Competitive failure reliability assessment method for multi-state power generation system

Abstract

The invention discloses a multi-state power generation system competitive failure reliability evaluation method, which comprises the following steps of: dividing failure modes of a multi-state power generation system into degradation failure caused by internal factors and sudden failure caused by external impact by combining historical failure data of the multi-state power generation system, establishing a degradation failure model and a sudden failure model of the multi-state power generation system; the interaction relation between degradation failure and sudden failure is researched, a reliability analysis model based on the semi-Markov process is established, and a multi-state system reliability analysis model based on a general generation function method is established; calculating the state probability, degradation failure reliability, impact failure reliability and competitive failure system reliability of the multi-state power generation system; the technical problems that the research on the competition failure mechanism of the reliability evaluation model of the multi-state power generation system and the comprehensive evaluation method aiming at the parameter uncertainty influence in the dependent competition failure model are incomplete and the like are solved.

Description

Technical Field

[0001] The invention belongs to the technical field of generator engineering, and in particular relates to a reliability assessment method for competitive failure of a multi-state power generation system. Background Art

[0002] As the main way of generating electricity in steam turbines, multi-state power generation systems may cause serious economic losses and environmental pollution if they fail. Some multi-state and multi-performance equipment systems, such as steam turbine power generation systems, have the characteristics of multi-state components due to the complexity of the use environment and working conditions. Therefore, the traditional two-state reliability analysis method has limitations in analyzing them, and their failure modes are often accompanied by degradation and random shocks. The two are related to each other and will compete with each other to cause system failures. Failure mechanisms such as corrosion, erosion, and fatigue will lead to different failure processes. These failure processes are often not independent, but competing and dependent on each other. This process is called a dependent competitive failure process. Ignoring the dependency between multiple failure processes may lead to an overestimation of system reliability.

[0003] The competitive relationship between degradation failure and sudden failure can be divided into degradation-shock correlation and shock-degradation correlation. In the prior art, a relatively comprehensive study has been conducted on the degradation-shock correlation, such as the increase in degradation amount or change in degradation rate caused by random shocks. However, there are relatively few studies on shock-degradation correlation. In addition, in the study of competitive failure reliability assessment, the parameter uncertainty of the distribution function is rarely considered. Due to the influence of uncertain factors such as the working environment and limited expert experience data, the parameters in the distribution function may also be uncertain. So far, the research on the competitive failure mechanism of the reliability assessment model of the multi-state power generation system and the comprehensive evaluation method for the influence of parameter uncertainty in the dependent competitive failure model are not perfect. Summary of the invention

[0004] The technical problem to be solved by the present invention is: to provide a reliability assessment method for competitive failures of a multi-state power generation system, taking into account the impact of the interaction between different failure factors on the multi-state power generation system, and realizing effective real-time assessment and prediction of the reliability of the multi-state power generation system, so as to solve the technical problems such as the research on the competitive failure mechanism of the reliability assessment model of the multi-state power generation system and the imperfect comprehensive assessment method for the influence of parameter uncertainty in the dependent competitive failure model.

[0005] The technical solution of the present invention is:

[0006] A method for evaluating the reliability of competitive failure of a multi-state power generation system, the method comprising:

[0007] Step 1: Combined with the historical failure data of the multi-state power generation system, the failure modes of the multi-state power generation system are divided into two types: degradation failure caused by internal factors and sudden failure caused by external impact, and a degradation failure model and a sudden failure model of the multi-state power generation system are established;

[0008] Step 2: Study the interaction between degradation failure and sudden failure, establish a reliability analysis model based on semi-Markov process, and establish a multi-state system reliability analysis model based on the general generating function method;

[0009] Step 3: Combined with the competitive failure mechanism of the multi-state power generation system, the state probability, degradation failure reliability, impact failure reliability and competitive failure system reliability of the multi-state power generation system are solved.

[0010] The multi-state power generation system degradation failure model includes:

[0011] The state transition process is modeled by a semi-Markov process, and the one-step transition probability is expressed as:

[0012] ξ jk =Pr{G t+1 =g k |G t =g j} j , g k ∈G

[0013] In the formula, ξ jk Represented by the state performance g j (1≤j≤n) transition to g k The probability of (1≤k≤n, k≠j), and the residence time before the two states are transformed is represented by the random variable T jk To express;

[0014] In the semi-Markov process, the relevant state chain is composed of the states of each discrete moment embedded in the continuous time history of the random process G(t), and the state transition probability is determined by the following formula:

[0015]

[0016] The degradation time T is expressed by the following formula:

[0017]

[0018] In the formula, (jk) and (kj) both represent the number of state transitions, that is, the number of states that need to be crossed; a and b represent their influencing factors.

[0019] The multi-state power generation system sudden failure model includes:

[0020] The Poisson model is used to describe the impact of random shocks on multi-state power generation systems. Assuming that the product is subjected to external environmental stress shocks, the process obeys the Poisson process as follows:

[0021]

[0022] Where θ is the number of random shocks at time t; λ is the frequency of shocks. Assuming that the shock intensity follows a normal distribution, denote mean and variance respectively;

[0023] Introducing critical threshold D 0 , the probability of normal operation of the system after an impact is:

[0024]

[0025] The impact of the internal degradation increment change caused by external shocks on the multi-state power generation system is:

[0026] The damage size is determined by the impact intensity and the cumulative degradation probability. The greater the cumulative degradation probability, the easier it is for the system to be weakened, making the system more susceptible to random shocks. Therefore, the damage size of the l-th shock to the one-step transition probability is expressed as:

[0027] Δξ jk (l) = cW l ·F(q l )

[0028] Where W l Indicates the impact intensity of the first impact; q l is the arrival time of the first impact; c is the impact factor;

[0029] Based on the principle of strength-stress interference model, random shocks can lead to a decrease in system strength, thereby increasing the probability of the system entering a degraded state. Therefore, the impact caused by random shocks can be attributed to a sudden increase in the probability of one-step transition due to degradation and a sudden decrease in the probability of one-step transition due to maintenance. If the system suffers l shocks at time point t, q l ≤t<q l+1 , the change in the probability of one-step transition caused by the impact is Δξ jk (r), (1≤r≤l), so the probability of one-step transition caused by degradation is given by the formula ξ jk (t r-1 )[1+Δξ jk (r)], and the probability of a one-step transition caused by maintenance is expressed by the formula ξ jk (t r-1 )[1-Δξ jk (r)], and the two equations are combined into the following equation:

[0030]

[0031] In the formula, ξ jk (0) represents ξ jk With the continuous impact, degradation causes the state transition rate to increase. In addition, the reduction in the transfer probability caused by maintenance will also continue to decrease with the impact. Therefore, the impact will make it more difficult to repair the product to a better state.

[0032] The reliability analysis model of multi-state power generation system based on semi-Markov process includes:

[0033] P(t)={P g1 (t),…,P gj (t),…,P gn (t)}, j = 1, ..., n

[0034] P gj (t) means that the system or component remains in state g at time t j The probability is P gj (t) = Pr{G t =g j}; At any time, the system or component should be in one of n states, namely

[0035] According to the Chapman-Kolmogorov equation, at time t the system or component is in state g j , within a time interval Δt or continue in g j state or transition to state g k (j≠k) the total probability is 1, that is:

[0036]

[0037] Where P jk (Δt) indicates the time interval of Δt. j → k The transition probability when a state change occurs;

[0038] At the next moment (t+Δt), there are two possibilities that may cause the product to be in state g j , first at time t the product is in state g k (k≠j) and in the time interval Δt, g k Transfer to g j By probability P gk (t) and ξ jk (t+Δt)F jk (τ jk +Δt); in this case, all except gj The state performance outside the state is accumulated; on the other hand, the product is in state g at time t j And no state transition occurs in the time interval Δt, the corresponding probabilities are expressed as P gj (t) and 1-Σ j≠k ξ jk (t+Δt)F jk (τ jk +Δt), then the total probability is expressed as:

[0039]

[0040] Define τ jk g j Transfer to g k The expected residence time is Divide both sides by Δt and take the limit to set Δt→0. Consider the initial condition F jk (0) = 0, F jk T jk Probability distribution function, get Substitute it into and then perform differential operations, as shown below:

[0041]

[0042] The expected shock arrival time is selected to solve the time-dependent one-step transition probability. The final result is expressed as a piecewise function divided by the expected shock arrival time, and the numerical calculation is performed using Matlab.

[0043] The established multi-state system reliability analysis model for multi-state power generation system based on the general generating function method includes: obtaining the system state performance probability requires two important elements, namely the probability function of all components and the system configuration function. The state space of component v is represented by g v = {g v1 , g v2 ,...,g v(kv)}, g vh For component v in state h(1≤h≤k v ), the steady-state probability of component v at any time is determined by a semi-Markov process, and the state probability set is expressed as P v (t) = {P v1 (t), P v2 (t),…P v(kv) (t)},P vh (t) = Pr{g v (t) = g vh}and Let L m = {g 11 ,g12 , …, g 1(k1)}×{g 21 , g 22 , …, g 2(k2)}×…×{g m1 , g m2 , …, g m(km)} is the possible state performance space of all components, and the state space G = {g 1 , g 2 , ..., g n}, mapping All possible performance levels of components and system states are connected by configuration functions. Depending on how the system is connected, the z-transformation function of the unit v is defined as follows:

[0044]

[0045] Introduce the universal generation operator and convert the unit UGF into the system Z transformation function:

[0046]

[0047] The operator Based on the structural configuration function of the system or subsystem,

[0048] The reliability of the degradation process, i.e. the soft failure process, is defined as the current state performance exceeding the system minimum required performance, given the system minimum required state g D, the corresponding system soft failure process reliability is expressed as:

[0049]

[0050] Similarly, define the minimum state requirement v of the component D , the reliability of the component soft failure process is

[0051] The reliability of the hard failure process caused by random impact on component v is expressed as follows:

[0052]

[0053] The corresponding system hard failure process reliability is

[0054] Considering the competitive failure process, that is, the system reliability of the system is affected by two failure processes that are related and competitive at the same time is as follows:

[0055]

[0056] The beneficial effects of the present invention are:

[0057] The present invention combines historical failure data of a multi-state power generation system, divides the failure modes of the multi-state power generation system into two types: degradation failure caused by internal factors and sudden failure caused by external impact, and establishes a degradation failure model and a sudden failure model for the multi-state power generation system; studies the interaction between degradation failure and sudden failure, establishes a reliability analysis model based on a semi-Markov process, and establishes a multi-state system reliability analysis model based on a universal generating function method; solves the system reliability of the state probability, degradation failure reliability, impact failure reliability and competitive failure of the multi-state power generation system; solves the technical problems of the research on the competitive failure mechanism of the reliability assessment model of the multi-state power generation system and the imperfect comprehensive assessment method for the influence of parameter uncertainty in the dependent competitive failure model. The present invention is in line with engineering practice for the reliability assessment of competitive failure of the multi-state power generation system, and the assessment result is more in line with engineering practice and has operability compared with the traditional method that does not consider failure coupling. At the same time, it has reference significance for the reliability assessment of other multi-state systems such as steam turbines, turbine systems and other products.

[0058] The technical problems such as the research on the competitive failure mechanism of the reliability assessment model of the multi-state power generation system and the imperfect comprehensive assessment method for the influence of parameter uncertainty in the dependent competitive failure model were solved. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a flow chart of a reliability assessment method for a multi-state power generation system disclosed in an embodiment of the present application;

[0060] Figure 2 It is a schematic diagram of the internal structure of the steam turbine power generation system disclosed in the embodiment of the present application. DETAILED DESCRIPTION

[0061] The specific scheme of the present invention is described in detail below in conjunction with the accompanying drawings:

[0062] like Figure 1 As shown in the figure, a real-time reliability assessment method for dependent competitive failure of a multi-state power generation system includes four major steps:

[0063] S1: Establish the failure mode of multi-state power generation system. Combined with the historical failure data of multi-state power generation system, the failure mode of multi-state power generation system is divided into two types: degradation failure caused by internal factors and sudden failure caused by external impact, and appropriate degradation and sudden failure models are selected.

[0064] The semi-Markov process is used to describe the degradation process of the multi-state power generation system. The intensity degradation time of the multi-state power generation system is a random variable T. The corresponding cumulative probability distribution function is F(T), which is the cumulative degradation probability, and f(T) is the probability density function. The intensity function, that is, the degradation rate, is expressed as f(T) / [1-F(T)]. The product has n performance states, and its state space is expressed as G={g 1 , g 2 ,... n}, state space order arrangement -g 1 Indicates that the product is completely ineffective, g n Indicates that the product is working perfectly. t is the performance status of the product at time t, T i (i=1,2…) is defined as the state performance conversion time point. From the initial state g 0 Jump to g 1 The corresponding residence time is T 1 , for time t∈[T i , T i+1 ), its state performance G t Keep in G Ti Considering the product degradation process, the residence time of the current state performance can be regarded as a random variable that obeys any specific distribution. Therefore, the state transition process can be modeled by a semi-Markov process. The one-step transition probability is expressed as:

[0065] ξ jk =Pr{G t+1 =g k |G t =g j} j , g k ∈G

[0066] In the formula, ξ jk Represented by the state performance g j (1≤j≤n) transition to g k The probability of (1≤k≤n,k≠j), and the residence time before the two states are transformed is represented by the random variable T jk To express.

[0067] In the semi-Markov process, the relevant state chain is composed of the states of each discrete moment embedded in the continuous time history of the random process G(t), also known as an embedded Markov chain, that is, the future state depends only on the current state and the corresponding residence time, and has nothing to do with the past state. Therefore, the state transition probability can be determined by the following formula:

[0068]

[0069] As for the degradation time random variable T, it reflects the internal coping performance of the product when it is subjected to stress. The smaller the degradation rate of the product, the smaller the cumulative degradation probability. Therefore, the smaller the T value, the worse its resistance to external impact, then the product will be more fragile when it degrades, and it will also increase the difficulty of recovering to better performance. Similarly, under the same cumulative degradation probability, the probability of 9k→gj for products with a smaller degradation rate is also smaller. Therefore, the smaller T is, the shorter the residence time in the current state when degradation occurs and causes a state transition. The degradation time T is inversely proportional to the duration of the state deviation caused by maintenance. It can be expressed by the following formula:

[0070]

[0071] In the formula, (jk) and (kj) both represent the number of state transitions, that is, the number of states that need to be crossed; a and b represent their influencing factors.

[0072] S2: The Poisson model is used to describe the impact of random shocks on the multi-state power generation system. Assuming that the product is subjected to external environmental stress (temperature, humidity, voltage, etc.), the process obeys the Poisson process as follows:

[0073]

[0074] Where θ is the number of random shocks at time t; λ is the frequency of shocks. Assume that the shock intensity follows a normal distribution, that is, represent mean and variance respectively.

[0075] In addition to degradation to complete failure, the system may also fail suddenly due to a shock exceeding the critical threshold. 0 , the probability of normal operation of the system after an impact is:

[0076]

[0077] The impact of the internal degradation increment change caused by the external shock of the multi-state power generation system is:

[0078] In order to analyze the impact of random shocks on the state transition process, it is assumed that random shocks cause a sudden change in the probability of one-step transition, making it easier for the system to transition to a degraded state. For the damage caused by the shock, the acceleration of the failure evolution process caused by the shock damage and the inherent tolerance of the system to resist random shocks are considered. Therefore, the damage size should be determined by the shock intensity and the cumulative degradation probability. The greater the cumulative degradation probability, the easier it is for the strength of the system to be weakened, making the system more susceptible to random shocks. Therefore, the damage size of the lth shock to the one-step transition probability should be expressed as:

[0079] Δξ jk (l) = cW l ·F(q l )

[0080] Where W l Indicates the impact intensity of the first impact; q l is the arrival time of the first impact; c is the impact factor.

[0081] Based on the principle of strength-stress interference model, random shocks can lead to a decrease in system strength, thereby increasing the probability of the system entering a degraded state. Therefore, the impact caused by random shocks can be attributed to a sudden increase in the probability of a one-step transition due to degradation and a sudden decrease in the probability of a one-step transition due to maintenance. l ≤t<q l+1 ) suffered l shocks, and the change in the probability of one-step transition caused by the shocks is Δξ jk (r), (1≤r≤l), so the probability of one-step transition caused by degradation can be expressed by this formula ξ jk (t r-1 )[1+Δξ jk (r)], similarly, the probability of a one-step transition due to maintenance can be expressed by this formula ξ jk (t r-1 )[1-Δξ jk (r)]. The two equations can be combined into the following equation:

[0082]

[0083] In the formula, ξ jk (0) represents ξ jk With the continuous impact, degradation leads to an increase in the state transition rate. In addition, the reduction in the transition probability caused by maintenance will also continue to decrease with the impact. Therefore, the impact will make it more difficult to repair the product to a better state.

[0084] S3: The reliability analysis model of multi-state power generation system based on semi-Markov process is:

[0085] P(t)={P g1 (t),…,P gj (t),…,P gn (t)}, j = 1, ..., n

[0086] P gj (t) means that the system or component remains in state g at time t j The probability is P gj (t) = Pr{G t =g j}.

[0087] At any time, a system or component should be in one of n states:

[0088] According to the Chapman-Kolmogorov equation, at time t the system or component is in state g j , within a time interval Δt, or continue to be in g j state or transition to state g k (j≠k) the total probability is 1, that is:

[0089]

[0090] Where P jk (Δt) indicates the time interval of Δt. j → k The transition probability when a state change occurs.

[0091] At the next moment (t+Δt), there are two possibilities that may cause the product to be in state g j First, at time t, the product is in state g k (k≠j) and in the time interval Δt, g k Transfer to g j By probability P gk (t) and ξ jk (t+Δt)F jk (τ jk +Δt). In this case, all the j The state performance outside the state is accumulated. On the other hand, the product is in state g at time t j And no state transition occurs in the time interval Δt, the corresponding probabilities are expressed as P gj (t) and 1-∑ j≠k ξ jk (y+Δt)F jk (τ jk +Δt). Then the total probability can be expressed as:

[0092]

[0093] Define τ jk g j Transfer to g k The expected residence time is Divide both sides of the above equation by Δt, and take the limit to set Δt→0. Consider the initial condition F jk (0) = 0, F jk T jk The probability distribution function can also be obtained Substitute it into the formula and then perform differential operation, as shown below:

[0094]

[0095] The expected shock arrival time is chosen to solve the time-dependent one-step transition probability. The final result is expressed as a piecewise function divided by the expected shock arrival time. The numerical calculations are performed using Matlab.

[0096] S4: The multi-state system reliability analysis model of the multi-state power generation system based on the general generating function method is:

[0097] Obtaining the probability of system state performance requires two important elements, namely the probability function of all components and the configuration function of the system. The state space of component v is represented by g v = {g v1 , g v2 , ..., g v(kv)}, g vh For component v in state h(1≤h≤k v The steady-state probability of component v at any time can be determined by the semi-Markov process of the present invention, and the state probability set is expressed as P v (t) = {P v1 (t), P v2 (t), ...P v(kv) (t)},P vh (t) = Pr{g v (t) = g vh}and Let L m = {g 11 , g 12 , ..., g 1(k1}×{g 21 , g 22 , ..., g 2(k2)}×…×{g m1 , g m2 , ..., g m(km)} is the space of all possible state performances of all components. State space G = {g 1 , g 2 , ..., g n}, mapping All possible performance levels of components and system states are connected using configuration functions. Configuration function Depends on how the system is connected. The z-transformation function of unit v is defined as follows:

[0098]

[0099] Introduce the universal generation operator and convert the unit UGF into the system Z transformation function:

[0100]

[0101] The operator Structural configuration functions based on systems or subsystems.

[0102] The reliability of the degradation process, i.e. the soft failure process, can be defined as the current state performance exceeding the system minimum required performance. Given the system minimum required state g D , the corresponding system soft failure process reliability is expressed as:

[0103]

[0104] Similarly, define the minimum state requirement v of the component D , the reliability of the component soft failure process is

[0105] The reliability of the hard failure process caused by random impact on component v is expressed as follows:

[0106]

[0107] The corresponding system hard failure process reliability is

[0108] Considering the competitive failure process, that is, the system reliability of the system is affected by two failure processes that are related and competitive at the same time is as follows:

[0109]

Claims

1. A method for evaluating the reliability of a multi-state power generation system under competitive failure, characterized in that: The method comprises: Step 1: Combined with the historical failure data of the multi-state power generation system, the failure modes of the multi-state power generation system are divided into two types: degradation failure caused by internal factors and sudden failure caused by external impact, and a degradation failure model and a sudden failure model of the multi-state power generation system are established; Step 2: Study the interaction between degradation failure and sudden failure, establish a reliability analysis model based on semi-Markov process, and establish a multi-state system reliability analysis model based on the general generating function method; Step 3: Calculate the state probability, degradation failure reliability, impact failure reliability and system reliability of competitive failure of the multi-state power generation system.

2. A method for evaluating reliability of competitive failure of a multi-state power generation system according to claim 1, characterized in that: The multi-state power generation system degradation failure model includes: The state transition process is modeled by a semi-Markov process, and the one-step transition probability is expressed as: ξ jk =Pr{G t+1 =g k |G t =g j }g j ,g k ∈G In the formula, ξ jk Represented by the state performance g j (1≤j≤n) transition to g k The probability of (1≤k≤n, k≠j), and the residence time before the two states are transformed is represented by the random variable T jk To express; In the semi-Markov process, the relevant state chain is composed of the states of each discrete moment embedded in the continuous time history of the random process G(t), and the state transition probability is determined by the following formula: The degradation time T is expressed by the following formula: In the formula, (jk) and (kj) both represent the number of state transitions, that is, the number of states that need to be crossed; a and b represent their influencing factors.

3. A method for evaluating reliability of competitive failure of a multi-state power generation system according to claim 1, characterized in that: The sudden failure model of multi-state power generation system includes: The Poisson model is used to describe the impact of random shocks on multi-state power generation systems. Assuming that the product is subjected to external environmental stress shocks, the process obeys the Poisson process as follows: Where θ is the number of random shocks at time t; λ is the frequency of shocks. Assuming that the shock intensity follows a normal distribution, denote mean and variance respectively; Introducing the critical threshold D0, the probability of normal operation of the system after an impact is: The impact of the internal degradation increment change caused by external shocks on the multi-state power generation system is: The damage size is determined by the impact intensity and the cumulative degradation probability. The greater the cumulative degradation probability, the easier it is for the system to be weakened, making the system more susceptible to random shocks. Therefore, the damage size of the l-th shock to the one-step transition probability is expressed as: Δξ jk (l)=cW l ·F(q l ) Where W l Indicates the impact intensity of the first impact; q l is the arrival time of the first impact; c is the impact factor; Based on the principle of strength-stress interference model, random shocks can lead to a decrease in system strength, thereby increasing the probability of the system entering a degraded state. Therefore, the impact caused by random shocks can be attributed to a sudden increase in the probability of one-step transition due to degradation and a sudden decrease in the probability of one-step transition due to maintenance. If the system suffers l shocks at time point t, q l ≤t<q l+1 , the change in the probability of one-step transition caused by the impact is Δξ jk (r), (1≤r≤l), so the probability of one-step transition caused by degradation is given by the formula ξ jk (t r-1 )[1+Δξ jk (r)], and the probability of a one-step transition caused by maintenance is expressed by the formula ξ jk (t r-1 )[1-Δξ jk (r)], and the two equations are combined into the following equation: In the formula, ξ jk (0) represents ξ jk With the continuous impact, degradation causes the state transition rate to increase. In addition, the reduction in the transfer probability caused by maintenance will also continue to decrease with the impact. Therefore, the impact will make it more difficult to repair the product to a better state.

4. A method for evaluating reliability of competitive failure of a multi-state power generation system according to claim 1, characterized in that: The reliability analysis model of multi-state power generation system based on semi-Markov process includes: P(t)={P g1 (t),…,P gj (t),…,P gn (t)},j=1,…,n P gj (t) means that the system or component remains in state g at time t j The probability is P gj (t) = Pr{G t =g j }; At any time, a system or component should be in one of n states: According to the Chapman-Kolmogorov equation, at time t the system or component is in state g j , within a time interval Δt or continue in g j state or transition to state g k (j≠k) the total probability is 1, that is: Where P jk (Δt) indicates the time interval of Δt. j → k The transition probability when a state change occurs; At the next moment (t+Δt), there are two possibilities that may cause the product to be in state g j , first at time t the product is in state g k (k≠j) and in the time interval Δt, g k Transfer to g j By probability P gk (t) and ξ jk (t+Δt)F jk (τ jk +Δt); in this case, all except g j The state performance outside the state is accumulated; on the other hand, the product is in state g at time t j And no state transition occurs in the time interval Δt, the corresponding probabilities are expressed as P gj (t) and 1-∑ j≠k ξ jk (t+Δt)F jk (τ jk +Δt), then the total probability is expressed as: Define τ jk g j Transfer to g k The expected residence time is Divide both sides by Δt and take the limit to set Δt→0. Consider the initial condition F jk (0) = 0, F jk T jk Probability distribution function, get Substitute it into and then perform differential operations, as shown below: The expected shock arrival time is selected to solve the time-dependent one-step transition probability. The final result is expressed as a piecewise function divided by the expected shock arrival time, and the numerical calculation is performed using Matlab.

5. The method for evaluating reliability of competitive failure of a multi-state power generation system according to claim 1, characterized in that: The established multi-state system reliability analysis model for multi-state power generation system based on the general generating function method includes: obtaining the system state performance probability requires two important elements, namely the probability function of all components and the system configuration function. The state space of component v is represented by g v = {g v1 , g v2 , ..., g v(kv) }, g vh For component v in state h(1≤h≤k v ), the steady-state probability of component v at any time is determined by a semi-Markov process, and the state probability set is expressed as P v (t) = {P v1 (t), P v2 (t), ...P v(kv) (t)},P vh (t) = Pr{g v (t) = g vh }and Let L m = {g 11 , g 12 , …, g 1(k1) }×{g 21 , g 22 , …, g 2(k2} }×…×{g m1 , g m2 , ..., g m(km) } is the possible state performance space of all components, and the state space G = {g1, g2, ..., g n }, mapping All possible performance levels of components and system states are connected by configuration functions. Depending on how the system is connected, the z-transformation function of the unit v is defined as follows: Introduce the universal generation operator and convert the unit UGF into the system Z transformation function: The operator Based on the structural configuration function of the system or subsystem, The reliability of the degradation process, i.e. the soft failure process, is defined as the current state performance exceeding the minimum required performance of the system. Given the minimum required state of the system g D , the corresponding system soft failure process reliability is expressed as: Similarly, define the minimum state requirement v of the component D , the reliability of the component soft failure process is The reliability of the hard failure process caused by random impact on component v is expressed as follows: The corresponding system hard failure process reliability is Considering the competitive failure process, that is, the system reliability of the system is affected by two failure processes that are related and competitive at the same time is as follows:

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