Sampling method suitable for advanced reactor continuous-discrete mixed variable design optimization

Abstract

The invention provides a sampling method suitable for continuous-discrete mixed variable design optimization of an advanced reactor. The sampling method comprises the following steps: (1) screening an effective discrete variable combination; (2) constructing a cumulative probability distribution function of the discrete variable combination; (3) hierarchically designing a space based on a cumulative probability distribution function interval; (4) distributing the number of samples according to the interval width proportion of the cumulative probability distribution function of each layer; (5) Latin hypercube sampling is carried out on the continuous variables in each layer; (6) integrating a global sample set and verifying the quality of the global sample set; and (7) constructing an agent model and evaluating precision. According to the method, the probability characteristic of the discrete variable and the space filling characteristic of the continuous variable are integrated, efficient exploration of the nuclear reactor design space is achieved, and compared with a traditional method, the sample quality and the calculation efficiency are remarkably improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of advanced reactor design optimization, and particularly relates to a sampling method suitable for continuous-discrete mixed variable design optimization of an advanced reactor. BACKGROUND

[0002] In the integrated optimization of the whole life cycle of a reactor, the collaborative optimization of continuous-discrete mixed variables is involved, such as the number of fuel assemblies and the arrangement mode of fuel assemblies as discrete variables, and the thickness of a reflector and the radial partition enrichment ratio of fuel assemblies as continuous variables. When optimization design and sensitivity analysis are carried out, the sampling method has a crucial influence on the accuracy of optimization and sensitivity analysis. Traditional sampling techniques such as simple random sampling and Latin hypercube sampling are suitable for single variable types (such as continuous or discrete) and cannot handle the sampling of continuous-discrete mixed variables.

[0003] The prior art has the following problems: (1) it cannot handle continuous variables and discrete variables simultaneously; (2) the balance between the number of samples and the calculation accuracy is difficult to grasp; and (3) it is difficult to simultaneously consider the probability characteristics of discrete variables and the space filling characteristics of continuous variables. Therefore, there is an urgent need to develop a method that can efficiently and uniformly handle the sampling of continuous-discrete mixed variable space. SUMMARY

[0004] The application aims to provide a sampling method suitable for continuous-discrete mixed variable design optimization of an advanced reactor to solve the problem that the prior art cannot sample continuous-discrete mixed variables. The method realizes efficient sampling of continuous-discrete mixed variable space by fusing the hierarchical strategy of cumulative probability distribution function and Latin hypercube sampling technology, and is suitable for nuclear reactor design optimization and sensitivity analysis. The technical scheme adopted by the application is as follows:

[0005] A sampling method suitable for continuous-discrete mixed variable design optimization of an advanced reactor comprises the following steps:

[0006] S110, among all discrete variable combinations, effective discrete variable combinations are screened, prior knowledge and constraint conditions are applied to eliminate physically infeasible, engineering unreasonable or practically meaningless combinations, and an effective combination set is determined ; for m discrete variables , each variable has possible values , the total number of original combinations is , and the number of effective combinations after screening is ;

[0007] S120, screening the effective discrete variable combination constructing a cumulative probability distribution function for representing the distribution characteristics of the discrete variable combination;

[0008] S130, designing a hierarchical space based on the cumulative probability distribution function interval of the effective discrete variable combination, each combination corresponds to a hierarchical, namely wherein is the total number of hierarchical, is the number of effective discrete variable combinations, and the cumulative probability distribution function interval corresponding to each layer is:

[0009] wherein is the discrete variable combination corresponding to the i-th layer;

[0010] S140, distributing the sample number according to the width proportion of the cumulative probability distribution function interval of each layer, using the formula to determine the sample number of the i-th layer, wherein is the width of the cumulative probability distribution function interval of the i-th layer, is the total sample number, is a function of rounding a value to the nearest integer; S150, performing Latin hypercube sampling on the continuous variable in each layer, and using the maximum minimum distance criterion to optimize the sample space filling, to ensure the uniform distribution of the sample in each dimension;

[0011] S160, integrating the samples of each layer to form a global sample set, and comprehensively verifying the sample quality through the discreteness index, the space filling index and the projection uniformity index;

[0012] S170, constructing a surrogate model based on the obtained sampling result, and evaluating the model accuracy through cross-validation, and returning to step S130 to re-adjust the sample distribution strategy and parameters if the accuracy does not meet the requirements.

[0013] 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 performs a sampling method suitable for advanced reactor continuous-discrete mixed variable design optimization.

[0014] A readable storage medium storing program instructions, when the program instructions are read and executed by a computing device, the computing device performs a sampling method suitable for advanced reactor continuous-discrete mixed variable design optimization.

[0015] A readable storage medium storing program instructions, when the program instructions are read and executed by a computing device, the computing device performs a sampling method suitable for advanced reactor continuous-discrete mixed variable design optimization.

[0016] ​​From the above technical solutions, the beneficial effects of the present application are:

[0017] First, the present application effectively solves the "dimension disaster" problem caused by high-dimensional discrete variable space through discrete variable combination screening and merging mechanism;

[0018] Second, the present application designs a stratified sampling strategy based on cumulative probability distribution function, which can reasonably allocate computing resources according to the importance of different discrete variable combinations;

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

[0020] Fourth, the present application optimizes Latin hypercube sampling using the maximum minimum distance criterion, which significantly improves the filling efficiency of the continuous variable space;

[0021] Fifth, the sample quality multi-dimensional evaluation system proposed by the present application ensures the representativeness and uniformity of the mixed variable space sample;

[0022] Sixth, the present application provides an adaptive optimization mechanism that can dynamically adjust the sampling strategy according to the model accuracy requirement.

[0023] The method can be applied to advanced reactor optimization design analysis and sensitivity analysis, and provides a high-confidence sample basis for advanced reactors involving continuous-discrete high-dimensional mixed variables, and has wide application prospects. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 The overall framework program flowchart of the sampling method of the present application suitable for continuous-discrete mixed variable design optimization of advanced reactors;

[0025] Figure 2 The Latin hypercube sampling optimization program flowchart of the present application. DETAILED DESCRIPTION

[0026] Exemplary embodiments of the present disclosure will be described in greater detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure can be implemented in various forms, and the present disclosure should not be limited by the embodiments described herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to convey the full scope of the present 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, integrate the samples of each layer to form a global sample set, and verify the quality of the samples by using the discreteness index, the space-filling index and the projection uniformity index;

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

[0036] Further, in step S110, the effective discrete variable combination is screened. The specific method is to construct a constraint matrix between discrete variables based on domain knowledge, and to screen the effective combination that meets all the constraints through matrix operation;

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

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

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

[0040] S120-3, the expert knowledge is quantified into weight coefficients of the discrete variable combination by fuzzy analytic hierarchy process, and the weight coefficients are used to construct the non-uniform discrete variable probability distribution.

[0041] Further, in S130, when the number of effective discrete variable combinations is too large to cause insufficient sample resources, the specific method is as follows: , set a weight threshold , and merge the discrete variable combinations with low weights that meet . The merging rule is: ① the same type (same variable value) combination is preferentially merged; ② the weight of the new layer after merging , the new layer refers to the layer formed by the merged discrete variable combinations;

[0042] Further, as shown in Figure 2 , the optimization of Latin hypercube sampling in S150 adopts the maximum minimum distance criterion, and iteratively optimizes the sample point distribution by simulated annealing algorithm to maximize the minimum Euclidean distance between sample points, so as to improve the filling efficiency of the continuous variable space. The implementation steps of S150 are as follows:

[0043] S150-1, initialization: generate an initial design scheme by using Latin hypercube sampling;

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

[0045] S150-3, iteratively optimize by simulated annealing algorithm:

[0046] 1) define initial temperature and cooling rate ;

[0047] 2) in each iteration, randomly swap the coordinate of a dimension of two sample points;

[0048] 3) calculate the objective function value of the new solution, and decide whether to accept the new solution according to the Metropolis criterion;

[0049] 4) reduce the temperature: ;

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

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

[0052] The sample quality is verified by the discreteness index, including calculating the distribution rationality index of the discrete variable, i.e. calculating the maximum value of the minimum distance between all sample points, and verifying the sample distribution rationality by comparing with the preset threshold, which is based on actual engineering experience and statistical theory:

[0053] ,

[0054] wherein, is the Euclidean distance (normalized) of sample points x i and x j .

[0055] The sample quality is verified by the space filling index, including calculating the space filling index of continuous variables: i.e. based on criterion, and confirming whether , wherein is the maximum allowed filling index value:

[0056] ,

[0057] The sample quality is verified by the projection uniformity index, including calculating the projection uniformity index, i.e. evaluating the uniformity of each dimension by Kolmogorov-Smirnov test:

[0058] ,

[0059] wherein, F emp is the sample empirical distribution, Funiform For the theoretical uniform distribution, For the upper bound, that is, the maximum value, For the value of the variable, For the KS test statistic, the smaller the value, the closer to the uniform distribution.

[0060] Further, in step S170, the model accuracy is evaluated by K-fold cross-validation, and if the accuracy does not meet the requirements, the total sample size or the sample allocation ratio is adjusted for optimization. The accuracy evaluation can use statistical quantities such as root mean square error (RMSE), maximum relative error (MRE) or determination coefficient (R 2 ) and the like.

[0061] Fuzzy Analytic Hierarchy Process (FAHP) is a multi-criteria decision-making method that effectively handles uncertainty and fuzziness in the decision-making process by combining traditional analytic hierarchy process (AHP) with fuzzy set theory. FAHP establishes a hierarchical structure model and uses fuzzy numbers to represent expert judgments to evaluate the importance of factors at each level and calculate their weights. Its advantage is that it can more accurately reflect the uncertainty of expert subjective judgments and organically combine qualitative and quantitative analysis, thus providing a more reasonable solution to complex decision-making problems.

[0062] Cumulative probability distribution function (CDF) is an important tool in probability theory, describing the probability of a random variable taking on a value less than or equal to a certain value. In this invention, CDF is innovatively applied to the probability representation of discrete variable combinations, by constructing a probability step function of discrete variable combinations, the design space is divided into different levels, realizing the reasonable allocation of computing resources. The uniqueness of this method lies in its ability to dynamically adjust the sample allocation strategy according to the importance of different discrete variable combinations, maximizing the utilization efficiency of limited computing resources.

[0063] Latin hypercube sampling is an efficient statistical sampling method that divides the value range of each dimension equally and ensures that the sample is uniformly distributed in the projection of each dimension, achieving efficient exploration of multi-dimensional space. This invention uses the maximum minimum distance criterion to optimize traditional Latin hypercube sampling, and iteratively optimizes the sample point distribution through simulated annealing algorithm, so that the minimum Euclidean distance between sample points reaches the maximum, significantly improving the filling efficiency and representativeness of continuous variable space.

[0064] In summary, the application provides a system method for efficient sampling of continuous-discrete mixed variable space in reactor optimization design, which realizes efficient exploration of complex design space of nuclear reactor by innovatively combining fuzzy analytic hierarchy process, cumulative probability distribution function stratification strategy and optimized Latin hypercube sampling technology.

[0065] The application theoretically proposes a method for sampling of continuous-discrete mixed variable space, which can be applied to reactor optimization design and parameter sensitivity analysis, and can significantly improve the calculation efficiency and reduce the number of design iterations, which is of great significance for promoting innovation of advanced nuclear energy technology.

[0066] The application 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 is caused to perform the sampling method suitable for advanced reactor continuous-discrete mixed variable design optimization.

[0067] The application also provides a readable storage medium storing program instructions, when the program instructions are read and executed by a computing device, the computing device is caused to perform the sampling method suitable for advanced reactor continuous-discrete mixed variable design optimization.

[0068] In the specification provided herein, a large number of specific details are described. However, it can be understood that the embodiments of the application can be practiced without these specific details. In some examples, well-known methods, structures and techniques are not shown in detail in order not to obscure the understanding of the present specification.

[0069] Although the application is described in terms of a limited number of embodiments, those skilled in the art, with the benefit of the description above, will appreciate that other embodiments are possible within the scope of the application described herein. Furthermore, it should be noted that the language used in the specification has primarily been chosen for readability and instructional purposes, and can not have been selected to convey an exclusive or exhaustive explanation of the subject matter.

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 1, 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 weight of the new layer after merging is... The new layer refers to the layer formed by the combination of discrete variables after merging.

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 (maximum number of iterations or temperature below the threshold).

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 The Euclidean distance; 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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