Failure probability determination method and apparatus, computer device, and storage medium

Abstract

The application relates to a failure probability determination method and device, computer equipment and a storage medium. The method comprises the following steps: constructing a GOTHIC model of a reactor containment according to structure information of the reactor containment in an EPS (passive containment cooling system); selecting a target influence parameter from each candidate influence parameter according to an importance level and a knowledge level of each candidate influence parameter; each candidate influence parameter is a parameter related to the failure probability of the EPS in the GOTHIC model; sampling the target influence parameter based on an importance sampling distribution to obtain at least two parameter values corresponding to the target influence parameter; the importance sampling distribution is determined based on an original probability density function of the target influence parameter and a failure boundary feature of the EPS; and determining the failure probability of the EPS according to the GOTHIC model, a failure determination criterion of the EPS and the at least two parameter values corresponding to the target influence parameter. The method can ensure the calculation accuracy and significantly improve the analysis efficiency of the extremely small probability failure event.

Description

Technical Field

[0001] This application relates to the field of nuclear power plant technology, and in particular to a method, apparatus, computer equipment, and storage medium for determining failure probability. Background Technology

[0002] In nuclear reactor safety systems, the Emergency Passive Safety System (EPS) is a key core system for ensuring reactor safety. Accurately determining the failure probability of the EPS is an important part of nuclear reactor probabilistic safety analysis and is of great significance for reactor safety design, operation and maintenance, and risk assessment.

[0003] Currently, existing technologies for calculating the failure probability of EPS mostly employ the traditional Monte Carlo sampling method, which combines thermal-hydraulic calculation programs to construct a reactor containment model. By randomly sampling relevant parameters that affect EPS failure, and substituting them into the model, a large number of case results are obtained. Then, the failure probability is finally determined by statistically analyzing the proportion of failure cases according to failure judgment criteria.

[0004] However, in practical engineering applications, EPS failure is an event with an extremely low probability. When using the traditional Monte Carlo sampling method to calculate its failure probability, there are obvious technical defects. Because the probability of failure events is extremely low, a massive number of parameter samples need to be extracted for calculation in order to ensure the accuracy and variance stability of the failure probability calculation results. This results in a very long calculation process and extremely high calculation costs, making it difficult to meet the high-efficiency calculation needs in practical engineering. Summary of the Invention

[0005] Therefore, it is necessary to provide a method, apparatus, computer equipment, and storage medium for determining the failure probability in response to the above-mentioned technical problems.

[0006] Firstly, this application provides a method for determining failure probability, including:

[0007] Based on the structural information of the reactor containment in the passive containment cooling system EPS, a GOTHIC model of the reactor containment is constructed.

[0008] Based on the importance level and knowledge level of each candidate impact parameter, a target impact parameter is selected from the candidate impact parameters; wherein, each candidate impact parameter is a parameter in the GOTHIC model related to the failure probability of EPS;

[0009] Based on the importance sampling distribution, the target impact parameter is sampled to obtain at least two parameter values ​​corresponding to the target impact parameter; wherein, the importance sampling distribution is determined based on the original probability density function of the target impact parameter and the failure boundary characteristics of EPS;

[0010] The failure probability of the EPS is determined based on the GOTHIC model, the failure criterion of the EPS, and the values ​​of at least two parameters corresponding to the target influence parameter.

[0011] In one embodiment, selecting the target impact parameter from the candidate impact parameters based on their importance level and knowledge level includes:

[0012] From the candidate impact parameters, preliminary screening parameters are selected; wherein, the importance level of the preliminary screening parameters is higher than that of the other candidate impact parameters, and the knowledge level of the preliminary screening parameters is lower than that of the other candidate impact parameters.

[0013] If the number of selected preliminary screening parameters is greater than the preset threshold, a sensitivity analysis is performed on each preliminary screening parameter to obtain the target influencing parameters;

[0014] If the number of selected preliminary screening parameters is less than or equal to the preset threshold, then the selected preliminary screening parameters will be used as the target influence parameters.

[0015] In one embodiment, the sensitivity analysis of each preliminary screening parameter to obtain the target influence parameter includes:

[0016] For each preliminary screening parameter, the local sensitivity corresponding to the preliminary screening parameter is determined based on the degree of influence of the value change of the preliminary screening parameter within its local value range on the failure probability of the EPS; and,

[0017] The global sensitivity corresponding to the preliminary screening parameters is determined based on the degree of influence of the changes in the values ​​of the preliminary screening parameters within the global value range on the failure probability of the EPS.

[0018] Based on the local and global sensitivity of each preliminary screening parameter, target influencing parameters are selected from the preliminary screening parameters.

[0019] In one embodiment, the failure determination criterion is determined based on a preset accident scenario;

[0020] When the preset accident scenario includes the Large Breach Loss of Water (LBLOCA) scenario, the failure determination criterion includes the criterion that the containment peak pressure exceeds the design pressure.

[0021] In one embodiment, determining the failure probability of the EPS based on the GOTHIC model, the failure determination criterion of the EPS, and the values ​​of at least two parameters corresponding to the target impact parameter includes:

[0022] For each parameter value corresponding to the target influence parameter, the parameter value is input into the GOTHIC model for thermo-hydraulic calculation to obtain the peak containment pressure corresponding to the parameter value;

[0023] Based on the failure determination criteria and the peak containment pressure corresponding to each parameter value, the failure value corresponding to the target influence parameter is selected from each parameter value;

[0024] The failure probability of the EPS is determined based on the failure value corresponding to the target impact parameter.

[0025] In one embodiment, selecting the failure value corresponding to the target influence parameter from the parameter values ​​based on the failure determination criteria and the peak containment pressure corresponding to each parameter value includes:

[0026] Determine the design pressure based on the aforementioned failure criteria;

[0027] For each parameter value, if the peak containment pressure corresponding to the parameter value is greater than the preset design pressure, then the parameter value is determined to be a failure value.

[0028] In one embodiment, constructing a GOTHIC model of the reactor containment based on the structural information of the reactor containment in the passive containment cooling system EPS includes:

[0029] Obtain structural information of the reactor containment structure in the EPS;

[0030] Based on the structural information, construct the basic geometric model of the reactor containment vessel;

[0031] The parameters of the basic geometric model are configured to obtain the GOTHIC model of the reactor containment.

[0032] Secondly, this application also provides a failure probability determination device, comprising:

[0033] The model building module is used to build a GOTHIC model of the reactor containment based on the structural information of the reactor containment in the passive containment cooling system EPS.

[0034] The parameter determination module is used to select the target impact parameter from the candidate impact parameters according to the importance level and knowledge level of each candidate impact parameter; wherein, each candidate impact parameter is a parameter related to the failure probability of EPS in the GOTHIC model;

[0035] The value determination module is used to sample the target influence parameter based on the importance sampling distribution to obtain at least two parameter values ​​corresponding to the target influence parameter; wherein, the importance sampling distribution is determined based on the original probability density function of the target influence parameter and the failure boundary characteristics of EPS;

[0036] The probability determination module is used to determine the failure probability of the EPS based on the GOTHIC model, the failure judgment criterion of the EPS, and the values ​​of at least two parameters corresponding to the target influence parameter.

[0037] Thirdly, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps:

[0038] Based on the structural information of the reactor containment in the passive containment cooling system EPS, a GOTHIC model of the reactor containment is constructed.

[0039] Based on the importance level and knowledge level of each candidate impact parameter, a target impact parameter is selected from the candidate impact parameters; wherein, each candidate impact parameter is a parameter in the GOTHIC model related to the failure probability of EPS;

[0040] Based on the importance sampling distribution, the target impact parameter is sampled to obtain at least two parameter values ​​corresponding to the target impact parameter; wherein, the importance sampling distribution is determined based on the original probability density function of the target impact parameter and the failure boundary characteristics of EPS;

[0041] The failure probability of the EPS is determined based on the GOTHIC model, the failure criterion of the EPS, and the values ​​of at least two parameters corresponding to the target influence parameter.

[0042] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the following steps:

[0043] Based on the structural information of the reactor containment in the passive containment cooling system EPS, a GOTHIC model of the reactor containment is constructed.

[0044] Based on the importance level and knowledge level of each candidate impact parameter, a target impact parameter is selected from the candidate impact parameters; wherein, each candidate impact parameter is a parameter in the GOTHIC model related to the failure probability of EPS;

[0045] Based on the importance sampling distribution, the target impact parameter is sampled to obtain at least two parameter values ​​corresponding to the target impact parameter; wherein, the importance sampling distribution is determined based on the original probability density function of the target impact parameter and the failure boundary characteristics of EPS;

[0046] The failure probability of the EPS is determined based on the GOTHIC model, the failure criterion of the EPS, and the values ​​of at least two parameters corresponding to the target influence parameter.

[0047] Fifthly, this application also provides a computer program product, including a computer program that, when executed by a processor, performs the following steps:

[0048] Based on the structural information of the reactor containment in the passive containment cooling system EPS, a GOTHIC model of the reactor containment is constructed.

[0049] Based on the importance level and knowledge level of each candidate impact parameter, a target impact parameter is selected from the candidate impact parameters; wherein, each candidate impact parameter is a parameter in the GOTHIC model related to the failure probability of EPS;

[0050] Based on the importance sampling distribution, the target impact parameter is sampled to obtain at least two parameter values ​​corresponding to the target impact parameter; wherein, the importance sampling distribution is determined based on the original probability density function of the target impact parameter and the failure boundary characteristics of EPS;

[0051] The failure probability of the EPS is determined based on the GOTHIC model, the failure criterion of the EPS, and the values ​​of at least two parameters corresponding to the target influence parameter.

[0052] The aforementioned failure probability determination method, apparatus, computer equipment, and storage medium ensure the realism and accuracy of the thermal-hydraulic simulation by constructing a GOTHIC model that matches the actual reactor containment. By selecting target influence parameters based on importance and knowledge level, the dimensionality of parameters can be effectively reduced while retaining key sources of uncertainty. The importance sampling distribution designed in conjunction with failure boundary characteristics significantly improves the sampling efficiency of failure area samples and greatly reduces the computational load. Finally, the failure probability of EPS is determined by combining failure judgment criteria, significantly improving the analysis efficiency of extremely low probability failure events while ensuring computational accuracy, making the entire method more efficient, reliable, and more practical for engineering applications. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments or related technologies of this application, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 This is a flowchart illustrating a method for determining failure probability in one embodiment;

[0055] Figure 2 This is a flowchart illustrating the process of selecting a target influence parameter from among candidate influence parameters in one embodiment.

[0056] Figure 3 This is a flowchart illustrating the process of determining target influence parameters in one embodiment;

[0057] Figure 4 This is a flowchart illustrating the process of determining the failure probability of EPS in one embodiment.

[0058] Figure 5 This is a schematic diagram of the process for constructing a GOTHIC model of a reactor containment structure in one embodiment;

[0059] Figure 6 This is a flowchart illustrating the failure probability determination method in another embodiment;

[0060] Figure 7 This is a structural block diagram of a failure probability determination device in one embodiment;

[0061] Figure 8 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0062] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0063] The failure probability determination method provided in this application can be applied to the reliability assessment of the passive containment cooling system of a nuclear power plant. The failure probability determination method provided in this application can be executed by a computer device, which can be a server or a terminal with powerful computing capabilities. The server can be a standalone server or a server cluster composed of multiple servers.

[0064] In one exemplary embodiment, such as Figure 1As shown, a method for determining failure probability is provided. Taking the application of this method to a server as an example, the specific steps include:

[0065] S101. Based on the structural information of the reactor containment in the passive containment cooling system EPS, a GOTHIC model of the reactor containment is constructed.

[0066] The passive containment cooling system is a safety system that requires no external power and relies on natural driving force to remove residual heat from the reactor containment. The structural information of the reactor containment is the core physical parameter used to build the model, including but not limited to the free volume of the containment body, annular cavity, sump, internal structure and wall dimensions, flow channel layout, and EPS heat exchanger arrangement parameters.

[0067] The GOTHIC (General Objective Thermal-Hydraulic Inside Containment) model is an engineering thermal-hydraulic model built on the GOTHIC program that is equivalent to the actual reactor containment. It can accurately simulate complex physical processes such as flow, heat transfer, and mass transfer inside the containment and is used for thermal-hydraulic calculations in subsequent accident scenarios.

[0068] Optionally, structural information about the containment can be comprehensively collected by consulting reactor containment design drawings, engineering specifications, and related technical documents. The key information to be collected includes the free volume of the containment body, the size of the annular cavity, the volume and location of the sump, the internal structures of the containment (such as baffles and supporting components) and the material / thickness of the walls, the flow channel layout (including resubmergence channels and natural circulation channels), and the arrangement height, quantity, and specifications of the EPS heat exchangers.

[0069] Furthermore, the GOTHIC program is launched to build a GOTHIC model of the reactor containment vessel based on the collected structural information. The completed GOTHIC model is then compared with the design parameters and historical experimental data of the reactor containment vessel. The model parameters are adjusted to ensure that the deviation between the model calculation results and the actual data is within the allowable range, thus verifying the effectiveness and accuracy of the model. Finally, a GOTHIC model that can be used for subsequent calculations is obtained.

[0070] S102, Select the target impact parameter from the candidate impact parameters according to the importance level and knowledge level of each candidate impact parameter.

[0071] Among them, each candidate influencing parameter is a parameter in the GOTHIC model related to the failure probability of EPS. The candidate influencing parameters are all input parameters in the GOTHIC model that may affect the failure probability of EPS, that is, parameters that can change the temperature and pressure changes inside the containment, affect the heat exchange efficiency of EPS, and thus lead to changes in the failure risk of EPS. In the embodiments of this application, the candidate influencing parameters include, but are not limited to, rupture size, decay heat release rate, EPS heat exchanger heat transfer coefficient, IRWST injection flow rate, containment wall heat transfer coefficient, etc.

[0072] Importance level is used to classify the degree of influence of candidate influencing parameters on EPS failure probability (e.g., high, medium, low). The higher the importance level, the more significant the impact of the parameter on EPS failure probability. Knowledge level is used to classify the level of understanding and data reliability of candidate influencing parameters (e.g., high, medium, low). The lower the knowledge level, the greater the uncertainty of the parameter, and the more attention it requires. Target influencing parameters are core parameters selected from candidate influencing parameters that have a significant impact on EPS failure probability and are subject to greater uncertainty.

[0073] Optionally, by combining the input parameters of the GOTHIC model, a comprehensive review of all candidate parameters that may affect the failure probability of EPS can be conducted, clarifying the physical meaning, value range, and correlation with EPS failure of each parameter (e.g., the larger the break size, the more mass energy is released, and the higher the risk of EPS failure).

[0074] Furthermore, the importance level and knowledge level of each candidate influencing parameter can be obtained based on a pre-built Phenomena Identification and Ranking Table (PIRT). The PIRT table is constructed by experts from multiple fields, combining engineering experience and experimental data, and can systematically and comprehensively evaluate the importance and uncertainty of each parameter.

[0075] Following a selection principle of high importance level + low knowledge level level, target impact parameters are selected from the candidate impact parameters. The core of this selection principle is to prioritize parameters that have a significant impact on EPS failure, are poorly understood, and have high uncertainty, ensuring that the selected parameters are targeted. The value range and distribution type (e.g., normal distribution, uniform distribution) of the target impact parameters are defined, and the original probability density function of each target impact parameter is determined by combining engineering practice and experimental data.

[0076] S103, based on the importance sampling distribution, sample the target influence parameters to obtain at least two parameter values ​​corresponding to the target influence parameters.

[0077] The importance sampling distribution is a proposed distribution designed to replace the original probability density function of the target influence parameter. Its core feature is that the distribution center is biased towards the failure boundary of the EPS, which can increase the proportion of sampling points in the failure area and solve the problem of low sampling efficiency for extremely low probability events. In the embodiments of this application, the importance sampling distribution is determined based on the original probability density function of the target influence parameter and the failure boundary characteristics of the EPS. The original probability density function is the natural distribution law of the target influence parameter in actual engineering, reflecting the true probability of the parameter value. The failure boundary of the EPS is the range of target influence parameter values ​​that can cause the EPS to fail; that is, when the target influence parameter falls within this range, the EPS cannot function properly. The failure boundary is determined by the failure judgment criteria of the EPS.

[0078] The parameter values ​​corresponding to the target impact parameters are obtained through sampling. Each set of parameter values ​​corresponds to a calculation case. At least two sets of parameter values ​​are required to statistically analyze the proportion of failure cases and calculate the failure probability.

[0079] Optionally, based on engineering practice, experimental data, and relevant specifications, the original probability density function of each target influence parameter can be defined. The original probability density function reflects the probability distribution of the target influence parameter under different values. Combining the original probability density function of the target influence parameter and the failure boundary characteristics of EPS, an importance sampling distribution is designed. The design principle is to shift the distribution center of the importance sampling distribution towards the failure boundary, making it easier for the sampled samples to fall in the failure area and increasing the proportion of failure samples.

[0080] In this embodiment, the importance sampling distribution can be constructed as follows: Obtain the original probability density function of the target influence parameter; determine the failure domain interval based on the critical parameter values ​​corresponding to the EPS failure boundary; and perform offset correction on the original probability density function based on the failure domain interval to obtain the importance sampling distribution. Here, the critical parameter value refers to the value of a single target influence parameter that, under the premise that other parameters take conservative or nominal values, just causes the peak containment pressure to reach the 550 kPa abs failure threshold. When the parameter value is greater than or less than this critical value (determined by the positive or negative effect of the parameter), it enters the failure domain; otherwise, it remains in the safe domain.

[0081] Optionally, collect basic uncertainty information on the parameters affecting each target, including equipment manufacturing deviations, test dispersion, operating condition fluctuations, and model applicability deviations. Secondly, determine the parameter distribution type based on general criteria for nuclear power uncertainty analysis. Finally, fit the complete original probability density function and the effective value range of the parameters, truncating physically meaningless out-of-range values ​​to ensure sampling rationality. Fix all non-target parameters to conservative engineering values ​​or nominal design values ​​to eliminate interference from other parameters. Perform multi-point uniform perturbation on the single target parameter within its original value range, successively substituting it into the GOTHIC model for thermal-hydraulic calculations, extracting the containment peak pressure for each calculation. Thirdly, solve for the parameter value corresponding to a peak pressure exactly equal to 550 kPa abs through interpolation fitting; this is the critical failure value for that parameter. Fourthly, determine the failure range direction based on the parameter's physical effect: if an increase in the parameter leads to overpressure failure, the range greater than the critical value is the failure domain; if a decrease in the parameter leads to insufficient cooling capacity and failure, the range less than the critical value is the failure domain, ultimately obtaining the precise failure domain range corresponding to each target parameter. The correction process involves several steps. First, the physical boundaries of the original distribution are preserved. The distribution center of the original probability density function is shifted towards the failure domain, and the distribution variance is appropriately scaled to ensure that more samples fall into the failure domain. Second, the distribution is normalized based on the optimal importance sampling theory to ensure that the corrected importance sampling distribution satisfies the mathematical condition that the probability density integral is 1. Finally, a weighted mapping relationship between the original distribution and the importance sampling distribution is established to provide a basis for subsequent weighted correction of failure probabilities, ensuring that the final statistical results are unbiased and reliable.

[0082] In this embodiment, by accurately obtaining the original probability density of the target impact parameters, quantifying the critical values ​​of the parameters corresponding to the EPS failure boundary, accurately dividing the parameter failure domain interval, and specifically correcting the offset of the original distribution, a dedicated importance sampling distribution adapted to the calculation of the failure probability of passive systems in reactor LBLOCA accidents is constructed.

[0083] Furthermore, based on the designed importance sampling distribution, a random sampling method is used to resample all target influence parameters to generate at least two sets of parameter values ​​(in actual engineering, thousands of samples are usually selected to balance accuracy and efficiency); each set of parameter values ​​corresponds to a combination of target influence parameters, representing a possible operating condition.

[0084] For each set of sampled parameters, calculate its corresponding weighting factor. The weighting factor corrects for the bias of importance sampling, restoring the proportion of failure cases obtained from the sampling to the true failure probability, thus ensuring the accuracy of the calculation results. Check the distribution of the sampled data to confirm that the samples are concentrated near the failure boundary and that the sample distribution conforms to the importance sampling distribution, avoiding sampling bias. If the sample distribution is unreasonable, adjust the importance sampling distribution parameters and resample.

[0085] S104. Determine the failure probability of EPS based on the GOTHIC model, the failure criterion of EPS, and the values ​​of at least two parameters corresponding to the target influence parameter.

[0086] Among them, the failure criteria for EPS are used as a quantitative standard to determine whether EPS has failed, and are usually determined in conjunction with the design requirements of the containment. The failure probability of EPS refers to the probability that EPS will fail under a preset accident scenario. It is a core indicator of probabilistic safety analysis of nuclear reactors, reflecting the safety and reliability of EPS, and its value is usually an extremely low probability (…). ~ (magnitude).

[0087] Optionally, the parameter values ​​of each group affecting the target are input into the constructed GOTHIC model. A Python program is coupled with the GOTHIC program to achieve parallel computation across multiple cases. The Python program is responsible for automatically modifying the parameter values ​​in the GOTHIC input card, calling the GOTHIC solver, and extracting the calculation results, achieving full automation and improving computational efficiency. Failure is assessed for each calculation condition based on preset EPS failure criteria. The failure samples are statistically analyzed and corrected using importance sampling weights, thereby quantitatively determining the failure probability of the passive containment cooling system's EPS.

[0088] In the above-mentioned method for determining failure probability, the authenticity and accuracy of the thermal-hydraulic simulation are ensured by constructing a GOTHIC model that matches the actual reactor containment structure. Target influence parameters are selected based on importance and knowledge level, effectively reducing parameter dimensionality while retaining key sources of uncertainty. An importance sampling distribution is designed in conjunction with failure boundary characteristics, significantly improving the sampling efficiency of failure area samples and greatly reducing computational load. Finally, the failure probability of EPS is determined by combining failure judgment criteria, significantly improving the analysis efficiency of extremely low probability failure events while ensuring computational accuracy, making the entire method more efficient, reliable, and more practical for engineering applications.

[0089] Optionally, in an exemplary embodiment, such as Figure 2 The present invention provides a method for selecting a target influence parameter from candidate influence parameters, which specifically includes the following steps:

[0090] S201. Select preliminary screening parameters from the candidate influence parameters.

[0091] The preliminary screening parameters are selected from all candidate influencing parameters based on the principle of high importance and low knowledge level. These parameters have a significant impact on the failure probability and are inherently uncertain. Therefore, the importance level of the preliminary screening parameters is higher than that of the other candidate influencing parameters, and the knowledge level of the preliminary screening parameters is lower than that of the other candidate influencing parameters.

[0092] Optionally, an existing PIRT can be pre-established or referenced, explicitly specifying the importance and knowledge level of each candidate impact parameter. All candidate impact parameters are sorted from highest to lowest importance and from lowest to highest knowledge level. Only parameters with the highest importance level and the lowest knowledge level are retained; parameters meeting both conditions are identified as preliminary screening parameters. Furthermore, non-critical parameters with low importance or high knowledge level (low uncertainty) are eliminated to avoid redundant subsequent calculations.

[0093] Using PIRT to screen uncertainty parameters has the following advantages:

[0094] a) Comprehensiveness: The establishment of PIRT is the result of joint efforts by experts from different fields, representing an understanding of the uncertainty parameters of passive system physical processes from different perspectives and fields. Consideration of all possible phenomena ensures the completeness of the candidate uncertainty parameters, thereby reducing the risk of omitting key parameters;

[0095] b) Systematicity: The establishment of PIRT is a recursive and systematic process from system to subsystem to phenomenon to parameter, which ensures the identification of all important phenomena and parameters.

[0096] As exemplary, Table 1 shows the PIRT of the EPS system provided in the embodiments of this application.

[0097] Table 1 PIRT of EPS System

[0098]

[0099] H, M, and L represent the scoring criteria for importance and knowledge level, as shown in Table 2.

[0100] Table 2 Ranking Criteria for Importance and Knowledge Level

[0101]

[0102] S202, determine whether the number of selected preliminary screening parameters is greater than the preset threshold; if yes, proceed to S203; if no, proceed to S204.

[0103] The initial screening parameters are the total number of parameters that meet the criteria of high importance and low knowledge level after screening. The preset threshold is a manually set critical value for the number of parameters, used to determine whether further sensitivity analysis is needed to simplify the parameters. The threshold is determined based on the engineering complexity, computational cost, and model coupling difficulty; for example, it can be set to 5, 6, or 8.

[0104] Optionally, the total number of preliminary screening parameters is counted and compared with a preset threshold. If the number of selected preliminary screening parameters is greater than the preset threshold, it indicates that there are still too many parameters, and direct sampling will lead to a combination explosion. Therefore, proceed to S203 for further sensitivity analysis and screening. If the number of selected preliminary screening parameters is less than or equal to the preset threshold, it indicates that the number of parameters is appropriate and can be directly used for subsequent importance sampling. Proceed to S204.

[0105] S203, Sensitivity analysis is performed on each preliminary screening parameter to obtain the target influence parameters.

[0106] Sensitivity analysis is a method for quantitatively analyzing the impact of each preliminary screening parameter on EPS failure-related outputs (such as containment peak pressure). In the embodiments of this application, sensitivity analysis includes local sensitivity analysis and global sensitivity analysis.

[0107] Optionally, sensitivity analysis can be performed on each preliminary screening parameter in turn to obtain the sensitivity of each preliminary screening parameter; further, the preliminary screening parameters can be sorted according to their sensitivity, and the few preliminary screening parameters with the highest sensitivity ranking can be retained, while redundant parameters with low sensitivity and weak impact on the output can be eliminated. The remaining parameters are the target impact parameters.

[0108] S204, use the selected preliminary screening parameters as the target influence parameters.

[0109] Optionally, since the number of preliminary screening parameters is already small and they are all high-importance, low-knowledge-level parameters, further simplification is unnecessary. All preliminary screening parameters can be directly identified as target influencing parameters, and a list of target influencing parameters can be compiled, clarifying the physical meaning, value range, and original probability distribution of each parameter.

[0110] In this embodiment, a three-level parameter simplification mechanism consisting of qualitative screening, quantitative screening, and adaptive quantity judgment is used to accurately identify key parameters affecting EPS failure. While ensuring that no important sources of uncertainty are overlooked, the subsequent sampling and calculation dimensions are significantly reduced, thereby improving the calculation efficiency and result accuracy of extremely low probability failure events.

[0111] Optionally, in an exemplary embodiment, such as Figure 3 As shown, a method for determining target influence parameters is provided, which specifically includes the following steps:

[0112] S301, for each preliminary screening parameter, determine the local sensitivity corresponding to the preliminary screening parameter based on the degree of influence of the value change of the preliminary screening parameter in the local value range on the failure probability of EPS.

[0113] The local value range is a small range of values ​​near the typical values ​​(or design reference values) of the initially screened parameters. This range corresponds to the normal operating fluctuation range of the parameters and does not cover all possible values, but focuses only on the vicinity of a specific operating point. Value variation refers to small disturbances (such as ±5%, ±10%, set according to parameter characteristics) applied to the initially screened parameters within the local value range. The disturbance amplitude must meet the principle of being small and not changing the physical meaning of the parameters.

[0114] Local sensitivity is a measure of the change in EPS failure probability caused by a unit change in the value of a preliminarily screened parameter within its local range. It reflects the strength of the parameter's influence on EPS failure probability near a specific operating point and is a quantitative indicator of the parameter's importance within a local range.

[0115] Optionally, for each preliminary screening parameter, consult engineering design documents and experimental data to determine its design baseline value (typical value) and set a local value range. Typically, the local range is set at ±5% to ±10% of the baseline value. For example, if the baseline value for a preliminary screening parameter is 100, the local range could be set to 90 to 110, ensuring that the range closely matches the parameter's normal operating fluctuation range. A uniform small disturbance amplitude can be determined based on the physical characteristics of the preliminary screening parameters, such as using ±5% disturbance for all preliminary screening parameters. This avoids calculation distortion due to excessively large disturbance amplitudes or failure to capture the parameter's influence due to excessively small amplitudes.

[0116] Adopting the principle of single-parameter perturbation and fixed other parameters, for each preliminary screening parameter, three key values ​​are taken in sequence within its local range: “baseline value - perturbation value”, “baseline value”, and “baseline value + perturbation value”. These values ​​are then input into the GOTHIC thermal-hydraulic model to simulate and calculate the EPS failure probability corresponding to each value.

[0117] Furthermore, local sensitivity can be calculated using the partial derivative method or the rate of change method. In one embodiment, the formula for calculating local sensitivity can be:

[0118]

[0119] in, For the first The local sensitivity of the initial screening parameters; For the first The parameter values ​​for the initial screening parameters; For the first The parameter values ​​of the initial screening parameters correspond to the EPS failure probability (or containment peak pressure).

[0120] S302, Determine the global sensitivity corresponding to the preliminary screening parameters based on the degree of influence of the changes in the values ​​of the preliminary screening parameters within the global value range on the failure probability of EPS.

[0121] The global value range encompasses all possible values ​​of the initially screened parameters, including design limits, normal operating fluctuations, and values ​​under abnormal conditions, fully reflecting all potential variations of the parameters in actual engineering projects. For example, the global range for a certain initially screened parameter can be set to 50~150, covering its minimum to maximum design value. Global sensitivity characterizes the overall impact of changes in the overall value of the initially screened parameter on the EPS failure probability within its global value range. It is not limited to a specific operating point and can capture the influence patterns of the parameter throughout its entire range of variation, as well as the nonlinear interactions between parameters. It is a quantitative indicator of the parameter's importance within the global scope.

[0122] Optionally, for each preliminary screening parameter, based on engineering specifications, design documents, and experimental data, its global value range should be defined to ensure that the range covers all potential values ​​of the parameter, including values ​​under normal operation, abnormal operating conditions, and extreme operating conditions, avoiding omission of key value ranges. The Latin hypercube sampling method can be used to generate [samples] within the global value range of all preliminary screening parameters. In the embodiments of this application, group sampling is used to select samples. Typically, 100 to 500 groups are selected to balance computational accuracy and efficiency. Each group of samples corresponds to a set of values ​​for all preliminary screening parameters, ensuring that the samples are evenly distributed in the global parameter space.

[0123] For each group of samples, a small perturbation is applied to each preliminary screening parameter in turn to obtain a new sample after the parameter perturbation; the original sample and the perturbed sample of each group are respectively input into the GOTHIC model to calculate the corresponding EPS failure probability (or containment peak pressure), and the output results of each group of samples are recorded.

[0124] Based on the model output results before and after the perturbation, the local effect of each preliminary screening parameter in each sample group is calculated. The formula for calculating the local effect is:

[0125]

[0126] in, It is the amount of change in the initial screening parameters input; These are standard basis vectors; It is the first The model output value corresponding to the original sampled group; For the first The model output value after initial parameter perturbation.

[0127] Based on the local effects of all samples, the mean sensitivity and variance of sensitivity for each preliminary screening parameter are calculated using the following formula:

[0128]

[0129]

[0130] in, For the first The average sensitivity of each initial screening parameter; The number of values ​​the parameter can take; For the first The sensitivity variance corresponds to each initial screening parameter. The sensitivity mean reflects the average strength of the global influence of the initial screening parameter; the larger the sensitivity mean, the stronger the global influence of the initial screening parameter. The sensitivity variance reflects the non-linearity of the influence of the initial screening parameter; the larger the sensitivity variance, the stronger the interaction between the initial screening parameter and other initial screening parameters, or the non-linearity of the parameter influence. The sensitivity mean is used as the core quantitative indicator of global sensitivity, and the sensitivity variance is used as an auxiliary indicator.

[0131] Record and archive the global sensitivity, sensitivity variance, and sampling calculation process for each preliminary screening parameter to form a global sensitivity statistics table, which corresponds to the local sensitivity results.

[0132] S303, based on the local and global sensitivity of each preliminary screening parameter, select the target influence parameter from each preliminary screening parameter.

[0133] Optionally, the local sensitivity and global sensitivity can be standardized to eliminate the dimensional differences in the sensitivity of different parameters, ensuring that the two can be directly combined for analysis. In the embodiments of this application, the local sensitivity is used for rough estimation and is only for reference, while the global sensitivity is used to determine the final calculation of the importance ranking of each preliminary screening parameter.

[0134] In this embodiment, local sensitivity can quickly identify parameters that significantly affect the failure probability of EPS under specific working conditions, while global sensitivity analysis covers the entire value range of the parameters, capturing the influence patterns of the parameters under different working conditions and the nonlinear interactions between parameters. By combining local and global sensitivity, accurate parameter screening is achieved, avoiding the screening bias caused by single sensitivity analysis and eliminating redundant parameters with weak impact on the failure probability of EPS. This significantly reduces the parameter dimensions for subsequent importance sampling, lowering the complexity and computational cost of sampling calculations.

[0135] Optionally, in one embodiment, the failure criterion is determined based on a preset accident scenario; if the preset accident scenario includes a Large Break Loss of Coolant Accident (LBLOCA) scenario, the failure criterion includes the criterion that the containment peak pressure exceeds the design pressure. In this embodiment, accident scenarios need to be screened. Based on the results of qualitative and quantitative analysis, the accident scenario should be selected as a typical reactor accident scenario with an envelope of accident consequences and a high frequency of occurrence. While determining the accident scenario, a criterion that can characterize the successful activation of the passive system is selected as the standard for failure. Based on the above criteria, the Large Break Loss of Coolant Accident (LBLOCA) is selected as the preset accident scenario, and based on relevant design parameters, the containment peak pressure exceeding the design pressure by 550 kPa abs is selected as the failure criterion. The LBLOCA accident process is as follows: When LBLOCA occurs, a large amount of mass energy is released from the rupture in a short period of time, causing the containment to heat up and pressurize rapidly. At the same time, due to insufficient early heat carrying capacity, the pressure reaches the first peak in a short period of time. Subsequently, as the breach flow decreases, the heat-carrying capacity of the containment structure and EPS exceeds the heat generation capacity from mass release, causing the containment temperature and pressure to drop. After the temperature difference decreases, the heat-carrying capacity declines briefly, and the containment temperature and pressure rise again, reaching a second peak (generally the maximum value after an LBLOCA event). After reaching the peak, due to factors such as the external temperature difference, the overall heat-carrying capacity of the containment increases, subsequently exceeding the heat generation capacity from mass release and core decay heat, causing the temperature and pressure to decrease until a new dynamic equilibrium is reached. During this period, the in-containment refueling water storage tank (IRWST) collects condensate from the containment walls and injects it into the bottom of the containment for recirculation and long-term cooling.

[0136] Based on the above embodiments, in one embodiment, such as Figure 4 As shown, a method for determining the failure probability of EPS is provided, which specifically includes the following steps:

[0137] S401, for each parameter value corresponding to the target influencing parameter, input the parameter value into the GOTHIC model for thermal-hydraulic calculation to obtain the peak containment pressure corresponding to the parameter value.

[0138] Among them, the peak containment pressure is the maximum pressure inside the containment calculated by the GOTHIC model under a preset accident scenario. It is the core quantitative indicator for judging whether the EPS has failed; its value directly determines whether the EPS can perform its residual heat discharge function normally.

[0139] Optionally, all obtained target influence parameters are categorized by case number, with each group of parameters corresponding to an independent calculation case. The specific values ​​of each target influence parameter and its corresponding weighting factor are clearly defined in each case group, and a parameter value statistics table is compiled. The GOTHIC program is launched, calling the constructed and validated GOTHIC model of the reactor containment to ensure the model can accurately simulate the thermal-hydraulic processes of the preset accident scenario (such as LBLOCA). By coupling the Python program with the GOTHIC program, automated batch input of parameter values ​​is achieved. The Python program reads the parameter value statistics table, automatically modifies the corresponding target influence parameter values ​​in the GOTHIC model input card, and generates GOTHIC input files (.SIN and / or .GIN format) for each calculation case group, avoiding errors caused by manual input and improving computational efficiency.

[0140] The GOTHIC solver is invoked to perform parallel calculations on all cases, simulating the temperature and pressure changes within the containment under a preset accident scenario. Convergence is monitored in real time during the calculation. If a case fails to converge, the parameter perturbation amplitude or model solution parameters for that case are adjusted, and the calculation is recalculated to ensure that all cases yield valid results. After the calculation is complete, the Python program automatically reads the GOTHIC output file (.GOT format) for each case set, extracts the containment pressure variation data over time, identifies and records the peak containment pressure corresponding to each set of parameter values, and archives the peak pressure with the corresponding case's parameter values ​​and case number to form a peak pressure calculation result table.

[0141] S402, based on the failure judgment criteria and the peak containment pressure corresponding to each parameter value, select the failure value corresponding to the target influence parameter from each parameter value.

[0142] Among them, the failure value is the value of the target influencing parameter that corresponds to the peak pressure of the containment that meets the failure judgment criterion (i.e., does not cause EPS failure), and is a valid case; conversely, the parameter value that causes the peak pressure of the containment to exceed the design pressure and EPS to fail is the failure value, and is a failure case.

[0143] Optionally, preset EPS failure criteria can be retrieved to define the decision logic. Based on whether each set of parameter values ​​meets the failure criteria, parameter values ​​that do not meet the failure criteria are taken as failure values.

[0144] For example, the design pressure is determined according to the failure judgment criteria. For each parameter value, if the peak containment pressure corresponding to the parameter value is greater than the preset design pressure, then the parameter value is determined to be a failure value. Specifically, if the peak containment pressure corresponding to a certain set of parameter values ​​is less than or equal to the preset design pressure, then the EPS has not failed, and the parameter value is a valid value; if the peak pressure is greater than the preset design pressure, then the EPS has failed, and the parameter value is a failure value. From all parameter values, the parameter values ​​with the judgment result of "failure" are selected and compiled into a failure value list, specifying the case number, peak pressure, and weight factor corresponding to each failure value; at the same time, a separate valid value list is compiled, recording the relevant information of valid cases.

[0145] S403, determine the failure probability of EPS based on the failure values ​​corresponding to the target impact parameters.

[0146] Optionally, the total number of all calculated cases and the number of failure cases (i.e., the number of failure values) are counted, and the weighting factor corresponding to each failure case is retrieved. The failure probability of EPS is calculated using an importance sampling correction formula.

[0147] In one embodiment, the sampling weighting factor for each failure value is determined based on the original probability density function and importance sampling distribution corresponding to each failure value; the failure probability of the EPS is determined based on each failure value and its weighting factor. The sampling weighting factor is the core correction coefficient of the importance sampling method, used to offset statistical biases caused by manual offset sampling distributions. The failure value sample refers to all target parameter samples obtained by sampling under the importance sampling distribution and, after being substituted into the GOTHIC model for calculation, where the containment peak pressure exceeds the 550 kPa abs design threshold and is determined to be an EPS system failure.

[0148] Optionally, for each valid parameter failure value sample, the true original probability density value and importance sampling probability density value of the corresponding target parameter are retrieved, and a unique corresponding sampling weight factor is calculated using the ratio method. After calculating the weight factors for all failure samples, the weighted probability contribution of all failure samples is accumulated based on the unbiased estimation formula for importance sampling, and combined with the total number of samples, the overall failure probability of the EPS system is solved.

[0149] In this embodiment, by accurately obtaining the original probability density of the target impact parameters, quantifying the critical values ​​of the parameters corresponding to the EPS failure boundary, accurately dividing the parameter failure domain interval, and specifically correcting the offset of the original distribution, a dedicated importance sampling distribution adapted to the calculation of the failure probability of passive systems in reactor LBLOCA accidents is constructed.

[0150] For example, suppose the failure area is The system's input variables are The probability density function of the input variable is The important sampling probability density function is selected and introduced artificially. Also known as the proposal distribution, this function increases the number of sampling points in the failure region, making it easier to sample failure points. Simultaneously, let... The function is Failure determination criteria are If the function This indicates the containment design pressure; generally, a containment pressure exceeding the design pressure is considered a failure. The indication function is... The number of sampling points is The failure probability of importance sampling can be expressed as:

[0151]

[0152] Among them, if , ,otherwise .in, , … obey They are distributed independently of each other. Let represent the expected value of the variable expressed as the importance sampling probability density function. The resulting probability estimate is:

[0153]

[0154] Its variance estimate is:

[0155]

[0156]

[0157] In this embodiment, based on clear failure judgment criteria, the parameter values ​​are accurately distinguished between valid and invalid values. The judgment logic is clear and the standards are unified, ensuring the accuracy of failure case statistics and providing reliable basic data for subsequent failure probability calculation. Combined with the weight factor correction of importance sampling, the true failure probability under the original distribution of target influence parameters is effectively restored. This overcomes the problems of poor calculation accuracy and large variance caused by the extremely low proportion of failure samples in traditional sampling methods. Under the premise of a small number of sampling cases, high-precision calculation of extremely low probability failure events is achieved, which greatly reduces the calculation cost.

[0158] Optionally, in one embodiment, such as Figure 5 As shown, a method for constructing a GOTHIC model of a reactor containment structure is provided, which specifically includes the following steps:

[0159] S501, obtain the structural information of the reactor containment structure in the EPS.

[0160] Optionally, the scope of structural information to be collected can be determined based on the requirements of the GOTHIC model's thermal-hydraulic simulation. This scope should focus on the containment's main geometric parameters, internal structural parameters, flow channel layout parameters, and EPS heat exchanger arrangement parameters. Structural information should be comprehensively collected by reviewing reactor containment design drawings, engineering design specifications, equipment manuals, and other technical documents. For some key parameters, verification should be performed using on-site measured data to ensure accuracy. If any parameters are missing, they should be supplemented appropriately based on design experience with similar reactor containments and relevant experimental data to ensure completeness.

[0161] S502, Based on the structural information, construct the basic geometric model of the reactor containment vessel.

[0162] The basic geometric model is a model built in the GOTHIC program based on the containment structure information. It only contains the containment geometry and does not include boundary conditions, initial conditions, or other parameter configurations. It forms the basic framework of the complete GOTHIC model.

[0163] Optionally, open the GOTHIC thermal hydraulic calculation software, create a new model project, and specify the model calculation scenario (preset accident scenario, such as a large breach loss-of-water accident LBLOCA). Set the calculation units for the model (such as pressure unit kPa, length unit m) to ensure consistency with the units in the structural information. Based on the containment body parameters in the structural information, draw the containment body structure in the geometric modeling module of the GOTHIC program, including the dome, shell, and bottom structure. Accurately input parameters such as inner diameter, height, and wall thickness to ensure that the geometric dimensions of the main body are consistent with the actual containment body. According to the structural information, build the internal components of the containment body (annular cavity, sump, diaphragm, and support components) in sequence, inputting the dimensions and position parameters of each component to ensure that the component layout is consistent with the actual layout. At the same time, build the flow channel structure. Based on the flow channel layout parameters, draw four flow channels from the bottom of the containment body to the bottom to simulate reflooding, and four three-dimensional flow channels from the bottom of the containment body to the dome to simulate natural circulation. Specify the cross-sectional dimensions and direction of the flow channels to ensure that the flow characteristics match the actual flow.

[0164] Based on the EPS heat exchanger layout parameters, a geometric model of the heat exchanger was built in the GOTHIC model. Twelve sets of coolers at two different heights were arranged according to the actual installation height and quantity. Key parameters such as the heat exchange area and pipe diameter of the heat exchangers were input to ensure that the geometric characteristics of the heat exchangers were consistent with the actual equipment. After the model was built, a 3D visualization check was performed on the basic geometric model to verify that the dimensions and positions of each structure, component, flow channel, and heat exchanger were consistent with the structural information. The flow channels were checked for unobstructed flow and whether there were any overlapping components, ensuring that the geometric model was free of deviations and omissions and could accurately reproduce the spatial structure of the actual reactor containment vessel.

[0165] S503 configures the parameters of the basic geometric model to obtain the GOTHIC model of the reactor containment.

[0166] Optionally, based on a preset accident scenario (such as LBLOCA), three types of core boundary conditions can be configured: first, the primary loop breach mass energy release boundary, simulating parameters such as leakage rate, temperature, and pressure of the primary loop working fluid during an accident; second, the containment refueling water storage tank (IRWST) injection boundary, simulating parameters such as flow rate and temperature of emergency makeup water after an accident; and third, the decay heat release boundary, simulating the change curve of core decay heat over time using heaters to ensure that the boundary conditions closely match the actual accident scenario. The initial state of the containment before the accident is set, inputting the initial temperature, pressure, and humidity of the containment atmosphere, as well as the initial temperature of the thermal components inside the containment, to closely match the initial state at the end of normal reactor operation, ensuring the realism of the simulation.

[0167] Input the material properties of the containment medium and components, including the specific heat capacity, thermal conductivity, and density of the containment atmosphere, as well as the specific heat capacity, thermal conductivity, and density of concrete and steel, to ensure the accuracy of heat and mass transfer calculations. Set the solution method, flow and heat transfer model, convergence criteria, and calculation time step to ensure stable calculation process and accurate results; simultaneously set the output parameters, specifying the required thermal and hydraulic parameters to be output.

[0168] After the parameters are configured, the GOTHIC model is run for trial calculation. The results of the trial calculation are compared with the experimental and design data of similar reactor containment structures. The model parameters are adjusted to ensure that the deviation between the model calculation results and the actual data is within the allowable range. After the verification is successful, the GOTHIC reactor containment model that can be used for subsequent EPS failure probability calculation is obtained, and the model file and parameter configuration records are archived.

[0169] In this embodiment, a basic geometric model is built based on real structural information, and through scientific parameter configuration, the final GOTHIC model can accurately simulate complex thermo-hydraulic processes such as flow, heat transfer, and mass transfer within the containment under preset accident scenarios. It can stably output core indicators such as the peak containment pressure, perfectly adapting to the needs of subsequent EPS failure probability calculation, and can be put into use directly without additional modifications.

[0170] Figure 6 This is a flowchart illustrating a failure probability determination method in another embodiment. Based on the above embodiments, this embodiment provides an optional example of a failure probability determination method. (Combined with...) Figure 6 The specific implementation process is as follows:

[0171] S601. Based on the structural information of the reactor containment in the passive containment cooling system EPS, a GOTHIC model of the reactor containment is constructed.

[0172] Optionally, obtain the structural information of the reactor containment vessel in the EPS; build a basic geometric model of the reactor containment vessel based on the structural information; configure the parameters of the basic geometric model to obtain the GOTHIC model of the reactor containment vessel.

[0173] S602, based on the importance level and knowledge level of each candidate impact parameter, select preliminary screening parameters from each candidate impact parameter.

[0174] Among them, the importance level of the preliminary screening parameters is higher than that of the other candidate impact parameters, and the knowledge level of the preliminary screening parameters is lower than that of the other candidate impact parameters.

[0175] S603, determine whether the number of selected preliminary screening parameters is greater than the preset threshold; if yes, execute S604; if no, execute S607.

[0176] S604, for each preliminary screening parameter, determine the local sensitivity corresponding to the preliminary screening parameter based on the degree of influence of the value change of the preliminary screening parameter in the local value range on the failure probability of EPS.

[0177] S605, determine the global sensitivity corresponding to the preliminary screening parameters based on the degree of influence of the changes in the values ​​of the preliminary screening parameters within the global value range on the failure probability of EPS.

[0178] S606, based on the local and global sensitivity of each preliminary screening parameter, select the target influencing parameter from each preliminary screening parameter, and execute S608.

[0179] S607, use the selected preliminary screening parameters as the target influence parameters, and execute S608.

[0180] S608, based on the importance sampling distribution, samples the target influence parameters to obtain at least two parameter values ​​corresponding to the target influence parameters.

[0181] The importance sampling distribution is determined based on the original probability density function of the target influence parameters and the failure boundary characteristics of EPS.

[0182] S609. Determine the failure probability of EPS based on the GOTHIC model, the failure criterion of EPS, and the values ​​of at least two parameters corresponding to the target influence parameter.

[0183] The specific processes of S601-S609 described above can be found in the description of the above method embodiments. Their implementation principles and technical effects are similar, and will not be repeated here.

[0184] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0185] Based on the same inventive concept, this application also provides a failure probability determination apparatus for implementing the failure probability determination method described above. The solution provided by this apparatus is similar to the implementation scheme described in the above method; therefore, the specific limitations in one or more failure probability determination apparatus embodiments provided below can be found in the limitations of the failure probability determination method described above, and will not be repeated here.

[0186] In one exemplary embodiment, such as Figure 7 As shown, a failure probability determination device 700 is provided, including: a model construction module 710, a parameter determination module 720, a value determination module 730, and a probability determination module 740, wherein:

[0187] Model building module 710 is used to build a GOTHIC model of the reactor containment based on the structural information of the reactor containment in the passive containment cooling system EPS.

[0188] The parameter determination module 720 is used to select the target impact parameter from the candidate impact parameters according to the importance level and knowledge level of each candidate impact parameter; wherein, each candidate impact parameter is a parameter in the GOTHIC model that is related to the failure probability of EPS;

[0189] The value determination module 730 is used to sample the target influence parameter based on the importance sampling distribution to obtain at least two parameter values ​​corresponding to the target influence parameter; wherein, the importance sampling distribution is determined based on the original probability density function of the target influence parameter and the failure boundary characteristics of EPS;

[0190] The probability determination module 740 is used to determine the failure probability of EPS based on the GOTHIC model, the failure judgment criteria of EPS, and the values ​​of at least two parameters corresponding to the target influence parameters.

[0191] In one embodiment, the parameter determination module 720 includes:

[0192] The preliminary determination unit is used to select preliminary screening parameters from the candidate impact parameters; wherein, the importance level of the preliminary screening parameters is higher than that of the other candidate impact parameters, and the knowledge level of the preliminary screening parameters is lower than that of the other candidate impact parameters.

[0193] The first determining unit is used to perform sensitivity analysis on each preliminary screening parameter to obtain the target influence parameter if the number of selected preliminary screening parameters is greater than a preset threshold.

[0194] The second determining unit is used to take the selected preliminary screening parameters as target influence parameters if the number of selected preliminary screening parameters is less than or equal to a preset threshold.

[0195] In one embodiment, the first determining unit is specifically used for:

[0196] For each preliminary screening parameter, the local sensitivity of the preliminary screening parameter is determined based on the degree of influence of the value change of the preliminary screening parameter within the local value range on the failure probability of EPS; and the global sensitivity of the preliminary screening parameter is determined based on the degree of influence of the value change of the preliminary screening parameter within the global value range on the failure probability of EPS; and the target influencing parameter is selected from each preliminary screening parameter based on the local sensitivity and global sensitivity of each preliminary screening parameter.

[0197] In one embodiment, the failure determination criteria are determined based on a preset accident scenario;

[0198] In the case of a pre-set accident scenario including the Large Breach Loss of Water (LBLOCA) scenario, the failure criterion includes the criterion that the peak containment pressure exceeds the design pressure.

[0199] In one embodiment, the probability determination module 740 includes:

[0200] The pressure determination unit is used to input the parameter values ​​corresponding to each target influencing parameter into the GOTHIC model for thermo-hydraulic calculations to obtain the peak containment pressure corresponding to the parameter values.

[0201] The value selection unit is used to select the failure value corresponding to the target influencing parameter from the parameter values ​​based on the failure judgment criteria and the peak containment pressure corresponding to each parameter value.

[0202] The probability determination unit is used to determine the failure probability of EPS based on the failure values ​​corresponding to the target influence parameters.

[0203] In one embodiment, the value selection unit is specifically used for:

[0204] The design pressure is determined according to the failure criteria. For each parameter value, if the peak containment pressure corresponding to the parameter value is greater than the preset design pressure, then the parameter value is determined to be the failure value.

[0205] In one embodiment, the model building module 710 is specifically used for:

[0206] Obtain the structural information of the reactor containment structure in the EPS; build the basic geometric model of the reactor containment structure based on the structural information; configure the parameters of the basic geometric model to obtain the GOTHIC model of the reactor containment structure.

[0207] Each module in the aforementioned failure probability determination device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the operations corresponding to each module.

[0208] In one exemplary embodiment, a computer device is provided, which may be a server, and its internal structure diagram may be as follows: Figure 8 As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and databases. The internal memory provides the environment for the operating system and computer programs stored in the non-volatile storage media to run. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communicating with external terminals via a network connection. When the computer program is executed by the processor, it implements a failure probability determination method.

[0209] Those skilled in the art will understand that Figure 8 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0210] In one exemplary embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps:

[0211] Based on the structural information of the reactor containment in the passive containment cooling system EPS, a GOTHIC model of the reactor containment is constructed.

[0212] Based on the importance level and knowledge level of each candidate impact parameter, the target impact parameter is selected from the candidate impact parameters; where each candidate impact parameter is a parameter in the GOTHIC model that is related to the failure probability of EPS.

[0213] Based on the importance sampling distribution, the target influence parameters are sampled to obtain at least two parameter values ​​corresponding to the target influence parameters; wherein, the importance sampling distribution is determined based on the original probability density function of the target influence parameters and the failure boundary characteristics of EPS;

[0214] The failure probability of EPS is determined based on the GOTHIC model, the failure criterion of EPS, and the values ​​of at least two parameters corresponding to the target impact parameter.

[0215] In one embodiment, when the processor executes a computer program to select a target impact parameter from among the candidate impact parameters based on the importance level and knowledge level of each candidate impact parameter, it also performs the following steps:

[0216] From the candidate impact parameters, preliminary screening parameters are selected. The importance level of the preliminary screening parameters is higher than that of the other candidate impact parameters, and the knowledge level of the preliminary screening parameters is lower than that of the other candidate impact parameters. If the number of selected preliminary screening parameters is greater than a preset threshold, sensitivity analysis is performed on each preliminary screening parameter to obtain the target impact parameter. If the number of selected preliminary screening parameters is less than or equal to the preset threshold, the selected preliminary screening parameters are used as the target impact parameters.

[0217] In one embodiment, when the processor executes a computer program to perform sensitivity analysis on each preliminary screening parameter and obtains the target influence parameters, it also performs the following steps:

[0218] For each preliminary screening parameter, the local sensitivity of the preliminary screening parameter is determined based on the degree of influence of the value change of the preliminary screening parameter within the local value range on the failure probability of EPS; and the global sensitivity of the preliminary screening parameter is determined based on the degree of influence of the value change of the preliminary screening parameter within the global value range on the failure probability of EPS; and the target influencing parameter is selected from each preliminary screening parameter based on the local sensitivity and global sensitivity of each preliminary screening parameter.

[0219] In one embodiment, the failure determination criterion is determined based on a preset accident scenario; in the case where the preset accident scenario includes the Large Breach Loss of Water (LBLOCA) scenario, the failure determination criterion includes the criterion that the peak containment pressure exceeds the design pressure.

[0220] In one embodiment, when the processor executes a computer program to determine the failure probability of the EPS based on the GOTHIC model, the failure determination criteria of the EPS, and the values ​​of at least two parameters corresponding to the target impact parameter, it also performs the following steps:

[0221] For each parameter value corresponding to the target influence parameter, the parameter value is input into the GOTHIC model for thermo-hydraulic calculation to obtain the peak containment pressure corresponding to the parameter value; based on the failure judgment criteria and the peak containment pressure corresponding to each parameter value, the failure value corresponding to the target influence parameter is selected from each parameter value; based on the failure value corresponding to the target influence parameter, the failure probability of EPS is determined.

[0222] In one embodiment, when the processor executes a computer program to select the failure value corresponding to the target influencing parameter from the parameter values ​​based on the failure determination criteria and the peak containment pressure corresponding to each parameter value, it also performs the following steps:

[0223] The design pressure is determined according to the failure criteria. For each parameter value, if the peak containment pressure corresponding to the parameter value is greater than the preset design pressure, then the parameter value is determined to be the failure value.

[0224] In one embodiment, when the processor executes a computer program to construct a GOTHIC model of the reactor containment based on the structural information of the reactor containment in the passive containment cooling system EPS, the following steps are also performed:

[0225] Obtain the structural information of the reactor containment structure in the EPS; build the basic geometric model of the reactor containment structure based on the structural information; configure the parameters of the basic geometric model to obtain the GOTHIC model of the reactor containment structure.

[0226] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0227] Based on the structural information of the reactor containment in the passive containment cooling system EPS, a GOTHIC model of the reactor containment is constructed.

[0228] Based on the importance level and knowledge level of each candidate impact parameter, the target impact parameter is selected from the candidate impact parameters; where each candidate impact parameter is a parameter in the GOTHIC model that is related to the failure probability of EPS.

[0229] Based on the importance sampling distribution, the target influence parameters are sampled to obtain at least two parameter values ​​corresponding to the target influence parameters; wherein, the importance sampling distribution is determined based on the original probability density function of the target influence parameters and the failure boundary characteristics of EPS;

[0230] The failure probability of EPS is determined based on the GOTHIC model, the failure criterion of EPS, and the values ​​of at least two parameters corresponding to the target impact parameter.

[0231] In one embodiment, when the processor executes a computer program to select a target impact parameter from among the candidate impact parameters based on the importance level and knowledge level of each candidate impact parameter, it also performs the following steps:

[0232] From the candidate impact parameters, preliminary screening parameters are selected. The importance level of the preliminary screening parameters is higher than that of the other candidate impact parameters, and the knowledge level of the preliminary screening parameters is lower than that of the other candidate impact parameters. If the number of selected preliminary screening parameters is greater than a preset threshold, sensitivity analysis is performed on each preliminary screening parameter to obtain the target impact parameter. If the number of selected preliminary screening parameters is less than or equal to the preset threshold, the selected preliminary screening parameters are used as the target impact parameters.

[0233] In one embodiment, when the processor executes a computer program to perform sensitivity analysis on each preliminary screening parameter and obtains the target influence parameters, it also performs the following steps:

[0234] For each preliminary screening parameter, the local sensitivity of the preliminary screening parameter is determined based on the degree of influence of the value change of the preliminary screening parameter within the local value range on the failure probability of EPS; and the global sensitivity of the preliminary screening parameter is determined based on the degree of influence of the value change of the preliminary screening parameter within the global value range on the failure probability of EPS; and the target influencing parameter is selected from each preliminary screening parameter based on the local sensitivity and global sensitivity of each preliminary screening parameter.

[0235] In one embodiment, the failure determination criterion is determined based on a preset accident scenario; in the case where the preset accident scenario includes the Large Breach Loss of Water (LBLOCA) scenario, the failure determination criterion includes the criterion that the peak containment pressure exceeds the design pressure.

[0236] In one embodiment, when the processor executes a computer program to determine the failure probability of the EPS based on the GOTHIC model, the failure determination criteria of the EPS, and the values ​​of at least two parameters corresponding to the target impact parameter, it also performs the following steps:

[0237] For each parameter value corresponding to the target influence parameter, the parameter value is input into the GOTHIC model for thermo-hydraulic calculation to obtain the peak containment pressure corresponding to the parameter value; based on the failure judgment criteria and the peak containment pressure corresponding to each parameter value, the failure value corresponding to the target influence parameter is selected from each parameter value; based on the failure value corresponding to the target influence parameter, the failure probability of EPS is determined.

[0238] In one embodiment, when the processor executes a computer program to select the failure value corresponding to the target influencing parameter from the parameter values ​​based on the failure determination criteria and the peak containment pressure corresponding to each parameter value, it also performs the following steps:

[0239] The design pressure is determined according to the failure criteria. For each parameter value, if the peak containment pressure corresponding to the parameter value is greater than the preset design pressure, then the parameter value is determined to be the failure value.

[0240] In one embodiment, when the processor executes a computer program to construct a GOTHIC model of the reactor containment based on the structural information of the reactor containment in the passive containment cooling system EPS, the following steps are also performed:

[0241] Obtain the structural information of the reactor containment structure in the EPS; build the basic geometric model of the reactor containment structure based on the structural information; configure the parameters of the basic geometric model to obtain the GOTHIC model of the reactor containment structure.

[0242] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, performs the following steps:

[0243] Based on the structural information of the reactor containment in the passive containment cooling system EPS, a GOTHIC model of the reactor containment is constructed.

[0244] Based on the importance level and knowledge level of each candidate impact parameter, the target impact parameter is selected from the candidate impact parameters; where each candidate impact parameter is a parameter in the GOTHIC model that is related to the failure probability of EPS.

[0245] Based on the importance sampling distribution, the target influence parameters are sampled to obtain at least two parameter values ​​corresponding to the target influence parameters; wherein, the importance sampling distribution is determined based on the original probability density function of the target influence parameters and the failure boundary characteristics of EPS;

[0246] The failure probability of EPS is determined based on the GOTHIC model, the failure criterion of EPS, and the values ​​of at least two parameters corresponding to the target impact parameter.

[0247] In one embodiment, when the processor executes a computer program to select a target impact parameter from among the candidate impact parameters based on the importance level and knowledge level of each candidate impact parameter, it also performs the following steps:

[0248] From the candidate impact parameters, preliminary screening parameters are selected. The importance level of the preliminary screening parameters is higher than that of the other candidate impact parameters, and the knowledge level of the preliminary screening parameters is lower than that of the other candidate impact parameters. If the number of selected preliminary screening parameters is greater than a preset threshold, sensitivity analysis is performed on each preliminary screening parameter to obtain the target impact parameter. If the number of selected preliminary screening parameters is less than or equal to the preset threshold, the selected preliminary screening parameters are used as the target impact parameters.

[0249] In one embodiment, when the processor executes a computer program to perform sensitivity analysis on each preliminary screening parameter and obtains the target influence parameters, it also performs the following steps:

[0250] For each preliminary screening parameter, the local sensitivity of the preliminary screening parameter is determined based on the degree of influence of the value change of the preliminary screening parameter within the local value range on the failure probability of EPS; and the global sensitivity of the preliminary screening parameter is determined based on the degree of influence of the value change of the preliminary screening parameter within the global value range on the failure probability of EPS; and the target influencing parameter is selected from each preliminary screening parameter based on the local sensitivity and global sensitivity of each preliminary screening parameter.

[0251] In one embodiment, the failure determination criterion is determined based on a preset accident scenario; in the case where the preset accident scenario includes the Large Breach Loss of Water (LBLOCA) scenario, the failure determination criterion includes the criterion that the peak containment pressure exceeds the design pressure.

[0252] In one embodiment, when the processor executes a computer program to determine the failure probability of the EPS based on the GOTHIC model, the failure determination criteria of the EPS, and the values ​​of at least two parameters corresponding to the target impact parameter, it also performs the following steps:

[0253] For each parameter value corresponding to the target influence parameter, the parameter value is input into the GOTHIC model for thermo-hydraulic calculation to obtain the peak containment pressure corresponding to the parameter value; based on the failure judgment criteria and the peak containment pressure corresponding to each parameter value, the failure value corresponding to the target influence parameter is selected from each parameter value; based on the failure value corresponding to the target influence parameter, the failure probability of EPS is determined.

[0254] In one embodiment, when the processor executes a computer program to select the failure value corresponding to the target influencing parameter from the parameter values ​​based on the failure determination criteria and the peak containment pressure corresponding to each parameter value, it also performs the following steps:

[0255] The design pressure is determined according to the failure criteria. For each parameter value, if the peak containment pressure corresponding to the parameter value is greater than the preset design pressure, then the parameter value is determined to be the failure value.

[0256] In one embodiment, when the processor executes a computer program to construct a GOTHIC model of the reactor containment based on the structural information of the reactor containment in the passive containment cooling system EPS, the following steps are also performed:

[0257] Obtain the structural information of the reactor containment structure in the EPS; build the basic geometric model of the reactor containment structure based on the structural information; configure the parameters of the basic geometric model to obtain the GOTHIC model of the reactor containment structure.

[0258] It should be noted that the data involved in this application (including but not limited to data used for analysis, data stored, data displayed, etc.) are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0259] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0260] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0261] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for determining failure probability, characterized in that, The method includes: Based on the structural information of the reactor containment in the passive containment cooling system EPS, a GOTHIC model of the reactor containment is constructed. Based on the importance level and knowledge level of each candidate impact parameter, a target impact parameter is selected from the candidate impact parameters; wherein, each candidate impact parameter is a parameter in the GOTHIC model related to the failure probability of EPS; Based on the importance sampling distribution, the target impact parameter is sampled to obtain at least two parameter values ​​corresponding to the target impact parameter; wherein, the importance sampling distribution is determined based on the original probability density function of the target impact parameter and the failure boundary characteristics of EPS; The failure probability of the EPS is determined based on the GOTHIC model, the failure criterion of the EPS, and the values ​​of at least two parameters corresponding to the target influence parameter.

2. The method according to claim 1, characterized in that, The selection of the target impact parameter from among the candidate impact parameters based on their importance level and knowledge level includes: From the candidate impact parameters, preliminary screening parameters are selected; wherein, the importance level of the preliminary screening parameters is higher than that of the other candidate impact parameters, and the knowledge level of the preliminary screening parameters is lower than that of the other candidate impact parameters. If the number of selected preliminary screening parameters is greater than the preset threshold, a sensitivity analysis is performed on each preliminary screening parameter to obtain the target influencing parameters; If the number of selected preliminary screening parameters is less than or equal to the preset threshold, then the selected preliminary screening parameters will be used as the target influence parameters.

3. The method according to claim 2, characterized in that, The sensitivity analysis of each preliminary screening parameter yields the target influence parameters, including: For each preliminary screening parameter, the local sensitivity corresponding to the preliminary screening parameter is determined based on the degree of influence of the value change of the preliminary screening parameter within its local value range on the failure probability of the EPS; and, The global sensitivity corresponding to the preliminary screening parameters is determined based on the degree of influence of the changes in the values ​​of the preliminary screening parameters within the global value range on the failure probability of the EPS. Based on the local and global sensitivity of each preliminary screening parameter, target influencing parameters are selected from the preliminary screening parameters.

4. The method according to any one of claims 1-3, characterized in that, The failure determination criteria are determined based on preset accident scenarios; When the preset accident scenario includes the Large Breach Loss of Water (LBLOCA) scenario, the failure determination criterion includes the criterion that the containment peak pressure exceeds the design pressure.

5. The method according to claim 4, characterized in that, The step of determining the failure probability of the EPS based on the GOTHIC model, the failure criterion of the EPS, and the values ​​of at least two parameters corresponding to the target impact parameter includes: For each parameter value corresponding to the target influence parameter, the parameter value is input into the GOTHIC model for thermo-hydraulic calculation to obtain the peak containment pressure corresponding to the parameter value; Based on the failure determination criteria and the peak containment pressure corresponding to each parameter value, the failure value corresponding to the target influence parameter is selected from each parameter value; The failure probability of the EPS is determined based on the failure value corresponding to the target impact parameter.

6. The method according to claim 5, characterized in that, The step of selecting the failure value corresponding to the target influence parameter from the parameter values ​​based on the failure determination criteria and the peak containment pressure corresponding to each parameter value includes: Determine the design pressure based on the aforementioned failure criteria; For each parameter value, if the peak containment pressure corresponding to the parameter value is greater than the preset design pressure, then the parameter value is determined to be a failure value.

7. The method according to any one of claims 1-3, characterized in that, The step of constructing a GOTHIC model of the reactor containment based on the structural information of the reactor containment in the passive containment cooling system EPS includes: Obtain structural information of the reactor containment structure in the EPS; Based on the structural information, construct the basic geometric model of the reactor containment vessel; The parameters of the basic geometric model are configured to obtain the GOTHIC model of the reactor containment.

8. The method according to claim 1, characterized in that, The importance sampling distribution is constructed in the following way: Obtain the original probability density function of the target influence parameters; The failure domain interval is determined based on the critical values ​​of the parameters corresponding to the EPS failure boundary. The original probability density function is offset and corrected based on the failure domain interval to obtain the importance sampling distribution.

9. The method according to claim 5, characterized in that, The number of failure values ​​is at least two. Determining the failure probability of the EPS based on the failure values ​​corresponding to the target influence parameter includes: Based on the original probability density function and importance sampling distribution corresponding to each failure value, determine the sampling weight factor for each failure value; The failure probability of EPS is determined based on each failure value and its weighting factor.

10. A failure probability determination device, characterized in that, The device includes: The model building module is used to build a GOTHIC model of the reactor containment based on the structural information of the reactor containment in the passive containment cooling system EPS. The parameter determination module is used to select the target impact parameter from the candidate impact parameters according to the importance level and knowledge level of each candidate impact parameter; wherein, each candidate impact parameter is a parameter related to the failure probability of EPS in the GOTHIC model; The value determination module is used to sample the target influence parameter based on the importance sampling distribution to obtain at least two parameter values ​​corresponding to the target influence parameter; wherein, the importance sampling distribution is determined based on the original probability density function of the target influence parameter and the failure boundary characteristics of EPS; The probability determination module is used to determine the failure probability of the EPS based on the GOTHIC model, the failure judgment criterion of the EPS, and the values ​​of at least two parameters corresponding to the target influence parameter.

11. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 9.

12. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 9.

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