction standard deviation). error , and the number N of predicted feasible points f , and the constraint boundary accuracy index value is calculated as follows:

[0096]

[0097] Specifically, the closer the value of R is to 0, the higher the fitting accuracy of the constraint surrogate model for the constraint boundary.

[0098] Preferably, the proposed constraint boundary accuracy index R can provide a real-time prediction value of the constraint boundary accuracy during the iteration process of the constraint optimization algorithm. The R index can provide new ideas for the design of expensive constraint optimization algorithms: that is, first consider the update of the constraint function when the constraint accuracy is poor; during the algorithm iteration process, the constraint boundary accuracy gradually improves, and thus the expensive constraint optimization can be gradually transformed into non-expensive constraint optimization to save the computing resources required by the optimization algorithm. Based on this, the "R-Believer" accuracy selection algorithm (Algorithm 1) for determining the accuracy of the constraint candidate supplementary point model is proposed: calculate the constraint boundary accuracy measurement index R according to the constraint boundary accuracy self-detection method, assume a supplementary point for low-precision model calculation, and assume that the low-precision predicted value of this point is the low-precision model value, update the variable credibility surrogate model, and calculate the constraint boundary accuracy measurement index accordingly Assume a supplementary point for high-precision model calculation, and assume that the high-precision predicted value of this point is the high-precision model value, update the variable credibility surrogate model, and calculate the constraint boundary accuracy measurement index accordingly Considering the calculation cost CR(t) of different precision models, determine the model accuracy of the constraint supplementary point according to the following formula

[0099]

[0100] Specifically, the "R-Believer" accuracy selection algorithm originally solves the problem of the accuracy level of the updated points in the multi-precision algorithm. Among them, and can respectively quantify the improvement in the constraint boundary accuracy when the constraint update points are of low and high precision. Considering that the computing resources required for different precision levels are not necessarily the same, when determining the accuracy level of the constraint supplementary points, and are respectively divided by the calculation cost C of the corresponding precision l 、C h, to calculate the improvement of the precision of each low and high precision for the constraint boundary precision under unit computing resources. Based on this, the precision level of the constraint candidate supplementary point x can be cleverly solved cons to maximize the utilization rate of computing resources.

[0101] Through mfplcb vf (x, t), mfmlcb(x) and the "R-Believer" precision selection algorithm, the update points for the objective function and their precision levels, and the update points for the constraint function and their precision levels can be determined respectively (it is worth mentioning that they can maximize the improvement of the objective and constraint boundary precision under unit computing resources). However, an important issue in expensive constraint optimization is how to balance the update of the objective function and the update of the constraint function under limited computing resources.

[0102] Preferably, the selection algorithm (Algorithm 2) for determining the update point (x new , t new ): If there is no feasible solution currently, select the update point as (x new , t new ) = (x cons , t cons ); If there is a feasible solution and the update point is determined based on the index value of the constraint precision self-detection: If R < 0.05, select the update point as (x new , t new ) = (x obj , t obj ); Otherwise, calculate the distance of the supplementary point determined according to the objective criterion and the constraint criterion to determine the update point: If the distance value is less than the preset critical value γ and the determined model precision levels are the same, select the update point as (x new , t new ) = (x obj , t obj ); Otherwise, select the update point as (x new , t new ) = (x obj , t obj ) ∪ (x cons , t cons ).

[0103] Example 1

[0104] A variable-fidelity constraint optimization method based on a surrogate model of the present invention for the buckling optimization of a variable-stiffness stiffened cylindrical shell includes the following steps:

[0105] Step 1: Determine the optimization mathematical model;

[0106] where the design variables and other parameters are shown in Table 1, and its structural schematic diagram is as attached Figure 2(a) and 2(b)As shown, the variable-stiffness stiffened cylindrical shell includes: an outer plate, large ribs, and small ribs. The schematic diagram of load application is shown in Figure 3 Figure (a) in the appendix and Figure 3 Figure (b) in the appendix. The load application directions include circumferential and longitudinal directions.

[0107] Table 1 Physical meanings and value ranges of design variables of variable-stiffness stiffened cylindrical shells

[0108]

[0109] Among them, P e (x) is the minimum buckling pressure, which is directly calculated by the finite element method; P crl is the actual critical load of local instability of the variable-stiffness stiffened cylindrical shell, which is approximately calculated by the theoretical calculation formula of the actual critical load of local instability of the equal-stiffness ring-ribbed stiffened cylindrical shell; P j = 3 Mpa is the calculation pressure; g1(x)-g3(x) are strength constraints, where σ1 is the circumferential stress at the mid-surface of the shell plate at the mid-span, σ2 is the longitudinal stress at the inner surface of the shell plate at the end of the span, σ f is the rib stress, σ s = 550 MPa is the material yield limit; g9(x) is the weight constraint of the variable-stiffness stiffened cylindrical shell, where w0 = 95 t is the allowable weight of the structure; the structural Poisson's ratio is 0.3, and the elastic modulus is 2.1×10 5 MPa, and the material density is 7.85×10 3 Kg / m 3 ; the radius of the cylindrical shell is 3500 mm, the rib spacing is 500 mm, and the total circumferential length is 12000 mm. When performing finite element analysis, the cost ratio of the high-precision model to the low-precision model is 5:1, and different precision finite element models are obtained by using different unit mesh densities.

[0110] Step 2: Use the Latin hypercube experimental design method to obtain a specified number of initial sample points and evaluate them using the corresponding precision simulation model, and update the feasible optimal solution. Specifically, the number of high-precision points is The number of low-precision points is d = 9 is the problem dimension.

[0111] Step 3: Use the information of the sample points in the current sample point library to establish a hierarchical Kriging surrogate model.

[0112] Step 4: Search for the target complementary point criterion mfplcb(x) through the particle swarm algorithm to determine the candidate points of the objective function and the precision level (x obj ,t obj ).

[0113] Step 5: Search for the constraint complementary point criterion mfmlcb(x) through the particle swarm algorithm to determine the candidate points x of the constraint function cons。

[0114] Table 2 Optimization to obtain the optimal solution information

[0115]

[0116] Step 6: Determine the accuracy level t of the candidate points of the constraint function through the "R-Believer" accuracy selection algorithm (Algorithm 1) cons 。

[0117] Step 7: Determine the updated point and accuracy level information (x new , t new ) through the updated point selection algorithm (Algorithm 2). The distance constraint γ is half of the minimum distance between the evaluated points.

[0118] Step 8: Search for the feasible optimal value in the current set of high-precision sample points. Then evaluate whether the stopping criterion is met. If the stopping criterion is met, the algorithm proceeds to Step 9; if the stopping criterion is not met, the algorithm returns to Step 3 to continue the iteration.

[0119] Step 9: Output the feasible optimal solution at the stop, that is, the structural parameters of the variable-stiffness stiffened cylindrical shell.

[0120] The optimization results of Example 1 are shown in Table 2.

[0121] The present invention consumes 69 high-precision sample points and 207 low-precision sample points to obtain the feasible optimal solution, which is equivalent to 110.40 high-precision model sample points, reflecting the high efficiency of using the multi-precision algorithm of the present invention.

[0122] It is easy for those skilled in the art to understand that the above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

Claims

1. A variable credibility constraint optimization method based on a surrogate model, characterized in that, It includes the following steps: (1) Taking the design parameters of the structure to be optimized as variables, imposing constraints on the structure to be optimized, establishing a constraint function, obtaining finite element models with different precisions by using different element mesh densities, calculating the optimization objective through finite element models with different precisions, and establishing an objective function; (2) Randomly generating initial design parameters within the range of design parameter values, substituting the initial design parameters into finite element models with different precisions, obtaining response values with different precisions for the optimization objective, taking the initial design parameters and their corresponding response values as initial sample points, forming a sample point library, and thus establishing a variable-fidelity surrogate model; (3) Combining the variable-fidelity lower confidence bound function of the objective function with the constraint function to establish an objective supplementary point criterion, combining the predicted mean and standard deviation of the surrogate model to establish a constraint supplementary point criterion, searching for the minimum value of the objective supplementary point criterion to determine the objective candidate supplementary points and the corresponding finite element model precision, searching for the minimum value of the constraint supplementary point criterion to determine the constraint candidate supplementary points, and selecting the corresponding finite element model precision; (4) Selecting updated points from the objective candidate supplementary points and the constraint candidate supplementary points, calculating the response values of the updated points using the finite element model with the precision corresponding to the updated points, and adding the updated points containing the response values to the sample point library; (5) Judging whether the stopping criterion is satisfied. If not, establishing a new surrogate model through the updated sample point library, and then entering step (3). If satisfied, selecting the design parameters corresponding to the optimal response value from the sample point library as the optimal design parameters of the structure to be optimized.

2. The variable credibility constraint optimization method based on an agent model according to claim 1, wherein In step (4), the updated points are selected in the following way: If there is no feasible solution in the current sample point library, select the constraint candidate supplementary points as the updated points; If there is a feasible solution in the current sample point library, select the updated points based on the constraint boundary accuracy index value R: If R < 0.05, select the objective candidate supplementary points as the updated points; otherwise, calculate the distance between the objective candidate supplementary points and the constraint candidate supplementary points to determine the updated points: If the distance is less than the preset critical value γ and the finite element model precision of the updated points is the same as that of the objective candidate supplementary points, select the objective candidate supplementary points as the updated points; otherwise, select the objective candidate supplementary points and the constraint candidate supplementary points as the updated points.

3. The variable credibility constraint optimization method based on an agent model according to claim 2, wherein The constraint boundary accuracy index value R is calculated in the following way: Randomly generate N test test points within the range of design parameter values, and count the number N test of the constraint boundary feasibility uncertain points that change from feasible points to infeasible points or from infeasible points to feasible points after considering the prediction standard deviation of the variable credibility surrogate model among the N error test points, as well as the number N f of the predicted feasible points, and the constraint boundary accuracy index value 4. A variable credibility constraint optimization method based on an agent model according to any one of claims 1-3, characterized in that, The objective supplementary point criterion is: Among them, the finite element models with different precisions are divided into high-precision and low-precision finite element models. t represents the precision level, t = l indicates the predicted value of the variable-fidelity surrogate model for the low-precision finite element model, and t = h indicates the predicted value of the variable-fidelity surrogate model for the high-precision finite element model, mfplcb vf (x, t) is the objective complementary point criterion value of point x when the precision of the variable-fidelity surrogate model is t. is the high-precision active constraint prediction value of the variable-fidelity surrogate model of point x. The active constraint is the constraint function with the largest predicted value among all constraint functions, lcb vf (x, t) is the variable-fidelity confidence lower bound function of the objective function, and α is the penalty coefficient of the constraint violation degree in the objective complementary point criterion.

5. The variable credibility constraint optimization method based on an agent model according to claim 4, characterized in that The variable-fidelity lower confidence bound function of the objective function is: where ω1 and ω2 are the local search weight coefficient and the global search weight coefficient respectively, is the predicted value of the variable credibility surrogate model at point x for the high-precision finite element model, and CR(t) is the cost function, is the variable credibility prediction error function of the objective function.

6. The variable credibility constraint optimization method based on an agent model according to claim 5, characterized in that The cost function is: Among them, C h and C l are the computational costs of the high-precision finite element model and the low-precision finite element model, respectively; The local search weight coefficient and the global search weight coefficient are calculated in the following way: Among them, CoV f and CoV rmse are respectively used to measure the fluctuation amplitude of the predicted value of the variable credibility surrogate model for the high-precision finite element model and the fluctuation amplitude of the predicted error function value of the variable credibility surrogate model for the high-precision finite element model.

7. The variable credibility constraint optimization method based on an agent model according to claim 6, characterized in that The constraint supplementary point criterion is: Among them, and are the predicted mean and the standard deviation of the predicted values of the variable credibility surrogate model for the high-precision finite element model, w1 and w2 are the local and global factors in the constrained complementary point criterion, and flag is the number of times the optimal response value appears in the current sample library.

8. A variable credibility constraint optimization method based on an agent model according to claim 7, characterized in that The accuracy t of the surrogate model corresponding to the constrained candidate supplementary point cons is selected in the following manner: where R is the constraint boundary accuracy index value. Assume the constrained candidate supplementary point x cons Perform low-precision finite element model calculation, and assume that the predicted value of the variable credibility surrogate model for this point with respect to the low-precision finite element model is the calculated value of the low-precision finite element model, and update the surrogate model and calculate the constraint boundary accuracy measurement index accordingly Assume the constrained candidate supplementary point x cons Perform high-precision finite element model calculation, and assume that the predicted value of the variable credibility surrogate model for this point with respect to the high-precision finite element model is the calculated value of the high-precision finite element model, and update the surrogate model and calculate the constraint boundary accuracy measurement index accordingly 9. A variable credibility constraint optimization system based on a surrogate model, characterized in that, It includes: A function establishment module, which takes the design parameters of the structure to be optimized as variables, imposes constraints on the structure to be optimized, establishes a constraint function, obtains finite element models with different precisions by using different element mesh densities, calculates the optimization objective through finite element models with different precisions, and establishes an objective function. A model establishment module, which randomly generates initial design parameters within the range of design parameter values, substitutes the initial design parameters into finite element models with different precisions, obtains response values with different precisions for the optimization objective, takes the initial design parameters and their corresponding response values as initial sample points, forms a sample point library, and thus establishes a variable-fidelity surrogate model. The supplementary point search module is used to combine the variable confidence lower bound function of the objective function with the constraint function to establish an objective supplementary point criterion, combine the predicted mean and standard deviation of the surrogate model to establish a constraint supplementary point criterion, search for the minimum value of the objective supplementary point criterion to determine the objective candidate supplementary points and the corresponding finite element model accuracy, search for the minimum value of the constraint supplementary point criterion to determine the constraint candidate supplementary points, and select the corresponding finite element model accuracy; The update module is used to select update points from the objective candidate supplementary points and the constraint candidate supplementary points, calculate the response values of the update points using the finite element model with the accuracy corresponding to the update points, and add the update points including the response values to the sample point library; The optimization module is used to determine whether the stopping criterion is satisfied. If not, a new surrogate model is established through the updated sample point library, and then the supplementary point search module is executed. If satisfied, the design parameters corresponding to the optimal response value are selected from the sample point library as the optimal design parameters of the structure to be optimized.

10. Application of a variable credibility constraint optimization method based on a surrogate model, characterized in that, The method is applied to the buckling optimization of a variable stiffness stiffened cylindrical shell. Taking the panel thickness, panel width, web thickness and web height of the small ribs, the panel thickness, panel width, web thickness and web height of the large ribs, and the plate thickness of the outer plate of the cylindrical shell of the variable stiffness stiffened cylindrical shell as design parameters, the strength, local stability, geometry and weight of the variable stiffness stiffened cylindrical shell are constrained to establish a constraint function, and an objective function is established with the maximum value of the minimum buckling pressure as the objective. The buckling optimization of the variable stiffness stiffened cylindrical shell is carried out using a variable confidence constraint optimization method based on a surrogate model as described in any one of claims 1-8 to obtain the optimal design parameters of the variable stiffness stiffened cylindrical shell.

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