A Complex Equipment Optimization Design Method Based on a Hybrid Adaptive Sampling Agent Model

Abstract

This invention discloses a method for optimizing the design of complex equipment based on a hybrid adaptive sampling surrogate model. This method divides the design space into several Voronoi polygons controlled by sample points. Three indices—leave-one-out error, local nonlinearity, and polygon region size—are used to evaluate the importance of each sample point region. An entropy-weighted distance method is used to select the most suitable sensitive region for adding points. A learning function based on error estimation is then combined to determine new sampling points. This iterative update constructs a high-precision surrogate model, establishing a mapping relationship between design parameters and optimization objectives, thereby solving the design optimization problem. This invention innovatively proposes a multi-index adaptive weight allocation method to select sensitive sample regions and proposes a novel learning function to determine the location of added points. This method can construct a high-precision surrogate model using fewer sample points and can be used for the optimization design of complex equipment, including but not limited to tunnel boring machines.

Description

Technical Field

[0001] This invention relates to the field of optimization design based on surrogate models, and more particularly to a method for optimizing complex equipment based on a hybrid adaptive sampling surrogate model. Background Technology

[0002] For complex practical engineering problems, such as optimization design, surrogate models are often used to replace physical experiments or numerical simulations to reduce resource and time consumption. The prediction accuracy of a surrogate model is highly dependent on the number and distribution of given sampling points. However, each sampling means conducting an expensive and time-consuming experiment or simulation. Therefore, a key issue is how to fully utilize sampling point information, minimize the number of sampling points, and simultaneously build a sufficiently accurate surrogate model. Adaptive sampling is a sequential sampling scheme that, during iteration, adds points gradually in undersampled regions based on spatial and error information, continuously improving model accuracy until a stopping criterion is met. In the process of sequentially adding points, selecting new sampling points based on existing sampling points and iteration process information is crucial. Summary of the Invention

[0003] The purpose of this invention is to overcome the aforementioned technical problems of existing technologies and propose a complex equipment optimization design method based on a hybrid adaptive sampling surrogate model. This invention divides the design space into several Vino polygon regions controlled by sample points. Three indicators—leave-one-out error, local nonlinearity, and polygon region size—are used to evaluate the importance of each sample point region. The most suitable sensitive region for adding points is selected using the entropy-weighted superior-inferiority distance method. New sampling points are determined by combining this with a learning function based on error estimation. A high-precision surrogate model is iteratively updated and constructed to solve the optimization design problem. This invention reduces the number of sampling points while maintaining the accuracy of the surrogate model, thus reducing the consumption of experimental or simulation computational resources.

[0004] The objective of this invention is achieved through the following technical solution:

[0005] A method for optimizing the design of complex equipment based on a hybrid adaptive sampling proxy model includes the following steps:

[0006] S1: Based on the design parameter space of the complex equipment optimization problem, a certain number of initial sample point sets X are randomly generated, and the target output value Y corresponding to each sample point is obtained to form the initial sample set S.

[0007] S2: Based on the sample point set X, the design parameter space of the complex equipment is divided into a Vino polygon region controlled by several sample points.

[0008] S3: Based on the initial sample set S, calculate the leave-one error, local nonlinearity, and polygon region size for each sample point;

[0009] S4: Based on the leave-one error, local nonlinearity and polygon region size calculated in S3 as evaluation indicators, the most sensitive region is selected as the new sampling point addition region using the entropy weight-good-bad solution distance method.

[0010] S5: Determine the new sampling point x using a learning function based on error estimation. new And obtain the target output value y corresponding to the new sampling point. new Add and update the sample set S;

[0011] S6: Determine whether the error convergence criterion has been met. If not, repeat steps S2 to S5; if it has been met, proceed to step S7.

[0012] S7: Based on the final sample set S, construct a Kriging surrogate model G to characterize the mapping relationship between the design parameters and optimization objectives of complex equipment;

[0013] S8: Based on the identified complex equipment optimization design problem, use a genetic algorithm to solve the optimization problem, determine the optimal design parameters, and verify them.

[0014] Furthermore, step S1 is specifically as follows:

[0015] S1.1: Use Latin hypercube sampling to randomly generate an initial sample point set X in the design parameter space, where the design parameters include structural dimensions and material properties;

[0016] S1.2 Obtain the target output value Y corresponding to each sample point.

[0017] Furthermore, step S3 is specifically as follows:

[0018] S3.1: Use leave-one-out cross-validation to calculate the cross-validation results for each sample point x in the sample point set X. i Leave one error

[0019] S3.2: Based on linear fitting residual analysis, calculate the local nonlinearity (NonL) of each sample point xi within the sample point set X. i :

[0020] S3.3: Based on Monte Carlo simulation, calculate the size Vol of the Vino polygon region controlled by each sample point xi within the sample point set X. i .

[0021] Furthermore, step S4 is specifically as follows:

[0022] S4.1: Construct decision matrix A based on the evaluation indices eLOO, NonL and Vol of each sample point in the sample set S;

[0023] S4.2: Normalize the decision matrix A to obtain the normalized decision matrix P;

[0024] S4.3: Calculate the information entropy of each evaluation index based on the normalized decision matrix P;

[0025] S4.4: Calculate the adaptive weight coefficient w for each evaluation index based on information entropy;

[0026] S4.5: Update the multi-attribute decision matrix Z according to the weight coefficients of each evaluation index;

[0027] S4.6: Based on the multi-attribute decision matrix Z, the superior-inferior solution distance method is used to calculate x for each sample point. i Comprehensive evaluation score s i ;

[0028] S4.7: Select the sample point x with the highest comprehensive evaluation score from the sample set. * As the most sensitive sample point, this sample point x... * The controlled polygonal region is used as the area for adding new sampling points.

[0029] Furthermore, step S5 is specifically as follows:

[0030] S5.1: The most sensitive sample point x is determined using the Delaunay triangulation algorithm. * Vino polygon adjacency set

[0031] S5.2: Leave-one-out cross-validation, calculate sample point x. * and its adjacent point set Leave one error;

[0032] S5.3: Based on the Monte Carlo simulation results obtained in S3.3, the points falling on the sensitive sample points x... * Points within the controlled polygonal region Using sample point x * The estimated error of a point is calculated by leaving one error between it and its adjacent points.

[0033] S5.4: Based on the Kriging surrogate model, obtain the output of the surrogate model at the point of distribution. Variance Var t * ;

[0034] S5.5: Sprinkle some Estimation error and variance Var t * Multiplication as a learning function;

[0035] S5.6 Select the point that maximizes the learning function as the new sampling point x. new New sampling points x are obtained through methods such as finite element analysis or experiments. new The corresponding target output value y new Add and update the sample set S.

[0036] Furthermore, the convergence criteria are as follows:

[0037] S6.1: Calculate the error of each sample point using the leave-one-out method.

[0038] S6.2: When At that point, it is considered that the error has converged;

[0039] Where m is the number of sample points and c is the error convergence constant.

[0040] Furthermore, step S8 is specifically as follows:

[0041] S8.1: Establish a mathematical model for the optimization design problem of complex equipment, including design parameters, optimization objectives and constraints;

[0042] S8.2: Use the surrogate model built in S7 to characterize the mapping relationship between design parameters and optimization objectives;

[0043] S8.3: Use a genetic algorithm to solve the optimization problem, determine the optimal design parameters, and verify them.

[0044] The beneficial effects of this invention are as follows:

[0045] (1) This invention proposes three evaluation indicators: leave-one error, local nonlinearity, and size of the Vino polygon region, to evaluate the impact of sample points on the accuracy of the surrogate model from the perspectives of local development and global exploration.

[0046] (2) This invention uses the entropy weight method to adaptively weight the three evaluation indicators, and uses the superior and inferior solution distance method to select the sample points that have the greatest impact on the proxy model, i.e. sensitive points, and adds new sampling points in their polygonal areas.

[0047] (3) The present invention adopts a novel learning function, which uses the leave-one error of the sensitive point and its adjacent points to approximate the error of any point in the polygonal region, and multiplies it with the variance output by the Kriging proxy model as the learning function to determine the final point position.

[0048] (4) Under the condition of constructing a proxy model with the same accuracy, the present invention can reduce the number of sampling points and improve sampling efficiency compared with other adaptive sampling schemes, establish the output mapping relationship between design parameters and optimization targets, and thus save computational resources and other costs for the optimization design of complex equipment such as tunnel boring machines. Attached Figure Description

[0049] Figure 1 This is a flowchart of the complex equipment optimization design method based on a hybrid adaptive sampling proxy model according to the present invention.

[0050] Figure 2 Schematic diagram of the Vino polygon and the Delaunay triangle;

[0051] Figure 3a This is a contour map showing the distribution of sample points in Example 1 of the present invention.

[0052] Figure 3b This is a contour map showing the sample point distribution of the method proposed by XU et al. in Example 1;

[0053] Figure 4 This is a schematic diagram of the optimized design parameters for the tunnel boring machine structure in Example 2; Detailed Implementation

[0054] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. The purpose and effects of the present invention will become clearer. It should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0055] like Figure 1 As shown, the complex equipment optimization design method based on the hybrid adaptive sampling surrogate model of the present invention divides the design parameter space of the optimization problem into a Vino polygon region controlled by several sample points. The importance of each sample point region is evaluated by three indicators: leave-one error, local nonlinearity, and polygon region size. The most suitable sensitive region for adding points is selected by the entropy weight-good solution distance method, and new sampling points are determined by combining the learning function based on error estimation. A high-precision surrogate model is constructed by iterative update, and then the optimization problem is solved.

[0056] The present invention specifically includes the following steps:

[0057] S1: Based on the design parameter space of the complex equipment optimization problem, a certain number of initial sample point sets X are randomly generated, and the target output value Y corresponding to each sample point is obtained. The two constitute the initial sample set S.

[0058] S1.1: Use Latin hypercube sampling to randomly generate an initial set of sample points X in the design parameter space, where the design parameters include structural dimensions, material properties, etc.

[0059] S1.2: Obtain the target output value Y corresponding to each sample point using empirical formulas, finite element simulation, or physical experiments.

[0060] S2: Based on the sample point set X, the design parameter space of the complex equipment is divided into a Vino polygon region controlled by several sample points.

[0061] S3: Based on the initial sample set S, calculate the leave-one-out error, local nonlinearity, and polygon region size for each sample point; specifically including the following sub-steps:

[0062] S3.1: Use leave-one-out cross-validation to calculate the cross-validation results for each sample point x in the sample point set X. i Leave one error

[0063]

[0064] Where m is the number of sample points in the initial sample point set X, and y i It is the sample point x i The actual response value at that location, It is to remove sample point x i and the Kriging proxy model G constructed from its output -i In x i The predicted value at that location.

[0065] A sample point x i Leave one error The larger the value, the greater the impact of the sample point on the accuracy of the surrogate model, and the more necessary it is to add new sample points within the polygonal region controlled by that point.

[0066] S3.2: Based on linear fitting residual analysis, calculate the x of each sample point in the sample point set X. i Local nonlinearity NonL i The Delaunay triangulation algorithm is used to determine the x-axis of each sample point. i Vino polygon adjacency set Fit sample points x using the least squares method (hyperplane). i and its adjacent point set The sum of the residuals of the true values ​​and the fitted values ​​used to characterize the sample point x i Local nonlinearity NonL i The calculation formula is as follows:

[0067]

[0068] Where k is the number of adjacent vertices, and when j is not 0, x ij For sample point x i The adjacent points of x; when j is 0, ij Degenerate into sample point x i itself, To fit the least squares (hyperplane) model in x ijThe fitted value, y ij Its true value.

[0069] A sample point x i Local nonlinearity NonL i The larger the value, the more difficult it is for the surrogate model to fit accurately at that point, and the more necessary it is to add new sample points within the polygonal region controlled by that point.

[0070] S3.3: Based on Monte Carlo simulation, calculate the size Vol of the Vino polygon region controlled by each sample point xi within the sample point set X. i Using Monte Carlo simulation, a large number of points are randomly scattered in the parameter space. Then, the number ni of points falling within the polygonal region controlled by each sample point xi is counted. The size of this polygonal region can then be calculated using the following formula:

[0071] Vol i =n i / N

[0072] Where N is the total number of points scattered.

[0073] The size of a polygonal region is the proportion of that region to the parameter space, representing the position of the sample point set at point x. i Density at the location, Vol i The larger the value, the sparser the distribution of the sample points in this area, and the more necessary it is to add new sample points in this region.

[0074] S4: Based on the leave-one error, local nonlinearity, and polygon region size calculated in S3 as evaluation indicators, the most sensitive region is selected as the new sampling point addition region using the entropy weight-good / bad solution distance method; specifically, it includes the following sub-steps:

[0075] S4.1: Based on the evaluation metrics eLOO, NonL, and Vol for each sample point in the sample set S, construct the decision matrix A as shown in the following formula:

[0076]

[0077] Where m is the number of sample points, and n is the dimension of the evaluation index; for this method, n = 3; a ij Let be the j-th evaluation index of the i-th sample point and the polygonal region it controls, where i∈[1,m] and j∈[1,n];

[0078] S4.2: Normalize the decision matrix A to obtain the normalized decision matrix P. The calculation formula is as follows:

[0079]

[0080] S4.3: Calculate the information entropy of each evaluation index based on the normalized decision matrix P. The calculation formula is as follows:

[0081]

[0082] Among them, e j Let be the information entropy of the j-th evaluation indicator. The smaller the information entropy, the more information the evaluation indicator contains.

[0083] S4.4: Based on information entropy, calculate the adaptive weight coefficient w for each evaluation index. The calculation formula is as follows:

[0084]

[0085] Among them, w j Let be the adaptive weight coefficient for the j-th evaluation index;

[0086] S4.5: Update the multi-attribute decision matrix Z based on the weight coefficients of each evaluation indicator. The calculation formula is as follows:

[0087]

[0088] Among them, z ij =w j ·p ij ;

[0089] S4.6: Based on the multi-attribute decision matrix Z, the best-inferior-best-solution distance method (TOPSIS) is used to calculate x for each sample point. i Comprehensive evaluation score s i ;

[0090] S4.7: Select the sample point x with the highest comprehensive evaluation score from the sample set. * As the most sensitive sample point, this sample point x... * The controlled polygonal region is used as the area for adding new sampling points;

[0091] S5: Determine the new sampling point x using a learning function based on error estimation. new And obtain the target output value y corresponding to the new sampling point. new Add and update the sample set S; specifically, this includes the following sub-steps:

[0092] S5.1: The most sensitive sample point x is determined using the Delaunay triangulation algorithm. * Vino polygon adjacency set

[0093] S5.2: Leave-one-out cross-validation, calculate sample point x. * and its adjacent point set The leave-one error is calculated using the following formula:

[0094]

[0095] Where k is the number of adjacent vertices, and when j is not 0, x j For sample point x * The adjacent points of x; when j is 0, ij Degenerate into sample point x * itself; To remove point x from the entire sample point set X j The agent model G constructed later -j At sample point x j The predicted value, y j For sample point x j The true value;

[0096] S5.3: Based on the Monte Carlo simulation results obtained in S3.3, the points falling on the sensitive sample points x... * Points within the controlled polygonal region Using sample point x * The estimated error of a point is calculated by leaving one error between it and its adjacent points. The calculation formula is as follows:

[0097]

[0098] Where, n * For falling on sample point x * The number of points within the controlled polygonal region. For sprinkling With the sample point or its adjacent point x j Euclidean distance;

[0099] S5.4: Based on the Kriging surrogate model, obtain the output of the surrogate model at the point of distribution. variance at location

[0100] S5.5: Sprinkle some The estimation error is multiplied by the variance to form the learning function, and the formula for the learning function is as follows:

[0101]

[0102] S5.6 Select the point that maximizes the learning function as the new sampling point x. new New sampling points x are obtained through methods such as finite element analysis or experiments. new The corresponding target output value y new Add and update the sample set S.

[0103] S6: Determine whether the error convergence criterion has been met. If not, repeat steps S2 to S5; if it has been met, proceed to step S7. The specific convergence criteria are as follows:

[0104] S6.1: Calculate the error of each sample point using the leave-one-out method.

[0105] S6.2: When At that time, it is considered that the error has converged.

[0106] Where m is the number of sample points and c is the error convergence constant.

[0107] S7: Based on the final sample set S, construct a Kriging surrogate model G to characterize the mapping relationship between the design parameters and optimization objectives of complex equipment.

[0108] S8: Based on the identified complex equipment optimization design problem, use a genetic algorithm to solve the optimization problem, determine the optimal design parameters, and verify them.

[0109] S8.1: Establish a mathematical model for the optimization design problem of complex equipment, including design parameters, optimization objectives and constraints;

[0110] S8.2: Use the surrogate model built in S7 to characterize the mapping relationship between design parameters and optimization objectives;

[0111] S8.3: Use a genetic algorithm to solve the optimization problem, determine the optimal design parameters, and verify them.

[0112] Throughout the implementation process, the system heavily relies on Vino polygons and Delaunay triangles: Firstly, in S4, calculating the local nonlinearity of a sample point requires obtaining its neighboring points using Delaunay triangles; secondly, in S4, calculating the size of the polygon region controlled by the sample points requires determining the boundaries of the Vino polygons; thirdly, in S5, estimating the error at any point within the polygon region also requires obtaining the neighboring points of the central sample point of that region, which is done using Delaunay triangles. Based on the sample point set, Vino polygons and Delaunay triangles are generated in the parameter space, and their relationships are as follows: Figure 2 As shown.

[0113] Example 1

[0114] To verify the effectiveness of the method of this invention, this implementation case adopts a two-dimensional numerical example given by Xu et al. (Xu S, Liu H, Wang X, et al. A robust error-pursuing sequential sampling approach for global metamodeling based on voronoi diagram and cross validation[J]. Journal of Mechanical Design, 2014, 136(7):071009.), and the optimization problem is as follows:

[0115] find x = [x1, x2]

[0116] min

[0117] st

[0118] In this embodiment, a surrogate model for f(x) needs to be established. Based on the characteristics of the two-dimensional numerical (x1, x2) instance, 20 initial sample points are randomly generated in the design parameter space using Latin hypercube sampling. Then, new sample points are added adaptively and sequentially using the method of this invention to construct a high-precision surrogate model that fits f(x). Compared with the method proposed by Xu et al. in the reference, under the same error stopping conditions, the total number of sample points required for stopping is compared, and the average of 5 tests is taken. The spatial distribution of sample points at the end of the method of this invention and the method of Xu et al. is shown in the form of a contour plot, as follows. Figure 3a and Figure 3b As shown in the figure, the sampling point distribution of the method proposed in this invention is more reasonable, and the probability of falling into the peak-valley zone is greater. Furthermore, under the same genetic optimization algorithm (GA), the optimal design parameters and optimal values ​​obtained by the two methods are compared, and the test results are shown in the table below:

[0119]

[0120] As can be seen from the results in the table above, the method proposed in this invention can construct a high-precision surrogate model more quickly, significantly reducing the number of sampling points required and substantially decreasing the consumption of computational resources for experiments or simulations. Furthermore, based on the constructed surrogate model, the optimal design results obtained by this invention are essentially consistent with Xu's method, with an error of approximately 0.3‰.

[0121] Example 2

[0122] The method of this invention was applied to the lightweight design of the cutterhead structure of a tunnel boring machine (TBM), demonstrating its effectiveness. Addressing the issues of low soil ingress rate and mud cake formation at the cutterhead center during actual TBM excavation, the opening ratio and mass of the cutterhead panel were selected as optimization objective functions to improve overall TBM operating efficiency and save material costs. A larger opening ratio results in higher cutting speed and efficiency. Design variables include the cutterhead opening angle θ, the cutterhead opening spacing l, and the cutterhead thickness w, etc. Figure 4 As shown. The multi-objective optimization mathematical model for the tunnel boring machine cutterhead is as follows:

[0123] find x = [θ, l, w]

[0124] min F(θ,l,w)=(-R open (θ,l),m c (θ,l,w))

[0125] st

[0126] In the embodiment, it is necessary to establish the relationship between the design parameter x and the average stress value of the hot spot area. and mass m c The surrogate model, thrust F, torque T, and aperture ratio R open These parameters can be calculated using (empirical) formulas. In the three-dimensional design parameter space, 30 initial sample points were randomly generated using Latin hypercube sampling. Then, new sample points were added adaptively and sequentially using the method described in this invention to construct... and m c A high-precision surrogate model was developed. Similarly, compared with the method proposed by Xu et al., under the same error stopping conditions, the total number of sample points required for stopping was compared, and the average of five tests was taken. Simultaneously, under the same multi-objective genetic optimization algorithm NSGA-II, the optimal design parameters and optimal values ​​obtained by the two methods were compared. The test results are shown in the table below:

[0127]

[0128] As can be seen from the results in the table above, the method proposed in this invention can construct a high-precision surrogate model more quickly, significantly reducing the consumption of computational resources for experiments or simulations. Furthermore, based on the constructed surrogate model, the design results obtained by this invention show a 12.1% increase in aperture ratio and a 21.2% reduction in mass compared to the original design, demonstrating significant optimization effects. Moreover, the optimization results are basically consistent with those based on the Xu method, with an error of approximately 7‰, but the required number of sampling points is greatly reduced, saving computational resources and time costs.

[0129] The above numerical values ​​and engineering examples effectively demonstrate the effectiveness and superiority of the complex equipment optimization design method based on the hybrid adaptive sampling proxy model proposed in this invention. It can significantly reduce the consumption of resources such as experimental or simulation calculations while ensuring accuracy, saving time and improving the efficiency of optimization design.

[0130] It will be understood by those skilled in the art that the above descriptions are merely preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A method for optimizing the design of complex equipment based on a hybrid adaptive sampling surrogate model, characterized in that... Includes the following steps: S1: Based on the design parameter space of the complex equipment optimization problem, a certain number of initial sample point sets X are randomly generated, and the target output value Y corresponding to each sample point is obtained to form the initial sample set S. S2: Based on the sample point set X, the design parameter space of the complex equipment is divided into a Vino polygon region controlled by several sample points. S3: Based on the initial sample set S, calculate the leave-one error, local nonlinearity, and polygon region size for each sample point; S4: Based on the leave-one error, local nonlinearity and polygon region size calculated in S3 as evaluation indicators, the most sensitive region is selected as the new sampling point addition region using the entropy weight-good-bad solution distance method. S5: Determine new sampling points using a learning function based on error estimation. And obtain the target output value corresponding to the new sampling point. Add and update the sample set S; S6: Determine whether the error convergence criterion has been met. If not, repeat steps S2 to S5; if it has been met, proceed to step S7. S7: Based on the final sample set S, construct a Kriging surrogate model G to characterize the mapping relationship between the design parameters and optimization objectives of complex equipment; S8: Based on the identified complex equipment optimization design problem, use a genetic algorithm to solve the optimization problem, determine the optimal design parameters, and verify them; The specific steps of S1 are as follows: S1.1: Use Latin hypercube sampling to randomly generate an initial sample point set X in the design parameter space, where the design parameters include structural dimensions and material properties; S1.2 Obtain the target output value Y corresponding to each sample point.

2. The complex equipment optimization design method based on a hybrid adaptive sampling surrogate model according to claim 1, characterized in that: Step S3 is as follows: S3.1: Use leave-one-out cross-validation to calculate the cross-validation results for each sample point in the sample point set X. Leave one error ; S3.2: Based on linear fitting residual analysis, calculate the residual values ​​of each sample point in the sample point set X. Local nonlinearity : S3.3: Based on Monte Carlo simulation, calculate the values ​​of each sample point in the sample point set X. Controlled size of the Vino polygon region .

3. The complex equipment optimization design method based on a hybrid adaptive sampling proxy model according to claim 2, characterized in that: Step S4 is as follows: S4.1: Evaluation indicators for each sample point in sample set S , and Construct decision matrix A; S4.2: Normalize the decision matrix A to obtain the normalized decision matrix P. The calculation formula is as follows: Where m is the number of sample points and n is the dimension of the evaluation index. Let j be the evaluation index for the i-th sample point and the polygonal region it controls. , ; S4.3: Calculate the information entropy of each evaluation index based on the normalized decision matrix P; S4.4: Calculate the adaptive weight coefficient w for each evaluation index based on information entropy; S4.5: Update the multi-attribute decision matrix Z based on the weight coefficients of each evaluation indicator. The formula for calculating the multi-attribute decision matrix Z is as follows: in, , Let be the adaptive weight coefficient of the j-th evaluation index. S4.6: Based on the multi-attribute decision matrix Z, the superior-inferior solution distance method is used to calculate the distance between each sample point. Comprehensive evaluation score ; S4.7: Select the sample point with the highest comprehensive evaluation score from the sample set. As the most sensitive sample point, this sample point The controlled polygonal region is used as the area for adding new sampling points.

4. The complex equipment optimization design method based on a hybrid adaptive sampling proxy model according to claim 3, characterized in that: Step S5 is as follows: S5.1: The most sensitive sample points are determined using the Delaunay triangulation algorithm. Vino polygon adjacency set ; S5.2: Use leave-one-out cross-validation to calculate sample points. and its adjacent point set Leave one error; S5.3: Based on the Monte Carlo simulation results obtained in S3.3, the points falling on sensitive sample points are... Points within the controlled polygonal region Using sample points Leave one error calculation point for its adjacent points estimation error ; S5.4: Based on the Kriging surrogate model, obtain the output of the surrogate model at the point of distribution. variance at location ; S5.5: Sprinkle some estimation error and variance Multiplication as a learning function; S5.6 Select the point that maximizes the learning function as the new sampling point. New sampling points are obtained through finite element method or experimental method. Corresponding target output value Add and update the sample set S.

5. The complex equipment optimization design method based on a hybrid adaptive sampling proxy model according to claim 4, characterized in that: The specific convergence criteria are as follows: S6.1: Calculate the error of each sample point using the leave-one-out method. ; S6.2: When At that point, it is considered that the error has converged; Where m is the number of sample points and c is the error convergence constant.

6. The complex equipment optimization design method based on a hybrid adaptive sampling proxy model according to claim 5, characterized in that: Step S8 is as follows: S8.1: Establish a mathematical model for the optimization design problem of complex equipment, including design parameters, optimization objectives and constraints; S8.2: Use the surrogate model built in S7 to characterize the mapping relationship between design parameters and optimization objectives; S8.3: Use a genetic algorithm to solve the optimization problem, determine the optimal design parameters, and verify them.

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