Data set adaptive optimization method for fuel cladding multi-physical coupling analysis

Abstract

A dataset adaptive optimization method for fuel cladding multi-physical coupling analysis is characterized in that aiming at the characteristics of MD, MSE and EI criteria, the descent speed of a model prediction error along with dataset expansion optimization is greatly improved through an overall-to-local thought and a two-stage adaptive expansion optimization strategy, and in combination with a newly developed ME criterion, the model prediction error can be predicted to be more accurate. According to the method, the model can have good global precision under the condition of small data volume, and the required sample size is greatly reduced while the construction of the high-precision fuel cladding agent model is supported.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of nuclear reactor control, and particularly relates to a data set adaptive optimization method for fuel cladding multi-physics coupling analysis. BACKGROUND

[0002] In the process of constructing a fuel cladding performance proxy model, one-time small data set selection is usually insufficient to make the proxy model achieve sufficient accuracy. If one-time data set selection is used, a large amount of data sets are certainly needed. However, due to the high complexity and high computing time characteristics in fuel cladding performance calculation, the time cost of generating a large data set is usually unbearable. Therefore, for the development of a fuel cladding performance proxy model, adaptive expansion optimization of the data set is indispensable. However, the existing adaptive expansion optimization method is low in efficiency, cannot well balance the allocation of the data set to the global accuracy and local details, cannot solve the problems of high model complexity and computing time in the construction of a fuel cladding performance proxy model, and cannot obviously help reduce the data demand and the accuracy improvement speed in the multi-physics coupling problem. SUMMARY

[0003] The present application proposes a data set adaptive optimization method for fuel cladding multi-physics coupling analysis to solve the defect that the existing expansion optimization criterion cannot simultaneously consider the overall and local accuracy, constructs a two-stage adaptive expansion optimization strategy based on multi-objective optimization based on the characteristics of fuel cladding multi-physics coupling analysis, and realizes the support for the construction of a high-precision fuel cladding proxy model while greatly reducing the required sample size.

[0004] The present application is implemented by the following technical solutions:

[0005] The present application relates to a data set adaptive optimization method for fuel cladding multi-physics coupling analysis, comprising:

[0006] In the initial stage, an initial data set is obtained based on an improved Latin hypercube experimental design method and an original fuel cladding multi-physics coupling analysis model, and a training set and a test set are divided.

[0007] In the first stage, after the candidate expansion sampling positions are evaluated by using a maximum minimum distance (MD) criterion and a mean square error (MSE) criterion in turn, the MD criterion and the MSE criterion are combined to search for the expansion sampling positions by using a multi-objective optimization algorithm (NSGA-II), the new sampling points generated by the adaptive expansion optimization are predicted based on the original fuel cladding multi-physics coupling analysis model, the prediction results are added to the initial data set, and the original fuel cladding multi-physics coupling analysis model is updated;

[0008] The first stage is repeatedly performed until the MD value of the user-provided data set or the test set normalized error MAE reaches the requirement, and the second stage is performed.

[0009] The second stage: the candidate expansion sampling positions are evaluated using the improved expectation improvement (EI) criterion and the ME criterion, the ME criterion and the EI criterion are combined again by using the NSGA-II to search for the expansion sampling positions, the local precision of the original fuel cladding multi-physics coupling analysis model prediction value is further improved in the second stage, and the new sampling points generated by the adaptive expansion optimization are predicted based on the original fuel cladding multi-physics coupling analysis model, and the prediction results are added to the data set, and the model is updated. When the precision of the surrogate model reaches the requirement, the adaptive expansion optimization is completed.

[0010] The original fuel cladding multi-physics coupling analysis model refers to a kind of analysis software that can be used to calculate the cladding thickness reduction, internal gas pressure, cladding strain, cladding peak temperature, irradiation elongation and protective oxide layer thickness performance parameters of the cladding of nuclear reactor under the conditions of neutron physics, heat transfer, corrosion dynamics, fission gas release theory, irradiation effect and mechanical coupling.

[0011] Technical effects

[0012] The present application is developed for fuel cladding performance, which is more in line with the characteristics of fuel cladding multi-physics coupling analysis. In view of the characteristics of MD, MSE and EI criteria, and in combination with the newly developed ME criterion, a two-stage adaptive expansion optimization strategy from the whole to the local is designed. The expansion optimization strategy can improve the efficiency of the fuel cladding multi-physics coupling analysis surrogate model while reducing the risk of model overfitting. Compared with the prior art, the two-stage adaptive expansion optimization strategy of the whole to the local idea greatly improves the descending speed of the model prediction error with the expansion optimization of the data set, and improves the utilization rate of the model to the data points. Based on the method, the model can have good global accuracy with less data amount. The method combines and uses the expansion optimization criterion in stages, which conforms to the characteristics of fuel cladding performance analysis, and greatly reduces the risk of overfitting of the surrogate model. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 The flowchart of the present application is shown. DETAILED DESCRIPTION

[0014] As shown in the figure, the present embodiment relates to a data set adaptive optimization method for fuel cladding multi-physics coupling analysis, which comprises: Figure 1

[0015] Step one, acquisition and division of initial data set, specifically including:

[0016] ​1.1 After randomly and discretely selecting the initial design points through the improved Latin hypercube experimental design method, the Latin hypercube experimental design is optimized by the MD criterion, specifically: ,in: is the design point parameter vector, and is the parameter vector Peacekeeping In the improved Latin hypercube experimental design, m random Latin hypercube experimental designs are performed, in which the data set with the largest MD value is selected as the final initial data set.

[0017] 1.2 The initial design points are predicted and analyzed one by one through the original fuel cladding multi-physics coupling analysis model, and the analysis results are summarized and counted to obtain the initial data set.

[0018] 1.3 The initial dataset obtained from the original fuel cladding multiphysics coupling analysis model was randomly divided into training and test sets in a 7:3 ratio. The datasets described below were obtained by adaptively expanding and optimizing the initial dataset. The optimized datasets were still divided into training and test sets in a 7:3 ratio.

[0019] Step 2: By quickly capturing the overall parameter change trend, the overall error of the proxy model is rapidly reduced, thereby improving the global predictive ability of the proxy model for the multi-physics coupling analysis of fuel cladding. Specifically,

[0020] 2.1 Use the MD criterion to evaluate the candidate expansion sampling positions, specifically: ,in: is the design point parameter vector, and is the parameter vector Peacekeeping dimension.

[0021] 2.2 Use the MSE criterion to evaluate the candidate expansion sampling positions, specifically: ,in: is the correlation matrix, which consists of the correlation function values ​​between all known sample points; is the correlation vector, which is composed of the correlation function values ​​between the unknown point and all known sample points; is the mean of the known design points. is the regression coefficient matrix.

[0022] 2.3 The multi-objective optimization algorithm (NSGA-II) is used to combine the MD criterion with the MSE criterion to search for expanded sampling positions and obtain the optimal expanded sampling positions to quickly improve the exploration breadth and overall accuracy of the K2K model in the design domain.

[0023] The multi-objective optimization algorithm includes initialization, second-generation generation and subsequent offspring iteration processes, specifically: randomly initialize the population and evaluate the fitness of each individual and perform non-dominated sorting on the individuals, select the parent generation based on the sorting and crowding, perform crossover and mutation to generate the second generation; merge the parent generation and offspring, calculate the crowding to maintain diversity, select the parent generation based on the sorting and crowding, perform crossover and mutation to generate a new offspring, and merge the new offspring and its parent generation again; repeat the above process until the termination condition is met.

[0024] The congestion level ,in: and The data points are and The numerical value of the indicator; and are the maximum and minimum values ​​of respectively; and are the maximum and minimum values ​​respectively.

[0025] 2.4 Predict new sampling points and update the data set: For the new sampling points generated by the adaptive expansion optimization obtained in step 1, predict them based on the original fuel cladding multi-physics coupling analysis model, add the prediction results to the data set, and update the model at the same time.

[0026] Step 3: Repeat step 2 until the MD value of the data set drops to 0.1 or the normalized error MAE of the test set drops to 0.05, and then perform step 4 for adaptive expansion optimization.

[0027] Step 4: Use the improved ME criterion and the improved EI criterion to evaluate the fitness of the sampling points. By mining the local key high error points, the prediction accuracy of the proxy model is further improved, including:

[0028] 4.1 Use the improved EI criterion to evaluate the candidate expansion sampling locations, specifically:

[0029] i) Assumptions The truth value is known, then the point The error caused by the true value of the model ,in: For the proxy model The estimated value at The original fuel cladding multi-physics coupling analysis model The calculated value of the fuel performance at the second stage. At the second stage accuracy level, it can be approximately considered that the error function value estimated by the model is approximately equal to the true error;

[0030] ii) Improvement function The expectation is obtained, and the improved The criteria are specifically: Wherein: And Cumulative probability function and probability density function of standard normal distribution respectively, Variance.

[0031] 4.2 The candidate expansion sampling position is evaluated using the ME criterion, specifically: Wherein: The corrected link prediction value.

[0032] 4.3 The ME criterion and the EI criterion are combined to search for an expansion sampling position using a multi-objective optimization algorithm (NSGA-II), and the local accuracy of the fuel cladding multi-physical coupling analysis proxy model prediction value is further improved in the second stage.

[0033] 4.4 The new sampling point is predicted and the data set is updated: after the new sampling point generated by the adaptive expansion optimization is predicted based on the original fuel cladding multi-physical coupling analysis model, the prediction result is added to the data set, and the model is updated.

[0034] Step five, when the fuel cladding performance proxy model training set error MAE decreases to 0.01, the accuracy of the proxy model meets the requirements, and the adaptive expansion optimization is completed.

[0035] Through specific actual experiments, in the specific environment setting of a typical lead-based fast reactor, the fuel cladding performance proxy model is constructed for the wide parameter range shown in Table 1 by using the above data set adaptive optimization method, and the final prediction accuracy of the fuel cladding performance proxy model reaches the level shown in Table 2 after only 192 iterations. Among them, the error reduction process in the iteration process is shown in Table 3, wherein the first 135 iterations correspond to the first stage of the two-stage adaptive expansion optimization, and the last 57 iterations correspond to the second stage of the two-stage adaptive expansion optimization.

[0036] Table 1

[0037] Table 2

[0038] Table 3

[0039] Compared with the prior art, the two-stage adaptive expansion optimization strategy proposed by the method captures the accuracy of the model into two parts: overall trend and local detail, so that the target of each stage is more clear and the utilization rate of data points is improved.

[0040] Specifically, in the initial dataset construction, the improved hypercube Latin experimental design guarantees the good spatial distribution of the initial data points, provides a good initial accuracy for the fuel cladding performance surrogate model, and provides a basic guarantee for the use of the MD criterion in the subsequent stage. In the first stage of adaptive expansion optimization, the MD criterion is used to control the distribution of data points to improve the spatial filling rate; the MSE criterion is used to make the position of the expansion sampling point tend to higher model accuracy improvement on the basis of considering the spatial filling. At the same time, the above advantages are consistent with the characteristics of the fuel cladding performance, that is, the overall trend is clear and the details change complex, which makes the fuel cladding performance surrogate model under this method have an observable accuracy even with a smaller sample size. In the second stage, the ME criterion can well capture the local maximum error position, and the EI criterion can balance the global and local to efficiently improve the overall local accuracy. At the same time, due to the control of the data distribution in the whole process, the risk of overfitting of the fuel cladding performance surrogate model is greatly reduced.

[0041] The above specific embodiments can be locally adjusted by those skilled in the art without departing from the principles and purposes of the present application. The protection scope of the present application is subject to the claims and is not limited by the above specific embodiments, and each implementation scheme within the scope is subject to the constraints of the present application.

Claims

1. A dataset adaptive optimization method for multi-physics coupled analysis of fuel cladding, characterized by: include: Initial stage: Based on the improved Latin hypercube experimental design method and the original fuel cladding multi-physics coupling analysis model, the initial data set is obtained and divided into training and test sets; Phase I: After evaluating candidate expanded sampling locations using the maximum-minimum distance (MD) criterion and the mean square error (MSE) criterion, a multi-objective optimization algorithm (NSGA-II) was used to combine the MD and MSE criteria to search for expanded sampling locations. The new sampling points generated by the adaptive expansion optimization were predicted based on the original fuel cladding multi-physics coupling analysis model. The predicted results were then added to the initial dataset, and the original fuel cladding multi-physics coupling analysis model was updated. Repeat the first stage until the MD value of the user-provided dataset or the normalized error MAE of the test set meets the requirements, and then execute the second stage; Phase II: The candidate expanded sampling locations are evaluated using the improved Expected Improvement (EI) criterion and the ME criterion. NSGA-II is again used to combine the ME and EI criteria to search for expanded sampling locations. In this second phase, the local accuracy of the predictions from the original fuel cladding multi-physics coupling analysis model is further improved. New sampling points generated by the adaptive expanded optimization are predicted based on the original fuel cladding multi-physics coupling analysis model. The prediction results are then added to the dataset and the model is updated. The adaptive expanded optimization ends when the proxy model accuracy meets the requirements.

2. The dataset adaptive optimization method for multi-physics coupling analysis of fuel cladding according to claim 1 is characterized in that: The obtaining of the initial data set specifically includes: 1.1 After randomly and discretely selecting the initial design points through the improved Latin hypercube experimental design method, the Latin hypercube experimental design is optimized by the MD criterion, specifically: ,in: is the design point parameter vector, and is the parameter vector Peacekeeping In the improved Latin hypercube experimental design, m random Latin hypercube experimental designs are performed, in which the data set with the largest MD value is selected as the final initial data set; 1.2 The initial design points are predicted and analyzed one by one through the original fuel cladding multi-physics coupling analysis model, and the analysis results are summarized and counted to obtain the initial data set.

3. The dataset adaptive optimization method for multi-physics coupling analysis of fuel cladding according to claim 1 is characterized in that: The evaluation of candidate expansion sampling locations described in the first stage specifically includes: 2.1 Use the MD criterion to evaluate the candidate expansion sampling positions, specifically: ,in: is the design point parameter vector, and is the parameter vector Peacekeeping dimension; 2.2 Use the MSE criterion to evaluate the candidate expansion sampling positions, specifically: ,in: is the correlation matrix, which consists of the correlation function values ​​between all known sample points; is the correlation vector, which is composed of the correlation function values ​​between the unknown point and all known sample points; is the mean of the known design points, is the regression coefficient matrix.

4. The dataset adaptive optimization method for multi-physics coupling analysis of fuel cladding according to claim 1 is characterized in that: The multi-objective optimization algorithm includes initialization, second-generation generation and subsequent offspring iteration processes, specifically: randomly initialize the population and evaluate the fitness of each individual and perform non-dominated sorting on the individuals, select the parent generation based on the sorting and crowding, perform crossover and mutation to generate the second generation; merge the parent generation and offspring, calculate the crowding to maintain diversity, select the parent generation based on the sorting and crowding, perform crossover and mutation to generate a new offspring, and merge the new offspring and its parent generation again; repeat the above process until the termination condition is met.

5. The dataset adaptive optimization method for multi-physics coupling analysis of fuel cladding according to claim 4 is characterized in that: The congestion level ,in: and The data points are and The numerical value of the indicator; and are the maximum and minimum values ​​of respectively; and are the maximum and minimum values ​​respectively.

6. The dataset adaptive optimization method for multi-physics coupling analysis of fuel cladding according to claim 1 is characterized in that: The requirement is met by repeatedly executing the first stage until the MD value of the data set drops to 0.1 or the normalized error MAE of the test set drops to 0.05, and then executing the second stage.

7. The dataset adaptive optimization method for multi-physics coupling analysis of fuel cladding according to claim 1 is characterized in that: The evaluation of candidate expansion sampling locations described in the second stage specifically includes: 4.1 Use the improved EI criterion to evaluate the candidate expansion sampling locations, specifically: i) Assumptions The truth value is known, then the point The error caused by the true value of the model ,in: For the proxy model The estimated value at The original fuel cladding multi-physics coupling analysis model The calculated value of fuel performance at the second stage accuracy level is approximately considered to be equal to the true error; ii) Improvement function Ask for expectations, get improved The guidelines are: ,in: and are the cumulative probability function and probability density function of the standard normal distribution, is the variance; 4.2 Use the ME criterion to evaluate the candidate expansion sampling locations, specifically: ,in: It is the predicted value of the correction link.

8. The dataset adaptive optimization method for multi-physics coupling analysis of fuel cladding according to claim 1 is characterized in that: The proxy model accuracy meets the requirement, which means that when the error MAE of the fuel cladding performance proxy model training set drops to 0.01, the proxy model accuracy meets the requirement and the adaptive expansion optimization ends.

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