Nuclear power plant passive system reliability analysis method based on meta-model adaptive sampling

Abstract

A nuclear power plant passive system reliability analysis method based on meta-model adaptive sampling comprises the following specific steps: 1, extracting a sample to establish a model, obtaining a response value through an optimal estimation program, and training an initial response surface; 2, extracting a sample, mapping by using a response surface, and selecting a response value as an intermediate event critical value; 3, selecting a design point from the samples within the critical value range as a new sampling center, generating a new sample, supplementing training data, and constructing a new response surface; 4, obtaining a sample obeying important sampling probability density function distribution by using new response surface mapping, obtaining sample points falling in a critical value range, and re-selecting a critical value; and 5, repeating the steps 3 and 4 until the critical value is less than 0, ending hierarchical calculation, and obtaining an estimated value of the failure probability. The method aims at reliability analysis and development of the passive system of the nuclear power plant, the precision of the response surface model is improved through the adaptive sampling algorithm, the calculation cost is low, and the calculation precision is high.

Description

Technical Field

[0001] The present invention relates to the technical field of research on whether a passive system can effectively realize its intended function, derive core residual heat, and analyze its reliability under accident conditions in a nuclear power plant, and specifically to a reliability analysis method for a passive system of a nuclear power plant based on metamodel adaptive sampling. Background Art

[0002] The passive safety systems introduced in third-generation reactors offer higher reliability than active systems, but this does not guarantee absolute reliability. In passive systems, the driving force and resistance are of similar magnitude, making physical process uncertainties, which are negligible in active systems, non-negligible. Even if all components in the system operate normally, there is still a risk that the intended safety functions may not be achieved. Therefore, studying the physical process failures in passive systems is of great significance.

[0003] Monte Carlo simulation (MCS) is a traditional reliability analysis method for the failure of passive system physical processes. Based on the law of large numbers, MCS is relatively simple and easy to implement. However, due to the extremely low probability of failure in passive systems, applying MCS often requires a very large number of simulation experiments to obtain practical analysis results. Furthermore, even the best estimate procedure takes a long time to run a single experiment, which undoubtedly consumes a large amount of computing resources.

[0004] In summary, it is necessary to develop an efficient computational method for the reliability analysis of passive systems. This method is expected to provide effective tools and technical support for safety analysis of nuclear power plants in my country, assisting in nuclear power plant design and safety analysis, effectively reducing potential accident risks, and ensuring the stable operation of nuclear power plants. Summary of the Invention

[0005] In order to overcome the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a reliability analysis method for the passive system of a nuclear power plant based on metamodel adaptive sampling. The method uses a response surface as a proxy model and uses advanced variance reduction technology to efficiently and accurately calculate the failure probability of the passive system of a nuclear power plant.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] 2. A nuclear power plant passive system reliability analysis method based on meta-model adaptive sampling, characterized by the following steps:

[0008] Step 1: Select failure criteria and best estimate procedure for modeling; determine the failure criteria based on the research object and use the best estimate procedure to build a system model;

[0009] Step 2: Identify and quantify uncertainty parameters; select key uncertainty parameters and their distributions based on the research object and working conditions;

[0010] Step 3: Sampling uncertainty parameters: Latin hypercube sampling is used to sample key uncertainty parameters to obtain N0 sample groups. For each variable, the range of values is divided into N0 intervals of equal probability. A value is randomly sampled in each interval to ensure that each variable has only one sample point in all divided intervals. The sampled values are mapped to obtain samples that obey the target distribution. Finally, the order of the samples is shuffled to obtain N0 sample groups.

[0011] Step 4: Best estimate program calculation and sensitivity analysis: Use the best estimate program to calculate the sample and obtain the output value, which together with the sample constitutes the training set of the response surface model. The response surface model is used as a proxy model for the thermal hydraulic program to achieve high-precision and fast calculation. The response surface used is a neural network response surface. After obtaining the output value, sensitivity analysis is also used to evaluate the impact of each parameter on the system output.

[0012] Step 5: Use the obtained training set to train the neural network response surface, and use the particle swarm optimization algorithm to optimize the neural network hyperparameters to obtain the optimal network structure for the current training data;

[0013] Step 6: Use the response surface model to perform direct Monte Carlo simulation and calculate the failure probability. The formula is:

[0014]

[0015] In the formula

[0016] N f ——Number of failed samples;

[0017] N0——the total number of samples obtained by Latin hypercube sampling;

[0018] — an estimate of the probability of failure;

[0019] Step 7: Repeat step 6 several times and observe Whether the value converges, if so, the calculation ends; if not, the subset simulation importance sampling process begins;

[0020] Step 8: Extract N1 sample points, map them using the response surface, and sort the output values from large to small, recorded as

[0021] Step 9: Let M1 = N1, and take the (1-p0)M1th response value as the critical value of the intermediate failure event F1 = {x:g(x)≤b1} At the same time, it is known p0 represents the probability level of the intermediate failure event;

[0022] Step 10: From Falling on F i-1 p0M in the domain (i=2,3,…,m) i-1 The point with the largest probability density value is selected from the samples as the important sampling density function h i (x) and generate N i The importance sampling density function h i (x) samples, which fall in the failure domain F i-1 M in (i=2,3,…,m) i The sample points follow the distribution condition density h i (x|F i-1 ), recorded as

[0023] Step 11: Alternately i-1 The samples of the domain are used to calculate the output values using the best estimation procedure and added to the response surface training data to construct a new response surface;

[0024] Step 12: Re-use the importance sampling density function to obtain N i Obey h i (x), use the new response surface to map the M i h i (x|F i-1 ) Sort the sample points from large to small;

[0025] Step 13: Take the (1-p0)Mth i The performance function value corresponding to the sample point is taken as the intermediate failure event F i ={x:g(x)≤b i The critical value b of i , and get F i-1 Under the conditions of occurrence F i The estimated value of the conditional failure probability for

[0026]

[0027] In the formula

[0028] ——The estimated value of the failure probability of the i-th layer, which means that the failure event F occurs under the known previous failure state i The estimated probability of

[0029] F i ——the i-th failure event or state;

[0030] F i-1 ——i-1th failure event or state;

[0031] N i ——The total number of samples obtained by the importance sampling of the i-th layer;

[0032] ——the jth sample in the i-th layer;

[0033] ——Indicates that the state F at the known i-1 step i-1 Next, sample The sampling distribution of , i.e., the conditional probability density function, is used to weight the importance of the samples;

[0034] ——The probability density function of important sampling, expressed as The target distribution function is used to standardize the weight of the samples;

[0035] - indicator function;

[0036] Expressed as

[0037]

[0038] In the formula

[0039] g(x) – performance function, replaced by response surface;

[0040] That is, when it falls into the failure area, the indicator function takes 1, and when it falls into the normal safety range, the indicator function takes 0;

[0041] Step 14: Repeat steps 10, 11, 12, and 13 until the (1-p0)Mth function value is sorted from large to small. m response values If the value is less than 0, then let b m =0, F m =F, automatic stratification ends;

[0042] Step 15: After the stratification is completed, the estimated failure probability of the passive system can be obtained for

[0043]

[0044] Probabilistic safety analysis of the reliability of passive systems in nuclear power plants has been implemented.

[0045] The principle of the particle swarm optimization algorithm used in step 5 is based on swarm intelligence. First, the neural network hyperparameters are regarded as the positions of particles in a multidimensional space. Each particle represents a set of hyperparameter combinations and has its own speed. The particle will update its speed based on its current speed, its distance from the individual extreme value, and its distance from the global extreme value, and move to a new position in the hyperparameter space. This process is continuously iterated, and the particle swarm will gradually explore and converge to a better area in the hyperparameter space, so that the neural network hyperparameter combination is continuously optimized, and finally a set of hyperparameters with better performance on the validation set is found, thereby improving the performance of the neural network.

[0046] The method of the present invention can make efficient and accurate analysis of the reliability of the passive system of a nuclear power plant, can provide effective tools and technical support for the safety analysis of the nuclear power plant, and ensure the stable operation of the nuclear power plant.

[0047] Compared with the prior art, the method of the present invention has the following advantages:

[0048] This method uses subset simulation to transform low-probability events into the product of multiple, larger conditional event probabilities, addressing the problem of small-batch experiments lacking failure samples. It also uses the response surface methodology as a proxy model for thermal-hydraulic programs, significantly improving computational efficiency. And through importance sampling, it expands the sample set in the failure region of the response surface, improving its accuracy. This method combines these three techniques to maintain computational accuracy while reducing computational costs to an acceptable level. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a flow chart of the reliability analysis of the passive system of a nuclear power plant according to the present invention. DETAILED DESCRIPTION

[0050] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] like Figure 1 As shown, the present invention is a nuclear power plant passive system reliability analysis method based on meta-model adaptive sampling. Its characteristics are that it uses a response surface model and a subset simulation importance sampling algorithm to accurately calculate low-probability failure events with a low computational cost, thereby improving the efficiency of reliability analysis. The steps are as follows:

[0052] Step 1: Select failure criteria and best estimate program for modeling. For the nuclear reactor passive system, based on its operating characteristics, a list of thermal parameters related to reliability under its operating state is compiled. Key parameters that directly reflect whether the system can function are selected as thresholds to establish failure criteria. An adapted thermal-hydraulic program is used as the best estimate program for passive system modeling.

[0053] Step 2: Identify and quantify uncertainty parameters. Based on the specific characteristics of the research object and its operating conditions, determine which parameters have a significant impact on the system's output or behavior. These parameters are called uncertainty parameters and may include material properties, geometric dimensions, and boundary conditions. Preliminary screening of key uncertainty parameters is done through literature research, experimental data, or expert experience. Quantitative analysis of these key uncertainty parameters is performed using probabilistic statistical methods, assuming that these parameters follow a certain probability distribution. Parameter estimation is then performed using experimental data or historical data.

[0054] Step 3: Sampling uncertainty parameters: Latin hypercube sampling is used to sample key uncertainty parameters to obtain N0 sample groups. For each variable, the range of values is divided into N0 intervals of equal probability. A value is randomly sampled from each interval to ensure that each variable has only one sample point selected from all its partitioned intervals. The sampled values are mapped to obtain samples that obey the target distribution. The sample order is then shuffled to obtain the final N0 sample groups.

[0055] Step 4: Best estimate program calculation and sensitivity analysis; use the best estimate program to calculate the sample and obtain the output value, which together with the sampled sample constitutes the training set of the response surface model. The response surface model serves as a proxy model for the thermal hydraulic program to achieve high-precision and fast calculation. The response surface used is a neural network response surface. After obtaining the output value, sensitivity analysis is also used to evaluate the influence of each parameter on the system output, further optimize the selection of input parameters of the response surface model, and thus optimize the neural network structure, such as the Spearman rank correlation coefficient. The Spearman rank correlation coefficient measures the monotonic relationship between the input parameter and the output result by converting the data into ranks and calculating its correlation coefficient, thereby evaluating the sensitivity of the parameter to the output.

[0056] Step 5: Use the obtained training set to train the neural network response surface, and use the particle swarm optimization algorithm to optimize the neural network hyperparameters to obtain the optimal network structure for the current training data; the principle of the particle swarm optimization algorithm is swarm intelligence. First, the neural network hyperparameters (such as learning rate, number of neurons, etc.) are regarded as the position of particles in a multidimensional space. Each particle represents a set of hyperparameter combinations and has its own speed. The particle will update its speed based on its current speed, its distance from the individual extreme value, and its distance from the global extreme value, and move to a new position in the hyperparameter space. This process is continuously iterated, and the particle swarm will gradually explore and converge to a better area in the hyperparameter space, so that the neural network hyperparameter combination is continuously optimized, and finally a set of hyperparameters with better performance on the validation set is found, thereby improving the performance of the neural network;

[0057] Step 6: Use the response surface model to perform direct Monte Carlo simulation and calculate the failure probability. The formula is:

[0058]

[0059] In the formula

[0060] N f ——Number of failed samples;

[0061] N0——the total number of samples obtained by Latin hypercube sampling;

[0062] — an estimate of the probability of failure;

[0063] Formula (1) is the equation for calculating the failure probability through direct Monte Carlo simulation;

[0064] Step 7: Repeat step 6 several times and observe Whether the value converges, if so, the calculation ends; if not, the subset simulation importance sampling process begins;

[0065] Step 8: Extract N1 sample points, map them using the response surface, and sort the output values from large to small, recorded as

[0066] Step 9: Let M1 = N1, and take the (1-p0)M1th response value as the critical value of the intermediate failure event F1 = {x:g(x)≤b1} At the same time, it is known p0 represents the probability level of the intermediate failure event, which is usually a small value and used as the step size of the subset simulation, affecting the accuracy and efficiency;

[0067] Step 10: From Falling on F i-1 p0M in the domain (i=2,3,…,m) i-1 The point with the largest probability density value is selected from the samples as the important sampling density function h i (x) and generate N i The importance sampling density function h i (x) samples, which fall in the failure domain F i-1 M in (i=2,3,…,m) i The sample points follow the distribution condition density h i (x|F i-1 ), recorded as

[0068] Step 11: Alternately i-1 The samples of the domain are used to calculate the output values using the best estimation procedure and added to the response surface training data to construct a new response surface;

[0069] Step 12: Re-use the importance sampling density function to obtain N i Obey h i (x), use the new response surface to map the M i h i (x|F i-1 ) Sort the sample points from large to small;

[0070] Step 13: Take the (1-p0)Mth i The performance function value corresponding to the sample point is taken as the intermediate failure event F i ={x:g(x)≤b i The critical value b of i , and get F i-1 Under the conditions of occurrence F i The estimated value of the conditional failure probability for

[0071]

[0072] In the formula

[0073] ——The estimated value of the failure probability of the i-th layer, which means that the failure event F occurs under the known previous failure state i The estimated probability of

[0074] F i ——the i-th failure event or state;

[0075] F i-1 ——i-1th failure event or state;

[0076] N i ——The total number of samples obtained by the importance sampling of the i-th layer;

[0077] ——the jth sample in the i-th layer;

[0078] ——Indicates that the state F at the known i-1 step i-1 Next, sample The sampling distribution of , i.e., the conditional probability density function, is used to weight the importance of the samples;

[0079] ——The probability density function of important sampling, expressed as The target distribution function is used to standardize the weight of the samples;

[0080] - indicator function;

[0081] Expressed as

[0082]

[0083] In the formula

[0084] g(x) – performance function, replaced by response surface;

[0085] That is, when it falls into the failure area, the indicator function takes 1, and when it falls into the normal safety range, the indicator function takes 0;

[0086] Step 14: Repeat steps 10, 11, 12, and 13 until the (1-p0)Mth function value is sorted from large to small. m response values If the value is less than 0, then let b m =0, F m =F, automatic stratification ends;

[0087] Step 15: Obtain the estimated failure probability of the passive system after the stratification is completed for

[0088]

[0089] In step 1, the failure criterion is selected and the best estimation model is established; in step 2, the uncertainty parameters are identified and quantified; in step 3, the Latin hypercube sampling method is used to sample the key uncertainty parameters; in step 4, the best estimation program is used to calculate, and the output value and the sample are combined to form the training set of the response surface model; in step 5, the training and optimization of the neural network response surface are completed; in step 6, the response surface model is used to perform Monte Carlo simulation; in step 7, the convergence is observed and whether to enter the subset simulation is decided; in steps 8 to 10, the sampling center of the first layer of important sampling is selected; in step 11, the training of the new response surface is completed; in steps 12 to 13, the conditional failure probability is calculated; in step 14, the iteration of subset simulation and importance sampling is completed; in step 15, the estimated value of the final failure probability is obtained; based on the above steps, the reliability analysis of the passive system is completed using the meta-model-based subset simulation importance sampling algorithm, and the failure probability of the system is calculated. Through the above steps, the probabilistic safety analysis of the reliability of the passive system of the nuclear power plant is realized.

Claims

1. A nuclear power plant passive system reliability analysis method based on metamodel adaptive sampling, characterized by: Here are the steps: Step 1: Select failure criteria and best estimate procedure for modeling; determine the failure criteria based on the research object and use the best estimate procedure to build a system model; Step 2: Identify and quantify uncertainty parameters; select key uncertainty parameters and their distributions based on the research object and working conditions; Step 3: Uncertainty parameter sampling; The Latin hypercube sampling method is used to sample the key uncertainty parameters and obtain N0 sample groups; For each variable, the range of values is divided into N0 intervals of equal probability. A value is randomly sampled in each interval to ensure that each variable has only one sample point in all the divided intervals. The sampled values are mapped to obtain samples that obey the target distribution. Finally, the order of the samples is shuffled to obtain N0 sample groups. Step 4: Best estimate program calculation and sensitivity analysis: Use the best estimate program to calculate the sample and obtain the output value, which together with the sample constitutes the training set of the response surface model. The response surface model is used as a proxy model for the thermal hydraulic program to achieve high-precision and fast calculation. The response surface used is a neural network response surface. After obtaining the output value, sensitivity analysis is also used to evaluate the impact of each parameter on the system output. Step 5: Use the obtained training set to train the neural network response surface, and use the particle swarm optimization algorithm to optimize the neural network hyperparameters to obtain the optimal network structure for the current training data; Step 6: Use the response surface model to perform direct Monte Carlo simulation and calculate the failure probability. The formula is: In the formula N f ——Number of failed samples; N0——the total number of samples obtained by Latin hypercube sampling; — an estimate of the probability of failure; Step 7: Repeat step 6 several times and observe Whether the value converges, if so, the calculation ends; if not, the subset simulation importance sampling process begins; Step 8: Extract N1 sample points, map them using the response surface, and sort the output values from large to small, recorded as Step 9: Let M1 = N1, and take the (1-p0)M1th response value as the critical value of the intermediate failure event F1 = {x:g(x)≤b1} At the same time, it is known p0 represents the probability level of the intermediate failure event; Step 10: From Falling on F i-1 p0M in the domain (i=2,3,…,m) i-1 The point with the largest probability density value is selected from the samples as the important sampling density function h i (x) and generate N i The importance sampling density function h i (x) samples, which fall in the failure domain F i-1 M in (i=2,3,…,m) i The sample points follow the distribution condition density h i (x|F i-1 ), recorded as Step 11: Alternately i-1 The samples of the domain are used to calculate the output values using the best estimation procedure and added to the response surface training data to construct a new response surface; Step 12: Re-use the importance sampling density function to obtain N i Obey h i (x), use the new response surface to map the M i h i (x|F i-1 ) Sort the sample points from large to small; Step 13: Take the (1-p0)Mth i The performance function value corresponding to the sample point is taken as the intermediate failure event F i ={x:g(x)≤b i The critical value b of i , and get F i-1 Under the conditions of occurrence F i The estimated value of the conditional failure probability for In the formula ——The estimated value of the failure probability of the i-th layer, which means that the failure event F occurs under the known previous failure state i The estimated probability of F i ——the i-th failure event or state; F i-1 ——i-1th failure event or state; N i ——The total number of samples obtained by the importance sampling of the i-th layer; ——the jth sample in the i-th layer; ——Indicates that the state F at the known i-1 step i-1 Next, sample x j (i) The sampling distribution of , i.e., the conditional probability density function, is used to weight the importance of the samples; ——The probability density function of important sampling, expressed as The target distribution function is used to standardize the weight of the samples; - indicator function; Expressed as In the formula g(x) – performance function, replaced by response surface; That is, when it falls into the failure area, the indicator function takes 1, and when it falls into the normal safety range, the indicator function takes 0; Step 14: Repeat steps 10, 11, 12, and 13 until the (1-p0)Mth function value is sorted from large to small. m response values If the value is less than 0, then let b m =0, F m =F, automatic stratification ends; Step 15: After the stratification is completed, the estimated failure probability of the passive system can be obtained for Probabilistic safety analysis of the reliability of passive systems in nuclear power plants has been implemented.

2. The method for reliability analysis of a nuclear power plant passive system based on metamodel adaptive sampling according to claim 1, characterized in that: The principle of the particle swarm optimization algorithm used in step 5 is based on swarm intelligence. First, the neural network hyperparameters are regarded as the positions of particles in a multidimensional space. Each particle represents a set of hyperparameter combinations and has its own speed. The particle will update its speed based on its current speed, its distance from the individual extreme value, and its distance from the global extreme value, and move to a new position in the hyperparameter space. This process is continuously iterated, and the particle swarm will gradually explore and converge to a better area in the hyperparameter space, so that the neural network hyperparameter combination is continuously optimized, and finally a set of hyperparameters with better performance on the validation set is found, thereby improving the performance of the neural network.

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