A method for optimizing DET branch step length based on Bayesian optimization search

Abstract

The present application discloses a method for optimizing the step length of a DET branch based on Bayesian optimization search, comprising: S1, constructing a DET model; S2, determining the time parameters of an operational branch event, simulating the DET model, and calculating the probability of core failure; S3, combining dynamic time warping with data stability classification to obtain the range of the risk failure space; S4, reconstructing the input-output mapping relationship using the Gaussian process model in S2; S5, predicting the DET output results of the entire space using the Gaussian process model; S6, gridding discretization and performing extreme value search to mark the entire grid space as a dangerous space and a safe space; S7, determining the boundaries of the safe and dangerous spaces based on the search results, and obtaining the parameter range of the envelope risk boundary as the Bayesian optimization search result; S8, combining the risk failure space range of S3 and the Bayesian optimization search range of S7 to narrow the problem space range, and updating the task time iterative calculation until it meets the standard. The method of the present application can automatically optimize the discrete step lengths of the operational branches in DET to obtain the key branch step lengths, reduce the repeated branches with similar accident simulation results under the equal step length branch rule, and improve the efficiency of DET calculation.

Description

Technical Field

[0001] The present invention belongs to the field of nuclear power plant safety simulation analysis, and in particular to an algorithm for optimizing and screening branch step lengths generated by a Discrete Dynamic Event Tree (DDET) model, that is, a method for optimizing DET branch step lengths based on Bayesian optimization search. Background Art

[0002] The Discrete Dynamic Event Tree (DDET) is a widely used dynamic event tree method in practical engineering applications. The DET method generates a series of time-dynamically changing event sequences based on its effective branching rules. The system evolution path is determined by defining branching conditions. When these conditions are met, the complex system evolves along different branching paths, resulting in a set of event sequences that are used to generate the DET model. Once the DET model is generated, all event sequences represented by the branches can be simulated using deterministic safety analysis methods, enabling deterministic analysis. By dynamically coupling DET with deterministic analysis software, in addition to obtaining traditional deterministic analysis results, the probability of occurrence of the calculated analysis results can also be determined, providing risk-informed decision support information for nuclear power plant design, operation, and management. The DET method typically requires significant computing resources and generates a large amount of accident sequence data. To ensure an envelope analysis of accident consequences, the DET method needs to generate a huge number of discrete branches for the time-related system / component operating states. Under the equal-step branch rule, a large number of invalid branches with similar states may be generated in absolutely safe or absolutely dangerous areas in the problem space composed of time parameters. These invalid branches will consume a lot of computing resources. Therefore, it is necessary to develop an efficient branch step optimization search method to automatically obtain the appropriate branch step so that it gradually approaches the risk boundary between the safe and dangerous areas in the problem space, comprehensively reflect the accident consequences with a small number of branches, and obtain accurate core failure probability values ​​under nuclear power plant accidents.

[0003] Bayesian optimization is an algorithm for finding the optimal value of a function. Its optimization methods have been recognized as state-of-the-art in hyperparameter optimization. Most existing hyperparameter optimization schemes that demonstrate superior efficiency and performance are based on the principles of Bayesian optimization. Its fundamental principle is to use a parameter tuning tool with a priori procedures (based on Bayesian processes) to perform parameter tuning and optimization, thereby accelerating parameter search and finding the parameters with optimal generalization. The process first establishes prior knowledge about the global behavior of the objective function (usually represented by a Gaussian process). This prior knowledge is then updated by observing the output of the objective function at different input points to form a posterior distribution. Based on the posterior distribution, the next sampling point is selected, taking into account both previously observed optimal values ​​(i.e., utilization) and globally unexplored areas (i.e., exploration). This selection strategy is typically defined by an acquisition function, such as the most commonly used expected improvement. As a result, Bayesian optimization not only efficiently searches the hyperparameter space but also guides the search based on existing knowledge, avoiding unnecessary attempts. Summary of the Invention

[0004] The purpose of this application is to solve the problem in existing nuclear power safety analysis that a large number of discrete branches are generated using the DET method, and a large number of invalid branches with similar states are generated using the equal-step branch rule. These invalid branches consume a lot of computing resources. In order to overcome the shortcomings of the DET equal-step branch rule in computational efficiency, the search efficiency is improved with the help of the Bayesian optimization algorithm. To this end, this application proposes a method for optimizing the DET branch step size based on Bayesian optimization search. This analysis method can realize automatic optimal search for the discrete step size of the time-related running branch in DET, obtain the key branch step size at the risk boundary, reduce the repeated branches with similar accident simulation results under the equal-step branch rule, and improve the DET computational efficiency.

[0005] To achieve the above-mentioned purpose of the invention, the present application proposes a method for optimizing the branch step size of DET based on Bayesian optimization search, which includes the following steps:

[0006] S1. Obtain time-related system / component information in the accident state of the nuclear power plant and use it as an operational branch event to construct a DET model;

[0007] S2. Determine the time parameters of the operational branch events in step S1, and find the shortest, longest, and median running times. Use these as the branch step lengths to construct a new DET model and perform simulation calculations. Simultaneously, calculate the core failure probability. The DET model here is defined as: where y i(t) is the calculated output of the nuclear power plant system in the corresponding problem space-time branch coordinates, t is the simulation model calculation time, i is the DET branch sequence number, F is the nuclear power plant accident system simulation program, is the time coordinate of the running branch;

[0008] S3. Based on the DET simulation output results of step S2, the output results are classified by the Dynamic Time Warping (DTW) method combined with the data stability test method, and the absolutely safe space and the absolutely dangerous space are excluded to obtain the range of the risk failure space. The risk failure space here is obtained by the following steps: S3-1. Based on the DET running branch time information obtained in step S2, the problem space is discretized into various subspaces, and each subspace vertex is the DET sequence simulation result composed of the branch time combination; S3-2. The DET sequence simulation results of the previous step are classified, and the safety variable extreme value max(y i (t)) exceeds the safety limit, and the branch results are divided into two states: "safe" and "failure". Since the actual simulation output result y i (t) is a set of data that changes with time. In order to more accurately judge the possible states in the subspace, the DTW method is used to classify the entire time series data; S3-3, the difference of the output results of each subspace vertex divided into the same category by the DTW method is calculated, and the stability of the difference data is judged by the unit root test (Augmented Dickey-Fuller, ADF) combined with the KPSS (Kwiatkowski-Phillips-Schmidt-Shin) test; when the subspace vertex data are all divided into the same category of "safe" state and the difference data is stable, the subspace is judged to be an absolutely safe space; when the subspace vertex data are all divided into the same category of "dangerous" state and the difference data is stable, the subspace is judged to be an absolutely dangerous space; S3-4, according to the division of S3-3, the absolutely safe space and the absolutely dangerous space are excluded from the problem space, and the remaining space is the failure risk space;

[0009] S4, obtain the branch time parameters of step S2 as input parameters, the extreme values ​​of the simulation output results of each branch of DET as output parameters, and train the generated Gaussian process model to reconstruct the mapping relationship between the input and output parameters; the training and construction method of the Gaussian process model is to use the branch time parameters is the extreme value max(y i (t)) is the training data. The Gaussian process method is used in the sklearn library of the Python program. After inputting the training data, the Gaussian process surrogate model ROM is fitted:

[0010] S5. Based on the mapping relationship in step S4, use the Gaussian process model to predict the extreme value of the DET simulation output result that envelops the entire problem space;

[0011] S6. Discretize the problem space in step S5 into grids and perform extreme value search on each grid space. If any parameter in the grid space exceeds the safety limit, the entire grid space is marked as a dangerous space, otherwise it is a safe space.

[0012] S7, determining the parameter range of the boundary between the envelope safe space and the dangerous space according to the grid space search result of step S6 as the search result of Bayesian optimization;

[0013] S8. Combine the parameter range of the Bayesian optimization search obtained in step S7 with the risk failure space range obtained in step S3, narrow the problem space range, update the system / component task time, and return to step S2 for iterative calculation until the criterion for stopping the iteration is met, that is, any of the following conditions is met: the stopping criterion is to meet any one of the following three conditions: (a) the probability value of the problem space is less than 0.05; (b) the relative error of the calculated failure probability value after two iterations is less than 0.01; (c) the calculation results of the updated DET branch model are all classified as "safe" state or "dangerous" state; finally, the DET branch step length optimization is achieved.

[0014] The advantages of the method of the present application are: (1) the traditional DET equal-step branch method selects the time-related running branch step based on human judgment, while the DET branch step search method based on Bayesian optimization can automatically search for subsequent branch steps based on data judgment after specifying the initial branch step, thereby reducing human intervention; (2) based on the DTW classification and data stability test method, the problem space composed of time parameters is classified and predicted, and the absolutely safe space and the absolutely dangerous space are excluded, thereby reducing the invalid branches of the traditional equal-step branch in the absolutely safe or absolutely dangerous space, and improving the DET calculation efficiency; (3) the DET branch step search method based on Bayesian optimization utilizes the characteristics of Bayesian optimization search to search for branch steps close to the risk boundary, and comprehensively simulates possible accident consequences with a small number of branches in the iterative calculation process, thereby further improving the DET calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a schematic diagram of the structural flow of the application method of the present invention;

[0016] Figure 2 It is a schematic diagram of the DET model structure of the nuclear power plant state evolution;

[0017] Figure 3 This is a schematic diagram of the dynamic coupling between DET and RELAP5 programs;

[0018] Figure 4 This is a schematic diagram of a single state transition of a DET simulation object; DETAILED DESCRIPTION

[0019] In order to more clearly explain the DET branch step size optimization method based on Bayesian optimization search proposed in this application, it is now described in conjunction with the accompanying drawings. Figure 1 A schematic diagram of the structure flow of the application method of the present invention is given, as shown in FIG. Figure 1 The method includes the following eight steps:

[0020] S1. Obtain time-related system / component information under the accident state of the nuclear power plant, including but not limited to system / component accident response actions and task time, and use these information parameters as operational branch events to construct a DET model;

[0021] S2. Determine the shortest and longest running times and median times of operational branch events, use them as branch step lengths to construct a DET model and perform simulation calculations, and simultaneously calculate the core failure probability;

[0022] S3. Based on the DET simulation output results, the output results are classified using the Dynamic Time Warping (DTW) method combined with the data stability test method to exclude the absolute safety space and the absolute failure space and obtain the risk failure space range;

[0023] S4. Obtain branch time parameters as input parameters, and the extreme values ​​of the simulation output results of each branch of DET as output parameters, and train and generate a Gaussian process model to reconstruct the mapping relationship between the input and output parameters;

[0024] S5. Use the Gaussian process model to predict the extreme values ​​of the DET simulation output results that envelop the entire problem space;

[0025] S6. Discretize the problem space into grids and perform extreme value search on each grid space. If any parameter in the grid space exceeds the safety limit, the entire grid space is marked as a dangerous space, otherwise it is a safe space.

[0026] S7. Determine the parameter range of the boundary between the enveloping safe space and the dangerous space according to the grid space search result, as the search result of Bayesian optimization;

[0027] S8. Combine the parameter range of the Bayesian optimization search obtained in step S7 with the risk failure space range obtained in step S3, narrow the problem space range, update the system / component task time, and return to step S2 for iterative calculation. During the iterative process of this step, the iteration stops when one of the following three criteria occurs: (a) the probability value of the problem space is less than 0.05; (b) the relative error of the calculated failure probability value after two iterations is less than 0.01; (c) the calculation results of the updated DET branch model are all classified as "safe" or "dangerous".

[0028] In the above steps, both S1 and S2 involve the construction of DET model. Figure 2 A schematic diagram of the DET model structure for the state evolution of a nuclear power plant is given. The branching time and the probability of the corresponding branching time at that time are defined as follows:

[0029] Ta_i, i=0, 1, 2: branch time of branch event Root1;

[0030] Tb_i, i=0, 1, 2: branch time of branch event Root2;

[0031] Pa_i, i=0, 1, 2: probability of branch event Root1 at branch time Ta_i;

[0032] Pb_i, i=0, 1, 2: probability of branch event Root2 at branch time Tb_i.

[0033] The specific implementation principles of steps S1 and S2 are as follows:

[0034] Assume that a DET model is constructed for two running branch events Root1 and Root2 for simulation calculation. The initial branch step data is obtained according to the task time of the branch time. Ta_0 is the shortest task time of the branch event Root1, Ta_2 is the longest task time, Ta_1 = Ta_0 + (Ta_2 - Ta_1) / 2; the time parameters of the branch event Root2 are the same.

[0035] The input parameters after constructing the DET branch combination are [Ta_0, Tb_0], [Ta_0, Tb_1], [Ta_0, Tb_2], [Ta_1, Tb_0], [Ta_1, Tb_1], [Ta_1, Tb_2], [Ta_2, Tb_0], [Ta_2, Tb_1], [Ta_2, Tb_2].

[0036] After constructing the DET model, simulations are performed on the sequences consisting of each branch to obtain the corresponding output results. The DET sequence probability is the product of the branch probabilities. For example, the probability of sequence 1 is Pa_0 × Pb_0. The DET sequence simulation results are used to determine whether a core failure has occurred. Sequences whose simulation results exceed the safety limit are marked as core failure sequences. The core failure sequence probabilities are summed to obtain the failure probability.

[0037] After completing the model construction through S1 and S2, step S3 begins to determine the scope of the failure risk space. For details, refer to Figure 3 As shown in the figure, under the combination of two branch events, the problem space consists of two-dimensional time parameters. The DET branch time divides the problem space into various subspaces. The state of each vertex in the subspace is determined based on the sequence state. The core failure sequence is marked as a dangerous point, and the remaining sequences are marked as safe points. The specific process is as follows:

[0038] S3-1: The DTW method classifies the entire time series data. The DTW method aims to address the problem that traditional distance metrics cannot effectively calculate similarity when the time series are of unequal length or have displacements on the time axis. It dynamically "bends" or "stretches" the time series to find the best matching path between the two series, minimizing the cumulative distance along this path.

[0039] S3-2: Obtain the output data that are classified into the same category by DTW in the output results corresponding to the four vertices of the subspace, calculate their data differences, and perform data stability tests on the difference data;

[0040] S3-3: The stability of the difference series data is tested using both the ADF test and the KPSS test. The ADF test is a statistical test used to determine whether time series data possess a unit root. A unit root indicates that the time series exhibits random walk properties, meaning that the series lacks a fixed mean and variance, exhibiting non-stationarity. The alternative hypothesis in the ADF unit root test is that the data generating process is an autoregressive model. A complementary method is the KPSS unit root test. Therefore, a combined ADF and KPSS test enhances the reliability of the test results. Subspaces that satisfy the stability test can be identified as either absolutely safe or absolutely dangerous, eliminating the possibility of subsequent branches from the problem space.

[0041] After the above-mentioned process from S3-1 to S3-3, the process from S4 to S8 is as follows: with the branch time parameters [Ta_0, Tb_0], [Ta_0, Tb_1], [Ta_0, Tb_2], [Ta_1, Tb_0], [Ta_1, Tb_1], [Ta_1, Tb_2], [Ta_2, Tb_0], [Ta_2, Tb_1], [Ta_2, Tb_2] and the extreme values ​​of the simulation results of each sequence of DET as training data, the Gaussian process method is used in the sklearn library of the Python program. After inputting the training data, the Gaussian process proxy model ROM is fitted; as shown in FIG. Figure 4 As shown, the problem space is discretized into grids, and the output results of the entire problem space are enveloping using ROM prediction. Bayesian optimization extreme value search is performed on each grid space. If any parameter in the grid space exceeds the safety limit, the entire grid space is marked as a dangerous space, otherwise it is marked as a safe space. Based on the grid space search results, the parameter range of the boundary between the enveloping safe space and the dangerous space is determined as the search result of Bayesian optimization, and combined with the risk failure space range obtained in step S3, the shortest and longest task times of the branch events are updated in the risk failure space. Based on the updated task time, the time parameters of each branch node of the new DET model are determined, and iterative calculation starts from step S2 until the iteration end condition is met.

[0042] The above-mentioned DET branch step search algorithm based on Bayesian optimization can be used to search and obtain key branch variables close to the risk boundary. Through a small number of branch calculations, the consequences of nuclear power plant accidents can be reflected efficiently and comprehensively.

[0043] The above description is merely a preferred embodiment of the present application; however, the scope of protection of the present application is not limited thereto. Any person skilled in the art who, within the technical scope disclosed in the present application, makes equivalent substitutions or modifications based on the technical solutions and improved concepts of the present application shall be covered by the scope of protection of the present application.

Claims

1. A method for optimizing DET branch step length based on Bayesian optimization search, characterized in that: The steps include: S1. Obtain time-related system / component information in the accident state of the nuclear power plant and use it as an operational branch event to construct a DET model; S2. Determine the time parameters of the operational branch events in step S1, and find the shortest, longest, and median running times. Use these as the branch step lengths to construct a new DET model and perform simulation calculations, while also calculating the core failure probability. S3. Based on the DET simulation output results in step S2, the output results are classified using the Dynamic Time Warping (DTW) method combined with the data stability test method to exclude the absolutely safe space and the absolutely dangerous space and obtain the risk failure space range; S4, obtaining the branch time parameters of step S2 as input parameters, the extreme values ​​of the simulation output results of each branch of DET as output parameters, and training the generated Gaussian process model to reconstruct the mapping relationship between the input and output parameters; S5. Based on the mapping relationship in step S4, use the Gaussian process model to predict the extreme value of the DET simulation output result that envelops the entire problem space; S6. Discretize the problem space in step S5 into grids and perform extreme value search on each grid space. If any parameter in the grid space exceeds the safety limit, the entire grid space is marked as a dangerous space, otherwise it is a safe space. S7, determining the parameter range of the boundary between the envelope safe space and the dangerous space according to the grid space search result of step S6 as the search result of Bayesian optimization; S8. Combine the parameter range of the Bayesian optimization search obtained in step S7 with the risk failure space range obtained in step S3, narrow the problem space range, update the system / component task time, and return to step S2 for iterative calculation until the criterion for iterative termination is met; thereby achieving DET branch step optimization.

2. The method for implementing DET branch step size optimization based on Bayesian optimization search according to claim 1, characterized in that: The DET model in step S2 is defined as: where y i (t) is the calculated output of the nuclear power plant system in the corresponding problem space-time branch coordinates, t is the simulation model calculation time, i is the DET branch sequence number, F is the nuclear power plant accident system simulation program, It is the time coordinate of the running branch.

3. The method for implementing DET branch step size optimization based on Bayesian optimization search according to claim 1, characterized in that: The risk failure space range in step S3 is obtained through the following steps: S3-1. According to the DET running branch time information obtained in step S2, the problem space is discretized into various subspaces, and each subspace vertex is a DET sequence simulation result composed of branch time combinations; S3-2, classify the DET sequence simulation results of the previous step, and classify the extreme value of the safety variable max(y i (t)) exceeds the safety limit, and the branch results are divided into two states: "safe" and "failure". Since the actual simulation output result y i (t) is a set of data that changes over time. In order to more accurately determine the possible states in the subspace, the DTW method is used to classify the entire time series data; S3-3. Calculate the difference in the output results of each subspace vertex classified into the same category using the DTW method, and determine the stability of the difference data using the unit root test (Augmented Dickey-Fuller, ADF) combined with the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test. If the data of all subspace vertices are classified into the same "safe" state and the difference data is stable, then the subspace is determined to be an absolutely safe space. If the data of all subspace vertices are classified into the same "dangerous" state and the difference data is stable, then the subspace is determined to be an absolutely dangerous space. S3-4. According to the division of S3-3, the absolutely safe space and the absolutely dangerous space are excluded from the problem space, and the remaining space is the failure risk space.

4. The method for implementing DET branch step size optimization based on Bayesian optimization search according to claim 2, characterized in that: In step S4, the training construction method of the Gaussian process model is to use the branch time parameter is the extreme value max(y i (t)) is the training data. The Gaussian process method is used in the sklearn library of the Python program. After inputting the training data, the Gaussian process surrogate model ROM is fitted:

5. The method for implementing DET branch step size optimization based on Bayesian optimization search according to claim 1, characterized in that: The criterion for stopping the iteration is to meet any of the following three conditions: (a) the probability value of the problem space is less than 0.05; (b) the relative error of the calculated failure probability value after two iterations is less than 0.01; (c) the calculation results of the updated DET branch model are all classified as "safe" or "dangerous".

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