Method and system for predicting residual life of redundant safety instrument system

Abstract

The invention discloses a method and system for predicting the residual life of a redundant safety instrument system, and the method comprises the steps: carrying out the life test of a to-be-predicted safety instrument system, and obtaining the residual life of the to-be-predicted safety instrument system according to the life data obtained through the test; constructing a mixed Weibull distribution model used for representing fault occurrence probability distribution characteristics of each device forming the safety instrument system to be predicted; performing maximum likelihood estimation on the mixed Weibull distribution model to obtain a maximum likelihood estimation value of a mixed Weibull distribution parameter; and constructing a fault distribution function of the to-be-predicted safety instrument system based on the fault equipment distribution characteristics corresponding to the failure of the to-be-predicted safety instrument system so as to obtain a failure probability density function, and based on the failure probability density function, obtaining the residual life of the current safety instrument system in combination with the maximum likelihood estimation value. The problem that the service life prediction of the redundant safety instrument system is limited to a single fault type and the application range is small is solved, and accurate prediction of the residual service life of the safety instrument system with multiple fault types at the same time is achieved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of safety equipment residual life prediction, and particularly relates to a method and system for predicting residual life of a redundant safety instrument system. BACKGROUND

[0002] With the development of petrochemical industry, safety problems inevitably become a key factor hindering production. In modern petrochemical plants, high-risk equipment determined based on risk assessment is widely equipped with a safety instrument system (SIS). However, the design of the safety instrument system does not have a perfect theory as a support, and is relatively more dependent on expert experience. Moreover, with the large-scale design of petrochemical plants, the structure of the safety instrument system is also becoming increasingly complex. Once the safety instrument system fails, the highly integrated and scaled petrochemical plants face the risk of causing significant property loss and personnel casualties. In order to further improve the reliability of the safety instrument system, the hardware redundancy method is usually used in engineering. The most common redundancy method is KooN structure, that is, N identical hardware devices are set, and the redundant system can work normally as long as no less than K devices are not faulty. Typical KooN structures include 1oo2, 2oo3 and 2oo4, etc. Due to the existence of the redundancy structure, the reliability of the safety instrument system is increasingly difficult to calculate, so a reliable model is constructed to predict the life of the KooN redundant safety instrument system, thereby guiding the maintenance and replacement of related components and devices, which can greatly improve the reliability of the safety instrument system and reduce maintenance costs and failure probability.

[0003] According to the requirements of the International Electrotechnical Commission standard IEC61508, the safety instrument system currently uses safety integrity level to measure reliability. Common simple formula method, reliability block diagram method and fault tree method all assume that the failure rate is constant, but in fact, due to equipment aging, wear and tear, etc., the failure rate of the safety instrument system and its component devices usually rises over time. Therefore, the construction of a reliable model to predict the life of the KooN redundant safety instrument system needs to consider the case that the failure rate is a time-varying parameter.

[0004] Currently, the mainstream safety instrument system life prediction methods are divided into three categories: expert experience method, artificial intelligence method and statistical method. The expert experience method is simple to implement, but the accuracy is related to the experience of relevant personnel, and generally the accuracy is low; the artificial intelligence method needs a large amount of equipment degradation data as training materials, and for safety instrument systems with high reliability, it is often difficult to obtain a large amount of degradation data; the statistical method obtains the failure time of the equipment through life test, and obtains the life prediction result based on the distribution model followed by the equipment. Among them, the commonly used distribution models in the statistical method are exponential distribution, Weibull distribution and Gamma distribution, and the life of most electronic, mechanical and electromechanical products can be considered to follow the Weibull distribution, so the Weibull distribution is the most commonly used model.

[0005] The safety instrument system internally contains many component devices, and each component device also has different fault types, so the safety instrument system can have multiple failures. These failures are usually determined by an analysis team using failure mode and effects analysis (FMEA). In the process of implementing the present application, the inventor found that the prior art for life prediction of KooN redundant safety instrument systems is mostly limited to a single fault type, without considering the condition that multiple fault types exist at the same time, which limits the universality of the life prediction method and cannot be widely applied to actual scenarios. Therefore, how to predict the life of a safety instrument system with multiple fault types existing at the same time is a difficult problem to be solved. SUMMARY

[0006] In order to solve the above problems, the embodiments of the present application provide a method for predicting the remaining life of a redundant safety instrument system, comprising: performing a life test on a safety instrument system to be predicted to construct a mixed Weibull distribution model representing the failure probability distribution characteristics of each device constituting the safety instrument system to be predicted according to the life data obtained by the test; performing maximum likelihood estimation on the mixed Weibull distribution model to obtain the maximum likelihood estimation value of the mixed Weibull distribution parameter; based on the failure device distribution characteristics corresponding to the failure of the safety instrument system to be predicted, constructing a failure distribution function of the safety instrument system to be predicted to obtain a failure probability density function, and based on this, combining the maximum likelihood estimation value to obtain the remaining life of the current safety instrument system.

[0007] Preferably, in the step of performing a life test on a safety instrument system to be predicted, a complete life test or a truncated life test is used to obtain the device operating time when different devices constituting the safety instrument system to be predicted fail, and the device operating time is taken as the life data of the corresponding device.

[0008] Preferably, in the step of constructing a mixed Weibull distribution model for representing the failure occurrence probability distribution characteristics of each device constituting the safety instrument system to be predicted, the step comprises: constructing a mixed Weibull distribution probability density function by using the number of failure types to form the mixed Weibull distribution model.

[0009] Preferably, in the process of forming the mixed Weibull distribution model, the step comprises: obtaining a corresponding cumulative distribution function according to the mixed Weibull distribution probability density function, and then obtaining a reliability function, so as to take the combination of the mixed Weibull distribution probability density function, the cumulative distribution function and the reliability function as the mixed Weibull distribution model.

[0010] Preferably, in the step of performing maximum likelihood estimation on the mixed Weibull distribution model, the step further comprises: obtaining a likelihood function of the mixed Weibull distribution parameters based on the mixed Weibull distribution model, and performing logarithmic processing on the likelihood function to determine an optimization objective for solving the maximum likelihood estimation value by using a logarithmic likelihood function, based on which a parameter estimation value at which the logarithmic likelihood function reaches a maximum value is obtained by using a heuristic search algorithm, and the parameter estimation value is taken as the maximum likelihood estimation value.

[0011] Preferably, the mixed Weibull distribution model is represented by the following expression:

[0012]

[0013] wherein f represents a mixed Weibull distribution probability density function, m represents the number of failure types, p i represents a weight of the i-th failure type sub-Weibull distribution, β i represents a shape parameter of the i-th failure type, η i represents a scale parameter of the i-th failure type, t represents a device operation time, and e represents a natural constant.

[0014] Preferably, the optimization objective is represented by the following expression:

[0015]

[0016] wherein γ represents a failure rate, lnL represents a logarithmic likelihood function, s.t. represents a constraint condition, and q represents a preset number of main failure types.

[0017] Preferably, the failure distribution function of the safety instrument system to be predicted is represented by the following expression:

[0018]

[0019] wherein F s represents a failure distribution function, N represents the total number of devices constituting the safety instrument system to be predicted, K represents the number of normal devices required for the safety instrument system to be predicted to work effectively, p and x represent random variables, C represents combination, and F represents a cumulative distribution function.

[0020] Preferably, in the step of obtaining the remaining life of the current safety instrument system, the step comprises: first, deriving the failure distribution function of the safety instrument system to be predicted to obtain the failure probability density function, and then substituting the maximum likelihood estimate into the failure probability density function to obtain an expected value representing the predicted remaining life of the current safety instrument system under the condition of multiple failure types, and further using the expected value to calculate the remaining life prediction value of the current safety instrument system at any time.

[0021] Preferably, the expected value is represented by the following expression:

[0022]

[0023] wherein E represents the expected value, t represents the running time of the device, f s represents the failure probability density function.

[0024] The application also provides a computer readable storage medium containing a series of instructions for the method steps of predicting the remaining life of the redundant safety instrument system.

[0025] In another aspect, the application also provides a system for predicting the remaining life of the redundant safety instrument system, the system comprising the following modules: a model construction module for conducting life tests on the safety instrument system to be predicted to construct a mixed Weibull distribution model representing the failure probability distribution characteristics of each device constituting the safety instrument system to be predicted according to the life data obtained by the tests; a likelihood estimation module for maximum likelihood estimation of the mixed Weibull distribution model to obtain the maximum likelihood estimate of the mixed Weibull distribution parameters; and a life prediction module for constructing a failure distribution function of the safety instrument system to be predicted based on the failure device distribution characteristics corresponding to the failure of the safety instrument system to be predicted, to obtain a failure probability density function, based on which, in combination with the maximum likelihood estimate, the remaining life of the current safety instrument system is obtained.

[0026] Compared with the prior art, one or more embodiments in the above scheme can have the following advantages or beneficial effects:

[0027] The application provides a method and system for predicting the residual life of a redundant safety instrument system. The application solves the problem that the life prediction of the redundant safety instrument system is limited to a single fault type and has a small application range, and realizes accurate prediction of the residual life of the safety instrument system with multiple fault types.

[0028] Other features and advantages of the present application will be set forth in the following description, and in part will be apparent from the description, or can be learned by practice of the present application. The objects and other advantages of the present application will be realized and attained by the structure particularly pointed out in the written description and claims thereof as well as the appended drawings. BRIEF DESCRIPTION OF DRAWINGS

[0029] The accompanying drawings are included to provide a further understanding of the present application, and are incorporated in and constitute a part of this specification, illustrate embodiments of the present application, and together with the description serve to explain the present application, and do not limit the present application. In the drawings:

[0030] Figure 1 A flow chart of the method for predicting the residual life of the redundant safety instrument system according to the embodiment of the present application.

[0031] Figure 2 An example of the probability density function of the two Weibull distribution of the method for predicting the residual life of the redundant safety instrument system according to the embodiment of the present application.

[0032] Figure 3 A schematic diagram of the correlation between the failure rate and the shape parameter of the Weibull distribution of the method for predicting the residual life of the redundant safety instrument system according to the embodiment of the present application.

[0033] Figure 4 A flow chart of the genetic algorithm of the method for predicting the residual life of the redundant safety instrument system according to the embodiment of the present application.

[0034] Figure 5 A module block diagram of a system for predicting the remaining life of a redundant safety instrumented system according to an embodiment of the present application. DETAILED DESCRIPTION

[0035] The embodiments of the present application will be described in detail with reference to the drawings and embodiments, so that the application can be understood as how to solve the technical problems and achieve the technical effects by applying technical means. It should be noted that, as long as there is no conflict, each embodiment in the present application and each feature in each embodiment can be combined with each other, and the technical solutions formed thereby are all within the protection scope of the present application.

[0036] In addition, the steps shown in the flowchart of the drawings can be executed in a computer system such as a set of computer executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described herein can be executed in an order different from that shown.

[0037] At present, the mainstream safety instrumented system life prediction methods are divided into three categories: expert experience method, artificial intelligence method and statistical method. The expert experience method is simple to implement, but the accuracy is related to the experience of the relevant personnel, and in general, the accuracy is low; the artificial intelligence method needs a large amount of equipment degradation data as training materials, and for safety instrumented systems with high reliability, degradation data is often difficult to obtain on a large scale; the statistical method is to obtain the failure time of the equipment through life test, and based on the distribution model followed by the equipment, the life prediction result is obtained. Among them, the commonly used distribution models in the statistical method are exponential distribution, Weibull distribution and Gamma distribution, etc., and the life of most electronic, mechanical and electromechanical products can be considered to follow the Weibull distribution, so the Weibull distribution is the most commonly used model.

[0038] The safety instrumented system contains many component devices, and each component device also has different fault types, so the safety instrumented system may have multiple failures. These failures are usually determined by an analysis team using failure mode and effects analysis (FMEA). In the process of implementing the present application, the inventors found that the prior art for life prediction of KooN redundant safety instrumented systems is mostly limited to a single fault type, without considering the condition that multiple fault types exist at the same time, which is more in line with the actual situation, limiting the universality of the life prediction method and making it unable to be widely applied to actual scenarios. Therefore, how to predict the life of a safety instrumented system with multiple fault types existing at the same time is a difficult problem that needs to be solved.

[0039] Therefore, in order to solve the above problems, the embodiment of the present application proposes a method and system for predicting the residual life of a redundant safety instrument system. The method considers the characteristics that multiple failure types exist at the same time in most cases of the actual safety instrument system, first performs reliability modeling on the safety instrument system to be detected with multiple failure types existing at the same time based on a mixed Weibull distribution; then, the maximum likelihood method is combined with a heuristic optimization algorithm to solve the maximum value for global optimization, so as to obtain the optimal parameters of the mixed Weibull distribution; finally, the failure probability density function is obtained based on the failure equipment distribution characteristics corresponding to the failure of the safety instrument system to be predicted, and the residual life of the current safety instrument system is further obtained in combination with the maximum likelihood estimate. The present application solves the problem that the life prediction of the redundant safety instrument system is limited to a single failure type and has a small applicable range, and realizes accurate prediction of the residual life of the safety instrument system with multiple failure types existing at the same time. At the same time, the present application only needs to obtain the life test data of the safety instrument system to be predicted and make full use of it, and can realize the prediction of the residual life without classifying the failure equipment, effectively reducing the workload. Moreover, compared with the traditional optimization algorithm, the heuristic optimization algorithm is not constrained by the initial conditions, effectively ensuring the reliability of the residual life prediction result of the present application.

[0040] Example One

[0041] Figure 1 The steps of the method for predicting the residual life of a redundant safety instrument system according to the embodiment of the present application are shown in the figure. The following will explain each step of the method with reference to Figure 1 .

[0042] As Figure 1 shown, in step S110, life test is performed on the safety instrument system to be predicted, so as to construct a mixed Weibull distribution model for representing the failure probability distribution characteristics of each device constituting the safety instrument system to be predicted according to the life data obtained by the test. The safety instrument system to be predicted in the embodiment of the present application is a KooN system composed of n devices. In the embodiment of the present application, life test is performed on the safety instrument system to be predicted until all the devices constituting the redundant structure of the safety instrument system to be predicted fail, and the life data of each device in the life test process is obtained. Then, the number m of failure types in the life data is used to construct an m-mixed Weibull distribution obeyed by each device, so as to obtain the mixed Weibull distribution model for representing the failure probability distribution characteristics of each device constituting the safety instrument system to be predicted.

[0043] In the step of performing life test on the to-be-predicted safety instrument system, full life test or truncated life test is adopted to obtain the running time of each device of the to-be-predicted safety instrument system when the device fails, and the running time is taken as the life data of the corresponding device. Specifically, the embodiment uses the conventional safety instrument system risk assessment method to assess the reliability of the to-be-predicted safety instrument system. For a safety instrument system with low reliability and easy to obtain all device life data, full life test is used to obtain the life data of each device, and for a safety instrument system with high reliability and difficult to obtain all device life data, truncated life test (for example, time truncated life test, number truncated life test, etc.) is used to obtain the life data of all devices including the right truncated data of part of the devices.

[0044] In the step of constructing a mixed Weibull distribution model for representing the failure probability distribution characteristics of each device of the to-be-predicted safety instrument system, the number of failure types is used to construct a mixed Weibull distribution probability density function to form a mixed Weibull distribution model. In the embodiment, the number of failure types m in the life data is used to construct an m-mixed Weibull distribution to which each device failure conforms, and a mixed Weibull distribution probability density function as shown in Figure 2 is formed to obtain a mixed Weibull distribution model Figure 2 (an example of the probability density function of the two Weibull distributions for the method for predicting the remaining life of the redundant safety instrument system in the embodiment). As shown in Figure 2 , there are two peaks in the image of the probability density function of the two Weibull distributions, which correspond to the failure probability of different failure types respectively, indicating that the failure probability of the two failure types is highest at the corresponding peak.

[0045] In the embodiment, the mixed Weibull distribution model is represented by the following expression:

[0046]

[0047] wherein f represents the mixed Weibull distribution probability density function, m represents the number of failure types, p i represents the weight of the i-th failure type sub-Weibull distribution, β i represents the shape parameter of the i-th failure type, η i represents the scale parameter of the i-th failure type, t represents the device running time, and e represents the natural constant.

[0048] In one specific embodiment of the application, p i , β i and ηi All are greater than 0, and

[0049] In the process of forming a hybrid Weibull distribution model, the corresponding cumulative distribution function is obtained based on the hybrid Weibull distribution probability density function, and then the reliability function is obtained. The combination of the hybrid Weibull distribution probability density function, cumulative distribution function, and reliability function constitutes the hybrid Weibull distribution model. In this embodiment, the corresponding cumulative distribution function is generated by differentiating the hybrid Weibull distribution probability density function, and the reliability function is obtained based on the generated cumulative distribution function. This forms a hybrid Weibull distribution model composed of the hybrid Weibull distribution probability density function, cumulative distribution function, and reliability function.

[0050] In this embodiment, the cumulative distribution function and the reliability function are represented by the following expressions:

[0051]

[0052] Where F represents the cumulative distribution function and R represents the reliability function.

[0053] Further, in step S120, maximum likelihood estimation is performed on the hybrid Weibull distribution model to obtain maximum likelihood estimates of the hybrid Weibull distribution parameters. In this embodiment, based on the maximum likelihood method, maximum likelihood estimation is performed on the hybrid Weibull distribution model to obtain maximum likelihood estimates of the hybrid Weibull distribution parameters, thereby obtaining the weights, shape parameters, and scale parameters of the sub-Weibull distributions for different fault types used to calculate the remaining lifetime of the current safety instrumented system.

[0054] In the step of performing maximum likelihood estimation on the mixed Weibull distribution model, the likelihood function of the mixed Weibull distribution parameters is obtained based on the mixed Weibull distribution model, and the logarithm of the likelihood function is taken. Using the log-likelihood function, the optimization objective for solving the maximum likelihood estimate is determined. Based on this, a heuristic search algorithm is used to obtain the parameter estimate that maximizes the log-likelihood function, and this estimate is used as the maximum likelihood estimate. Specifically, in this embodiment, the likelihood function of the mixed Weibull distribution parameters is listed based on the number m of fault types in the lifetime data, and the logarithm of the likelihood function is taken to determine the optimization objective for solving the maximum likelihood estimate. Next, based on the optimization objective, a heuristic search algorithm is used to optimize the weights, shape parameters, and scale parameters of the sub-Weibull distributions for different fault types used to calculate the remaining lifetime of the current safety instrumented system. This yields the parameter estimate that maximizes the log-likelihood function, which is the optimal estimate, and this estimate is used as the maximum likelihood estimate. Therefore, this invention effectively reduces the difficulty of obtaining the maximum likelihood estimate while ensuring the validity of the obtained maximum likelihood estimate.

[0055] In one specific embodiment of this application, the maximum number of lifetime data obtained in step S110 is n. However, due to the high reliability characteristics of the safety instrumented system under study, the lifetime test process is terminated after obtaining only r actual lifetime data (i.e., complete lifetime data), denoted as t. j At this point (determined based on the end time of the life test), the number of right-truncated data points is nr, denoted as t. k The corresponding likelihood function is expressed by the following expression:

[0056]

[0057] Among them, L(p i ,β i ,η i ) represents the likelihood function.

[0058] Furthermore, in a specific embodiment of this application, the log-likelihood function is expressed using the following expression:

[0059]

[0060] Where lnL represents the log-likelihood function.

[0061] In practical applications, the failure rate of the Weibull distribution has a relationship with its shape parameter as follows: Figure 3 The correlation shown is in the form of a "bathtub curve" ( Figure 3This is a schematic diagram illustrating the correlation between the failure rate and shape parameters of the Weibull distribution in the method for predicting the remaining lifetime of a redundant safety instrumented system according to an embodiment of this application. Figure 3 As shown, when the shape parameter is less than 1, it indicates that a new device has just been put into operation and testing. At this time, the failure rate is relatively high and decreases with the increase of operating time. When the shape parameter is equal to 1, it indicates that the failure of the device is an accidental failure, unrelated to aging. At this time, the failure rate is constant and does not increase with the passage of operating time. When the shape parameter is greater than 1, it indicates that the failure of the device is caused by aging. At this time, the failure rate increases with the increase of operating time. Accordingly, this embodiment is based on β. i The principle ∈ (1,10) is used to describe the reliability of the safety instrumented system to be predicted. Therefore, the optimization objective of this embodiment is expressed by the following expression:

[0062]

[0063] Where γ represents the failure rate, st represents the constraint condition, and q represents the number of preset main failure types.

[0064] In one specific embodiment of this application, a genetic algorithm is used as a heuristic search algorithm to optimize the weights, shape parameters, and scale parameters of the sub-Weibull distributions for different fault types. Figure 4 This is a flowchart of a genetic algorithm for predicting the remaining lifetime of a redundant safety instrumented system, as described in an embodiment of this application. Figure 4 As shown, firstly, in this embodiment, similar to the individual encoding in a genetic algorithm, the parameters to be optimized are encoded in binary form, generating a chromosome-like sequence to represent the parameters of individuals in the population. Then, similar to population initialization in a genetic algorithm, the population size NP is set, and NP individuals are randomly generated as the initial population, ensuring that the aforementioned encoding results (individual encodings) satisfy the optimization objective of this embodiment. Next, similar to the initial population fitness evaluation in a genetic algorithm, the optimization objective is used as the fitness of each individual in the initial population and calculated, at which point the iteration count iter is 0. Then, following a method similar to the selection, crossover, and mutation operations in a genetic algorithm, a roulette wheel selection method is used to select the parents of the next generation individuals based on their fitness, starting with the crossover probability p. c The chromosome sequences of the father and mother are crossed to generate the next generation of individuals. Then, the generated next generation individuals are sorted according to the mutation probability p. vThe mutation operation, which changes the encoding at a specific point on the chromosome, prevents the genetic algorithm from entering local optima. Next, similar to the fitness evaluation operation in the genetic algorithm, the fitness of each individual in the current population is calculated based on the optimization objective. Then, similar to the termination condition in the genetic algorithm, a preset termination condition is established, such as reaching a maximum number of iterations or the highest fitness of the population remaining unchanged for multiple consecutive iterations. Finally, if the termination condition is met, the individual with the highest fitness is output; otherwise, the next generation population is generated again, following a process similar to the selection, crossover, and mutation operations in the genetic algorithm, with the iteration count incremented by one. Based on this, the weights, optimal shape parameters, and optimal scale parameters of the optimal sub-Weibull distribution for different fault types are obtained.

[0065] Further, in step S130, based on the distribution characteristics of the faulty devices corresponding to the predicted failure of the safety instrumented system, a fault distribution function of the safety instrumented system is constructed to obtain a failure probability density function. Based on this, combined with the maximum likelihood estimate, the remaining lifetime of the current safety instrumented system is obtained. In a specific embodiment of this application, according to the working principle of the KooN system, when at least N-K+1 devices in the system fail, the entire system enters a fault state, thereby constructing a fault distribution function of the safety instrumented system to be predicted. Then, mathematical operations are performed on the constructed fault distribution function of the safety instrumented system to be predicted to construct a function (i.e., the failure probability density function of the KooN system) capable of obtaining the failure probability of the N-K+1th device among the N devices constituting the safety instrument to be predicted in the order of failure occurrence. Finally, the failure probability density function is combined with the maximum likelihood estimate in step S120 to calculate the remaining lifetime of the current safety instrumented system.

[0066] In this embodiment, the fault distribution function of the safety instrumented system to be predicted is represented by the following expression:

[0067]

[0068] Among them, F s Let represent the fault distribution function, N represent the total number of devices that make up the safety instrumented system to be predicted, K represent the number of normal devices required for the effective operation of the safety instrumented system to be predicted, p and x represent random variables, and C represent the combination.

[0069] In the step of obtaining the remaining lifetime of the current safety instrumented system, the fault distribution function of the system to be predicted is first differentiated to obtain the failure probability density function. Then, the maximum likelihood estimate is substituted into the failure probability density function to obtain the expected value representing the predicted remaining lifetime of the current safety instrumented system under the condition of multiple fault types. The expected value is then used to calculate the predicted remaining lifetime of the current safety instrumented system at any given time. Specifically, in this embodiment, the constructed fault distribution function is first differentiated to obtain the failure probability density function. Next, the maximum likelihood estimate (the weights, optimal shape parameters, and optimal scale parameters of the optimal sub-Weibull distributions corresponding to different fault types) from step S120 is substituted into the failure probability density function, and the expected value of the current failure probability density function is obtained to obtain the expected value of the failure time. Finally, the expected value is used to obtain the remaining lifetime of the current safety instrumented system at any given time.

[0070] In this embodiment, the failure probability density function is represented by the following expression:

[0071]

[0072] Among them, f s This represents the failure probability density function. The weights of the optimal sub-Weibull distribution for the i-th fault type are represented. This represents the optimal shape parameter for the i-th fault type. The optimal scale parameter represents the i-th fault type.

[0073] In this embodiment of the application, the expected value is represented by the following expression:

[0074]

[0075] Where E represents the expected value.

[0076] Furthermore, the predicted remaining lifetime of the current safety instrumented system when its actual operating time is δ is obtained using the following expression:

[0077]

[0078] Where RUL represents the predicted remaining lifetime and δ represents the actual operating time.

[0079] Example Two

[0080] In one specific embodiment of this application, the safety instrumented system to be predicted is a 2004 type safety instrumented system under two fault types (i.e., N=4, K=2). The number of lifetime data points is 1000. Fault type 1 follows a Weibull distribution with shape parameter β=5 and scale parameter η=2000, while fault type 2 follows a Weibull distribution with shape parameter β=2 and scale parameter η=800.

[0081] First, construct the mixed Weibull distribution probability density function, cumulative distribution function, and reliability function for the lifetime of individual devices within this 2oo4 system:

[0082]

[0083]

[0084] Subsequently, since the 1000 lifetime data points include 900 complete lifetime data points and 100 right-truncated data points, the corresponding likelihood function, log-likelihood function, and optimization objective are as follows:

[0085]

[0086] Next, the mutation probability p of the genetic algorithm is preset. v The crossover probability is 0.2, and the crossover probability is p. c The optimal value is 0.8, the population size NP is 500, and the maximum number of iterations is 1000. Optimizing the aforementioned objective yields the optimal weights, shape parameters, and scale parameters of the optimal sub-Weibull distributions for fault types 1 and 2.

[0087] Based on the working principle of the 2oo4 system, when at least three devices in the system fail, the entire system enters a fault state. Therefore, the failure probability density function of the 2oo4 system is obtained in a manner similar to that of Example 1:

[0088]

[0089] Finally, the weights, optimal shape parameters, and optimal scale parameters of the optimal sub-Weibull distributions corresponding to the different failure types are substituted into the failure probability density function, and the expectation of the current failure probability density function is calculated to obtain the expected value of the failure time (the expected lifetime of the 2oo4 system under the aforementioned two failure types is 790.6 days). Ultimately, the remaining lifetime of the current safety instrumented system at any given time can be obtained using the expected value.

[0090] In addition, this embodiment simulates the lifespan of 100,000 sets of the 2oo4 system and obtains an actual average lifespan of 790.1 days, with an error of 0.06% compared to the prediction result of this embodiment, further proving the feasibility of the remaining lifespan prediction method proposed in this invention.

[0091] Example Three

[0092] In one specific embodiment of this application, the safety instrumented system to be predicted is a 2oo3 type safety instrumented system (i.e., N=3, K=2) under two fault types. The number of lifetime data points is 1000. Fault type 1 follows a Weibull distribution with shape parameter β=3 and scale parameter η=1500, while fault type 2 follows a Weibull distribution with shape parameter β=5 and scale parameter η=600.

[0093] The expected lifetime of the 2oo3 system under the aforementioned two failure types was obtained in a manner similar to that of Example 1, which is 554.7 days.

[0094] In addition, this embodiment conducted a lifetime simulation on 100,000 sets of the 2oo3 system and obtained an actual average lifetime of 545.3 days, with an error of 1.7% compared with the prediction result of this embodiment. This also proves the feasibility of the remaining lifetime prediction method proposed in this invention.

[0095] Example Four

[0096] In one specific embodiment of this application, the safety instrumented system to be predicted is a 1oo2 type safety instrumented system (i.e., N=2, K=1) under two fault types. The number of lifetime data points is 1000. Fault type 1 follows a Weibull distribution with shape parameter β=3 and scale parameter η=1000, while fault type 2 follows a Weibull distribution with shape parameter β=5 and scale parameter η=1400.

[0097] The expected lifespan of the 1oo2 system under the aforementioned two failure types was obtained in a manner similar to that of Example 1, which is 1028.5 days.

[0098] In addition, this embodiment simulates the lifespan of 100,000 sets of the 2oo3 system and obtains an actual average lifespan of 1,008.9 days, which is 1.9% less than the prediction result of this embodiment. This also proves the feasibility of the remaining lifespan prediction method proposed in this invention.

[0099] Example Five

[0100] In one specific embodiment of this application, the safety instrumented system to be predicted is a 3005 type safety instrumented system (i.e., N=5, K=3) under two fault types. The number of lifetime data points is 1000. Fault type 1 follows a Weibull distribution with shape parameter β=2 and scale parameter η=1200, while fault type 2 follows a Weibull distribution with shape parameter β=4 and scale parameter η=1400.

[0101] The expected lifetime of the 3oo5 system under the aforementioned two failure types was obtained in a manner similar to that of Example 1.

[0102] In addition, this embodiment conducted a lifetime simulation on 100,000 sets of the 2oo3 system and obtained an actual average lifetime of 878.5 days, with an error of 0.15% compared with the prediction result of this embodiment, which also proves the feasibility of the remaining lifetime prediction method proposed in this invention.

[0103] Example Six

[0104] This invention also provides a computer-readable storage medium storing at least one instruction that is loaded and executed by a processor to perform the operation of predicting the remaining lifetime of a redundant safety instrumented system as performed in the method of the above embodiments. For example, the computer-readable storage medium may be ROM (Read Only Memory), RAM (Random Access Memory), CD-ROM (Compact Disc-Read Only Memory), magnetic tape, floppy disk, and optical data storage device, etc.

[0105] Example Seven

[0106] Based on the method for predicting the remaining lifetime of a redundant safety instrumented system described in Embodiment 1 above, this embodiment of the invention also provides a system for predicting the remaining lifetime of a redundant safety instrumented system (hereinafter referred to as the "remaining lifetime prediction system"). Figure 5 This is a block diagram of a system for predicting the remaining lifetime of a redundant safety instrumented system, according to an embodiment of this application.

[0107] like Figure 5As shown, the remaining lifetime prediction system in this embodiment of the invention includes: a model building module 51, a likelihood estimation module 52, and a lifetime prediction module 53. Specifically, the model building module 51 is implemented according to the method described in step S110 above, and is configured to conduct a lifetime test on the safety instrumented system to be predicted, so as to construct a hybrid Weibull distribution model representing the failure probability distribution characteristics of each device constituting the safety instrumented system to be predicted based on the lifetime data obtained from the test; the likelihood estimation module 52 is implemented according to the method described in step S120 above, and is configured to perform maximum likelihood estimation on the hybrid Weibull distribution model to obtain the maximum likelihood estimate value of the hybrid Weibull distribution parameters; the lifetime prediction module 53 is implemented according to the method described in step S130 above, and is configured to construct a failure distribution function of the safety instrumented system to be predicted based on the distribution characteristics of the faulty devices corresponding to the failure of the safety instrumented system to be predicted, so as to obtain a failure probability density function, and based on this, combined with the maximum likelihood estimate value, obtain the remaining lifetime of the current safety instrumented system.

[0108] This invention discloses a method and system for predicting the remaining lifetime of redundant safety instrumented systems (SIS). The method considers the characteristic that real-world SIS often exhibits multiple fault types simultaneously. First, it models the reliability of the SIS under test based on a mixed Weibull distribution with multiple fault types. Then, it uses a maximum likelihood method combined with a heuristic optimization algorithm to solve for the maximum value and perform global optimization, thereby obtaining the optimal parameters of the mixed Weibull distribution. Finally, based on the distribution characteristics of the faulty equipment corresponding to the predicted SIS failure, it obtains the failure probability density function and further combines it with the maximum likelihood estimate to obtain the remaining lifetime of the current SIS. This invention solves the problem that the lifetime prediction of redundant SIS is limited to a single fault type and has a small scope of application, achieving accurate prediction of the remaining lifetime of SIS with multiple fault types. Furthermore, this invention only requires acquiring and fully utilizing the lifetime test data of the SIS under test, without needing to classify faulty equipment to achieve the prediction of remaining lifetime, effectively reducing workload. Moreover, compared to traditional optimization algorithms, the heuristic optimization algorithm is not constrained by initial conditions, effectively ensuring the reliability of the remaining lifetime prediction results of this invention.

[0109] The above description represents a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

[0110] Of course, the present invention may have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications should all fall within the protection scope of the claims of the present invention.

[0111] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. Optionally, they can be implemented using computer-executable program code, thereby storing them in a storage device for execution by a computing device, or fabricating them separately as individual integrated circuit modules, or fabricating multiple modules or steps as a single integrated circuit module. Thus, the present invention is not limited to any particular hardware and software combination.

[0112] While the embodiments disclosed in this invention are as described above, the content is merely for the purpose of facilitating understanding of the invention and is not intended to limit the invention. Any person skilled in the art to which this invention pertains may make any modifications and variations in form and detail of the implementation without departing from the spirit and scope disclosed herein; however, the scope of patent protection for this invention shall still be determined by the scope defined in the appended claims.

Claims

1. A method for predicting the remaining life of a redundant safety instrumented system, characterized by, The method comprises the following steps: Performing life test on a safety instrumented system to be predicted to build a mixed Weibull distribution model for representing failure probability distribution characteristics of each device constituting the safety instrumented system to be predicted according to life data obtained in the test; Performing maximum likelihood estimation on the mixed Weibull distribution model to obtain maximum likelihood estimation values of mixed Weibull distribution parameters; Based on failure device distribution characteristics corresponding to the safety instrumented system to be predicted, constructing a failure distribution function of the safety instrumented system to be predicted to obtain a failure probability density function, based on which, combined with the maximum likelihood estimation values, the residual life of the current safety instrumented system is obtained.

2. The method of claim 1, wherein, In the step of performing life test on the safety instrumented system to be predicted, the following steps are included: Using complete life test or truncated life test to obtain device running time when different devices constituting the safety instrumented system to be predicted fail, and taking the device running time as life data of the corresponding device.

3. The method of claim 2, wherein, In the step of building the mixed Weibull distribution model for representing failure probability distribution characteristics of each device constituting the safety instrumented system to be predicted, the following steps are included: Using the number of failure types to construct a mixed Weibull distribution probability density function to form the mixed Weibull distribution model.

4. The method of claim 3, wherein, In the process of forming the mixed Weibull distribution model, the following steps are included: According to the mixed Weibull distribution probability density function, a corresponding cumulative distribution function is obtained, and then a reliability function is obtained, so that the combination of the mixed Weibull distribution probability density function, the cumulative distribution function and the reliability function is taken as the mixed Weibull distribution model.

5. The method of claim 4, wherein, In the step of performing maximum likelihood estimation on the mixed Weibull distribution model, the following steps are included: Based on the mixed Weibull distribution model, a likelihood function of the mixed Weibull distribution parameters is obtained, and the likelihood function is logarithmically processed to use the logarithmic likelihood function to determine an optimization objective for solving the maximum likelihood estimation values, based on which, a heuristic search algorithm is used to obtain parameter estimation values when the logarithmic likelihood function reaches a maximum value, and the parameter estimation values are taken as the maximum likelihood estimation values.

6. The method of claim 5, wherein, The mixed Weibull distribution model is represented by the following expression: where f denotes the mixed Weibull distribution probability density function, m denotes the number of failure types, p i denotes the weight of the i-th failure type sub-Weibull distribution, β i denotes the shape parameter of the i-th failure type, η i denotes the scale parameter of the i-th failure type, t denotes the equipment running time, and e denotes the natural constant.

7. The method of claim 6, wherein, The optimization objective is represented by the following expression: Wherein, γ represents failure rate, lnL represents logarithmic likelihood function, s.t. represents constraint condition, and q represents the number of preset main failure types.

8. The method of claim 7, wherein, The failure distribution function of the safety instrumented system to be predicted is represented by the following expression: where F s represents a failure distribution function, N represents the total number of devices that constitute the safety instrument system to be predicted, K represents the number of normal devices required for the safety instrument system to be predicted to work effectively, p and x represent random variables, C represents combination, and F represents a cumulative distribution function.

9. The method according to any one of claims 1 to 8, characterized in that, In the step of obtaining the residual life of the current safety instrumented system, the following steps are included: The derivative of the failure distribution function of the safety instrument system to be predicted is calculated to obtain the failure probability density function, and then the maximum likelihood estimation value is substituted into the failure probability density function to obtain an expected value representing the predicted residual life of the current safety instrument system under the condition of multiple failure types, and the expected value is used to calculate the residual life prediction value of the current safety instrument system at any time.

10. The method of claim 9, wherein, The expected value is represented by the following expression: where E represents the expected value, t represents the equipment running time, f s represents the failure probability density function.

11. A computer readable storage medium, characterized in that, It comprises a series of instructions for executing the method steps for predicting the residual life of a redundant safety instrument system as claimed in any one of claims 1-10.

12. A system for predicting the remaining life of a redundant safety instrumented system, comprising: The system comprises the following modules: A model construction module is configured to perform life tests on a safety instrument system to be predicted to construct a mixed Weibull distribution model representing the failure probability distribution characteristics of each device constituting the safety instrument system to be predicted based on the life data obtained from the tests; A likelihood estimation module is configured to perform maximum likelihood estimation on the mixed Weibull distribution model to obtain the maximum likelihood estimation value of the mixed Weibull distribution parameters; A life prediction module is configured to construct a failure distribution function of the safety instrument system to be predicted based on the failure device distribution characteristics corresponding to the failure of the safety instrument system to be predicted, to obtain a failure probability density function, and based on this, in combination with the maximum likelihood estimation value, to obtain the residual life of the current safety instrument system.

Images