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

Abstract

A dataset adaptive optimization method for fuel cladding multi-physics coupling analysis is provided. According to the characteristics of MD, MSE and EI criteria, the two-stage adaptive expansion optimization strategy greatly improves the descending speed of model prediction error with dataset expansion optimization through the idea of overall to local. Combined with the newly developed ME criterion, the model has good global accuracy with less data, which greatly reduces the required sample size while supporting the construction of high-precision fuel cladding proxy model.

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 initial design points using the improved Latin hypercube experimental design method, the Latin hypercube experimental design is optimized using the MD criterion, specifically as follows: ,in: To design the point parameter vector, and For the parameter vector of the first peacekeeping In the improved Latin hypercube experimental design, m randomized Latin hypercube experiments are conducted, and the dataset with the largest MD value is selected as the final initial dataset.

[0017] 1.2 The initial design points were predicted and analyzed one by one using the original fuel cladding multi-physics coupling analysis model, and the results of the analysis were summarized and statistically analyzed to obtain the initial dataset.

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

[0019] Step 2: By rapidly capturing the overall parameter change trend, the overall error of the surrogate model is quickly reduced, thereby improving the surrogate model's global prediction capability for multi-physics coupling analysis of fuel cladding. Specifically, this includes:

[0020] 2.1 The candidate augmentation sampling locations are evaluated using the MD criterion, specifically as follows: ,in: To design the point parameter vector, and For the parameter vector of the first peacekeeping dimension.

[0021] 2.2 The candidate augmentation sampling locations are evaluated using the MSE criterion, specifically as follows: ,in: The correlation matrix consists of the correlation function values ​​between all known sample points; The correlation vector is composed of the correlation function values ​​between the unknown point and all known sample points; The mean value of the known design points. This is the regression coefficient matrix.

[0022] 2.3 The multi-objective optimization algorithm (NSGA-II) is used to combine the MD criterion and the MSE criterion to search for the extended sampling position and obtain the optimal extended sampling position, so as to rapidly improve the breadth of the K2K model's exploration of the design domain and the overall accuracy.

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

[0024] The crowding degree , wherein: and are the numerical values of the data points in and ; and are the maximum and minimum values of and are the maximum and minimum values of

[0025] 2.4 Predict new sampling points and update the dataset: for the new sampling points generated by adaptive expansion optimization in step one, based on the original fuel cladding multi-physics coupling analysis model, the prediction results are added to the dataset, and the model is updated.

[0026] Step three, repeat step two until the MD value of the dataset decreases to 0.1 or the normalized error MAE of the test set decreases to 0.05, then perform step four of adaptive expansion optimization.

[0027] Step four, use the improved ME criterion and the improved EI criterion to evaluate the fitness of the sampling points. By digging local key high error points, the prediction accuracy of the surrogate model is further improved, specifically including:

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

[0029] i) Assuming that the true value at is known, then the true value of point brings error to the model, wherein: is the estimated value of the surrogate model at , and is the calculated value of the original fuel cladding multi-physics coupling analysis model at . At the accuracy level of the second stage, it can be approximately considered that the error function value estimated by the model is approximately equal to the true error;

[0030] ii) For the improved function The expectation is obtained, and the improved The criteria are specifically: wherein: and are the cumulative probability function and the probability density function of the standard normal distribution, respectively, is the variance.

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

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

[0033] 4.4 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.

[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 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]

[0038] Table 2

[0039]

[0040] Table 3

[0041]

[0042] 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 of overall trend and local detail by the idea of whole to part, so that the target of each stage is more clear and the utilization rate of data points is improved.

[0043] Specifically, in the initial data set construction, the improved hypercube Latin experimental design guarantees good spatial distribution of the initial data points, provides good initial accuracy for the fuel cladding performance proxy model, and provides a basic guarantee for the use of the subsequent MD criterion. In the first stage of adaptive expansion optimization, the distribution of data points is controlled by using the MD criterion to tend to improve the spatial filling rate; by using the MSE criterion, the position of the expansion sampling point tends to a higher model accuracy improvement amount 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 "overall trend clear and detail change complex", which makes the fuel cladding performance proxy model with observable accuracy can be obtained under the method even with less sample amount. The second stage can capture the local maximum error position by the ME criterion, and balance the global through the EI criterion auxiliary, so as to realize the efficient improvement of overall and local accuracy. At the same time, due to the control of data distribution in the whole process, the overfitting risk of the fuel cladding performance proxy model is greatly reduced.

[0044] The above specific implementation can be adjusted in different ways 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 implementation, each implementation scheme within the scope is subject to the constraint of the present application.

Claims

1. A data set adaptive optimization method for fuel cladding multi-physics coupling analysis, characterized in that, The application relates to a method for self-adaptive expanding optimization of a fuel cladding performance surrogate model. The method comprises the following steps: An initial stage: obtaining an initial data set and dividing a training set and a test set based on an improved Latin hypercube design method and an original fuel cladding multi-physical coupling analysis model; A first stage: using a maximum-minimum distance (MD) criterion and a mean square error (MSE) criterion to evaluate candidate expanding sampling positions in sequence, combining the MD criterion and the MSE criterion to search for expanding sampling positions by using a multi-objective optimization algorithm (NSGA-II), predicting new sampling points generated by self-adaptive expanding optimization based on the original fuel cladding multi-physical coupling analysis model, adding the prediction results to the initial data set, updating the original fuel cladding multi-physical coupling analysis model, and repeating the first stage until a second stage is performed when a MD value of a user-provided data set or a test set normalized error MAE reaches a requirement; The second stage: using an improved expected improvement (EI) criterion and a ME criterion to evaluate candidate expanding sampling positions, combining the ME criterion and the EI criterion to search for expanding sampling positions by using the NSGA-II again, further improving the local precision of prediction values of the original fuel cladding multi-physical coupling analysis model in the second stage, predicting new sampling points generated by self-adaptive expanding optimization based on the original fuel cladding multi-physical coupling analysis model, adding the prediction results to the data set, updating the model, and ending the self-adaptive expanding optimization when the precision of the surrogate model reaches the requirement; The method further comprises the following steps: 4.1 using the improved EI criterion to evaluate the candidate expanding sampling positions, specifically as follows: i) Assumptions truth value at If it is known, then point The true value contributes to the error in the model. ,in: For proxy model The estimated value at that location, For the original fuel cladding multi-physics coupling analysis model The calculated values ​​of fuel performance, at the second-stage accuracy level, are approximately considered to be equal to the actual error value estimated by the model. ii) the improvement function The expected value of the improvement function is given by The criterion is given by where and are the cumulative probability function and the probability density function of the standard normal distribution, respectively, is the variance. 4.2 Evaluate the candidate augmented sampling locations using the ME criterion, in particular: where: is the corrected link prediction value.

2. The data set adaptive optimization method for fuel cladding multi-physics coupling analysis of claim 1, wherein, The method further comprises the following steps: 1.1 After randomly and discretely selecting initial design points using the improved Latin hypercube experimental design method, the Latin hypercube experimental design is optimized using the MD criterion, specifically as follows: ,in: To design the point parameter vector, and For the parameter vector of the first peacekeeping In the improved Latin hypercube experimental design, m randomized Latin hypercube experiments are conducted, and the dataset with the largest MD value is selected as the final initial dataset. 1.2 predicting and analyzing the initial design points one by one by using the original fuel cladding multi-physical coupling analysis model, collecting and counting the analysis results, and obtaining the initial data set.

3. The data set adaptive optimization method for fuel cladding multi-physics coupling analysis of claim 1, wherein, The method further comprises the following steps: 2.1 Evaluate the candidate augmented sample locations using the MD criterion, specifically: where: is the design point parameter vector, and are the first dimension and the first dimension of the parameter vector, respectively. 2.2 Evaluate the candidate augmented sampling locations using the MSE criterion, which is given by: where: is the correlation matrix, which is composed 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 data set adaptive optimization method for fuel cladding multi-physics coupling analysis of claim 1, wherein, The multi-objective optimization algorithm comprises initialization, second-generation generation and subsequent offspring iteration processes, specifically as follows: randomly initializing a population, evaluating the fitness of each individual, and non-dominantly sorting the individuals; selecting parents based on the sorting and crowding degree, generating the second generation through crossover and mutation; merging the parents and the offspring, calculating the crowding degree to maintain diversity, selecting the parents based on the sorting and crowding degree, generating new offspring through crossover and mutation, and merging the new offspring and the parents again; and constantly repeating the above process until a termination condition is met.

5. The data set adaptive optimization method for fuel cladding multi-physics coupling analysis of claim 4, wherein, The crowdedness wherein: and are the values of the data points in and respectively; and are the maximum and minimum values of and are the maximum and minimum values of 6. The data set adaptive optimization method for fuel cladding multi-physics coupling analysis of claim 1, wherein, The requirement is that the first stage is repeatedly executed until the MD value of the data set drops to 0.1 or the test set normalized error MAE drops to 0.05, and the second stage is executed.

7. The data set adaptive optimization method for fuel cladding multi-physics coupling analysis of claim 1, wherein, The requirement that the precision of the surrogate model reaches the requirement is that the fuel cladding performance surrogate model training set error MAE drops to 0.01, the precision of the surrogate model reaches the requirement, and the self-adaptive expanding optimization is ended.

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