A method, procedure, equipment, and storage medium for uniform experimental design in a design space with complex constraints.

Abstract

This invention belongs to the field of engineering optimization design technology, specifically relating to a method, program, equipment, and storage medium for uniform experimental design within a design space with complex constraints. By accurately representing the boundary of the constrained design space and gradually reducing the relaxation of constraints based on the sequential Monte Carlo method, this invention ensures that after a finite number of iterations, the selected priority sample points fully satisfy all constraints. This prevents individual sample points from not belonging to the actual constraint space due to inaccurate boundary condition definitions, thus avoiding unreasonable sample point selection. By introducing the "maximize minimum distance" criterion, uniform and orthogonal sampling can be achieved for a given number of samples, ensuring good representativeness of the sample selection. Progressive sampling can be implemented, preventing the need for complete resampling due to insufficient initial sample point selection, while simultaneously ensuring that all sample points maintain good uniformity and orthogonality after progressive sampling.

Description

Technical Field

[0001] This invention belongs to the field of engineering optimization design technology, and specifically relates to a uniform experimental design method, program, equipment and storage medium in a design space with complex constraints. Background Technology

[0002] In the field of engineering optimization design, the feasible region of design variables in optimization problems is often not a regular hypercubic design space, but an irregular design space containing various equality or inequality constraints. For example, in the optimization of large wind farm layout, it is required that all wind turbines be located within the outer boundary of the wind farm, but the outer boundary of the wind farm may contain areas that cannot be placed, which implies some complex geometric constraints; in the optimization of ship hydrostatic resistance, it is usually required that the relative changes in the ship's displacement volume and wetted surface area cannot exceed a certain range; in the optimization of the slamming load of the connecting bridge of a multihull ship, it is required that the sum of the lengths of the arc segments and straight segments of the connecting bridge does not exceed a certain value, etc.

[0003] The constraints mentioned above are essentially equality or inequality restrictions between design variables in optimization problems. This directly leads to the feasible region of the design variables no longer being a regular design space. In optimization based on approximation models, the experimental design methods commonly used are for regular design spaces. It is foreseeable that this method may waste some computational resources, because points outside the irregular design space have a relatively small impact on the approximation model built within that space. In other words, to achieve the same level of accuracy as the approximation model built when the sample points are entirely within the irregular design space, it is necessary to use methods such as Optimal Latin Hypercube Sampling (OLHS) and Sobol to sample more points in a relatively larger regular design space.

[0004] A search revealed that Wuhan University of Technology has disclosed a method, system, and terminal for selecting sample points based on ship hull constraint space (Chinese Patent, Publication No. CN117150652A, Publication Date 20231201). This invention first uses a uniform design method to generate initial ship hull sample points, and then calculates the corresponding ship hull hydrodynamic data based on these sample points. It then determines feasible and infeasible points according to the ship hull constraint conditions. Next, it uses the K-nearest neighbor classification algorithm, commonly used in machine learning, to extract boundary points. Then, based on these boundary points, it uses the least squares method to fit the boundary information of feasible and infeasible points, obtaining the feasible space range. Finally, it fills the sample space within the ship hull feasible space. However, the uniform design method used in this invention has a relatively small impact on the sampling of points outside the constraint space for subsequent surrogate model construction, and the fitting near boundary points cannot guarantee the accuracy of the constraint conditions. Furthermore, it is difficult to guarantee uniform, orthogonal, and progressive sampling under any given number of samples in an irregular design space, which weakens the rationality and repeatability of sample selection. Summary of the Invention

[0005] The purpose of this invention is to provide a uniform experimental design method in a design space with complex constraints.

[0006] A method for uniform experimental design within a design space with complex constraints includes the following steps:

[0007] Step 1: For the initial M-dimensional rule design space D M Define the constraint Ω in this space, and obtain D. M Point x∈D within M The deviation function C between the constraint Ω and the constraint Ω Ω (x);

[0008] Step 2: For the initial M-dimensional rule design space D M Perform dense sampling to obtain an initial set of sample points;

[0009] Step 3: Use the sequential constraint Monte Carlo method to iteratively update the coordinates of each sample point in the initial sample point set;

[0010] Step 4: For the updated initial set of sample points, the "maximize minimum distance" criterion is used for further filtering to obtain a given number of sample points with good uniformity and orthogonality.

[0011] Further, step 1 specifically includes:

[0012] This represents the original M-dimensional rule-based design space, which contains constraints, forming a constrained design space.

[0013] If the constraint is a single inequality g(x)≤0, that is, Ω={(x1,x2,…,x…) M For any point x∈D, |g(x)≤0} M The deviation function between it and the constraint is defined as C. Ω (x) = g(x);

[0014] If the constraints are n inequalities and g1(x)≤0, g2(x)≤0,...,g n (x)≤0, that is, the intersection of multiple regions: Ω={(x1,x2,…,x M )|max{g1(x),g2(x),…,g n For any point x∈D, (x)}≤0} M The deviation function between it and the constraint is defined as follows:

[0015] If the constraints are n inequalities and g1(x)≤0, or g2(x)≤0,…, or g… n (x)≤0, that is, the union of multiple regions: Ω={(x1,x2,…,x M )|min{g1(x),g2(x),...,g n For any point x∈D, (x)}≤0} M The deviation function between it and the constraint is defined as C. Ω (x)=min{g1(x),g2(x),...,g n (x)}≤0;

[0016] If the constraint is an equality constraint h(x) = 0, for some point x ∈ D M The deviation function between it and the constraint is defined as C. Ω (x)=|h(x)|-ε; among them, 0<ε<<1.

[0017] Furthermore, in step 2, dense sampling is performed using optimized Latin hypercube sampling or Sobol sampling methods.

[0018] Furthermore, step 3 specifically includes:

[0019] Step 3.1: Set the threshold τ T Number of steps N MH Initialize t=1, initialize weights. N is the initial set of sample points. The number of sample points in the middle;

[0020] Step 3.2: Solve the ESS equation for the effective sample number to obtain τ. t ;

[0021]

[0022] in, The coordinates of the nth sample point at time step t-1;

[0023] Step 3.3: Update Weights And after normalization, we obtain

[0024] Step 3.4: Perform importance resampling and select random numbers.

[0025] For j, k = 1, 2, ..., N, if but

[0026] Step 3.5: After completing the resampling, set the weights.

[0027] Step 3.6: For each dimension, calculate N samples. Standard deviation in the m-th dimension Select random number For each sample in turn The offset operation is performed on the m-th dimension, and the coordinates of the sample after offset are:

[0028]

[0029] Among them, e m It is a basic matrix in which the m-th component is 1 and all other components are 0;

[0030] Calculate the acceptance probability α, select a random number u2∈U[0,1], and if u2≤α, then accept the sample coordinates after a slight offset. Otherwise, do not move; the sample coordinates remain the same.

[0031]

[0032] Step 3.7: Repeat step 3.6, performing the operation on each dimension of all samples in sequence. MH This process yields N samples in total. The coordinates corresponding to time step t;

[0033] Step 3.8: If τ t ≤τ T If the result is positive, let t = t + 1 and return to step 3.2; otherwise, end the calculation and output N samples. Updated coordinates.

[0034] Furthermore, step 4 specifically includes:

[0035]

[0036] To solve the above optimization problem, the sample points in the updated initial sample point set are filtered to obtain N1 sample points with good uniformity and orthogonality; among them, p m With q m Let p and q represent the coordinate components of the m-th dimension of sample points p and q, respectively.

[0037] Furthermore, if the N1 sample points obtained in step 4 do not meet the design requirements, then based on the N1 sample points, N2 points are further sampled asymptotically using the "maximize minimum distance" criterion to construct a more accurate surrogate model, i.e., to optimize and solve the following problem:

[0038]

[0039] in, r m With s m Let r and s represent the coordinate components of the m-th dimension of the sample points r and s, respectively.

[0040] A computer device / apparatus / system includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above-described uniform experimental design method in a design space with complex constraints.

[0041] A computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements the steps of the above-described uniform experimental design method in a design space with complex constraints.

[0042] A computer program product includes a computer program / instructions that, when executed by a processor, implement the steps of the above-described uniform experimental design method in a design space with complex constraints.

[0043] The beneficial effects of this invention are as follows:

[0044] This invention accurately expresses the boundary of the constraint design space and gradually reduces the relaxation of constraints based on the sequential Monte Carlo method. This ensures that after a finite number of iterations, the selected priority sample points can fully satisfy all constraint conditions, preventing individual sample points from not belonging to the actual constraint space due to inaccurate boundary condition definitions, thus avoiding unreasonable sample point selection. By introducing the "maximize minimum distance" criterion, uniform and orthogonal sampling under a given number of samples can be achieved, making the sample selection highly representative. Progressive sampling can be implemented to prevent the need for complete resampling due to insufficient initial sample point selection, while ensuring that all sample points maintain good uniformity and orthogonality after progressive sampling. Attached Figure Description

[0045] Figure 1 This is a flowchart of the present invention.

[0046] Figure 2 This is a two-dimensional illustration of the constraint space in an example of the present invention.

[0047] Figure 3 In an example of the present invention, in space D 2 The image shows the coordinates of sample points obtained by dense sampling using the optimized Latin hypercube sampling method.

[0048] Figure 4 The diagram illustrates the coordinates of sample points after one or two iterations using the SCMC method in an example of this invention.

[0049] Figure 5 In an example of the present invention, the "maximize minimum distance" criterion is used to obtain a preset number of N1 = 120 sample points with good orthogonality and uniformity in a complex constrained space.

[0050] Figure 6 The figure shows the results of asymptotic sampling of N2=80 in a complex constrained space using the "maximize minimum distance" criterion in an example of the present invention. Detailed Implementation

[0051] The present invention will now be further described with reference to the accompanying drawings.

[0052] To overcome the shortcomings of existing related technologies, this invention provides a uniform experimental design method in a design space with complex constraints. Based on Monte Carlo methods and the "maximize minimum distance" criterion, it obtains a preset with good homogeneity and orthogonality in an irregular constraint space, as well as a larger number of samples.

[0053] S1, for the initial rule design space D M Define the constraints in this space, and relax the constraints according to different situations to form a mathematical expression of a space Ω with complex constraints;

[0054] S2, for the initial design space D M Perform dense sampling;

[0055] S3, for D obtained in S2 M The initial sample points within the time step t are iteratively processed according to the Sequentially Constrained Monte Carlo (SCMC) method for each time step t. This involves updating the weights of each component of each sample point, normalizing them, resampling their importance, accepting / rejecting transition steps, obtaining all sample positions for the current step t, until a threshold is reached.

[0056] S4. For the large number of sample points within Ω obtained in S3, the "maximize minimum distance" criterion is used for further screening to obtain a given number of sample points with good uniformity and orthogonality.

[0057] S5. For the small number of sample points within Ω obtained in S4, additional samples can be filled in as needed to obtain any number of sample points within Ω with good uniformity and orthogonality.

[0058] In step S1, This represents the original M-dimensional rule-based design space, which contains constraints to form a constrained design space. The constraints can be inequality constraints, resulting in the original rule design space D. M The constraint can be a subregion; it can also be an equality constraint, resulting in a high-dimensional manifold; or it can be a combination of two constraint types. Uniform sampling within a constrained design space Ω can actually be viewed as a regular design space D. M Sampling where the internal sample distribution is uneven.

[0059] When the constraint is a single inequality g(x)≤0, i.e. Ω={(x1,x2,…,x…)} M For any point x∈D, |g(x)≤0} M Define the deviation function between it and the constraint:

[0060] C Ω (x)=g(x)

[0061] When the constraints consist of n inequalities, one case is g1(x)≤0, g2(x)≤0,...,g n (x)≤0, that is, the intersection of multiple regions: Ω={(x1,x2,…,x M )|max{g1(x),g2(x),…,g n For any point x∈D, (x)}≤0} M Define the deviation function between it and the constraint:

[0062]

[0063] Another case is when g1(x)≤0, or g2(x)≤0,…, or g n (x)≤0, that is, the union of multiple regions: Ω={(x1,x2,…,x M )|min{g1(x),g2(x),...,g n For any point x∈D, (x)}≤0} M Define the deviation function between it and the constraint:

[0064] C Ω (x)=min{g1(x),g2(x),...,g n (x)}≤0

[0065] In step S1, when the constraint is an equality constraint h(x) = 0, due to the parameter τ T It can be set very large, which can relax the equality constraint into an inequality constraint with a very small deviation function magnitude (e.g., 0 < ε << 1). For a point x ∈ D M Define the deviation function between it and the constraint:

[0066] C Ω (x)=|h(x)|-ε

[0067] The above relaxation can effectively prevent sampling failures caused by the probability of points satisfying the equality constraint being 0.

[0068] Introducing the standard normal cumulative function, i.e.

[0069]

[0070] It is then transformed into a constraint index function Φ(-τC) Ω (x)), where the parameter τ (τ≥0) controls the stiffness of the constraint.

[0071] Construct a monotonically increasing sequence and the corresponding series of probability density distributions Its form is

[0072]

[0073] If there are multiple constraints, such as The above probability density distribution can be generalized to the following definition:

[0074]

[0075] According to the deviation function defined above, a sample point satisfies the constraint condition if and only if all its deviation function values ​​are non-positive. Therefore, when τ TWhen the size is sufficiently large, the sample distribution tends to be a uniform distribution within the constrained design space Ω.

[0076] In step S2, the initial design space D is given. M Sample size N, threshold τ T Accept / reject transition step number N MH Set the initial conditions t = 0, τ t =0, and in a space D with a sample size of N. M In this study, dense sampling was performed using methods such as Optimal Latin Hypercube Sampling (OLHS) and Sobol sampling to obtain D. M Coordinates of sample points with good homogeneity and orthogonality and initial weights Where n = 1, ..., N.

[0077] In step S3, the concept of Efficient Sampling Sum (ESS) is introduced to determine the sequence density distribution, ensuring that the number of effective samples is not less than a given value (e.g., half of the total number of samples N). The τ in the following equation is solved numerically. t accomplish:

[0078]

[0079] in

[0080]

[0081] Solve for τ t Then, update the weights. And after normalization, we obtain

[0082]

[0083] To effectively remove samples with low probability, importance resampling is implemented:

[0084] Select a random number:

[0085] For j,k=1,2,…,N, if but

[0086] After completing the above resampling process, set the weights. Where n = 1, 2, ..., N.

[0087] In step S3, to prevent sample degradation, i.e., some points may be repeatedly copied in the resampling step, the specific implementation method is to perform NMH The Metropolis-Hastings acceptance / rejection transition step causes the position of each sample to shift slightly within step t with a certain probability.

[0088] For a transition step, it is necessary to sequentially... The operation is performed on the k-th dimension (k = 1, 2, ..., M) of the sample:

[0089] Assuming the above-obtained sample The standard deviation in the k-th dimension is Select random number The offset sample coordinates are

[0090]

[0091] Where e k It is the basic matrix where the k-th component is 1 and all other components are 0.

[0092] Calculate the probability of acceptance:

[0093]

[0094] Select a random number u∈U[0,1]. If u≤α, accept the sample value after a small offset. Otherwise, do not move; the sample value remains the same. The probability of each sample remains unchanged during this step.

[0095] Perform the operation N sequentially on each dimension of all samples. MH N times, that is, completed N MH After several Metropolis-Hastings accept / reject transition steps, the sample corresponding to time step t can be obtained. Proceed to the next iteration to update the samples, until τ t Greater than a specific value τ T .

[0096] In step S4, a large number of relatively uniform sample points can be obtained within the restricted area through the SCMC method. In order to obtain a number of N1 (<<N) sample points with good orthogonality and uniformity, the "maximize minimum distance" criterion can be used for further screening.

[0097] If an experimental design maximizes the minimum distance between each pair of sample points, then it is a "maximize minimum distance" experimental design, which satisfies the condition.

[0098]

[0099] in

[0100]

[0101] By employing intelligent optimization algorithms such as genetic algorithms to solve the above optimization problem, the dense sampling in the irregular design space can be further filtered to obtain a given number of samples with good uniformity and orthogonality, not exceeding the total number of samples.

[0102] In step S5, a predetermined number of samples N1 (<< N) are selected based on the "maximize minimum distance" criterion. After constructing a surrogate model of the objective function with respect to the sample points based on numerical simulation, experimental measurement, etc., if the accuracy does not meet the requirements, N2 points can be further sampled asymptotically based on the original sample points using the "maximize minimum distance" criterion to construct a more accurate surrogate model, that is, to optimize and solve the following problem:

[0103]

[0104] in

[0105]

[0106] Example 1:

[0107] This embodiment provides a method and system for uniform experimental design within a design space with complex constraints, such as... Figure 1 As shown, the system consists of a constraint construction module for constructing mathematical expressions based on different constraints, a hypercubic space sampling module for uniform and orthogonal dense sampling of the initial regular space, an SCMC dense sampling module for obtaining a large number of sample points within the constraint space, a sampling module for obtaining a preset number of samples within the constraint space using the "maximize minimum distance" criterion, and an asymptotic sampling module for obtaining more uniform and orthogonal sample points based on a finite number of samples within the constraint space. This invention, based on methods such as OLHS, can obtain dense sampling within an initial regular space containing irregular design spaces. Based on the improved SCMC method, it can achieve uniform, orthogonal, and asymptotic sampling within irregular design spaces containing various constraints (single / multiple constraints, single / complex connectivity, convex / non-convex regions, equality / inequality constraints).

[0108] S1, for the initial rule design space D M Define the constraints in this space, and relax the constraints according to different situations to form a mathematical expression of a space Ω with complex constraints;

[0109] S2, for the initial design space D M Perform dense sampling;

[0110] S3, for D obtained in S2 MThe initial sample points within the time step t are iteratively processed according to the SCMC method for each time step t, which involves updating the weights of each component of each sample point, normalizing, resampling the importance, accepting / rejecting transition steps, obtaining all sample positions of the current step t, until the threshold is reached.

[0111] S4. For the large number of sample points within Ω obtained in S3, the "maximize minimum distance" criterion is used for further screening to obtain a given number of sample points with good uniformity and orthogonality.

[0112] S5. For the small number of sample points within Ω obtained in S4, additional samples can be filled in as needed to obtain any number of sample points within Ω with good uniformity and orthogonality.

[0113] In this embodiment, step S1: as Figure 2 The constrained space shown is a two-dimensional multi-connected region Ω enclosed by the letters H, E, and U, i.e., Ω = Ω1 ∪ Ω2 ∪ Ω3. We can form a mathematical expression for the complex constrained space Ω using the maximum and minimum value functions:

[0114] Ω={(x1,x2)|min{g1(x),g2(x),...,g 10 (x)}≤0}

[0115] in:

[0116] g1(x)=max{0.1-x1,x1-0.2,-x2,x2-1}

[0117] g2(x)=max{0.2-x1,x1-0.8,0.45-x2,x2-0.55}

[0118] g3(x)=max{0.8-x1,x1-0.9,-x2,x2-1}

[0119] g4(x)=max{1.1-x1,x1-1.2,-x2,x2-1}

[0120] g5(x)=max{1.2-x1,x1-1.9,-x2,x2-0.1}

[0121] g6(x)=max{1.2-x1,x1-1.9,0.45-x2,x2-0.55}

[0122] g7(x)=max{1.2-x1,x1-1.9,0.9-x2,x2-1}

[0123] g8(x)=max{2.1-x1,x1-2.2,0.4-x2,x2-1}

[0124] g9(x)=max{2.8-x1,x1-2.9,0.4-x2,x2-1}

[0125] g 10 (x) = max{(x1 - 2.5)} 2 +(x2-0.4) 2 -0.16, 0.09 - (x1 - 2.5) 2 -(x2-0.4) 2 ,-x2,x2-0.4}

[0126] Define its deviation function from the constraints:

[0127] C Ω (x)=min{g1(x),g2(x),...,g 10 (x)}≤0

[0128] In step S2, for the initial design space D 2 = [0,3]×[0,1], set the sample size to N=10000, and the threshold τ T =10 6 Metropolis-Hastings accept / reject transition step number N MH =10, set initial conditions t=0, τ t =0, and as Figure 3 In a space D with a sample size of N = 10000 2 D was obtained by dense sampling using the OLHS method. 2 Coordinates of sample points with good homogeneity and orthogonality and initial weights Where n = 1, ..., 10000.

[0129] In step S3, the solution is obtained numerically:

[0130]

[0131] in:

[0132]

[0133] Solving for τ1, we get 20.534, and then update the weights. And after normalization, we obtain

[0134]

[0135] To effectively remove samples with low probability, importance resampling is implemented:

[0136] Select a random number:

[0137] For j, k = 1, 2, ..., 10000, if but

[0138] After completing the above resampling process, set the weights. Where n = 1, 2, ..., 10000.

[0139] Then perform 10 more Metropolis-Hastings acceptance / rejection transition steps, so that the position of each sample is slightly shifted with a certain probability within step 1.

[0140] Need to be done in sequence Perform operations on the k-th dimension of the sample (k=1,2):

[0141] Assuming the above-obtained sample The standard deviation in the k-th dimension is Select random number The offset sample coordinates are:

[0142]

[0143] Where e k It is the basic matrix where the k-th component is 1 and all other components are 0.

[0144] Calculate the probability of acceptance:

[0145]

[0146] Select a random number u∈U[0,1]. If u≤α, accept the sample value after a small offset. Otherwise, do not move; the sample value remains the same. The probability of each sample remains unchanged during this step.

[0147] The results after the above processing are as follows Figure 4 .

[0148] Since τ1 < 10 6 Therefore, proceed to the next iteration to update the samples:

[0149]

[0150] in:

[0151]

[0152] Solving for τ2, we get 10. 6 The threshold has been reached.

[0153] Similar to the previous step, after updating the weights of each component for each sample point, normalizing, resampling for importance, and accepting / rejecting the transition step, the result is as follows: Figure 4 .

[0154] In step S4, as described above... Figure 5 The method shown uses the "maximize minimum distance" criterion to obtain a preset number of N1 = 120 sample points with good orthogonality and uniformity, thus satisfying the condition:

[0155]

[0156] In step S5, based on the pre-set number N1 = 120 samples selected by the "maximize minimum distance" criterion, N2 = 80 points can be sampled asymptotically by the "maximize minimum distance" criterion, i.e., the following optimization problem can be solved:

[0157]

[0158] Progressive sampling results as follows Figure 6 As shown, it can be foreseen that, with the same number of samples, the sample points obtained by this system have good uniformity and orthogonality, and will have higher accuracy than the surrogate model constructed by the traditional sampling method. Therefore, this invention can be used for sampling in spaces with various complex constraints.

[0159] This invention accurately expresses the boundary of the constraint design space and gradually reduces the relaxation of constraints based on the sequential Monte Carlo method. This ensures that after a finite number of iterations, the selected priority sample points can fully satisfy all constraint conditions, preventing individual sample points from not belonging to the actual constraint space due to inaccurate boundary condition definitions, thus avoiding unreasonable sample point selection. By introducing the "maximize minimum distance" criterion, uniform and orthogonal sampling under a given number of samples can be achieved, making the sample selection highly representative. Progressive sampling can be implemented to prevent the need for complete resampling due to insufficient initial sample point selection, while ensuring that all sample points maintain good uniformity and orthogonality after progressive sampling.

[0160] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for uniform experimental design within a design space with complex constraints, characterized in that, The application to ship hydrostatic resistance optimization includes the following steps: Step 1: For the initial M-dimensional rule design space D M Define the constraint Ω in this space, and obtain D. M Point x∈D within M The deviation function C between the constraint Ω and the constraint Ω Ω (x); Step 2: For the initial M-dimensional rule design space D M Perform dense sampling to obtain an initial set of sample points; Step 3: Use the sequential constraint Monte Carlo method to iteratively update the coordinates of each sample point in the initial sample point set; Step 3.1: Set the threshold τ T Number of steps N MH Initialize t=1, initialize weights. N is the initial set of sample points. The number of sample points in the middle; Step 3.2: Solve the ESS equation for the effective sample number to obtain τ. t ; in, The coordinates of the nth sample point at time step t-1; Step 3.3: Update Weights And after normalization, we obtain Step 3.4: Perform importance resampling and select random numbers. For j, k = 1, 2, ..., N, if but Step 3.5: After completing the resampling, set the weights. Step 3.6: For each dimension, calculate N samples. Standard deviation in the m-th dimension Select random number For each sample in turn The offset operation is performed on the m-th dimension, and the coordinates of the sample after offset are: Among them, e m It is a basic matrix in which the m-th component is 1 and all other components are 0; Calculate the acceptance probability α, select a random number u2∈U[0,1], and if u2≤α, then accept the sample coordinates after a slight offset. Otherwise, do not move; the sample coordinates remain the same. Step 3.7: Repeat step 3.6, performing the operation on each dimension of all samples in sequence. MH This process yields N samples in total. The coordinates corresponding to time step t; Step 3.8: If τ t ≤τ T If the result is positive, let t = t + 1 and return to step 3.2; otherwise, end the calculation and output N samples. Updated coordinates; Step 4: For the updated initial sample point set, the "maximize minimum distance" criterion is used for further screening to obtain N1 sample points with good uniformity and orthogonality; If the obtained N1 sample points do not meet the design requirements, then based on the N1 sample points, N2 points are further sampled progressively using the "maximize minimum distance" criterion to build a more accurate surrogate model.

2. The uniform experimental design method in a design space with complex constraints according to claim 1, characterized in that: Step 1 specifically involves: This represents the original M-dimensional rule-based design space, which contains constraints, forming a constrained design space. If the constraint is a single inequality g(x)≤0, that is, Ω={(x1,x2,…,x…) M For any point x∈D, |g(x)≤0} M The deviation function between it and the constraint is defined as C. Ω (x) = g(x); If the constraints are n inequalities and g1(x)≤0, g2(x)≤0,...,g n (x)≤0, that is, the intersection of multiple regions: Ω={(x1,x2,…,x M )|max{g1(x),g2(x),…,g n For any point x∈D, (x)}≤0} M The deviation function between it and the constraint is defined as follows: If the constraints are n inequalities and g1(x)≤0, or g2(x)≤0,…, or g… n (x)≤0, that is, the union of multiple regions: Ω={(x1,x2,…,x M )|min{g1(x),g2(x),...,g n For any point x∈D, (x)}≤0} M The deviation function between it and the constraint is defined as C. Ω (x)=min{g1(x),g2(x),...,g n (x)}≤0; If the constraint is an equality constraint h(x) = 0, for some point x ∈ D M The deviation function between it and the constraint is defined as C. Ω (x)=|h(x)|-ε; among them, 0<ε<<1.

3. The uniform experimental design method in a design space with complex constraints according to claim 1, characterized in that: In step 2, dense sampling is performed using optimized Latin hypercube sampling or Sobol sampling.

4. The uniform experimental design method in a design space with complex constraints according to claim 1, characterized in that: In step 4, the updated initial sample point set is further filtered using the "maximize minimum distance" criterion to obtain N1 sample points with good uniformity and orthogonality, i.e., optimizing the following problem: in, p m With q m Let p and q represent the coordinate components of the m-th dimension of sample points p and q, respectively.

5. The uniform experimental design method in a design space with complex constraints according to claim 4, characterized in that: If the N1 sample points obtained in step 4 do not meet the design requirements, then based on the N1 sample points, N2 points are further sampled asymptotically using the "maximize minimum distance" criterion to construct a more accurate surrogate model, i.e., to optimize and solve the following problem: in, r m With s m Let r and s represent the coordinate components of the m-th dimension of the sample points r and s, respectively.

6. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 5.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When executed by a processor, the computer program implements the steps of the method according to any one of claims 1 to 5.

8. A computer program product comprising computer instructions, characterized in that: When executed by a processor, the computer instructions implement the steps of the method according to any one of claims 1 to 5.

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