A method for dissipative analysis of system failure processes

Abstract

The present application relates to the field of safety science and technology, and provides a dissipative analysis method of system failure process, the system failure evolution process is a changing process influenced by the outside world, and the method is provided for determining the dissipative property thereof; the characteristics of the system failure evolution process are discussed, the dissipative property of the evolution is studied, and a calculation method of key parameters in the dissipative structure is proposed; the evolution process satisfies four conditions of the dissipative structure; the calculation method of the key parameters can be constructed with the aid of the physical meaning of the evolution process and the mathematical method of the spatial failure network, so as to quantitatively calculate and judge the dissipative property of the evolution process; and the method can be used to judge and predict the influence of the final result of the system failure evolution process on subsequent events. The present application can quantitatively calculate and judge the dissipative property of the system failure evolution process, and according to the result of the dissipative property, whether the system failure evolution process is stable and whether there is a failure overflow risk can be judged.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of safety science and technology, in particular to a dissipative analysis method of system failure process, which can judge and predict the influence of the final result of system failure evolution process on subsequent events. BACKGROUND

[0002] The occurrence and development of system failure is a dynamic, nonlinear and uncertain system function state change process, which changes between reliable and failure states. The system failure process is not isolated and must exchange energy, information and matter with the outside of the system. Moreover, the system formed as a research object is only a part divided in a larger system, which depends on the boundary conditions of research requirements. Therefore, after the system is affected by the outside, it experiences system failure evolution and reaches stability without continuing to affect the occurrence of subsequent events; or the unbalanced instability evolves the result to continue to transmit to the outside, leading to the occurrence of failure events outside the studied system. Safety science emphasizes essential safety, that is, even after failure, it is hoped that subsequent accidents will not expand. Therefore, it is necessary to study whether the system failure evolution process transmits the failure result to the outside in the process of changes in external influencing factors. This is the key to predicting the system failure evolution process and the basis for taking measures in advance. Existing research has achieved system failure analysis through different theories and methods, including related research on causes and results, prediction, prevention and management. However, these methods do not study whether the system failure evolution process is stable, whether there is a risk of failure overflow, and only remain in the process and mechanism research of system failure evolution itself.

[0003] To study whether the system failure evolution result is stable and whether there is an overflow risk, the present application provides a dissipative analysis method of system failure process based on dissipative structure. The calculation method of key parameters of dissipative structure is established based on the spatial failure network theory. This method provides a method for determining the effect of system failure evolution process on the outside and a prediction basis for the occurrence of subsequent events. SUMMARY

[0004] The present application aims to provide a dissipative analysis method of system failure process to solve the problem that the existing system failure process analysis method does not consider whether the system failure evolution process is stable and whether there is a risk of failure overflow.

[0005] Firstly, the characteristics of system failure evolution process are described:

[0006] The system failure evolution process is a concept set describing the change of system function in the running process. The corresponding theory and mathematical method proposed is the spatial failure network theory. The system failure evolution process describes the fluctuation of system function state in the process of environmental factor change, which is a continuous change set of system function state.

[0007] The system fault evolution process has complex structure and hierarchy. The structure includes experience events, influence factors, logical relations and evolution conditions. Experience events are the specific manifestations of the system fault evolution process, and different events in different stages constitute the main body of the evolution process, which are the initiators and implementers of the evolution process. Generally, events are divided into cause events and result events, and cause events lead to result events. Events in different positions in the evolution process can be divided into edge events, process events and final events. Events without cause events are edge events; events without result events are final events; events that are both cause events and result events are process events. Influence factors are the reasons for the change of the evolution process. They mainly affect the state of experience events. Since the main body of the event is a physical element, different factors lead to different element performances, and finally lead to different abilities of events to realize their own functions. In fact, factors affect experience events, logical relations and evolution conditions, but the most obvious is experience events. Logical relations represent the action relationship between events, such as multiple cause events leading to single result events. Logical relations are a comprehensive representation of the action relationship between multiple events. Evolution conditions represent the conditions required for cause events to lead to result events. Therefore, the system fault evolution process is a process in which cause events lead to result events according to logical relations and meet evolution conditions in the factor change process. The evolution process formed by the connection of the most basic unit of all cause events and all result events is the system fault evolution process, which is generally a network topology structure.

[0008] The hierarchy of the system fault evolution process is divided into system evolution layer, event layer, factor layer, factor phase layer and factor phase value layer from top to bottom. The state of the object in a certain layer depends on the superposition of the state of the object in the lower layer. The invention uses the superposition of quantum states to realize this superposition. It can be seen that the system function state in the system fault evolution process mainly depends on events and factors, and events represent the entity of evolution, and factors represent the reason of evolution.

[0009] The invention proposes a spatial fault network theory to describe the system fault evolution process, which is the third stage of the spatial fault tree theory. Experience events, influence factors, logical relations and evolution conditions are abstracted as nodes, connections and their contained attributes. The spatial fault network is analyzed by mathematical methods, so as to study the inherent characteristics of the system fault evolution process and carry out numerical analysis.

[0010] The system failure evolution process is influenced by external factors, and is uninterrupted and continuous. The complex structure and hierarchy lead to complex internal evolution process. The system function state in evolution represents the change rule, range and period of evolution. The system function state is always in the superposition state of complete failure and complete reliability, and fluctuates around the core of change. Once the fluctuation is large, it will lead to the final result of evolution continuing to affect the system, and failure spillover occurs. This is the same as the basic idea of dissipative structure, so the system failure evolution process can be studied based on the idea of dissipative structure.

[0011] Secondly, the analysis of failure evolution and dissipative conditions is described:

[0012] Generally, dissipative structure refers to an open system far from equilibrium, which forms and maintains an ordered structure state in time, space or function from a disordered state through internal nonlinear dynamic mechanism in the process of continuously exchanging matter and energy with the outside world. Therefore, dissipative nature must meet four conditions, including non-equilibrium state, nonlinear relationship, open system and fluctuation state.

[0013] The requirement of non-equilibrium state is due to the need of dissipative structure to form an ordered stable structure in a non-equilibrium state. The system failure evolution process has complex structure and hierarchy. In the evolution process, the system function state will always change due to the change of factors. In this process, with the change of factors, the state of each event in the system also changes. When the factors remain unchanged, a relatively stable evolution process can be formed, that is, a certain evolution process and final result, realizing the so-called interpretability, transparency and risk-free of analysis results. But in the actual process, this is difficult to achieve, and there is no environment where factors remain unchanged. Therefore, the system function state of the system failure evolution process is always changing between reliability and failure, and it is difficult to determine a suitable equilibrium state. Even if the theoretical equilibrium state is obtained, it can only be in this state for a moment, and the non-equilibrium state is the norm. It can be seen that the system failure evolution process meets the requirement of non-equilibrium state.

[0014] Nonlinear relationship generally refers to the complex relationship between system input and output, which does not have a simple linear mapping relationship. In terms of calculation, single factor change and event state form a characteristic function, and all factor influences form a failure probability distribution when all characteristic functions are used, which is numerical calculation; the interaction between events is represented by logical relationship, including the most basic and or relationship, or more detailed 20 kinds of flexible logical relationship, which is logical operation; the condition that the cause event meets to lead to the result event also needs to be converted into probability for operation. Further, the system function state is the superposition of event state and factor state, which is realized by using the superposition of quantum state wave function. Therefore, from the aspects of calculation, structure and state, the causes and results of the system failure evolution process cannot be linearly related.

[0015] The so-called open system is a system itself and the outside environment have energy, information and material exchange. In theory, any system has openness and must be open. Taking the system failure evolution process as the object, although the events, logical relationships and evolution conditions in the system structure are basically fixed after the system is formed, the influencing factors are constantly changing. The results of failure evolution also constantly affect the events outside the system. A system failure evolution process is inevitably part of a larger system failure evolution process, only because the research target needs to define the research scope. Therefore, the system failure evolution process is an open system.

[0016] The fluctuation state is reflected in the system input and output. The input in the system failure evolution process is the value of the influencing factor changing in the value range, and the output is the change state of the system function state between reliability and failure in the evolution. Whether there is a so-called stable value or intermediate value, the system failure evolution is bound to fluctuate at any time, and its results also fluctuate at any time.

[0017] As can be seen from the above, the system failure evolution process meets the conditions of dissipative structure, and therefore can be studied as a dissipative structure.

[0018] Based on the above principles, the invention analyzes the dissipative nature of the system failure process to determine whether the system failure process is stable and whether the system failure has an overflow risk.

[0019] Specifically, the invention provides a dissipative analysis method for a system failure process, which is also called a system failure evolution process. The system failure evolution process is a constantly changing process affected by the outside world. The invention proposes a dissipative analysis method for the system failure process to determine its dissipative nature; discusses the characteristics of the system failure evolution process, studies the dissipative nature of the evolution, and proposes a calculation method for the key parameters in the dissipative structure; the evolution process meets the four conditions of the dissipative structure; with the physical meaning of the evolution process and the mathematical method of the spatial failure network, the calculation method of the key parameters is constructed, so as to quantitatively calculate and judge the dissipative nature of the evolution process; used for judging and predicting the influence of the final result of the system failure evolution process on the subsequent events.

[0020] Dissipative structure analysis:

[0021] The dissipative structure theory is used to study various problems, and the Brusselator is used to construct the dynamic equation required for analysis.

[0022]

[0023] The formula (1) is the reaction equation group of Brussels model. A and B are reactants, which are consumed and replenished in the reaction process; D and E are products, which are taken away in the reaction process; x and y are intermediate products; k1, k2, k3 and k4 are catalysts in the reaction, and their quantity influences the reaction speed. The kinetic equation of the reaction is shown in the formula (2).

[0024]

[0025] It is further assumed that b=k2B / k4, τ=k4t, and the formula (2) is converted to the formula (3).

[0026]

[0027] The formula (3) has a unique singular point (a, b / a), and the coordinate conversion is carried out with the point as the origin, i.e. γ=u-a, η=v-b / a, and the formula (3) is converted to the formula (4).

[0028]

[0029] In the formula (4), the nonlinear term is not considered, the system stability is determined by solving the linear equation, the formula (4) is converted to the formula (5), and the solving process is shown in the formula (6).

[0030]

[0031]

[0032] The research considers that when λ 1,2 is negative real part, i.e. b-1-a 2 <0, the system is non-dissipative structure; when λ 2 is positive real part, i.e. b-1-a >0, the system is dissipative structure. Therefore, the values of a and b need to be determined to determine whether the system is dissipative structure, and the values of k1, k2, k3 and k4 and A and B need to be determined, which are the key parameters for determining the dissipative structure. It can be seen that the parameters need to be determined to complete the dissipative research of the system failure evolution process, and the physical meaning of the parameters in the evolution process needs to be understood.

[0033] Dissipative parameter determination:

[0034] In combination with the characteristics of the system failure evolution process, the evolution and dissipative conditions, and the analysis process of the dissipative structure, the key parameters for determining the dissipative structure of the system failure evolution process are determined. According to the formula (1) and the characteristics of the system failure evolution process, the parameters in the formula (1) are explained and described. A is the reason event for increasing the failure probability, and (↑) is used to represent the state of increasing the probability, i.e. the reason event (↑), N ANumber of events representing cause events (↑). x: Evolution result event failure probability increase, represented as result event (↑). B: Cause event with failure probability decrease, represented as state of probability decrease, i.e. cause event (↓), N B Number of events representing cause events (↓). y: Evolution result event failure probability decrease, represented as result event (↓). D: Failure consequence of system failure evolution process. E: Failure overflow of system failure evolution process. The number of A, B needs to be normalized, using A, B as the normalization value without causing ambiguity, i.e. The above definitions are brought into equation (1), which can explain the physical meaning contained in the four equations.

[0035] Determine the values of k1, k2, k3 and k4. In equation (1), they identify the catalyst of the reaction, i.e. they only change the speed of the reaction, but do not change themselves. Corresponding to the system failure evolution process, the speed of evolution transmission between events in the evolution process can be used, or the inverse of the time required for evolution transmission. To realize quantitative calculation, the spatial failure network theory needs to be introduced.

[0036] The spatial failure network theory is a set of mathematical methods proposed by the present invention to describe the system failure evolution process. The failure evolution process is abstracted as a network topology structure. In the network structure, events are represented by nodes, evolution transmission processes are represented by connections, factor influences are represented by characteristic functions and failure probability distributions, and logical relationships are represented by result events.

[0037] Let the event set of the spatial failure network be E = {e1, …, e I}, I represents the total number of events. The path set is L = {l1, …, l N}, N is the number of paths. The network structure is decomposed into paths. The transmission time set is T = {t1, …, t M}, M is the number of transmissions, t represents the time for a cause event to achieve evolution transmission to a result event. The overflow transmission time set after the final result event is T' = {t M+1 ,…,t M+Δ}, Δ is the overflow transmission number, representing the transmission time caused by other events after the system failure evolution process. The transmission time set of a certain path is M n , which is the number of transmissions. According to the spatial failure network simplification method, when a cause event leads to a result event with an or relationship, multiple independent paths can be formed; when a cause event leads to a result event with an and relationship, only one path is still formed, and the transmission time of these cause events leading to the result event is the maximum value of all transmission times, t = Max{t i ,t j}.

[0038] The determination of k1, k2, k3 and k4 is illustrated by the change of system fault evolution in an evolution time.

[0039] k1: the average value reciprocal of the total sum of transmission time in all paths from the cause event (↑) to the final result event (↑), as shown in equation (7).

[0040]

[0041] In the formula: l n The first ↑ in (↑↑) represents the cause event state, and the second ↑ represents the final result event state.

[0042] k2: the average value reciprocal of the total sum of transmission time in all paths from the cause event (↓) to the final result event (↓), as shown in equation (8).

[0043]

[0044] In the formula: l n The first ↓ in (↓↓) represents the cause event state, and the second ↓ represents the final result event state.

[0045] k3: the average value reciprocal of the total sum of transmission time in all paths from the cause event (↑↓) to the final result event (↑), as shown in equation (9).

[0046]

[0047] In the formula: l n The first ↑ in (↑↑) represents the cause event state, and the second ↑ represents the final result event state. n The first ↓ in (↓↑) represents the cause event state, and the second ↑ represents the final result event state.

[0048] k4: the maximum value of the reciprocal of each transmission time caused by the final result event (↑) to the subsequent event, as shown in equation (10).

[0049] k4 = Max {1 / t M+1 ,…, 1 / t M+Δ} (10)

[0050] The above method based on the characteristics of system fault evolution process and the spatial fault network realizes the determination of the values of k1, k2, k3 and k4 and the values of A and B.

[0051] Of course, other forms of calculation methods can also be constructed according to their physical meanings, and the calculation of these parameters is not unique.

[0052] The letters not specially marked for meaning in this application are intermediate variables.

[0053] The system fault evolution process dissipative analysis method provided by the application can judge the dissipative nature of the system fault evolution process through quantitative calculation, and the system fault evolution process can be judged to be stable or not to have a fault overflow risk according to the dissipative result. BRIEF DESCRIPTION OF DRAWINGS

[0054] Figure 1 A schematic diagram of a system fault evolution process example is shown. DETAILED DESCRIPTION

[0055] The above method is used to judge the dissipative nature of the evolution process through a simple electrical system fault evolution process as follows.

[0056] Figure 1 e1, e2, e4, and e6 are edge events, e3 and e5 are process events, and e7 is a final event, i.e., a final result event. "+" and "·" represent the or and relationship of the cause events. ↑ and ↓ represent the increase and decrease of the corresponding event failure probability. t1, t2, t3, t4, t5, and t6 are evolution transmission times, and T = {t1, t2, t3, t4, t5, t6}. t7 and t8 are overflow transmission times. It is assumed that t1 = 2, t2 = 3, t3 = 4, t4 = 3, t5 = 5, t6 = 4, t7 = 3, and t8 = 2 time units.

[0057] According to the space fault network theory, e7 is taken as the final result event, and simplification is performed to obtain e7 = e6 + e5 = e6 + e3 · e4 = e6 + (e1 + e2) e4 = e6 + e1 e4 + e2 e4. This indicates that there are three paths that lead to the occurrence of the final result event in the evolution process. Referring to Figure 1 , the three paths L = {l1, l2, l3} are l1(↑↑): e6↑→e7↑, l1(↑↑) = {t6} = {4}; l2(↑↑): e1↑→e3·e4↓→e5→e7↑, l2(↑↑) = {t1, Max{t3, t4}, t5} = {2, 4, 5}; and l3(↓↑): e2↓→e3·e4↓→e5→e7↑, l3(↓↑) = {t2, Max{t3, t4}, t5} = {3, 4, 5}.

[0058] According to formulas (7) to (10), respectively, k2 = 0, N A = N B = 2, so A = 0.5 and B = 0.5. Further according to b = k2B / k4, and k1, k2, k3, and k4 are brought in to obtain b = 0. The result satisfies b < 1 + a 2The system failure evolution process is not a dissipative structure under the condition, so the system failure evolution process in the system does not produce failure overflow, and does not cause t7 and t8 to appear, and the evolution process has no influence on the outside world.

[0059] The system failure evolution process is the change process of the system function state under the influence of multiple factors, and the state fluctuates between reliability and failure. As a part of the evolution process in a larger range, the evolution process may continue to evolve and affect the occurrence of subsequent failure events, or may reach self-dynamic balance and not continue to develop. The above characteristics meet the condition of dissipative structure, so the dissipative theory is used to analyze the dissipation of the system failure evolution process. With the help of the mathematical method of the space failure network, the calculation method of the key parameters is given, so that the dissipation of the system failure evolution process can be judged by quantitative calculation.

[0060] The cause event in the application can be aging and damage of the insulating layer of the wire, loosening of the wire connection, oxidation, mold, etc., and the result event can be power failure, line failure, component failure, etc.

[0061] The application is also applicable to the analysis of the system failure process other than the system failure evolution process of the electrical system. When the failure system is judged to be a dissipative system, it is considered that the system failure evolution process is stable, and there is no risk of failure overflow; when the failure system is judged to be a dissipative system, it is considered that the system failure evolution process is unstable, and there is a risk of failure overflow.

Claims

1. A method for dissipative analysis of system failure processes, characterized in that, The system failure evolution process is a constantly changing process influenced by external factors. This method is proposed to determine its dissipative nature. The characteristics of the system failure evolution process are discussed, the dissipative nature of the evolution is studied, and a method for calculating key parameters in the dissipative structure is proposed. The evolutionary process satisfies the four conditions of dissipative structures; by leveraging the physical meaning of the evolutionary process and the mathematical methods of spatial fault networks, a calculation method for key parameters is constructed, thereby quantitatively calculating and judging the dissipativeness of the evolutionary process; Used to determine and predict the impact of the final outcome of a system failure evolution process on subsequent events; Use the Brussels apparatus to construct the dynamic equations required for the analysis; Equation (1) is the Brussels model reaction equation set; A and B are reactants, which are continuously consumed and replenished during the reaction; D and E are products, which are continuously removed during the reaction; x and y are intermediate products; k1, k2, k3 and k4 are catalysts in the reaction, and their quantity affects the reaction rate; the kinetic equation of the reaction is shown in Equation (2). Further set Substituting b = k2B / k4 and τ = k4t into equation (2), we obtain equation (3). Equation (3) has a unique singularity (a, b / a). Using this point as the origin, we perform coordinate transformation γ = ua and η = vb / a, and substitute them into equation (3) to obtain equation (4). In equation (4), nonlinear terms are not considered. The stability of the system is determined by solving the linear equation, and equation (4) is transformed into equation (5). The solution process is shown in equation (6); When λ 1,2 When the real part is negative, i.e., b-1-a 2 <0, the system is a non-dissipative structure; when it is a positive real part, i.e., b⁻¹-a 2 >0 indicates that the system is a dissipative structure; to determine the dissipative structure, we need to determine the values ​​of a and b, and further determine the values ​​of k1, k2, k3 and k4 and the values ​​of A and B. These are the key parameters for determining dissipativeness. Dissipation parameters determined; The analysis process combines the characteristics of system failure evolution, evolution and dissipation conditions, and dissipation structure. Identify the key parameters for assessing the dissipative nature of the system's fault evolution process; Based on equation (1) and the characteristics of the system fault evolution process, the parameters in equation (1) are explained; A is the causal event for the increased fault probability, and (↑) represents the state of increased probability, i.e., the causal event (↑), N A N represents the number of events that are causal events (↑); x: the evolutionary result event with increased failure probability, represented as the result event (↑); B: the causal event with decreased failure probability, represented by (↓), i.e., the causal event (↓). B Indicates the number of events that cause the event (↓); y: The probability of failure decreases as a result event (↓); D: The failure consequences of the system failure evolution process; E: Fault spillover during the system fault evolution process; the quantities of A and B need to be normalized, and A and B should be used as normalization values ​​without causing ambiguity. Substitute the above definition into equation (1) to explain the physical meaning of the four equations therein; Determine the values ​​of k1, k2, k3 and k4; in equation (1), they identify the catalyst of the reaction, which only changes the rate of the reaction and does not change itself; corresponding to the system failure evolution process, the rate of evolution and transmission between events in the evolution process is used, or the reciprocal of the time required for evolution and transmission is used. To achieve quantitative calculation, it is necessary to introduce spatial fault network theory, which is a set of mathematical methods for describing the fault evolution process of a system. The fault evolution process is abstracted into a network topology. In the network structure, nodes represent events, connections represent the transmission process of evolution, factor influences are represented by characteristic functions and fault probability distributions, and logical relationships are represented by result events. Let the event set of the spatial fault network be E = {e1, ..., e}. I }, where I represents the total number of events; the path set is L = {l1, ..., l N }, where N is the number of paths; the network structure is decomposed into paths; the set of transmission times is T = {t1, ...,t}. M }, M is the number of events transmitted, and t represents the time it takes for the cause event to evolve and propagate to the result event; The set of spillover propagation times after the final result event is T' = {t} M+1 ,…,t M+Δ }, where Δ is the spillover propagation quantity, representing the propagation time of other events caused after the system failure evolution process; the set of propagation times for a certain path is... M n To transmit the quantity; According to the spatial fault network simplification method, when a causal event leads to an outcome event via an OR relationship, multiple independent paths are formed; when a causal event leads to an outcome event via an AND relationship, only one path is formed. The propagation time of these causal events leading to the outcome event is the maximum of all propagation times, t = Max{t i ,t j }; The determination of k1, k2, k3, and k4 is explained by the changes in system fault evolution over a certain period of time; k1: The reciprocal of the average of the total transit times in all paths from the cause event (↑) to the final result event (↑), as shown in equation (7); In the formula: l n In (↑↑), the first ↑ indicates the state of the cause event, and the second ↑ indicates the state of the final result event. k2: The reciprocal of the average of the total transit times in all paths from the cause event (↓) to the final result event (↓), as shown in equation (8); In the formula: l n In (↓↓), the first ↓ indicates the state of the cause event, and the second ↓ indicates the state of the final result event; k3: The reciprocal of the average of the total transit times in all paths from the cause event (↑↓) to the final result event (↑), as shown in equation (9); In the formula: l n In (↑↑), the first ↑ indicates the state of the cause event, and the second ↑ indicates the state of the final result event; n In (↓↑), the first ↓ indicates the state of the cause event, and the second ↑ indicates the state of the final result event. k4: The maximum value of the reciprocal of the propagation time of each subsequent event caused by the final result event (↑), as shown in equation (10); k4=Max{1 / t M+1 ,…,1 / t M+Δ } (10) The above-mentioned method based on the characteristics of system fault evolution process and spatial fault network has enabled the determination of the values ​​of k1, k2, k3 and k4 and the values ​​of A and B.

2. The dissipative analysis method for system failure processes according to claim 1, characterized in that, The failure evolution process of electrical systems is analyzed using the dissipative analysis method of system failure process; Let e1, e2, e4, e6 be edge events, e3, e5 be process events, and e7 be the final event, i.e., the final result event; "+" and "·" represent the OR and AND relationships of their causal events; ↑ and ↓ represent the increase and decrease of the corresponding event failure probability; t1, t2, t3, t4, t5, t6 are the evolution propagation times, T = {t1, t2, t3, t4, t5, t6}; t7 and t8 are the spillover propagation times; let t1 = 2, t2 = 3, t3 = 4, t4 = 3, t5 = 5, t6 = 4, t7 = 3, and t8 = 2 time units; According to the spatial fault network theory, taking e7 as the final result event, the simplification yields e7 = e6 + e5 = e6 + e3·e4 = e6 + (e1 + e2)e4 = e6 + e1e4 + e2e4. This indicates that there are three paths leading to the final result event during the evolution process. These three paths L = {l1, l2, l3} are: l1(↑↑): e6↑ → e7↑, l1(↑↑) = {t6} = {4}; l2(↑↑): e1↑ → e3·e4↓ → e5 → e7↑, l2(↑↑) = {t1, Max{t3, t4}, t5} = {2, 4, 5}; l3(↓↑): e2↓ → e3·e4↓ → e5 → e7↑, l3(↓↑) = {t2, Max{t3, t4}, t5} = {3, 4, 5}. We obtain the results from equations (7) to (10) respectively. k2 = 0, N A =N B =2, so A=0.5, B=0.5; according to b = k2B / k4. Substituting k1, k2, k3, and k4 into the equation, we get... b = 0; the result satisfies b < 1 + a 2 Under the given conditions, the failure evolution process of this system is not a dissipative structure; This indicates that the system fault evolution process within the system will not cause fault spillover and will not lead to the subsequent occurrence of t7 and t8. This evolution process has no impact on the outside world.

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