Method and equipment for calculating reliability of steam generator system based on digital simulation method

Abstract

According to the method and the equipment for calculating the reliability of the steam generator system based on the digital simulation method, the fault-free time interval and task reliability evaluation of the whole steam generator system can be realized. The method comprises the following steps: firstly, establishing a reliability block diagram of the steam generator, and then establishing a reliability mathematical analysis model of a steam generator complete machine system about each component subsystem; secondly, fitting a failure time probability density function by utilizing a failure time sample of a component subsystem and a Bootstrap-based sample virtual augmentation evaluation method; and according to the failure time probability density function, an MCMC digital simulation method is adopted to extract a failure time sample, the failure time sample is substituted into the system reliability analysis model, and finally the average fault-free interval and the task reliability of the whole machine are obtained through calculation. According to the method, reliability simulation evaluation can be effectively carried out on the steam generator, and when a task reliability threshold value is given, early warning can be effectively carried out on the operation reliability of the steam generator through the method.

Description

Technical Field

[0001] The present invention relates to the technical field of reliability analysis of steam generator systems, and in particular to a method and device for calculating the reliability of a steam generator system 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. As a key equipment of nuclear industry thermal energy devices, steam generators are not only the main pressure equipment, but also an important safety barrier to isolate the first and second circuits and prevent radioactive substances from polluting the environment. However, steam generators are under the harsh working conditions of high temperature and high pressure for a long time, and are affected by factors such as vibration, scouring, and corrosion, and are often damaged. This not only reduces the service life of steam generators, but also leads to the power reduction operation of nuclear energy devices and even unplanned shutdowns, hindering the improvement of the safety and economy of the overall nuclear energy device. Therefore, quantitatively evaluating its reliability indicators, predicting its failure time in advance, tracking and mastering the operating status of steam generators, and providing guidance and support for preventive maintenance have become issues of concern to all parties in the field of nuclear energy devices. The traditional equipment reliability analysis method based on statistical methods relies on a large number of equipment failure samples. For nuclear-grade equipment, its system is highly complex and expensive, and it is impossible to conduct full life cycle tests and destructive life tests on it. Therefore, the cost of obtaining its failure samples is extremely high, which makes the traditional reliability analysis method 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 a digital simulation method, 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 a steam generator, which can be applied to the calculation of the mean time between failures and mission reliability of the steam generator and the failure warning during the operation process.

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

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

[0008] Step 3: Virtually augment the failure time samples of steam generator components and resample based on the Bootstrap method to simulate the real distribution of the failure time and obtain the parameter estimation of the distribution probability density function;

[0009] Step 4: Determine the probability density function of the failure time distribution of the component subsystem based on the failure time sample of the component subsystem, and use the MCMC digital simulation method to perform random sampling to obtain the component failure time sample;

[0010] Step 5: Bring the component failure time samples in step 4 into the reliability analysis mathematical model of the whole system for each component subsystem, obtain the failure time sample set of the whole system, and finally complete the system reliability simulation of the steam generator whole machine.

[0011] On the other hand, the present invention further discloses a computer device, including 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.

[0012] It can be seen from the above technical scheme that the present invention proposes a reliability calculation method for a steam generator system based on a digital simulation method. This method can realize the efficient evaluation of the fault-free interval and mission reliability of the steam generator system based on a small number of failure samples of system components by constructing a reliability mathematical model of the whole system about the component subsystem. The basic process of this method is as follows: according to the physical structure of the steam generator and its 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 system is established; secondly, according to the failure time samples of each subsystem component in the reliability mathematical model of the steam generator system, the failure time probability density function of the subsystem / component is fitted; according to the failure time probability density function, the Monte Carlo (MC) method is used to extract the failure time samples, and the samples are substituted into the system reliability analysis model to calculate the mean fault-free interval and mission reliability of the whole machine. Since the mission reliability finally obtained is a function of the steam generator operation time, if the steam generator mission reliability threshold is given, this method can effectively warn the operation reliability of the steam generator.

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

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

[0015] b) The present invention can obtain the function of the whole machine mission reliability with respect to the mission time by calculating the mission reliability, and can provide early warning for the operation reliability of the steam generator;

[0016] c) The present invention establishes a reliability block diagram and uses a visual graphic representation of the steam fault transmission path of the steam generator, which is more intuitive;

[0017] d) The present invention performs virtual augmentation on the failure samples of steam generator components based on the Bootstrap method, which effectively solves the reliability evaluation problem under the condition of small samples;

[0018] d) The present invention adopts the Monte Carlo digital simulation method to extract samples according to the probability distribution density function. The algorithm has clear principles, simple operation and high credibility.

[0019] e) The present invention uses a digital simulation method to reduce the cost of quantitative evaluation and analysis of steam generator reliability indicators and improve the evaluation efficiency; BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 Algorithm flow chart of digital simulation method for steam generator system reliability assessment;

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

[0022] Figure 3 is the variation curve of steam generator system mission reliability over time, where T t For a given steam generator reliability threshold R t The moment when the steam generator reaches unacceptable reliability. DETAILED DESCRIPTION

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

[0024] In order to evaluate the reliability of steam generators, the embodiment of the present invention proposes a method for calculating the mean time between failures and time-varying task reliability of steam generators based on a digital simulation method. The method constructs a mathematical model of the reliability of the whole system for each subsystem component by drawing a reliability block diagram of the steam generator, and extracts failure time samples using the MCMC digital simulation method, and substitutes them into the mathematical model of the reliability of the whole system, and finally calculates the mean time between failures and time-varying task reliability of the steam generator. The algorithm proposed in the embodiment of the present invention is as follows:

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

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

[0027] Step 3: Virtually augment the failure time samples of steam generator components and resample based on the Bootstrap method to simulate the real distribution of the failure time and obtain the parameter estimation 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 sample of the component subsystem, and use the Monte-Carlo digital simulation method to perform random sampling to obtain the component failure time sample;

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

[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. 1 . 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 steam generator reliability block diagram and reliability analysis mathematical model

[0033] According to the corresponding relationship between steam generator functions and structural levels, based on the physical structure and logical connection mode of the steam generator system, and considering the fault transmission path, a 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 barrel 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, that is, the reliability of the whole system is a function of the reliability of the subsystem components. The mathematical model for the reliability analysis of the whole system is established as follows:

[0035] T s =G(t)=G(t 1 ,t 2 ,...t 6 ) (1)

[0036] In formula (1), t = {t 1 ,t 2,...t 6} T , represents the joint vector of failure time samples of subsystem components, 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 actual 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 failure sample of the steam generator component, the virtual augmentation sample method is used to expand the failure sample of the steam generator according to 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 sub-sample. The failure sample capacity is expanded to n ≥ 10, and the augmented failure time sample set is recorded as F se ={x 1 ,x 2 ,...x n};

[0040] 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 new observation information. The implementation steps are as follows:

[0041] f) For the failure sample set F se ={x 1 ,x 2 ,...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 i =i / n, from which the empirical cumulative distribution function of the sample can be constructed as

[0042]

[0043] g) Generate a random number η uniformly distributed in the interval [0,1], let 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) ), and 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)}, fit the key parameters in the probability density function, and then obtain 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 computing 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, and the failure sample distribution is obtained.

[0050] Figure 2 The typical probability density distribution of mechanical components is given. If the exponential distribution is selected to fit the failure time samples, 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 unit under this simulation. si ;

[0053] Step 2: Use the MC digital simulation method to repeat the simulation sampling N times to obtain the failure time sample set T of the whole system s ={T s1 ,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 overall 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 whole 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 figure 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 realizing the reliability prediction and evaluation of the steam generator system in an efficient and low-cost manner. By constructing a reliability block diagram of the whole system, augmenting the Bootstrap virtual sample, and random sampling by digital simulation method, the problems of small number of failure samples, high cost, and low efficiency in the reliability evaluation of the steam generator system are overcome. The algorithm flow of the present invention is reasonable and clear, efficient and easy to implement, and has a wide range of applications. It can be used not only in the field of nuclear industry thermal energy devices, but also in the fields of thermal power, chemical industry, petroleum and petrochemical industry, etc.

[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 flow of the present invention is reasonable and clear, efficient and easy to implement, with a wide range of applications and certain innovation.

[0063] On the other hand, the present invention further discloses a computer device, including 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 method 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 in the above methods.

[0066] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions may be transmitted from a website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) mode to another website site, computer, server or data center. The computer-readable storage medium may be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated. The available medium may be a magnetic medium, (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive Solid State Disk (SSD)), etc.

[0067] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0068] Each embodiment in this specification is described in a related manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0069] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A steam generator system reliability calculation method based on digital simulation method, characterized in that: The following steps are included: Step 1: According to the physical structure of the steam generator and its logical connection mode, the reliability block diagram and reliability line diagram of its component subsystem and the whole system are established, and the physical relationship of each unit in the system is constructed by graphical means; Step 2: Based on the steam generator task reliability block diagram constructed in step 1, a reliability analysis mathematical model of the whole system for each component subsystem is established; Step 3: Virtually augment the failure time samples of steam generator components and resample based on the Bootstrap method to simulate the real distribution of the failure time and obtain the parameter estimation of the distribution probability density function; Step 4: Determine the probability density function of the failure time distribution of the component subsystem based on the failure time sample of the component subsystem, and use the MCMC digital simulation method to perform random sampling to obtain the component failure time sample; Step 5: Bring the component failure time samples in step 4 into the reliability analysis mathematical model of the whole system for each component subsystem, obtain the failure time sample set of the whole system, and finally complete the system reliability simulation of the steam generator whole machine.

2. The method for calculating the reliability of a steam generator system based on digital simulation method 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 joint 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 method according to claim 1, characterized in that: In step 2, the reliability analysis mathematical model of the whole system for each component subsystem is established as follows: T s =G(t)=G(t1,t2,...t6)(1) In formula (1), t = {t1, t2, ... t6} T , represents the joint vector of failure time samples of subsystem components, and G(.) is the operator.

4. The method for calculating the reliability of a steam generator system based on digital simulation method according to claim 1, characterized in that: Virtual augmentation of failure time samples for steam generator components, including, Let the failure time sample set be denoted as F s ; Step 2.1: Virtual augmentation of failure samples: Considering the small sample size of the failure sample of the steam generator component, the virtual augmentation sample method is used to expand the failure sample of the steam generator according to 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 sub-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 }; 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 new observation information.

5. The method for calculating the reliability of a steam generator system based on digital simulation method according to claim 4 is characterized in that: Step 2.2 specifically includes: a) 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 i =i / n, the empirical cumulative distribution function of the sample is constructed as follows: b) 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; c)x F =x (i) +(β-i+1)(x (i+1) -x (i) ), and the obtained x F That is the required random sample point; d) Repeat n times to get a Bootstrap sample X = {x F1 , x F2 ,...x Fn }; e) Repeat steps b)-d) N times to obtain the failure time sample set Y={X (1) , X (2) , ...X (N) }.

6. The method for calculating the reliability of a steam generator system based on digital simulation method according to claim 5, characterized in that: Resampling based on the Bootstrap method is used to simulate the true distribution of the approximate failure time and obtain 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 Y = {X (1) , X (2) , ...X (N) }, fit the key parameters in the probability density function, and then obtain the probability density distribution function f(t). 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 computing 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, and the failure sample distribution is obtained.

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

8. The method for calculating the reliability of a steam generator system based on digital simulation method according to claim 3 is characterized in that: The reliability simulation steps of step 5 are as follows: Step 1: Based on the fitted component failure time probability density function f(t), use the MC digital simulation method to sample and obtain a single failure time sample t i ={t i1 ,t i2 ,...t i6 } T , i = 1, 2, ... N, and then substitute the sample into formula (1) to obtain the failure time response sample of the steam generator under this simulation Step 2: Use the MC digital simulation method to repeat the simulation sampling N times to obtain the failure time sample set of the whole system Calculate the whole machine failure time sample set T s The mean of the failure interval of the whole system is obtained 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 ); 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 overall 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 whole system. The calculation expression is as follows: From the above formula, we can know that the mission reliability of the whole system R s is a variable related to task time; Step 5: Given the steam generator reliability threshold R t , determine the time T corresponding to the steam generator system reaching unacceptable reliability t :

9. 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 5.

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