A sampling method suitable for advanced reactor continuous-discrete hybrid variable design optimization

Abstract

The application provides a sampling method suitable for advanced reactor continuous-discrete mixed variable design optimization, comprising (1) screening effective discrete variable combination; (2) constructing a cumulative probability distribution function of the discrete variable combination; (3) designing a space based on a cumulative probability distribution function interval; (4) distributing sample numbers according to the width proportion of the cumulative probability distribution function interval of each layer; (5) performing Latin hypercube sampling on the continuous variable in each layer; (6) integrating a global sample set and verifying the quality thereof; and (7) constructing a surrogate model and evaluating the accuracy thereof. The application realizes efficient exploration of the nuclear reactor design space by integrating the probability characteristics of the discrete variable and the space filling characteristics of the continuous variable, and significantly improves the sample quality and the calculation efficiency compared with the traditional method.

Description

Technical Field

[0001] This invention belongs to the field of advanced reactor design optimization technology, specifically relating to a sampling method suitable for the design optimization of continuous-discrete mixed variables in advanced reactors. This method solves the sample coverage problem in the continuous-discrete mixed variable space of advanced reactors by fusing a hierarchical strategy based on the cumulative probability distribution function with Latin hypercube sampling techniques. Background Technology

[0002] Integrated optimization throughout the reactor's entire lifecycle involves the coordinated optimization of a mixture of continuous and discrete variables. Discrete variables include the number of fuel assemblies and their arrangement, while continuous variables include reflector thickness and the radial enrichment ratio of fuel assemblies. When conducting optimization design and sensitivity analysis, the sampling method has a crucial impact on the accuracy of both the optimization and sensitivity analysis. Traditional sampling techniques, such as simple random sampling and Latin hypercube sampling, are suitable for single variable types (e.g., continuous or discrete) but cannot handle sampling of mixed continuous and discrete variables.

[0003] The existing technology has the following problems: (1) it cannot handle continuous and discrete variables at the same time; (2) it is difficult to balance the sample size and the calculation accuracy; (3) it is difficult to take into account both the probabilistic characteristics of discrete variables and the spatial filling characteristics of continuous variables at the same time. Therefore, it is urgent to develop a method that can efficiently and uniformly handle spatial sampling of continuous-discrete mixed variables. Summary of the Invention

[0004] The purpose of this invention is to provide a sampling method suitable for the design optimization of continuous-discrete mixed variables in advanced reactors, thereby solving the problem that existing technologies cannot sample continuous-discrete mixed variables. This method achieves efficient sampling of the continuous-discrete mixed variable space by integrating a stratified strategy based on the cumulative probability distribution function with Latin hypercube sampling techniques, making it suitable for nuclear reactor design optimization and sensitivity analysis. The technical solution adopted by this invention is as follows:

[0005] A sampling method applicable to continuous-discrete hybrid variable design optimization for advanced reactors, comprising:

[0006] S110, among all combinations of discrete variables, screen for effective combinations, apply prior knowledge and constraints to eliminate combinations that are physically infeasible, engineering unreasonable, or practically meaningless, and determine the set of effective combinations. For m discrete variables Each variable have One possible value Total number of original combinations The number of valid combinations after screening is ;

[0007] S120, for the selected effective discrete variable combinations Perform probability modeling and construct the cumulative probability distribution function. , used to characterize the distributional properties of combinations of discrete variables;

[0008] S130, based on the interval design of the cumulative probability distribution function of effective discrete variable combinations, spatial stratification is performed, with each combination corresponding to one stratum, i.e. ,in It is the total number of layers. The effective number of discrete variable combinations, and the corresponding cumulative probability distribution function interval for each layer are:

[0009] ,in It is the combination of discrete variables corresponding to the i-th layer;

[0010] S140, the number of samples is allocated according to the proportion of the interval width of the cumulative probability distribution function of each layer, using the formula... Determine the first The number of samples in the layer, of which For the first The interval width of the cumulative probability distribution function of the layer. The total number of samples, A function to round a number to the nearest integer;

[0011] S150 performs Latin hypercube sampling on continuous variables within each layer and uses the maximum-minimum distance criterion to optimize sample space filling, ensuring uniform distribution of samples in all dimensions.

[0012] S160 integrates samples from each layer to form a global sample set, and comprehensively verifies the sample quality through discreteness index, space filling index and projection uniformity index.

[0013] S170: Construct a surrogate model based on the obtained sampling results, and evaluate the model accuracy through cross-validation. If the accuracy does not meet the requirements, return to step S130 to readjust the sample allocation strategy and parameters.

[0014] A computing device includes: at least one processor and a memory storing program instructions; when the program instructions are read and executed by the processor, the computing device causes the computing device to perform a sampling method suitable for continuous-discrete hybrid variable design optimization of advanced reactors.

[0015] A readable storage medium storing program instructions that, when read and executed by a computing device, cause the computing device to perform a sampling method suitable for continuous-discrete hybrid variable design optimization of advanced reactors.

[0016] As can be seen from the above technical solution, the beneficial effects of the present invention are as follows:

[0017] First, this invention effectively solves the "curse of dimensionality" problem caused by high-dimensional discrete variable space through a discrete variable combination screening and merging mechanism;

[0018] Second, this invention designs a stratified sampling strategy based on the cumulative probability distribution function, which can reasonably allocate computing resources according to the importance of different combinations of discrete variables.

[0019] Third, the present invention employs a method based on intra-layer Latin hypercube sampling and maximum-minimum distance optimization to ensure uniform filling of the continuous variable space;

[0020] Fourth, this invention uses the maximum-minimum distance criterion to optimize Latin hypercube sampling, which significantly improves the filling efficiency of continuous variable space;

[0021] Fifth, the multidimensional evaluation system for sample quality proposed in this invention ensures the representativeness and homogeneity of samples in the mixed variable space;

[0022] Sixth, this invention provides an adaptive optimization mechanism that can dynamically adjust the sampling strategy according to the model's accuracy requirements.

[0023] This method can be applied to advanced reactor optimization design analysis, sensitivity analysis, etc., and provides a high-confidence sample basis for advanced reactors involving continuous-discrete high-dimensional mixed variables, and has broad application prospects. Attached Figure Description

[0024] Figure 1 This is a flowchart illustrating the overall framework of the sampling method for design optimization of continuous-discrete mixed variables in advanced reactors, as described in this invention.

[0025] Figure 2 This is a flowchart of the Latin hypercube sampling optimization procedure of the present invention. Detailed Implementation

[0026] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0027] Figure 1This is a flowchart illustrating the overall framework of the sampling method for the design optimization of continuous-discrete mixed variables in advanced reactors, applicable to this invention. This method primarily combines fuzzy hierarchical analysis, a hierarchical strategy based on the cumulative probability distribution function, and an optimized Latin hypercube sampling technique to achieve efficient sampling. Figure 1 As shown, the method includes the following steps:

[0028] S110, among all combinations of discrete variables, screen for effective combinations, apply prior knowledge and constraints to eliminate combinations that are physically infeasible, engineering unreasonable, or practically meaningless, and determine the set of effective combinations. For m discrete variables Each variable have One possible value Total number of original combinations The number of valid combinations after screening is ;

[0029] S120, for the selected effective discrete variable combinations Perform probability modeling and construct the cumulative probability distribution function. , used to characterize the distributional properties of combinations of discrete variables;

[0030] S130, based on the interval design of the cumulative probability distribution function of effective discrete variable combinations, spatial stratification is performed, with each combination corresponding to one stratum, i.e. ,in Total number of layers The effective number of discrete variable combinations, and the corresponding cumulative probability distribution function interval for each layer are:

[0031] ,in It is the combination of discrete variables corresponding to the i-th layer;

[0032] S140, the number of samples is allocated according to the proportion of the interval width of the cumulative probability distribution function of each layer, using the formula... Determine the number of samples in the i-th layer, where For the first The interval width of the cumulative probability distribution function of the layer. The total number of samples, A function to round a number to the nearest integer;

[0033] S150 performs Latin hypercube sampling on continuous variables within each layer and uses the maximum-minimum distance criterion to optimize sample space filling, ensuring uniform distribution of samples in all dimensions.

[0034] S160 integrates samples from each layer to form a global sample set, and comprehensively verifies the sample quality through discreteness index, space filling index and projection uniformity index.

[0035] S170: Construct a surrogate model based on the obtained sampling results, and evaluate the model accuracy through cross-validation. If the accuracy does not meet the requirements, return to step S130 to readjust the sample allocation strategy and parameters.

[0036] Furthermore, in step S110, the selection of effective discrete variable combinations is specifically carried out by constructing a constraint matrix between discrete variables based on domain knowledge, and then selecting effective combinations that satisfy all constraints through matrix operations.

[0037] Furthermore, S120 specifically includes the following steps:

[0038] S120-1, Analyze the joint probability distribution characteristics of discrete variables, and establish a probability distribution model of discrete variables based on expert knowledge or the uniform distribution assumption.

[0039] S120-2, Based on the probability distribution model in step S120-1, generate the cumulative probability ladder function of the discrete variable combination, ensuring that each discrete variable combination corresponds to a unique cumulative probability distribution function interval;

[0040] S120-3, expert knowledge is quantified into weight coefficients for combinations of discrete variables through fuzzy hierarchical analysis. These weight coefficients are used to construct the probability distribution of non-uniform discrete variables.

[0041] Furthermore, in S130, when the number of effective discrete variable combinations is too large, resulting in insufficient sample resources, the specific method adopted is: based on the weight coefficients of the discrete variable combinations obtained in step S120-3... Set weight threshold , for satisfying The low-weight discrete variable combinations are merged according to the following rules: ① Combinations of the same type (with the same variable values) are merged first; ② The weights of the new layer after merging are... The new layer refers to the layer formed by the combination of discrete variables after merging;

[0042] Furthermore, such as Figure 2 As shown, the optimization of Latin hypercube sampling in S150 adopts the maximum-minimum distance criterion. The sample point distribution is iteratively optimized through simulated annealing algorithm to maximize the minimum Euclidean distance between sample points, thereby improving the filling efficiency of the continuous variable space. The implementation steps of S150 are as follows:

[0043] S150-1, Initialization: Initial design scheme is generated using Latin hypercube sampling;

[0044] S150-2, Define the objective function: maximize the minimum Euclidean distance between sample points;

[0045] S150-3 is optimized iteratively using a simulated annealing algorithm:

[0046] 1) Define the initial temperature and cooling rate ;

[0047] 2) In each iteration, randomly swap the coordinates of one dimension of two sample points;

[0048] 3) Calculate the objective function value of the new scheme and decide whether to accept the new scheme based on the Metropolis criterion;

[0049] 4) Lower the temperature: ;

[0050] 5) Stop when the termination condition is met (maximum number of iterations or temperature below the threshold).

[0051] Furthermore, the comprehensive verification in S160 includes:

[0052] Verifying sample quality using discreteness indicators includes: calculating the reasonableness index of discrete variable distribution, which involves calculating the minimum and maximum distances between all sample points and comparing them with a preset threshold to verify the reasonableness of the sample distribution. The threshold is derived from practical engineering experience and statistical theory.

[0053] ,

[0054] in, For sample point x i and x j The Euclidean distance (after normalization).

[0055] Verifying sample quality using space-filling indices includes: calculating the space-filling index for continuous variables; that is, based on... The criteria are calculated, and it is confirmed whether... ,in Maximum allowed fill index value:

[0056] ,

[0057] Validating sample quality using projection homogeneity indices includes: calculating the projection homogeneity index, i.e., assessing the homogeneity of each dimension using the Kolmogorov-Smirnov test:

[0058] ,

[0059] Among them, F emp For the empirical distribution of the sample, Funiform For a theoretically uniform distribution, This is the supremum, i.e., the maximum value. For the values ​​that the variable can take, This is the KS test statistic; the smaller the value, the closer it is to a uniform distribution.

[0060] Furthermore, in step S170, the model accuracy is evaluated using K-fold cross-validation. If the accuracy does not meet the requirements, optimization is performed by increasing the total number of samples or adjusting the sample allocation ratio. Accuracy evaluation can use root mean square error (RMSE), maximum relative error (MRE), or coefficient of determination (R²). 2 Statistics such as )

[0061] Fuzzy Hierarchical Analysis (FAHP) is a multi-criteria decision-making method that effectively addresses uncertainty and fuzziness in the decision-making process by combining traditional analytic hierarchy process (AHP) with fuzzy set theory. FAHP establishes a hierarchical model and uses fuzzy numbers to represent expert judgments, evaluating the importance and calculating the weights of factors at each level. Its advantage lies in its ability to more accurately reflect the uncertainty of expert subjective judgments, organically combining qualitative and quantitative analysis to provide more reasonable solutions to complex decision-making problems.

[0062] The cumulative probability distribution function (CDF), an important tool in probability theory, describes the probability that a random variable will take a value less than or equal to a specific value. In this invention, the CDF is innovatively applied to the probabilistic representation of combinations of discrete variables. By constructing a probability ladder function for these combinations, the design space is divided into different levels, enabling a rational allocation of computational resources. The unique feature of this method is its ability to dynamically adjust the sample allocation strategy based on the importance of different combinations of discrete variables, maximizing the utilization efficiency of limited computational resources.

[0063] Latin hypercube sampling is an efficient statistical sampling method that achieves efficient exploration of multidimensional space by equally dividing the range of values ​​for each dimension and ensuring that the projection of the sample is uniformly distributed in each dimension. This invention optimizes traditional Latin hypercube sampling using the maximum-minimum distance criterion and iteratively optimizes the sample point distribution through simulated annealing algorithm, maximizing the minimum Euclidean distance between sample points, thus significantly improving the filling efficiency and representativeness of continuous variable space.

[0064] In summary, this invention provides a systematic method for efficiently handling spatial sampling of continuous-discrete mixed variables in reactor optimization design. By innovatively integrating fuzzy hierarchical analysis, a cumulative probability distribution function hierarchical strategy, and optimized Latin hypercube sampling technology, it achieves efficient exploration of the complex design space of nuclear reactors. This method addresses the limitations of traditional sampling methods in handling mixed variable problems, effectively balancing the probabilistic characteristics of discrete variables with the spatial filling characteristics of continuous variables. Furthermore, through a multi-dimensional sample quality assessment system and an adaptive optimization mechanism, it significantly improves the accuracy and reliability of the surrogate model.

[0065] This invention theoretically proposes a methodology for continuous-discrete hybrid variable spatial sampling, which can be applied to reactor optimization design and parameter sensitivity analysis, and can significantly improve computational efficiency and reduce the number of design iterations, which is of great significance for promoting innovation in advanced nuclear energy technology.

[0066] The present invention also provides a computing device, comprising: at least one processor and a memory storing program instructions; when the program instructions are read and executed by the processor, the computing device causes the computing device to perform a sampling method suitable for continuous-discrete hybrid variable design optimization of advanced reactors.

[0067] The present invention also provides a readable storage medium storing program instructions that, when read and executed by a computing device, cause the computing device to perform a sampling method suitable for continuous-discrete hybrid variable design optimization of advanced reactors.

[0068] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0069] Although the invention has been described with respect to a limited number of embodiments, those skilled in the art will understand from the foregoing description that other embodiments are conceivable within the scope of the invention described herein. Furthermore, it should be noted that the language used in this specification has been chosen primarily for readability and instructional purposes, and not for the purpose of explaining or limiting the subject matter of the invention.

Claims

1. A sampling method applicable to continuous-discrete mixed-variable design optimization for advanced reactors, characterized in that, include: S110, among all combinations of discrete variables, screen for effective combinations, apply prior knowledge and constraints to eliminate combinations that are physically infeasible, engineering unreasonable, or practically meaningless, and determine the set of effective combinations. For m discrete variables Each variable have One possible value Total number of original combinations The number of valid combinations after screening is ; S120, for the selected effective discrete variable combinations Perform probability modeling and construct the cumulative probability distribution function. , used to characterize the distributional properties of combinations of discrete variables; S130, based on the interval design of the cumulative probability distribution function of effective discrete variable combinations, spatial stratification is performed, with each combination corresponding to one stratum, i.e. ,in It is the total number of layers. The effective number of discrete variable combinations, and the corresponding cumulative probability distribution function interval for each layer are: ,in It is the combination of discrete variables corresponding to the i-th layer; S140, the number of samples is allocated according to the proportion of the interval width of the cumulative probability distribution function of each layer, using the formula... Determine the first The number of samples in the layer, of which For the first The interval width of the cumulative probability distribution function of the layer. The total number of samples, A function to round a number to the nearest integer; S150 performs Latin hypercube sampling on continuous variables within each layer and uses the maximum-minimum distance criterion to optimize sample space filling, ensuring uniform distribution of samples in all dimensions. S160 integrates samples from each layer to form a global sample set, and comprehensively verifies the sample quality through discreteness index, space filling index and projection uniformity index. S170: Construct a surrogate model based on the obtained sampling results, and evaluate the model accuracy through cross-validation. If the accuracy does not meet the requirements, return to step S130 to readjust the sample allocation strategy and parameters.

2. The sampling method for continuous-discrete hybrid variable design optimization of advanced reactors according to claim 1, characterized in that, S110 includes: constructing a constraint matrix between discrete variables based on domain knowledge, and filtering out effective combinations that satisfy all constraints through matrix operations.

3. The sampling method for continuous-discrete hybrid variable design optimization of advanced reactors according to claim 1, characterized in that, S120 includes the following steps: S120-1, Analyze the joint probability distribution characteristics of discrete variables, and establish a probability distribution model of discrete variables based on expert knowledge or the uniform distribution assumption. S120-2, Based on the probability distribution model in step S120-1, generate the cumulative probability ladder function of the discrete variable combination, ensuring that each discrete variable combination corresponds to a unique cumulative probability distribution function interval; S120-3, the expert knowledge is quantified into weight coefficients of discrete variable combinations through fuzzy hierarchical analysis, and the weight coefficients are used to construct the probability distribution of non-uniform discrete variables.

4. The sampling method for continuous-discrete hybrid variable design optimization of advanced reactors according to claim 3, characterized in that, In S130, when the number of effective discrete variable combinations is too large, resulting in insufficient sample resources, the specific method adopted is: based on the weight coefficients of the discrete variable combinations obtained in S120-3. Set weight threshold , for satisfying Low-weight combinations are merged, with the following merging rule: combinations of the same type (i.e., with the same variable values) are merged first; the weights of the new layer after merging are... The new layer refers to the layer formed by the combination of merged discrete variables.

5. The sampling method for continuous-discrete hybrid variable design optimization of advanced reactors according to claim 1, characterized in that, The optimization of Latin hypercube sampling in S150 adopts the maximum-minimum distance criterion. The distribution of sample points is iteratively optimized through simulated annealing algorithm to maximize the minimum Euclidean distance between sample points, thereby improving the filling efficiency of continuous variable space.

6. The sampling method for continuous-discrete hybrid variable design optimization of advanced reactors according to claim 5, characterized in that, S150 includes: S150-1, Initialization: Initial design scheme is generated using Latin hypercube sampling; S150-2, Define the objective function: maximize the minimum Euclidean distance between sample points; S150-3 is optimized iteratively using a simulated annealing algorithm: 1) Define the initial temperature and cooling rate ; 2) In each iteration, randomly swap the coordinates of one dimension of two sample points; 3) Calculate the objective function value of the new scheme and decide whether to accept the new scheme based on the Metropolis criterion; 4) Lower the temperature: ; 5) Stop when the termination condition is met.

7. The sampling method for continuous-discrete hybrid variable design optimization of advanced reactors according to claim 1, characterized in that, The comprehensive verification in S160 includes: Verifying sample quality using dispersion indicators includes: calculating the reasonableness index of the discrete variable distribution, which involves calculating the minimum and maximum distances between all sample points and comparing them with a preset threshold to verify the reasonableness of the sample distribution. ， in, For sample point x i and x j Euclidean distance, This represents the total number of samples. Validating sample quality using space-filling indices includes: calculating the space-filling index for continuous variables, i.e., based on... The criteria are calculated, and the verification process includes confirmation. ,in Maximum allowed fill index value: ， Validating sample quality using projection homogeneity indices includes: calculating the projection homogeneity index, i.e., assessing the homogeneity of each dimension using the Kolmogorov-Smirnov test: ， Among them, F emp For the empirical distribution of the sample, F uniform For a theoretically uniform distribution, This is the supremum, i.e., the maximum value. For the values ​​that the variable can take, This is the KS test statistic; the smaller the value, the closer it is to a uniform distribution.

8. The sampling method for continuous-discrete hybrid variable design optimization of advanced reactors according to claim 1, characterized in that, In S170, the model accuracy is evaluated through K-fold cross-validation. If the accuracy does not meet the requirements, it is optimized by increasing the total number of samples or adjusting the sample allocation ratio.

9. A computing device, characterized in that, include: At least one processor and a memory storing program instructions; When the program instructions are read and executed by the processor, the computing device performs the sampling method for design optimization of continuous-discrete hybrid variables for advanced reactors as described in any one of claims 1-8.

10. A readable storage medium storing program instructions, characterized in that, When the program instructions are read and executed by the computing device, the computing device performs the sampling method applicable to the continuous-discrete hybrid variable design optimization of advanced reactors as described in any one of claims 1-8.

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