Steam generator system reliability calculation method and device based on digital simulation method

Abstract

The application discloses a steam generator system reliability calculation method and equipment based on a digital simulation method, which can realize the failure-free time interval and task reliability evaluation of the whole steam generator system. The method first establishes a reliability block diagram of the steam generator, and then establishes a reliability mathematical analysis model of the whole steam generator system about each component subsystem. Secondly, the failure time sample of the component subsystem and a sample virtual extension evaluation method based on Bootstrap are used to fit the failure time probability density function. According to the failure time probability density function, the MCMC digital simulation method is used to extract the failure time sample, which is substituted into the system reliability analysis model to finally calculate the average failure-free interval and task reliability of the whole machine. The method can effectively evaluate the reliability simulation of the steam generator, and when the task reliability threshold value is given, the method can give a warning for the operation reliability of the steam generator.

Description

Technical Field

[0001] The present invention relates to the technical field of steam generator system reliability analysis, and in particular to a steam generator system reliability calculation method and equipment based on a digital simulation method. Background Art

[0002] With the rapid development and utilization of nuclear energy, the reliability and safety of nuclear pressure equipment are becoming increasingly important. Steam generators, as key components of nuclear thermal power plants, are not only the primary pressure-bearing equipment but also serve as a critical safety barrier separating primary and secondary circuits and preventing radioactive contamination. However, steam generators are subject to long-term, harsh operating conditions of high temperature and high pressure, subject to vibration, erosion, corrosion, and other factors, and are often subject to damage and breakage. This not only shortens the steam generator's service life but also leads to reduced power operation and even unplanned shutdowns of nuclear power plants, hindering the overall safety and economic efficiency of nuclear power plants. Therefore, quantitatively assessing reliability indicators, predicting failure times in advance, tracking steam generator operating status, and providing guidance and support for preventive maintenance have become a key concern within the nuclear power plant industry. Traditional statistically based equipment reliability analysis methods rely on a large number of equipment failure samples. However, for nuclear-grade equipment, the high system complexity and high cost make full lifecycle testing and destructive life testing impossible. Consequently, the high cost of obtaining failure samples makes traditional reliability analysis methods inapplicable. Summary of the Invention

[0003] The present invention proposes a method and device for calculating the reliability of a steam generator system based on digital simulation, which can solve at least one of the technical problems in the background technology; the present invention provides a highly efficient method for quantitative analysis and evaluation of system reliability indicators for steam generators, which can be applied to the calculation of the mean time between failures and mission reliability of steam generators and failure warning during operation.

[0004] To achieve the above object, the present invention adopts the following technical solutions:

[0005] A method for calculating the reliability of a steam generator system based on a digital simulation method comprises the following steps:

[0006] Step 1: Based on the physical structure of the steam generator and its logical connection mode, establish the reliability block diagram and reliability line diagram of its component subsystems and the entire system, and use graphical means to construct the physical relationship between each unit in the system;

[0007] Step 2: Based on the steam generator mission reliability block diagram constructed in step 1, establish a reliability analysis mathematical model for each component subsystem of the entire system;

[0008] Step 3: Virtual augmentation is performed on the failure time sample of the steam generator assembly, and a bootstrap method is used for resampling to simulate the true distribution of the failure time, so that the parameter estimation of the distribution probability density function is obtained;

[0009] Step 4: The probability density function of the component subsystem failure time distribution is determined according to the component subsystem failure time sample, and the MCMC digital simulation method is used for random sampling to obtain the component failure time sample;

[0010] Step 5: The component failure time sample in step 4 is brought into the reliability analysis mathematical model of the whole machine system with respect to each component subsystem, and the failure time sample set of the whole machine system is obtained, and finally the system reliability simulation of the steam generator whole machine is completed.

[0011] In another aspect, the application also discloses a computer device comprising a memory and a processor, wherein the memory stores a computer program, and the computer program is executed by the processor to make the processor execute the steps of the above method.

[0012] From the above technical solution, the application proposes a steam generator system reliability calculation method based on digital simulation method. The method can realize efficient evaluation of the failure interval and task reliability of the steam generator whole machine system based on a small amount of failure samples of system components by constructing a reliability mathematical model of the whole machine system with respect to the component subsystem. The basic flow of the method is as follows: according to the physical structure of the steam generator and the logical connection mode, a reliability block diagram of the steam generator is established, and on this basis, a reliability mathematical analysis model of the steam generator whole machine system is established; secondly, the failure time probability density function of the subsystem / component is fitted according to the failure time sample of each subsystem component in the steam generator whole machine system reliability mathematical model; according to the failure time probability density function, the failure time sample is extracted by using the Monte Carlo (MC) method, and the average failure interval and task reliability of the whole machine are calculated by substituting the system reliability analysis model. Since the final obtained task reliability is a function of the running time of the steam generator, if the task reliability threshold of the steam generator is given, the method can effectively warn the running reliability of the steam generator.

[0013] Specifically, the advantages of the application can be embodied in the following aspects:

[0014] a) The application can realize quantitative reliability index evaluation of the steam generator whole machine system, which meets the actual engineering needs;

[0015] b) The application can obtain the function of the whole machine task reliability with respect to the task time by calculating the task reliability, and can warn the running reliability of the steam generator;

[0016] c) The present application is more intuitive by establishing a reliability block diagram, and characterizing the steam generator steam failure transmission path by a visual graph;

[0017] d) The present application effectively solves the reliability evaluation problem under the condition of small sample by virtually augmenting the failure sample of the steam generator component based on the Bootstrap method;

[0018] d) The present application uses the Monte Carlo digital simulation method to extract samples according to the probability distribution density function, and the algorithm principle is clear, simple to operate and high in reliability.

[0019] e) The present application uses the digital simulation method to reduce the cost of quantitative evaluation and analysis of the reliability index of the steam generator, and improves the evaluation efficiency; BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 The algorithm flowchart of the digital simulation method for the reliability evaluation of the steam generator system;

[0021] Figure 2 The reliability block diagram and reliability line diagram of the steam generator;

[0022] Figure 3 The curve of the time-varying task reliability of the steam generator system, wherein T t R is the given steam generator reliability threshold t The time when the steam generator reaches the unacceptable reliability. DETAILED DESCRIPTION

[0023] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all the embodiments.

[0024] For the reliability evaluation of the steam generator, the embodiments of the present application propose a calculation method of the steam generator average failure-free interval and time-varying task reliability based on the digital simulation method. The method draws the reliability block diagram of the steam generator to construct the reliability mathematical model of the whole system about each subsystem component, and uses the MCMC digital simulation method to extract the failure time sample, which is substituted into the reliability mathematical model of the whole system, and finally the steam generator average failure-free interval and time-varying task reliability are calculated. The algorithm content proposed in the embodiments of the present application is as follows:

[0025] Step 1: According to the physical structure and logical connection mode of the steam generator, the reliability block diagram and reliability line diagram of the component subsystem-whole system are established, and the physical relationship of each unit in the system is constructed by graphical means;

[0026] Step 2: Based on the steam generator reliability block diagram constructed in step 1, establish a reliability analysis mathematical model for each component subsystem of the entire system;

[0027] Step 3: Virtually augment the failure time samples of steam generator components and perform resampling based on the Bootstrap method to simulate the true distribution of failure times and obtain parameter estimates of the distribution probability density function;

[0028] Step 4: Determine the probability density function of the failure time distribution of the component subsystem based on the failure time samples of the component subsystem, and use the Monte-Carlo digital simulation method to perform random sampling to obtain the component failure time samples;

[0029] Step 5: Bring the component failure time samples in step 4 into the reliability analysis mathematical model of each component subsystem of the whole system to obtain the failure time sample set of the whole system, and finally complete the system reliability simulation of the steam generator whole unit.

[0030] The following are specific instructions:

[0031] like Figure 1 The algorithm flow of the digital simulation method for steam generator system reliability evaluation is shown in FIG. The specific steps of the present invention for realizing the reliability analysis and calculation of the steam generator system are as follows:

[0032] (1) Establishing a steam generator reliability block diagram and reliability analysis mathematical model

[0033] According to the corresponding relationship between steam generator function and structural level, based on the physical structure and logical connection mode of the steam generator system, considering the fault transmission path, the following is established: Figure 2 The steam generator system reliability block diagram and line diagram shown include a feedwater assembly, a header assembly, a support assembly, a heat transfer tube assembly, a cylinder assembly, and a steam pipe assembly.

[0034] Depend on Figure 1 The reliability modeling results show that the steam generator system is a series model, that is, all subsystem components in the system must operate normally for the entire system to operate normally. In other words, the reliability of the entire system is a function of the reliability of the subsystem components. The mathematical model for the reliability analysis of the entire system is established as follows:

[0035] T s =G(t)=G(t1,t2,...t6) (1)

[0036] In formula (1), t = {t1, t2, ... t6} T, represents the joint vector of subsystem component failure time samples, G(.) is an operator. Since the steam generator reliability analysis model in this example is a series model, G(.) represents the minimum value operation.

[0037] (2) Virtual augmentation of failure samples based on the Bootstrap method

[0038] The failure time samples of steam generator components can be obtained based on the development test results, engineering experience feedback, relevant public databases, etc. The failure time sample set is denoted as F s .

[0039] Step 2.1: Virtual augmentation of failure samples. Considering the small sample size of the steam generator component failure sample, the virtual augmentation sample method is used to expand the steam generator failure sample based on the principle that the mean of the virtual augmented sample is the same as the original sample mean and the standard deviation of the virtual augmented sample is equal to the standard deviation of the similar component sample. The failure sample capacity is expanded to n ≥ 10, and the augmented failure time sample set is recorded as F se ={x1,x2,...x n};

[0040] Step 2.2: Resampling of failed samples based on the Bootstrap method. The Bootstrap method relies only on existing sample information and does not require other assumptions or new observations. The implementation steps are as follows:

[0041] f) For the failure sample set F se ={x1,x2,...x n}, arranged in ascending order, and the order statistics {x (1) ,x (2) ,...x (n)}. Use the simplest estimation method to get x (i) The cumulative probability value at is F i =i / n, from this we can construct the empirical cumulative distribution function of the sample as

[0042]

[0043] g) Generate a random number η uniformly distributed in the interval [0, 1], set β = (n-1)η, i = [β] + 1, where [β] is β rounded down;

[0044] h)x F =x (i) +(β-i+1)(x (i+1) -x (i) ), the obtained x F That is the required random sample point;

[0045] i) Repeat n times to get a Bootstrap sample X={x F1 ,x F2 ,...x Fn}

[0046] j) Repeat steps b)-d) N times to obtain the failure time sample set Y={X (1) ,X (2) ,...X (N)}.

[0047] (3) Estimation of failure sample distribution parameters.

[0048] For the components included in the steam generator system, based on the failure sample set Y={X (1) ,X (2) ,...X (N)}, fitting the key parameters in the probability density function, and then obtaining the probability density distribution function f(t). The specific process is as follows:

[0049] Based on the failure samples obtained in the above steps, the parameter density estimation method is used to fit the failure distribution. Based on the distribution fitting toolbox in the mathematical calculation software MATLAB, the failure distribution of the failure samples is fitted according to different distribution assumptions. The distribution fitting results under different distribution assumptions are obtained to obtain the failure sample distribution.

[0050] Figure 2 The typical probability density distribution of mechanical components is given. If the exponential distribution is selected to fit the failure time sample, the parameter λ in the exponential distribution is estimated, and the failure time distribution probability density function f(t) = λe is obtained. -λt ; If the lognormal distribution is selected, the mean μ and variance in the distribution model are estimated.

[0051] (4) System reliability simulation

[0052] Step 1: Based on the component failure time probability density function f(t) obtained by fitting in (2), the single failure time sample t is obtained by sampling using the MC digital simulation method. i ={t i1 ,t i2 ,...t i6} T Then, the sample is substituted into formula (1) to obtain the failure time response sample T of the steam generator under this simulation. si ;

[0053] Step 2: Repeat the simulation sampling N times using the MC digital simulation method to obtain the failure time sample set T of the entire system s ={Ts1 ,T s2 ,....T sN}, calculate the whole machine failure time sample set T s The mean of the failure interval of the whole system can be obtained

[0054]

[0055] Step 3: Given the whole system task time T d Next, calculate the failure time sample set T of the whole machine s The system failure time is less than T d Sample T f (T f ∈{T≤T d}), denoted as M(T d );

[0056] Step 4: According to the law of large numbers, when the failure time sample set T s When it is large enough, it can be considered that the ratio of the number of samples whose system failure time is greater than the specified task time to the number of samples in the total failure time sample set is equal to the probability that the system failure time is greater than the specified task time, that is, the task reliability of the entire system. The calculation expression is as follows:

[0057]

[0058] From the above formula, we can know that the mission reliability of the whole system R s is a variable related to task time, and its change over time is shown in the following diagram Figure 3 As shown in the figure, the reliability of the whole machine is a non-increasing variable with respect to time. The horizontal axis in the figure is the mission time of the steam generator whole machine, and the vertical axis is the reliability of the whole machine system. d = 0, the reliability of the whole system is R s =1; As the mission time increases, the reliability of the entire system gradually decreases.

[0059] Step 5: Given the steam generator reliability threshold R t , determine the time T corresponding to the steam generator system reaching unacceptable reliability t :

[0060]

[0061] In summary, the purpose of the embodiments of the present invention is to solve the problem of achieving efficient and low-cost prediction and evaluation of the reliability of a steam generator complete system. By constructing a complete system reliability block diagram, augmenting bootstrap virtual samples, and random sampling using digital simulation methods, the problems of limited failure samples, high cost, and low efficiency in steam generator complete system reliability assessment are overcome. The algorithm of the present invention has a reasonable and clear process flow, high efficiency, and is easy to implement. It has a wide range of applications, not only in the field of nuclear industry thermal energy devices, but also in thermal power, chemical industry, petrochemical industry, and other fields.

[0062] The present invention can be widely used in reliability analysis of steam generators in the fields of nuclear energy, petroleum, chemical industry, etc. The algorithm of the present invention has a reasonable and clear process, high efficiency and easy implementation, wide application range and certain innovation.

[0063] On the other hand, the present invention further discloses a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the above method.

[0064] In another embodiment provided in the present application, a computer program product including instructions is also provided, which, when executed on a computer, enables the computer to execute any of the steam generator system reliability calculation methods based on digital simulation methods in the above embodiments.

[0065] It is understandable that the system, device and storage medium provided in the embodiments of the present invention correspond to the method provided in the embodiments of the present invention, and the explanation, examples and beneficial effects of the relevant contents can refer to the corresponding parts of the above methods.

[0066] In the embodiments described above, all or some of the steps can be implemented by hardware, software, firmware or any combination thereof. When implemented by software, all or some of the steps can be implemented in the form of one or more computer programs or program elements. The computer programs reside (at least temporarily) in a memory of a computer during execution. The memory can be a RAM memory, a flash memory, a ROM memory, an EPROM memory, or any other suitable memory. The memory can be integral to or separate from the computer. The computer programs can be written in any suitable programming language, such as C, C++, Java, Visual Basic, etc. The computer programs can be written in assembly or machine language, if desired. The computer programs can be distributed over network coupled file servers, or can be distributed by any other suitable means.

[0067] It is to be noted that, in the present document, relational terms such as first and second and the like can be used solely to distinguish one entity or action from another entity or action without necessarily implying any actual relationship or order between such entities or actions. Also, the terms "comprises", "comprising", or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can include other elements not expressly listed or inherent to such process, method, article, or apparatus. In addition, terms such as "first" and "second" are used herein only to distinguish one entity or action from another entity or action without necessarily implying any actual relationship or order between such entities or actions.

[0068] Each of the embodiments described in the present specification is described in an associated manner, and the same or similar parts among the embodiments can be referred to each other. Each of the embodiments focuses on the difference from other embodiments. In particular, for the system embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the part of the description of the method embodiments.

[0069] The above examples are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that the technical solutions recorded in the foregoing examples can be modified, or some technical features can be replaced by equivalent features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A steam generator system reliability calculation method based on digital simulation method, characterized in that: The following steps are included: Step 1: Based on the physical structure of the steam generator and its logical connection mode, establish the reliability block diagram and reliability line diagram of its component subsystems and the entire system, and use graphical means to construct the physical relationship between each unit in the system; Step 2: Based on the steam generator mission reliability block diagram constructed in step 1, establish a reliability analysis mathematical model for each component subsystem of the entire system; Step 3: Virtually augment the failure time samples of steam generator components and perform resampling based on the Bootstrap method to simulate the true distribution of failure times and obtain parameter estimates of the distribution probability density function; Step 4: Determine the probability density function of the component subsystem failure time distribution based on the component subsystem failure time sample, and use the MC digital simulation method to perform random sampling to obtain the component failure time sample; Step 5: Substitute the component failure time samples from step 4 into the reliability analysis mathematical model of each component subsystem of the entire system to obtain the failure time sample set of the entire system, and finally complete the system reliability simulation of the steam generator. In step 2, the reliability analysis mathematical model of the whole system for each component subsystem is established as follows: （1） In formula (1), , represents the joint vector of subsystem component failure time samples, is an operator; The reliability simulation steps of step 5 are as follows: Step 1: Calculate the probability density function of component failure time obtained by fitting , using MC digital simulation method to sample and obtain single failure time samples , Then, the sample is substituted into formula (1) to obtain the failure time response sample of the steam generator under this simulation. ; Step 2: Repeat using MC digital simulation method Simulate sampling times to obtain the failure time sample set of the entire system , calculate the whole machine failure time sample set The mean of the failure interval of the whole system is obtained （3） Step 3: At the given system task time Calculate the failure time sample set of the whole machine System failure time is less than Sample , The number of ; Step 4: According to the law of large numbers, when the failure time sample set of the whole machine When it is large enough, it can be considered that the ratio of the number of samples whose system failure time is greater than the specified task time to the number of samples in the total failure time sample set is equal to the probability that the system failure time is greater than the specified task time, that is, the task reliability of the entire system. The calculation expression is as follows: （4） From the above formula, we can see that the mission reliability of the whole system is is a variable related to task time; Step 5: Given the steam generator reliability threshold , determine the time when the steam generator system reaches unacceptable reliability : （5）。 2. The method for calculating the reliability of a steam generator system based on digital simulation according to claim 1, characterized in that: The reliability block diagram and reliability line diagram established in step 1 comprehensively consider the impact of component subsystems including water supply components, header components, heat transfer tube components, support components, cylinder components and steam pipe components on the reliability of the steam generator system.

3. The method for calculating the reliability of a steam generator system based on digital simulation according to claim 1, characterized in that: Virtual augmentation of failure time samples for steam generator components, including, Assume that the failure time sample set is recorded as ; Step 2.1: Virtual augmentation of failure samples: Considering the failure sample of steam generator components, the virtual augmentation sample method is used to expand the failure sample of steam generator according to the principle that the mean of the virtual augmented sample is the same as the mean of the original sample and the standard deviation of the virtual augmented sample is equal to the standard deviation of the similar sub-sample. The failure sample capacity is expanded to , the augmented failure time sample set is recorded as ; Step 2.2: Resampling of failed samples based on the Bootstrap method. The Bootstrap method only relies on the existing sample information and does not require other assumptions or the addition of new observation information.

4. The method for calculating the reliability of a steam generator system based on digital simulation according to claim 3, characterized in that: Step 2.2 specifically includes: a) For the failure sample set , arranged in order from small to large, to obtain the order statistics ; Using the simplest estimation method to obtain The cumulative probability value at , the empirical cumulative distribution function of the sample is constructed as （2） b) Generate uniformly distributed random numbers in the interval [0,1] ,make , ,in For Round down; c) , obtained That is the required random sample point; d) Repeat n times to get a Bootstrap sample ; e) Repeat steps b)-d) times, we can get the failure time sample set obtained by resampling using the Bootstrap method. .

5. The method for calculating the reliability of a steam generator system based on digital simulation according to claim 4, characterized in that: Resampling based on the Bootstrap method is used to simulate the true distribution of the failure time and obtain the parameter estimates of the distribution probability density function, including: For the components included in the steam generator system, based on the acquired failure sample set , fitting the key parameters in the probability density function, and then obtaining the probability density distribution function The specific process is as follows: Based on the failure samples obtained in the above steps, the parameter density estimation method is used to fit the failure distribution. Based on the distribution fitting toolbox in the mathematical calculation software MATLAB, the failure distribution of the failure samples is fitted according to different distribution assumptions. The distribution fitting results under different distribution assumptions are obtained to obtain the failure sample distribution.

6. The method for calculating the reliability of a steam generator system based on digital simulation according to claim 5, characterized in that: In step 4, the probability density function of the component subsystem failure time distribution is determined based on the component subsystem failure time sample, including: The failure time samples of steam generator components are obtained based on the development test results, engineering experience feedback, and relevant public databases. For the components included in the steam generator system, the key parameters in the probability density function are fitted through a small number of failure samples, and then the probability density distribution function is obtained. ; If the exponential distribution is selected to fit the failure time sample, the parameters of the exponential distribution are estimated. , thus obtaining the failure time distribution probability density function ; If the lognormal distribution is selected, the mean in the estimated distribution model is and variance.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the computer program is executed by the processor, the processor is caused to perform the steps of the method according to any one of claims 1 to 6.

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