Dynamic reliability analysis methods, systems, equipment and media for reactor protection systems

Abstract

This invention discloses a method, system, equipment, and medium for dynamic reliability analysis of reactor protection systems, relating to the field of nuclear energy engineering. The method includes: obtaining a dynamic fault tree based on the fault sources and results of the reactor protection system; constructing a fuzzy dynamic Bayesian model of the reactor protection system based on the dynamic fault tree; obtaining the conditional probability table and state transition matrix of the fuzzy dynamic Bayesian model based on Markov chains, and determining the prior probabilities of the fuzzy dynamic Bayesian model using D-S evidence theory, thus obtaining a fuzzy dynamic Bayesian model with determined parameters; and applying the Latin hypercube sampling rule to perform fuzzy Bayesian forward inference on the fuzzy dynamic Bayesian model with determined parameters to obtain the reliability-time relationship curve of the reactor protection system. This invention can dynamically reflect the reliability of reactor protection systems.

Description

Technical Field

[0001] This invention relates to the field of nuclear energy engineering, and in particular to a method, system, equipment and medium for dynamic reliability analysis of reactor protection systems. Background Technology

[0002] The Hualong One is currently the world's most advanced third-generation nuclear reactor. The world's first Hualong One has been put into operation at the Fuqing Nuclear Power Plant. The Reactor Protection System (RPS) is a crucial safety-related system in the Hualong One. Its main function is to ensure timely and reliable protective actions from the reactor shutdown system in the event of an accident, keeping the reactor under control. Because the digital instrumentation and control system is installed within the RPS, it contains a large number of components. The hardware components include sensors, relay cabinets, and power supplies, while the software includes communication, signal logic voting, and processors. This results in a complex system structure and dynamic characteristics. Therefore, conducting dynamic reliability analysis of the Hualong One RPS is of great significance. Summary of the Invention

[0003] The purpose of this invention is to provide a method, system, equipment, and medium for dynamic reliability analysis of reactor protection systems, which can dynamically reflect the reliability of reactor protection systems.

[0004] To achieve the above objectives, the present invention provides the following solution:

[0005] A method for dynamic reliability analysis of a reactor protection system, the method comprising:

[0006] A dynamic fault tree is obtained based on the sources and results of faults in the reactor protection system;

[0007] Based on the dynamic fault tree, a fuzzy dynamic Bayesian model of the reactor protection system is constructed.

[0008] The conditional probability table and state transition matrix of the fuzzy dynamic Bayesian model are obtained based on the Markov chain, and the prior probability of the fuzzy dynamic Bayesian model is determined by applying the DS evidence theory, thus obtaining the fuzzy dynamic Bayesian model with determined parameters.

[0009] By applying the Latin hypercube sampling rule, fuzzy Bayesian forward inference is performed on the fuzzy dynamic Bayesian model with determined parameters to obtain the reliability-time relationship curve of the reactor protection system.

[0010] Optionally, obtaining a dynamic fault tree based on the fault sources and fault outcomes of the reactor protection system specifically includes:

[0011] The top event of the reactor protection system is determined based on the source and result of the fault in the reactor protection system.

[0012] Based on the fault sources and fault results of the reactor protection system, the intermediate events and basic events of the reactor protection system are determined by applying the potential failure mode and effects analysis method.

[0013] Static and dynamic logic gates are used to connect the logical relationships between the top event, the intermediate event, and the basic event to obtain the logic gate connection relationship;

[0014] A dynamic fault tree for the reactor protection system is established based on the top event, the intermediate events, the basic events, and the logic gate connections.

[0015] Optionally, constructing a fuzzy dynamic Bayesian model of the reactor protection system based on the dynamic fault tree specifically includes:

[0016] A transformation strategy is applied to convert the basic events, intermediate events, and top events of the dynamic fault tree into nodes, and to convert the logic gate connection relationships into conditions of non-root nodes; the nodes include root nodes, intermediate nodes, and leaf nodes;

[0017] Based on the nodes and conditions, a fuzzy dynamic Bayesian model is established.

[0018] Optionally, the conditional probability table and state transition matrix of the fuzzy dynamic Bayesian model are obtained based on the Markov chain, and the prior probabilities of the fuzzy dynamic Bayesian model are determined by applying DS evidence theory, resulting in a fuzzy dynamic Bayesian model with determined parameters, specifically including:

[0019] Based on expert knowledge, the failure rate of the node is determined, and the node failure rate is obtained.

[0020] Based on the expected value and standard deviation of the node failure rate, the judgment information based on the interval type II fuzzy set is determined;

[0021] Based on the judgment information, establish a judgment matrix for the node failure rate based on interval type II fuzzy sets;

[0022] An evidence matrix is ​​established by assigning basic probability values ​​to the judgment information in the judgment matrix;

[0023] The evidence matrix is ​​fused using the DS evidence theory to determine the prior probability of the root node;

[0024] Based on Markov chains, the logic gate connection relationships in the dynamic fault tree are converted into a conditional probability table of non-root nodes.

[0025] Based on Markov chains and in accordance with the international standards for reactor protection systems, the state transition matrix of the root node based on interval type II fuzzy sets is determined.

[0026] Based on the conditional probability table, the state transition matrix, and the prior probabilities, a fuzzy dynamic Bayesian model with determined parameters is obtained.

[0027] Optionally, the algorithm for fusing the evidence matrix using DS evidence theory is as follows:

[0028]

[0029]

[0030]

[0031]

[0032] in, The result of the fusion of membership functions; m L* (x i ) represents the fusion result of the membership function; n is the number of indicators; e is the number of experts; K L K represents the conflict coefficient of the membership function. U The conflict coefficient of the membership function; Let be the membership function of the z-th expert evidence; Let L be the upper membership function of the z-th expert evidence; L and U are the lower and upper bounds, respectively.

[0033] Optionally, the application of the Latin hypercube sampling rule to perform fuzzy Bayesian forward inference on the fuzzy dynamic Bayesian model with determined parameters to obtain the reliability-time relationship curve of the reactor protection system specifically includes:

[0034] The Latin hypercube sampling rule is applied to determine the prior probability sample;

[0035] Based on the prior probability samples, apply the formula Calculate the probability of leaf node T occurring in the k-th prior probability sample; where P k (X i P is a prior probability sample; k (T|X i P represents the conditional probability. k (T) represents the probability of leaf node T occurring; P k (X i |T) represents node X i The posterior probability;

[0036] According to the formula ΔPk (X i )=|P k (X i |T)-P k (X i )|, calculate the posterior probability of the root node of the k-th prior probability sample; where P k (T) represents the probability of leaf node T occurring; P k (X i |T) represents node X i The posterior probability; ΔP k (X i ) is node X i The rate of change of probability;

[0037] The reliability of the root node of the k-th prior probability sample is determined based on the posterior probability of the root node of the k-th prior probability sample.

[0038] The reliability of all the prior probability samples is determined based on the reliability of the root node of the k-th prior probability sample.

[0039] Based on the reliability of all the prior probability samples, the reliability-time relationship curve of the reactor protection system is obtained.

[0040] Optionally, the method further includes:

[0041] By applying the Latin hypercube sampling rule, fuzzy Bayesian inverse reasoning is performed on the fuzzy dynamic Bayesian model with determined parameters to obtain the key components affecting the reliability of the reactor protection system.

[0042] A dynamic reliability analysis system for reactor protection systems, applied to the aforementioned dynamic reliability analysis method for reactor protection systems, the system comprising:

[0043] The dynamic fault tree building module is used to generate a dynamic fault tree based on the fault sources and fault results of the reactor protection system.

[0044] The fuzzy dynamic Bayesian model building module is used to construct a fuzzy dynamic Bayesian model of the reactor protection system based on the dynamic fault tree.

[0045] The parameter determination module is used to obtain the conditional probability table and state transition matrix of the fuzzy dynamic Bayesian model based on the Markov chain, and to determine the prior probability of the fuzzy dynamic Bayesian model by applying DS evidence theory, so as to obtain the fuzzy dynamic Bayesian model after parameter determination.

[0046] The prediction module is used to apply the Latin hypercube sampling rule to perform fuzzy Bayesian forward inference on the fuzzy dynamic Bayesian model after the parameters are determined, so as to obtain the reliability-time relationship curve of the reactor protection system.

[0047] An electronic device includes a memory and a processor, the memory storing a computer program, and the processor running the computer program to enable the electronic device to perform the above-described dynamic reliability analysis method for reactor protection systems.

[0048] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described dynamic reliability analysis method for reactor protection systems.

[0049] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0050] This invention provides a dynamic reliability analysis method for a reactor protection system, comprising: obtaining a dynamic fault tree based on the fault sources and fault results of the reactor protection system; constructing a fuzzy dynamic Bayesian model of the reactor protection system based on the dynamic fault tree; obtaining the conditional probability table and state transition matrix of the fuzzy dynamic Bayesian model based on Markov chains, and applying DS evidence theory to determine the prior probability of the fuzzy dynamic Bayesian model to obtain a fuzzy dynamic Bayesian model with determined parameters; and applying the Latin hypercube sampling rule to perform fuzzy Bayesian forward inference on the fuzzy dynamic Bayesian model with determined parameters to obtain the reliability-time relationship curve of the reactor protection system. This invention applies Dynamic Fault Tree Analysis (DFTA) to establish a DFT characterizing the dynamic interactivity of a system; it applies Dynamic Bayesian Network (DBN), Interval Type II Fuzzy Sets (IT2FSs), and an improved DS evidence theory to establish a DFT-based fuzzy DBN model representing the dynamic interactivity, time dependence, and fuzziness of the system; and it applies an improved Latin hypercube sampling method to perform fuzzy Bayesian forward inference, i.e., RPS dynamic prediction analysis, on a "Hualong One" reactor protection system in eastern China, obtaining the reliability-time relationship curve of the reactor protection system. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 Flowchart of the dynamic reliability analysis method for reactor protection system provided by the present invention;

[0053] Figure 2 A flowchart illustrating a specific embodiment of the present invention;

[0054] Figure 3 Dynamic fault tree for APU power supply failure;

[0055] Figure 4 A fuzzy dynamic Bayesian model was established using APU power supply failure as an example.

[0056] Figure 5 This is a schematic diagram illustrating the conversion strategy of the FDEP gate from DFT to DBN model in this invention;

[0057] Figure 6 This is a schematic diagram of the conversion strategy of the PAND gate from DFT to DBN model in this invention;

[0058] Figure 7 The fuzzy DBN model diagram of the "Hualong One" RPS based on DFT provided by this invention;

[0059] Figure 8 A block diagram of the dynamic reliability analysis system for reactor protection provided by this invention.

[0060] Symbol explanation:

[0061] Dynamic fault tree building module—1, fuzzy dynamic Bayesian model building module—2, parameter determination module—3, prediction module—4. Detailed Implementation

[0062] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0063] The purpose of this invention is to provide a method, system, equipment, and medium for dynamic reliability analysis of reactor protection systems, which can dynamically reflect the reliability of reactor protection systems.

[0064] Currently, traditional static methods are mainly used to analyze RPS reliability. These methods can characterize the static interaction characteristics of the system, but they are difficult to characterize the dynamic interaction of the system.

[0065] To address this issue, several researchers used Dynamic Fault Tree Analysis (DFTA) and Markov modeling methods to conduct dynamic reliability analysis (RPS) of two other national nuclear power plants. In DFTA, four dynamic logic gates (including spare parts gate, function-dependent gate, priority AND gate, and sequence-dependent gate) were introduced to express the dynamic logical relationships between system events. DFTA solves the problem that traditional static fault trees cannot characterize the dynamic interactions between system events. The DBN model derived from DFTA uses conditional independence relationships between non-parent-child nodes, which greatly reduces the computational load. Simultaneously, DBN has powerful time-dependent modeling and forward and backward reasoning capabilities. Therefore, DBN is very suitable for dynamic reliability analysis of complex systems. However, traditional DBN is based on accurate sets and probabilities. Due to system complexity and the fuzziness of expert thinking, reliability analysis will inevitably generate multi-source fuzzy information. Therefore, it is necessary to modify the DBN model and establish a fuzzy DBN model to handle fuzzy information.

[0066] Type I fuzzy sets are widely used to process fuzzy information. The membership function of a Type I fuzzy set is a crisp value in the range [0, 1]. However, in complex situations, it is difficult to determine the precise membership function of a Type I fuzzy set. Type II fuzzy sets (considered an extension of Type I fuzzy sets) are an effective method for processing complex fuzzy information because their membership function is a fuzzy set. However, the cumbersome calculations of Type II fuzzy sets hinder their practical application. IT2FSs (Integrated Time Between Faults and Effects Analysis) are defined by interval-valued membership functions, thus capturing highly fuzzy information and possessing relatively simple formulas and lower computational complexity. Therefore, IT2FSs have become a research hotspot in processing fuzzy information. Notably, some researchers have improved methods within the IT2FSs framework (such as Failure Mode and Effects Analysis (FMEA), Monte Carlo simulation, multi-criteria decisionmaking, and the success likelihood index method), and these methods have been applied in many research fields. These fields include: risk analysis for NPP (Non-Power Processing), reliability analysis of power distribution systems in the power industry, reliability analysis of recycling facilities systems in the infrastructure industry, and human error in maritime transportation. Given the advantages and successful applications of interval type II fuzzy sets, we apply interval type II fuzzy sets to handle highly fuzzy information in the dynamic reliability evaluation process of the "Hualong One" RPS.

[0067] It should be noted that when experts hold differing opinions, the multi-source IT2FSs information generated from the dynamic reliability analysis of the "Hualong One" RPS must be fused. Therefore, the DS evidence theory is applied to fuse the IT2FSs information.

[0068] like Figure 2 As shown, this invention is divided into three stages: Stage A: Applying Dynamic Fault Tree Analysis (DFTA) to establish a dynamic fault tree characterizing the dynamic interactivity of the "Hualong One" Reactor Protection System (RPS); Stage B: Applying Dynamic Bayesian Network (DBN), Interval Type-2 Fuzzy Sets (IT2FSs), and improved Dempster-Shafer (DS) evidence theory to establish a fuzzy DBN model of the "Hualong One" RPS based on Dynamic Fault Tree; Stage C: Applying improved LHS (Latin hypercube sampling), defining a new fuzzy Bayesian inference algorithm to perform fuzzy Bayesian inference of the fuzzy DBN model.

[0069] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0070] Example 1

[0071] like Figure 1 As shown, the present invention provides a method for dynamic reliability analysis of a reactor protection system, the method comprising:

[0072] Step S1: Obtain the dynamic fault tree based on the fault sources and fault results of the reactor protection system.

[0073] In practical applications, based on the fault sources and fault results of the reactor protection system, the fault causes in the fault sources are defined as the bottom events in the dynamic fault tree, the fault modes in the fault sources are defined as the intermediate events in the dynamic fault tree, and the fault results are defined as the top events. Static logic gates and dynamic logic gates are used to connect the events (bottom events, intermediate events, and top events) to obtain the dynamic fault tree.

[0074] S1 specifically includes:

[0075] Step S11: Determine the top event of the reactor protection system based on the fault source and fault result. The top event of the reactor protection system can be determined based on the relevant probabilistic safety assessment report. Assuming we take a component in the system, the Acquisition and Processing Unit (APU), as an example, let the fault result of APU power supply failure be considered a top event.

[0076] Step S12: Based on the fault sources and results of the reactor protection system, apply the Potential Failure Mode and Effects Analysis (FMEA) method to determine the intermediate events and basic events of the reactor protection system. Specifically, apply FMEA to analyze the RPS failure modes and causes, and define them as intermediate events and basic events in the DFT, respectively. Failure modes are defined as intermediate events, and failure causes are defined as basic events. Taking the dynamic fault tree of APU power supply failure as an example, FMEA analysis shows that the failure modes are PU sensor failure preceding main power supply failure and APU power backup failure, which are defined as intermediate events in the dynamic fault tree. The failure causes are APU sensor failure, APU main power supply failure, and APU cold backup power supply failure, which are defined as basic events.

[0077] Step S13: Apply static and dynamic logic gates to connect the logical relationships between the top event, the intermediate event, and the basic event to obtain the logic gate connection relationship. Specifically, static and dynamic logic gates are introduced to analyze and characterize the static and dynamic interactions between RPS components. Analysis shows that a cold standby relationship exists between APU main power supply failure and APU cold standby power supply failure; a cold standby gate is used to connect APU main power supply failure and APU cold standby power supply failure. A priority AND relationship exists between APU sensor failure and APU main power supply failure; a priority AND gate is used to connect APU sensor failure and APU main power supply failure.

[0078] Step S14: Based on the top event, the intermediate events, the basic events, and the logic gate connections, establish a dynamic fault tree for the reactor protection system. Specifically, through S11, S12, and S13, a dynamic fault tree characterizing the dynamic interactivity of the RPS is established. Taking the dynamic fault tree of APU power supply failure as an example, the established dynamic fault tree is shown in Figure 3.

[0079] exist Figure 3 In the diagram, node M17 indicates APU power supply failure, node M18 indicates APU sensor failure before main power supply failure, node M19 indicates APU power backup failure, node X12 indicates APU sensor failure, node X13 indicates APU main power supply failure, and node X14 indicates APU cold backup power supply failure.

[0080] Step S2: Based on the dynamic fault tree, construct a fuzzy dynamic Bayesian model of the reactor protection system.

[0081] S2 specifically includes:

[0082] Step S21: Apply a transformation strategy to convert the basic events, intermediate events, and top event of the dynamic fault tree into nodes, and convert the logic gate connection relationships into conditions for non-root nodes; the nodes include root nodes, intermediate nodes, and leaf nodes. Specifically, using the DFT to DBN model transformation strategy, the basic events, intermediate events, and top event in the RPS system dynamic fault tree are converted into root nodes, intermediate nodes, and leaf nodes in the DBN model, respectively. Basic events correspond to leaf nodes, intermediate events correspond to intermediate nodes, and top events correspond to root nodes. Based on the static and dynamic transformation processes from the dynamic fault tree to the DBN model, static and dynamic logic gates are converted into conditions for non-root nodes in the DBN model.

[0083] Step S22: Based on the nodes and conditions, establish a fuzzy dynamic Bayesian model. Taking APU power supply failure as an example, a fuzzy dynamic Bayesian model was established, as shown in Figure 4.

[0084] Step S3: Based on the Markov chain, obtain the conditional probability table and state transition matrix of the fuzzy dynamic Bayesian model, and apply DS evidence theory to determine the prior probability of the fuzzy dynamic Bayesian model, thus obtaining the fuzzy dynamic Bayesian model with determined parameters.

[0085] S3 specifically includes:

[0086] Step S31: Based on expert knowledge, determine the failure rate of the node to obtain the node failure rate.

[0087] As shown in formula (3):

[0088]

[0089] in, It is an interval type II fuzzy set (IT2FSs); Let be the membership function of IT2FSs; The membership function of IT2FSs; The reference point for the interval type II fuzzy set; This is the upper bound of the membership function; This is the lower bound of the membership function. This is the upper limit of the membership function; This is the lower bound of the membership function.

[0090] Step S32: Determine the judgment information based on the expected value and standard deviation of the node failure rate, as shown in formulas (4) and (5):

[0091]

[0092]

[0093] in, Let be the membership degree of a type of fuzzy set; K is a constant, K = 0, 1, 2, 3; Ex is the expected value of the node failure rate; σ is the standard deviation of the node failure rate; Ex 2 The square of the expected value; Let be the upper membership degree of a fuzzy set.

[0094] Step S33: Based on the judgment information, establish a judgment matrix for the node failure rate based on interval type II fuzzy sets.

[0095] In practical applications, the expected value and standard deviation of the failure rate of RPS system components are determined based on expert scores. Formulas (3), (4), (5), and (6) are applied iteratively to calculate the IT2FSs-based judgment information for the failure rate of all nodes. An IT2FSs-based judgment matrix is ​​then established.

[0096]

[0097] Where Ex is the expected value; σ is the standard deviation; K = 0, 1, 2, 3; It is an interval type II fuzzy set.

[0098] Step S34: Assign basic probabilities to the judgment information in the judgment matrix to establish an evidence matrix.

[0099] In practical applications, according to formula (7) The judgment information set based on IT2FSs is defined by basic probability assignment, and then the evidence matrix M is established. The evidence matrix M is shown in formula (8).

[0100]

[0101]

[0102] Step S35: Apply DS evidence theory to fuse the evidence matrix to determine the prior probability of the root node; specifically, the algorithm for fusing the evidence matrix using DS evidence theory is as follows:

[0103]

[0104]

[0105]

[0106]

[0107] Among them, is the fusion result of the upper membership function; is the fusion result of the lower membership function; n is the number of indicators; e is the number of experts; K L is the conflict coefficient of the lower membership function; K U is the conflict coefficient of the upper membership function; is the lower membership function of the z-th expert evidence; is the upper membership function of the z-th expert evidence; L and U are the lower limit and the upper limit respectively; U* is the upper limit of the fusion result; L* is the lower limit of the fusion result.

[0108] According to formulas (9) - (12), an evidence fusion algorithm is obtained. Applying this evidence fusion algorithm, {m * (x1), …, m * (x i ), …, m * (x n )} is obtained. Among them, m * (x i ) is the evidence fusion rule for the i-th indicator. For the evidence fusion rule of the i-th indicator, the specific algorithm steps are as follows:

[0109] Let represent the probability assignment function value corresponding to the membership degree of the z-th expert to the i-th indicator IT2FSs-CM. Calculate K L and fuse The input is The output is result / sum(Fusion result).

[0110] 1. Calculate the matrix

[0111] 2. Calculate Let z = 3.

[0112] 3. Update the matrix

[0113] 4. Calculate Let z = z + 1.

[0114] 5. If z < e + 1, return to 3; otherwise, proceed to the next step.

[0115] 6. Calculate

[0116] 7. If 0 ≤ K L < 0.95, the fusion result is Fusion result = diag log(R L ) / (1 - K L ).

[0117] Otherwise, the fusion result is

[0118] Formula (13) was used to determine the prior probability of the root node in the fuzzy DBN model. The specific formula (13) is as follows:

[0119] P(X i )=m * (x i (13)

[0120] Step S36: Based on the Markov chain, convert the logic gate connection relationship in the dynamic fault tree into a conditional probability table of non-root nodes.

[0121] Specifically, based on the static and dynamic transformation processes from dynamic fault trees to DBN models, static and dynamic logic gates are transformed into conditions for non-root nodes in the DBN model. Markov chains are applied to obtain the conditional probabilities of non-root nodes, thus determining the conditional probability table for non-root nodes. The transformation strategies for FDEP gates and PAND gates are as follows: Figure 5 and Figure 6 As shown. The conditional probability table of the FDEP gate in the DBN model is shown in Equation (1), and the conditional probability table of the PAND gate in the DBN model is shown in Equation (2).

[0122]

[0123]

[0124] Where, λ J , and Representing nodes J, A1, and A respectively. n The failure rate; J(t) is the probability of output node J(t) occurring; A1(t) is the probability of output node A1(t) occurring; A n (t) represents the output node A. n G(t) is the probability of occurrence of the output node G(t); G(t) is the probability of occurrence of the output node G(t).

[0125] Step S37: Based on the Markov chain and in accordance with the international standard for the reactor protection system, determine the state transition matrix of the root node based on the interval type II fuzzy set.

[0126] Referring to international standards NUREG / CR-6928 and NUREG / CR-6883, the periodic testing and preventive maintenance cycles for RPS components are determined. Without considering periodic testing and preventive maintenance, formula (14) is used to determine the state transition probability of the root node based on IT2FSs. Considering periodic testing and preventive maintenance, formula (15) is applied to determine the state transition probability of the root node based on IT2FSs. Specifically:

[0127]

[0128]

[0129] in, μ represents the failure rate based on IT2FSs; W represents the maintenance rate; and F represents the working state.

[0130] Step S38: Based on the conditional probability table, the state transition matrix, and the prior probability, obtain the fuzzy dynamic Bayesian model with determined parameters.

[0131] Based on steps S2 and S3, a DFT-based fuzzy DBN model characterizing the dynamic interaction, time dependence, and fuzziness of the "Hualong One" RPS is established. The parameters in this model are determined. Figure 7 As shown.

[0132] Step S4 applies the Latin hypercube sampling rule to perform fuzzy Bayesian forward inference on the fuzzy dynamic Bayesian model after the parameters are determined, and obtains the reliability-time relationship curve of the reactor protection system.

[0133] S4 specifically includes:

[0134] Step S41: Apply the Latin hypercube sampling rule to determine the prior probability sample.

[0135] Step S42: Based on the prior probability sample, apply formula (16) to calculate the probability of occurrence of leaf node T of the k-th prior probability sample.

[0136]

[0137] Step S43: Calculate the posterior probability of the root node of the k-th prior probability sample according to formula (17).

[0138] ΔP k (X i )=|P k (X i |T)-P k (X i (17)

[0139] Among them, P k (X i P is a prior probability sample; k (T|X i P represents the conditional probability. k (T) represents the probability of leaf node T occurring; P k (X i |T) represents node X i The posterior probability; ΔP k (X i ) is node X i The rate of change of probability.

[0140] In practical applications, a new fuzzy Bayes inference algorithm is defined based on the Latin hypercube sampling rule and formulas (16) and (17). The specific solution steps are as follows:

[0141] Define a row of Latin hypercube matrices as a prior probability sample space.

[0142] 1. Initialize the number of samples to zero.

[0143] 2. Define an interval [0,] in the sample space, and divide the interval into s equal intervals.

[0144] 3. Sample each of the s random samples in [0,1], and record the k-th random number as u. ki .

[0145] 4. Use the formula Generate a random value x ki Then, the s random values ​​(sample values) are randomly arranged.

[0146] 5. Use the formula F(x) i )=P{X i ≤x i} Calculate the cumulative distribution function of s random values ​​(samples).

[0147] 6. Use formula P k (X i ) = p ki =F -1 (x ki ), generate s prior probability samples.

[0148] 7. If no s prior probability samples of n root nodes are generated, return 1; otherwise, save the result to the Latin hypercube matrix.

[0149] 8. For any sample space, initialize the structure and parameters in the BN model based on CM-IT2FSs.

[0150] 9. Assign the prior probability samples to the root node and use formula (16) to calculate the probability of occurrence of the leaf nodes.

[0151] 10. Use formula (17) to calculate the posterior probability.

[0152] 11. Calculate the sensitivity performance metric using formula (18). Specifically, formula (18) is shown below:

[0153]

[0154] Among them, P k (T|X i P represents the conditional probability. k (T) represents the probability of leaf node T occurring; SPM k (X i (T) represents node X i The sensitivity performance metric expresses its sensitivity to leaf nodes.

[0155] 12. If all prior probability sample spaces have been computed, output the result; otherwise, return to step 7.

[0156] Step S44: Determine the reliability of the root node of the k-th prior probability sample based on the posterior probability of the root node of the k-th prior probability sample.

[0157] Step S45: Determine the reliability of all the prior probability samples based on the reliability of the root node of the k-th prior probability sample.

[0158] Step S46: Based on the reliability of all the prior probability samples, obtain the reliability-time relationship curve of the reactor protection system.

[0159] Furthermore, the dynamic reliability analysis method for reactor protection systems provided by this invention also includes:

[0160] By applying the Latin hypercube sampling rule, fuzzy Bayesian inverse reasoning is performed on the fuzzy dynamic Bayesian model with determined parameters to obtain the key components affecting the reliability of the reactor protection system.

[0161] Specifically, the fuzzy Bayesian inference algorithm is applied to a "Hualong One" reactor in eastern China to perform forward fuzzy Bayesian inference and predict dynamic reliability (RPS). The defined fuzzy Bayesian inference algorithm is also applied to the same reactor to perform inverse fuzzy Bayesian inference and analyze RPS dynamic sensitivity. The purpose of forward fuzzy Bayesian inference is to predict RPS reliability as accurately as possible before system failure, obtaining the RPS reliability change curve over time. The purpose of inverse fuzzy Bayesian inference is to obtain the dynamic impact of component failure on system failure, and then identify the key components affecting RPS reliability.

[0162] Example 2

[0163] To implement the method corresponding to Embodiment 1 above and achieve the corresponding functions and technical effects, a dynamic reliability analysis system for reactor protection is provided below, such as... Figure 8 As shown, the system includes:

[0164] The dynamic fault tree building module 1 is used to obtain a dynamic fault tree based on the fault sources and fault results of the reactor protection system.

[0165] The fuzzy dynamic Bayesian model building module 2 is used to construct a fuzzy dynamic Bayesian model of the reactor protection system based on the dynamic fault tree.

[0166] The parameter determination module 3 is used to obtain the conditional probability table and state transition matrix of the fuzzy dynamic Bayesian model based on the Markov chain, and to determine the prior probability of the fuzzy dynamic Bayesian model by applying DS evidence theory, so as to obtain the fuzzy dynamic Bayesian model after parameter determination.

[0167] Prediction module 4 is used to apply the Latin hypercube sampling rule to perform fuzzy Bayesian forward inference on the fuzzy dynamic Bayesian model after the parameters are determined, so as to obtain the reliability-time relationship curve of the reactor protection system.

[0168] Example 3

[0169] This invention provides an electronic device, including a memory and a processor. The memory stores a computer program, and the processor runs the computer program to enable the electronic device to execute the dynamic reliability analysis method for a reactor protection system according to Embodiment 1.

[0170] Alternatively, the aforementioned electronic device may be a server.

[0171] In addition, this embodiment of the invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the dynamic reliability analysis method for the reactor protection system of Embodiment 1.

[0172] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0173] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for dynamic reliability analysis of a reactor protection system, characterized in that, The method includes: A dynamic fault tree is obtained based on the sources and results of faults in the reactor protection system; Based on the dynamic fault tree, a fuzzy dynamic Bayesian model of the reactor protection system is constructed. The conditional probability table and state transition matrix of the fuzzy dynamic Bayesian model are obtained based on Markov chains, and the prior probabilities of the fuzzy dynamic Bayesian model are determined by applying DS evidence theory, resulting in a fuzzy dynamic Bayesian model with determined parameters. Specifically, this process includes: determining the failure rate of nodes based on expert knowledge; determining judgment information based on interval type II fuzzy sets based on the expected value and standard deviation of the node failure rate; and establishing a fuzzy dynamic Bayesian model with determined parameters based on the judgment information. The algorithm for fusing the evidence matrix based on interval type II fuzzy sets to determine the failure rate of the root node is as follows: An evidence matrix is ​​established using the judgment information in the judgment matrix as basic probability values; the evidence matrix is ​​fused using DS evidence theory to determine the prior probability of the root node; based on Markov chains, the logic gate connection relationships in the dynamic fault tree are converted into a conditional probability table for non-root nodes; based on Markov chains and according to the international standard for reactor protection systems, the state transition matrix of the root node based on interval type II fuzzy sets is determined; based on the conditional probability table, the state transition matrix, and the prior probability, a fuzzy dynamic Bayesian model with determined parameters is obtained; the algorithm for fusing the evidence matrix using DS evidence theory is as follows: in, This is the fusion result of the membership function; This represents the fusion result of the membership function; n is the number of indicators; e is the number of experts; The conflict coefficient of the membership function; The conflict coefficient of the membership function; Let be the membership function of the z-th expert evidence; Let L be the upper membership function of the z-th expert evidence; L and U are the lower and upper bounds, respectively. By applying the Latin hypercube sampling rule, fuzzy Bayesian forward inference is performed on the fuzzy dynamic Bayesian model with determined parameters to obtain the reliability-time relationship curve of the reactor protection system.

2. The dynamic reliability analysis method for reactor protection system according to claim 1, characterized in that, The process of obtaining a dynamic fault tree based on the fault sources and fault outcomes of the reactor protection system specifically includes: The top event of the reactor protection system is determined based on the source and result of the fault in the reactor protection system. Based on the fault sources and fault results of the reactor protection system, the intermediate events and basic events of the reactor protection system are determined by applying the potential failure mode and effects analysis method. Static and dynamic logic gates are used to connect the logical relationships between the top event, the intermediate event, and the basic event to obtain the logic gate connection relationship; A dynamic fault tree for the reactor protection system is established based on the top event, the intermediate events, the basic events, and the logic gate connections.

3. The dynamic reliability analysis method for reactor protection system according to claim 2, characterized in that, The step of constructing a fuzzy dynamic Bayesian model of the reactor protection system based on the dynamic fault tree specifically includes: A transformation strategy is applied to convert the basic events, intermediate events, and top events of the dynamic fault tree into nodes, and to convert the logic gate connection relationships into conditions of non-root nodes; the nodes include root nodes, intermediate nodes, and leaf nodes; Based on the nodes and conditions, a fuzzy dynamic Bayesian model is established.

4. The dynamic reliability analysis method for a reactor protection system according to claim 1, characterized in that, The Latin hypercube sampling rule is applied to perform fuzzy Bayesian forward inference on the fuzzy dynamic Bayesian model with determined parameters to obtain the reliability-time relationship curve of the reactor protection system, specifically including: The Latin hypercube sampling rule is applied to determine the prior probability sample; Based on the prior probability samples, apply the formula Calculate the probability of leaf node T occurring in the k-th prior probability sample; where, For a prior probability sample; For conditional probability; leaf node T The probability of occurrence; For nodes X i The posterior probability; According to the formula Calculate the posterior probability of the root node of the k-th prior probability sample; where, For a prior probability sample; For nodes X i The posterior probability; For nodes X i The rate of change of probability; The reliability of the root node of the k-th prior probability sample is determined based on the posterior probability of the root node of the k-th prior probability sample. The reliability of all the prior probability samples is determined based on the reliability of the root node of the k-th prior probability sample. Based on the reliability of all the prior probability samples, the reliability-time relationship curve of the reactor protection system is obtained.

5. The dynamic reliability analysis method for a reactor protection system according to claim 4, characterized in that, The method further includes: By applying the Latin hypercube sampling rule, fuzzy Bayesian inverse reasoning is performed on the fuzzy dynamic Bayesian model with determined parameters to obtain the key components affecting the reliability of the reactor protection system.

6. A dynamic reliability analysis system for a reactor protection system, characterized in that, The system includes: The dynamic fault tree building module is used to generate a dynamic fault tree based on the fault sources and fault results of the reactor protection system. The fuzzy dynamic Bayesian model building module is used to construct a fuzzy dynamic Bayesian model of the reactor protection system based on the dynamic fault tree. The parameter determination module is used to obtain the conditional probability table and state transition matrix of the fuzzy dynamic Bayesian model based on the Markov chain, and to determine the prior probability of the fuzzy dynamic Bayesian model by applying DS evidence theory, thus obtaining the fuzzy dynamic Bayesian model with determined parameters. Specifically, obtaining the conditional probability table and state transition matrix of the fuzzy dynamic Bayesian model based on the Markov chain, and determining the prior probability of the fuzzy dynamic Bayesian model by applying DS evidence theory, thus obtaining the fuzzy dynamic Bayesian model with determined parameters includes: determining the node failure rate based on expert knowledge, thus obtaining the node failure rate; determining judgment information based on the expected value and standard deviation of the node failure rate using interval type II fuzzy sets; and determining the judgment information based on the judgment information. A judgment matrix based on interval type-2 fuzzy sets is established to determine the failure rate of the nodes. An evidence matrix is ​​established using the judgment information in the judgment matrix as basic probability values. The evidence matrix is ​​fused using DS evidence theory to determine the prior probability of the root node. Based on Markov chains, the logic gate connection relationships in the dynamic fault tree are converted into conditional probability tables for non-root nodes. Based on Markov chains and according to the international standard for reactor protection systems, the state transition matrix of the root node based on interval type-2 fuzzy sets is determined. Based on the conditional probability tables, the state transition matrix, and the prior probabilities, a fuzzy dynamic Bayesian model with determined parameters is obtained. The algorithm for fusing the evidence matrix using DS evidence theory is as follows: in, This is the fusion result of the membership function; This represents the fusion result of the membership function; n is the number of indicators; e is the number of experts; The conflict coefficient of the membership function; The conflict coefficient of the membership function; Let be the membership function of the z-th expert evidence; Let L be the upper membership function of the z-th expert evidence; L and U are the lower and upper bounds, respectively. The prediction module is used to apply the Latin hypercube sampling rule to perform fuzzy Bayesian forward inference on the fuzzy dynamic Bayesian model after the parameters are determined, so as to obtain the reliability-time relationship curve of the reactor protection system.

7. An electronic device, characterized in that, The device includes a memory and a processor, wherein the memory stores a computer program and the processor runs the computer program to enable the electronic device to perform the dynamic reliability analysis method for a reactor protection system according to any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that, It stores a computer program that, when executed by a processor, implements the dynamic reliability analysis method for reactor protection systems as described in any one of claims 1 to 5.

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