A reliability importance analysis method and device for a multi-state complex system

Abstract

The present application belongs to the field of software system technology, and specifically discloses a reliability importance analysis method and device for a multi-state complex system. The present application improves the generating function of the units constituting the multi-state complex system by introducing a state-reachable threshold parameter, and based on the improved generating function of the unit, improves the traditional multi-state reliability generating function analytical algorithm to obtain reliability measurement parameters, and performs reliability importance analysis on the multi-state complex system, thereby constructing a general solution system for the reliability importance of multi-state complex systems that has a wide range of applications, high resolution accuracy and computational efficiency, is easy to implement through computer programming, and can adapt to the constraints of different state reachable threshold parameters.

Description

Technical Field

[0001] The present application belongs to the field of software system technology, and more specifically, relates to a reliability importance analysis method and device for a multi-state complex system. Background Art

[0002] In recent years, with the rapid development of engineering technologies such as design, materials, and manufacturing, the structures of industrial products have become increasingly large, their internal couplings have become increasingly complex, and their mission and functional states have become increasingly diverse. Traditional reliability engineering theories based on "binary" state assumptions are far from meeting the needs of high-precision reliability modeling, analysis, and evaluation of modern large-scale and complex industrial products. There is an urgent need for technological breakthroughs in the reliability modeling, analysis, and evaluation of "multi-state" complex systems (complex product entities). At the same time, given that "multi-state" complex systems often have numerous built-in components and complex and changeable state transmission relationships, achieving refined management of their mission functions and state performance is extremely difficult, and has become a technical bottleneck in the field of reliability engineering.

[0003] Studying the reliability importance of "multi-state" complex systems will help clarify the technical state coupling relationship between different built-in units of the system and the whole, help identify key mission components and underlying units in the system's built-in complex structure, and help track potential weak links in the system's multi-state transition process. It has important engineering application value for scientifically ensuring and controlling the excellent reliability characteristics of the system during its life cycle, improving its utilization efficiency and reducing potential risks. It has important technical guidance value for optimizing the system engineering design level and improving the effectiveness of refined management work.

[0004] While relevant research on reliability importance has yielded substantial results, most are limited to the basic assumptions of binary-state performance in complex systems. Clearly, this falls short of achieving the goal of refined management of the functional states of complex systems. The reliability importance analysis model for multi-state complex systems constructed in the relevant art, suitable for Birnbaum importance calculations, lacks sufficient technical elaboration on other types of reliability importance. While the relevant art provides a class of normalized analytical algorithms that can effectively distinguish the reliability importance of different internal units in multi-state complex systems, the modeling process is overly complex and cumbersome, and the technical difficulty of relying on computer programming is high.

[0005] In summary, at present, the research work on the reliability importance of complex systems is still mainly concentrated on binary-state systems, with a small amount of research work on the reliability importance of multi-state complex systems. The relevant technical research content is far from rich enough, and it is urgently needed to be expanded and improved in terms of applicability, resolution accuracy and solution efficiency. Summary of the Invention

[0006] In response to the defects of the existing technology, the purpose of this application is to provide a method and device for reliability importance analysis of multi-state complex systems, aiming to solve the problems of small applicability, low resolution accuracy and low computational efficiency in the existing technology when performing reliability importance analysis on complex systems.

[0007] To achieve the above objectives, in a first aspect, the present application provides a reliability importance analysis method for a multi-state complex system, comprising:

[0008] Based on the state reachability threshold parameters of the units in the multi-state complex system, the generating function of the units is improved;

[0009] Based on the improved generating function of the unit and the generating functions of the remaining units constituting the multi-state complex system, a specific operator for determining the reliability measurement parameter of the multi-state complex system when the unit is in a below-threshold state and an above-threshold state;

[0010] According to the state performance requirements of the multi-state complex system to meet the task function requirements, the improved generating function of the unit, the generating functions of the remaining units and the specific operators, the reliability measurement parameters corresponding to the unit when it is in the lower threshold state and the upper threshold state are determined respectively;

[0011] According to the reliability measurement parameters corresponding to the unit in the below-threshold state and above-threshold state, the reliability importance analysis of the multi-state complex system is carried out.

[0012] In some embodiments, based on the state reachability threshold parameters of the units constituting the multi-state complex system, the generating function of the units is improved, including:

[0013] The state in which the state performance output of the unit is less than or equal to the state reachable threshold parameter is set as the threshold lower state, and the state in which the state performance output of the unit is greater than the state reachable threshold parameter is set as the threshold upper state;

[0014] The generating function of the unit is improved based on the generating functions when the unit is in the underthreshold state and the overthreshold state.

[0015] In some embodiments, the reliability measurement parameters corresponding to the unit being in the below-threshold state and the above-threshold state include:

[0016] According to the reliability measurement parameters corresponding to the unit in the below-threshold state and above-threshold state, the Birnbaum importance and Fussel-Vesely importance of the multi-state complex system are determined;

[0017] Reliability importance analysis is performed on multi-state complex systems based on Birnbaum importance and / or Fussel-Vesely importance.

[0018] In some embodiments, the reliability measurement parameters include at least the availability, expected performance output, and expected performance failure of the multi-state complex system.

[0019] In some embodiments, a method for obtaining a generating function when a unit is in a below-threshold state and an above-threshold state includes:

[0020] The generating function of the unit when it is in the below-threshold state and the above-threshold state is determined according to the generating function of the unit, the state performance cutoff number of the unit, the cumulative probability sum of the unit in the below-threshold state and the cumulative probability sum of the unit in the above-threshold state.

[0021] In some embodiments, a method for obtaining a generating function of a unit includes:

[0022] The generating function of the unit is determined according to the probability distribution law of the unit's performance in different states.

[0023] In a second aspect, the present application provides a device for analyzing the reliability importance of a multi-state complex system, comprising:

[0024] An improvement module, for improving the generating function of a unit based on the state reachability threshold parameter of the unit constituting the multi-state complex system;

[0025] A first determining module is used to determine a specific operator of a reliability measurement parameter of the multi-state complex system when the unit is in a below-threshold state and an above-threshold state based on the improved generating function of the unit and the generating functions of the remaining units constituting the multi-state complex system;

[0026] The second determination module is used to determine the reliability measurement parameters corresponding to the unit when it is in a below-threshold state and above-threshold state respectively according to the state performance requirements of the multi-state complex system to meet the task function requirements, the improved generating function of the unit, the generating functions of the remaining units and the specific operator;

[0027] The analysis module is used to perform reliability importance analysis on a multi-state complex system according to the reliability measurement parameters corresponding to the units when they are in the below-threshold state and the above-threshold state.

[0028] In a third aspect, the present application provides an electronic device comprising: at least one memory for storing programs; and at least one processor for executing the programs stored in the memory. When the programs stored in the memory are executed, the processor is used to execute the reliability importance analysis method for a multi-state complex system described in the first aspect or any embodiments of the first aspect.

[0029] In a fourth aspect, the present application provides a computer-readable storage medium storing a computer program. When the computer program runs on a processor, the processor executes the reliability importance analysis method for a multi-state complex system described in the first aspect or any embodiments of the first aspect.

[0030] In a fifth aspect, the present application provides a computer program product, which, when running on a processor, enables the processor to execute the reliability importance analysis method of a multi-state complex system described in the first aspect or any embodiments of the first aspect.

[0031] In general, the above technical solutions conceived by this application have the following beneficial effects compared with the existing technologies:

[0032] The reliability importance analysis method and device provided in the present application improve the generating function of the units constituting the multi-state complex system by introducing state-reachable threshold parameters, and based on the improved generating function of the units, improve the traditional multi-state reliability generating function analytical algorithm to obtain reliability measurement parameters, and perform reliability importance analysis on the multi-state complex system, thereby constructing a general solution system for the reliability importance of multi-state complex systems with a wide range of applications, high resolution accuracy and computational efficiency, and ease of computer programming implementation, and adaptable to the constraints of different state reachable threshold parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 Schematic diagram of the process of analyzing the reliability importance of a multi-state complex system provided by an embodiment of the present application;

[0034] Figure 2 This is a schematic diagram of the task reliability of a multi-state complex energy transmission system provided by an embodiment of the present application;

[0035] Figure 3 Schematic diagram of the change of system availability A under different requirements w provided in an embodiment of the present application;

[0036] Figure 4 Schematic diagram of the change of the expected performance output E of the system under different requirements w provided in the embodiment of the present application;

[0037] Figure 5 Schematic diagram of the change of expected performance failure D of the system under different requirements w provided in the embodiment of the present application;

[0038] Figure 6 Schematic diagram of the importance change of availability parameters under different requirements w provided in an embodiment of the present application;

[0039] Figure 7This is a Birnbaum importance comparison diagram between different built-in units provided in an embodiment of the present application;

[0040] Figure 8 This is a Fussel-Vesely importance comparison diagram between different built-in units provided in an embodiment of the present application;

[0041] Figure 9 Schematic diagram of the structure of the device for analyzing the reliability importance of a multi-state complex system provided by an embodiment of the present application;

[0042] Figure 10 It is a structural diagram of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0044] The term "and / or" as used herein describes an association between related objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A exists alone, A and B exist simultaneously, or B exists alone. The symbol " / " as used herein indicates that the related objects are in an "or" relationship, for example, A / B means either A or B.

[0045] In the embodiments of this application, words such as "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of this application should not be interpreted as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0046] In the description of the embodiments of the present application, unless otherwise specified, “plurality” means two or more.

[0047] Reliability importance is used to analyze potential technical weaknesses in large, complex industrial systems. Decades of technological enrichment and continuous development have led to the development of various reliability importance concepts, including Birnbaum importance, Fussel-Vesely importance, critical importance, redundancy importance, cost importance, and comprehensive importance. Currently, research on reliability importance analysis for complex industrial systems is limited.

[0048] In terms of theoretical research, related technologies have developed a Birnbaum importance analysis algorithm for complex systems based on the classical reliability importance analysis theory, which takes into account the correlation of built-in units; studied the importance solution model under conditional reliability constraints; based on the general Birnbaum importance analysis model, successfully solved the reliability optimization allocation problem of built-in units in complex systems; for traditional kn configuration systems (where k represents the number of states of each unit in a multi-state complex system, and n represents the number of units in a multi-state complex system), a random weight factor was introduced to explore the reliability importance modeling and analysis method of complex systems considering the influence of uncertain factors; for linearly overlappable mkn continuous configuration task function systems (where m represents that at least m units need to be in a predetermined normal state to ensure the normal operation of the multi-state complex system or complete the task), reliability importance modeling and analysis research was carried out.

[0049] In terms of application practice, relevant technologies have explored the impact of different failure modes on the mission reliability of aviation power systems by applying the reliability importance analysis theory to the aviation industry; the reliability importance analysis theory has been used to identify the technical weaknesses of the mission functions of drone clusters, and the intelligent and autonomous collaborative management of drone clusters has been realized; reliability importance has been used as an important factor to consider in planning the preventive maintenance guarantee strategy of industrial bearing systems, and a type of global optimization maintenance guarantee strategy has been proposed; by introducing the concept of cost-effectiveness importance, a type of optimal funding allocation strategy that can be used to scientifically plan preventive maintenance activities for complex systems has been constructed; the reliability importance analysis theory has been successfully applied to the coal industry, and an efficient operation and maintenance management strategy for coal transportation systems has been constructed that can effectively constrain operating costs and fully guarantee high-reliability operation.

[0050] The reliability importance analysis method and device of a multi-state complex system provided in the embodiment of the present application are intended to further enrich and develop the existing reliability importance analysis theory of a multi-state complex system at the technical level. By introducing an improved generating function for state-reachable threshold parameters, the traditional analytical algorithm for the multi-state reliability generating function is improved, and then a general solution system for the reliability importance of a multi-state complex system is constructed, which has a wide range of applications, high resolution accuracy and computational efficiency, is easy to implement by relying on computer programming, and can adapt to the constraints of different state-reachable threshold parameters. At the same time, combined with the verification of typical cases of industrial systems and the quantitative simulation comparative analysis of different types of reliability importance, it is strived to be based on the solution system in the embodiment of the present application, so as to be able to more completely interpret the core components and key technical elements that affect the mission-performing capability of a multi-state complex system, and then provide engineering and technical guidance at the refined management level for scientifically optimizing the system engineering design structure, effectively avoiding potential system use risks, efficiently mobilizing key system supply guarantee resources, and rationally planning system preventive maintenance work activities.

[0051] The embodiments of the present application are described below in conjunction with the drawings in the embodiments of the present application.

[0052] See also Figure 1 , an embodiment of the present application provides a reliability importance analysis method for a multi-state complex system, which may include: steps 110 to 140.

[0053] Step 110 improves the generating function of the unit based on the state reachable threshold parameter of the unit constituting the multi-state complex system;

[0054] Step 120 determines a specific operator of a reliability measurement parameter of the multi-state complex system when the unit is in a below-threshold state and an above-threshold state based on the improved generating function of the unit and the generating functions of the remaining units constituting the multi-state complex system;

[0055] Step 130 determines the reliability measurement parameters corresponding to the unit when it is in a below-threshold state and above-threshold state, respectively, based on the state performance requirements of the multi-state complex system that meet the task function requirements, the improved generating function of the unit, the generating functions of the remaining units, and the specific operator;

[0056] Step 140 performs reliability importance analysis on the multi-state complex system according to the reliability measurement parameters corresponding to the units being in the below-threshold state and the above-threshold state, respectively.

[0057] In the embodiment of the present application, the so-called multi-state complex system generally refers to a special time-varying task function system with complex physical structure design, numerous built-in units (components) and multiple (>2) state performance output. For a multi-state complex system S composed of n units i, i = 1, 2, ..., n, assuming that the state performance output G of unit i at instant t i (t) satisfies the probability distribution law shown in formula (1), then the state performance output G(t) of the multi-state complex system S has K possibilities and satisfies the mathematical association shown in formula (2).

[0058]

[0059] Where pr(·) is the absolute probability function, k i is the total number of multivariate state performance of unit i, g ir and p ir (t) are the state performance and state probability of unit i when it is in the rth state, r = 1, 2, ..., k i .

[0060]

[0061] where f(·) is the logical configuration function that reflects the state performance transfer relationship between unit i and the multi-state complex system S.

[0062] When the transition interval Δt between the states of unit i satisfies the random statistical characteristics of the continuous-time Markov chain, the state probability p in formula (1) ir (t) can be determined by formula (3).

[0063]

[0064] Where, is the transition intensity of unit i from the mth state to the rth state, p im (t) is the state probability when unit i is in the mth state.

[0065] Furthermore, combining equations (1) and (2), we can see that the state performance output G(t) of the instantaneous multi-state complex system S satisfies the probability distribution law shown in equation (4).

[0066]

[0067] Where g l and p l (t) are the state performance and state probability of the multi-state complex system S when it is in the lth state, l = 1, 2, .., K.

[0068] In engineering, we generally pay more attention to the probability distribution law of a multi-state complex system S in a steady state. In this case, Equation (4) can be rewritten as Equation (5).

[0069]

[0070] Generating function models are a type of engineering solution model in the form of numerical sequences. Due to their wide applicability, convenient computational process, low computational resource requirements, and high computational speed, they are widely used in the reliability modeling, analysis, and assessment of large, multi-state complex systems with multi-layered structures. Generating function models define a generating function u(z) that can characterize the multi-state probability distribution characteristics of any unit (component) in a multi-state complex system S, and a specific generating operator Ω that accurately transfers state-performance relationships between different hierarchical levels, such as "unit-component, component-subsystem, and subsystem-system." Generating function models are then deduced layer by layer to obtain a generating function U(z) that directly characterizes the multi-state probability distribution characteristics of the multi-state complex system S. Furthermore, leveraging the intrinsic numerical sequence characteristics of generating function U(z), various reliability measurement parameters of the multi-state complex system S over a specific mission period are analyzed and calculated.

[0071] Furthermore, in some embodiments, in the above steps, the method of obtaining the generating function of the unit may include:

[0072] The generating function of the unit is determined according to the probability distribution law of the unit's performance in different states.

[0073] In the embodiment of the present application, for any unit i, if the probability distribution law of its performance in different states is known (as shown in formula (1)), a type of numerical sequence polynomial with symbol z as the base can be constructed, as shown in formula (6). In engineering, this special polynomial that embeds the probability distribution information of performance in different states is called the generating function of unit i, denoted by u i (z).

[0074]

[0075] The generating functions of different units can be coupled by the generating operator Ω. Taking unit i and unit j as an example, we have:

[0076]

[0077] Where, ψ ij (·) is the logical configuration function that reflects the state performance relationship between unit i and unit j. It is easy to see that the polynomial numerical sequence in formula (7) is the generation operator Ω that realizes the coupling operation between unit i and unit j. ij The numerical operation properties are completely inherited from the logical configuration function ψ ij (·) has numerical operation properties, and is generated by the operator Ω ij The polynomial numerical sequence output after the action still conforms to the symbolic definition of the generating function shown in formula (6). To distinguish it from the generating function of the unit, the generating function of the component composed of unit i and unit j is often recorded as u ij (z), that is:

[0078] u ij (z)=Ω ij [u i (z),u j (z)] (8)

[0079] Based on the definition of the generating function and generating operator of the aforementioned unit, it is easy to know that the generating function of the multi-state system level can be solved layer by layer using the nested operation process. Assuming that the multi-state complex system S can be divided into four levels of "unit-component-subsystem-multi-state complex system" at the physical structure level, and any component e is composed of unit i and unit j, then the generating function U of the multi-state complex system S is S (z) can be written as:

[0080] U S (z)=Ω S {Ω sub <Ω e [ui (z),u j (z)],…>,…} (9)

[0081] Where, Ω S ,Ω sub and Ω e are the generating operators that reflect the state coupling between the multi-state complex system and subsystems, subsystems and components, and components and units. It should be noted that the generating function U of the multi-state complex system S is S After being sorted out, (z) can maintain the following mathematical expression, as shown in formula (10).

[0082]

[0083] Where, K, g l and p l (t) still uses the same symbolic meaning as in formula (4) and will not be repeated here.

[0084] Combining the above deduction process, it can be found that the multi-state complex system S generates the function U S The mathematical generation process of (z) is solely related to the unit-level generating functions and the logical definitions of operators between these levels, and is unrelated to the transition strengths between the performance states at the system level. Therefore, this method cleverly avoids the numerical computation of large-dimensional differential equations required to directly solve the probability distribution characteristics of the multi-state performance of a multi-state complex system S, while also enabling the rapid and easy deduction of the multi-state probability distribution characteristics of the multi-state complex system S. Compared to traditional Markov models, this solution offers significant advantages.

[0085] The traditional reliability importance analysis of complex systems in "binary" states, by comparing the quantitative impact of the loss of task functions of different built-in units on the state output performance of the binary state system, distinguishes the corresponding importance of different built-in units in the system technical design and quality management. When the "binary" state system is derived into a "multi-state" state complex system, the constraint condition of "loss of task function" in the "binary" state evolves into "transition changes between different task function states". At this time, in order to more realistically and accurately examine the impact of changes in the task function states of different built-in units on the state output performance of the multi-state complex system, it is necessary to improve the traditional "binary" state system reliability importance analysis method. The embodiment of the present application achieves this engineering analysis goal at the level of limited technical constraints by appropriately constructing an improved generating function that fits the "multi-state" state reliability importance analysis.

[0086] Furthermore, in some embodiments, step 110 of improving the generating function of a unit based on the state reachable threshold parameter of the unit constituting the multi-state complex system may include:

[0087] The state in which the state performance output of the unit is less than or equal to the state reachable threshold parameter is set as the threshold lower state, and the state in which the state performance output of the unit is greater than the state reachable threshold parameter is set as the threshold upper state;

[0088] The generating function of the unit is improved based on the generating functions when the unit is in the underthreshold state and the overthreshold state.

[0089] In the embodiment of the present application, in order to realize the reliability importance analysis of the multi-state complex system S, the state reachable threshold parameter β is introduced here, and the state performance output G in the built-in unit i of the multi-state complex system S is converted into i (t) All states that are not higher than β are unified into the lower threshold state, and vice versa, the remaining states higher than β are unified into the upper threshold state. Then, the generating function u of the built-in unit i of the multi-state complex system S can be calculated as i (z) Make the following improvements to obtain the improved generating function.

[0090] Furthermore, in some embodiments, in the above steps, the method of obtaining the generating function when the unit is in the below-threshold state and the above-threshold state may include:

[0091] The generating function of the unit when it is in the below-threshold state and the above-threshold state is determined according to the generating function of the unit, the state performance cutoff number of the unit, the cumulative probability sum of the unit in the below-threshold state and the cumulative probability sum of the unit in the above-threshold state.

[0092] In the specific implementation, the generating function u of the built-in unit i of the multi-state complex system S is i (z) is improved as follows to obtain the improved generating function, as shown in formula (11):

[0093]

[0094] Where, and are the lower threshold and upper threshold generating functions of the improved model of “state reachable threshold parameter” for unit i, N(β,i) is the state performance cutoff number of unit i, satisfying g iN(β,i) ≤β <g i[N(β,i)+1] , and are the cumulative probabilities of unit i being in the lower threshold state and the upper threshold state, p ih (t) is the state probability when unit i is in the hth state.

[0095] Assuming that the state performance requirement of the multi-state complex system S that meets the task function requirements is w, then based on the aforementioned generating function model, it is easy to know that the arbitrary reliability measurement parameter O of the multi-state complex system S is w It can be expressed as:

[0096]

[0097] Where, It is a specific operator for solving the reliability measurement parameter of the multi-state complex system S based on the generating function of different built-in units. w When the availability A is taken, formula (12) can be written as:

[0098]

[0099] In the formula, 1(·) is the logical discriminant function, which takes the value 1 when the logical criterion is established and takes the value 0 when the logical criterion is not established. w When taking the expected performance output E, formula (12) can be written as:

[0100]

[0101] When the measurement parameter O w When the expected performance failure D is taken, formula (12) can be written as:

[0102]

[0103] Furthermore, the improved generating function model for multi-state complex systems oriented to “state reachability” is introduced, and the reliability measurement parameters of the built-in unit i of the multi-state complex system S in the state below the threshold and the state above the threshold are respectively and

[0104]

[0105] Furthermore, in some embodiments, step 140 of performing reliability importance analysis on the multi-state complex system based on the reliability measurement parameters corresponding to the units in the below-threshold state and the above-threshold state may include:

[0106] According to the reliability measurement parameters corresponding to the unit in the below-threshold state and above-threshold state, the Birnbaum importance and Fussel-Vesely importance of the multi-state complex system are determined;

[0107] Reliability importance analysis is performed on multi-state complex systems based on Birnbaum importance and / or Fussel-Vesely importance.

[0108] In the embodiment of the present application, the reliability measurement parameters corresponding to the state below the threshold and the state above the threshold obtained above are respectively and Birnbaum importance can be obtained by the following formula and Fussel-Vesely importance I O f i βw :

[0109]

[0110] According to the obtained Birnbaum importance and Fussel-Vesely importance I O f i βw At least one of them performs reliability importance analysis on a multi-state complex system.

[0111] Furthermore, in some embodiments, the reliability measurement parameters include at least the availability, expected performance output, and expected performance failure of the multi-state complex system.

[0112] For example, the reliability measurement parameters may be the availability A, expected performance output E, and expected performance failure D of a multi-state complex system, or other parameters.

[0113] Taking a typical multi-state complex energy (electrical energy, thermal energy, fluid working medium, etc.) transmission system as an example, the reliability block diagram of the relevant task function level is as follows: Figure 2 As shown, it includes units 1 to 6, an input end and an output end.

[0114] The mission function system consists of 6 built-in units with multi-state performance. The rated energy transmission ratio is used as the state performance parameter of interest. The state performance of different built-in units in the multi-state complex energy transmission system is g. ih As listed in Table 1.

[0115] Table 1: Multivariate state performance g of built-in units ih (Unit: 1)

[0116]

[0117] Furthermore, combined with the statistical data of engineering practices of similar systems in the past, and assuming that the transition process between the performance states of the built-in units of the multi-state complex energy transmission system only has the possibility of "minor failure" and "minor repair", the relevant state transition strengths of different built-in units are given as listed in Table 2.

[0118] Table 2: State transition strength of built-in units (Unit: year -1 )

[0119]

[0120] Substituting the values ​​listed in Table 2 into Equation (3) and taking the task time t→+∞, we can obtain the steady-state probability distribution p of the performance of the built-in units in the multi-state complex energy transmission system in different states: ih As listed in Table 3.

[0121] Table 3: Multivariate steady-state probability distribution p of built-in units ih

[0122]

[0123]

[0124] In addition, considering the logical transmission association of different built-in units in the multi-state complex energy transmission system at the energy transmission task level, it can be known that the logical configuration function ψ between different built-in units i and j in the multi-state complex energy transmission system ij (·)As listed in Table 4.

[0125] Table 4: Logical configuration function ψ between different built-in units ij (·)

[0126]

[0127] Taking the state reachability threshold parameter β = 0.8, the generating function of the improved model for the built-in unit i in the system for "state reachability" can be constructed based on formula (11). Here, unit 3 is selected as an example. At this time, the state performance boundary number N(β,3) = 2, from which we can know the improved generating function when unit 3 is in the two special states of below threshold and above threshold. and They are:

[0128]

[0129] Furthermore, based on the inherent good mathematical operation characteristics of the generating function model, referring to formula (9), the generating function of this type of multi-state energy transmission system can be nested and solved layer by layer. That is, the system generating function when unit 3 is in the threshold below and threshold above states is and They can be written as:

[0130]

[0131] Where u 12 (z) is the generating function of the component composed of unit 1 and unit 2 in parallel, u 46 (z) is the generating function of the component composed of unit 4 and unit 6 in series, and are the generating functions of the components formed by connecting unit 3 in series with unit 5 when unit 3 is in the below-threshold and above-threshold states, respectively.

[0132]

[0133] In summary, after sorting and simplifying, we have:

[0134]

[0135] First, various system reliability measurement parameters based on the improved generating function are constructed as follows:

[0136]

[0137] Where, and and and are the availability, expected performance output and expected performance failure of the energy transmission system when unit 3 is in the below-threshold and above-threshold states, respectively. and are specific operators, and their corresponding definitions are shown in Equations (13), (14), and (15). Further, different state performance requirements w are selected to solve various reliability measurement parameters of the energy transmission system, such as Figure 3-Figure 5 shown.

[0138] Depend on Figure 3-Figure 5 It can be seen that: (1) As the state performance demand w changes, the system availability A and expected performance failure D will also change, but the expected performance output E remains unchanged; (2) When unit 3 is in two different states, below the threshold and above the threshold, the values ​​of the reliability measurement parameters of the system related to it are significantly different, corresponding to the "fault" state and "functional intact" state in the "binary" state system respectively; (3) When unit 3 is in the below-threshold state, the system expected performance output E is stable at 0.7858, and when it is in the above-threshold state, it is stable at 0.874 7; (4) With the increase of the state performance requirement w, the system availability A shows a step-by-step monotonically decreasing trend, and the system expected performance failure D shows a linear monotonically increasing trend. When the state performance requirement w is greater than 0.9, the system availability A is always 0; (5) When the state performance requirement w∈[0.1,1], the minimum difference between the system availability A of unit 3 in the two different states of below-threshold and above-threshold is 0, and the maximum difference is 0.9125. The minimum difference between the system expected performance failure D is 0.0311, and the maximum difference is 0.4731.

[0139] Given that availability parameters are one of the most important measurement parameters that reflect the mission-performing capabilities of a complex system with multiple states, the following focuses on the importance analysis of the availability parameters of the energy transmission system. and Fussel-Vesely importance The solution result is as follows Figure 6 shown.

[0140] Depend on Figure 6 It can be seen that: (1) As the state performance requirement w increases, the impact of unit 3 on system availability gradually increases; (2) When the state performance requirement w is greater than 0.8, the importance of unit 3 will increase significantly, and when w is greater than 0.85, the importance will reach its peak, which are Birnbaum importance 0.9125 and Fussel-Vesely importance 1 respectively; (3) When the state performance requirement w∈[0.1,0.85], the Birnbaum importance of unit 3 is slightly higher than the Fussel-Vesely importance, but when w is greater than 0.85, the Birnbaum importance of unit 3 is significantly lower than the Fussel-Vesely importance.

[0141] In order to further deconstruct the different technical status of different built-in units in affecting the reliability characteristics of the energy transmission system, find out the built-in units and weak links that need to be focused on during the daily operation and maintenance of the system, and provide decision support for the refined management of the system's technical integrity, a comparison chart of important metrics between different built-in units of the system is given here, such as Figure 7 and Figure 8 shown.

[0142] Depend on Figure 7It can be seen that: (1) When the state performance requirement w∈[0.1,0.8], the state performance change of unit 5 dominates among the many built-in units that affect the system availability, and it is necessary to pay special attention to it in the daily operation and maintenance management of the system; (2) When the state performance requirement w∈(0.8,0.9], the state performance change of unit 3 dominates among the many built-in units that affect the system availability, and it is necessary to pay special attention to it in the daily operation and maintenance management of the system; (3) When the state performance requirement w∈[0.1,0.6]∪(0.8,0.85], the state performance change of unit 3 dominates among the many built-in units that affect the system availability, and it is necessary to pay special attention to it in the daily operation and maintenance management of the system. The state performance changes of 1 and 2 have the least impact on system availability; when the state performance requirement w∈(0.6,0.8], the change to unit 3 has the least impact on system availability; when the state performance requirement w∈(0.85,0.9], the change to units 4 and 6 has the least impact on system availability; (4) In general, unit 5 has a greater impact on system availability under different state performance requirements and occupies a dominant position among many built-in units. Therefore, under the constraint of limited guarantee resources, the guarantee requirements of unit 5 should be met first; (5) When the state performance requirement w∈[0.1,0.6], the refined optimization guarantee strategy of this type of energy transmission system is: unit 5→unit 4→unit 6→unit 3→unit 2, unit 1; (6) When the state performance requirement w∈(0.6,0.8], the refined optimization guarantee strategy of this type of energy transmission system is: unit 5→unit 2, unit 1→unit 4→unit 6→unit 3; (7) When the state performance requirement w∈(0.8,0.85], the refined optimization guarantee strategy of this type of energy transmission system is: unit 3→unit 5→unit 4→unit 6→unit 2, unit 1; (8) When the state performance requirement w∈(0.85,0.9], the refined optimization guarantee strategy of this type of energy transmission system is: unit 3→unit 5→unit 2, unit 1→unit 4, unit 6; (9) The state performance requirement w=0.8 is the “inflection point” of the importance analysis of unit 3. When w is less than 0.8, the impact of unit 3 on system availability is small; when w is greater than 0.8, its impact on system availability is large, and it jumps to a dominant position among the six built-in units of the system.

[0143] Depend on Figure 8 It can be seen that: (1) when the state performance requirement w∈[0.1,0.9], the Fussel-Vesely important metric values ​​of unit 4 and unit 6 converge to the same value; (2) when the state performance requirement w∈(0.8,0.9], the Fussel-Vesely important metric values ​​of unit 3 and unit 5 converge to the same value; (3) except for the case where some of them converge to the same value, Figure 8 and Figure 7The ranking of the impact of different built-in units on system availability is consistent, and the clear refined optimization guarantee strategy is also consistent. Specifically, when the state performance requirement w∈[0.1,0.6], unit 5→unit 4, unit 6→unit 3→unit 2, unit 1; when the state performance requirement w∈(0.6,0.8], unit 5→unit 2, unit 1→unit 4, unit 6→unit 3; when the state performance requirement w∈(0.8,0.85], unit 3, unit 5→unit 4, unit 6→unit 2, unit 1; when the state performance requirement w∈(0.85,0.9], unit 3, unit 5→unit 2, unit 1→unit 4, unit 6.

[0144] In summary, when the state reachability threshold parameter β is taken as 0.8 and the reliability measurement parameter is availability A, the solution conclusions of Birnbaum's importance and Fussel-Vesely's importance can both be used to guide the daily "fine-tuning" management and "high efficiency and cost-effectiveness" guarantee work of this type of energy transmission system; and when the state performance requirement w∈[0.1,0.9] is taken, the fine-tuning management resolution of the solution conclusion of Birnbaum's importance is slightly better than that of Fussel-Vesely's importance, but the overall fine-tuning management strategies of the two remain consistent.

[0145] (1) Computing resource requirements

[0146] The multi-state complex energy transmission system in the above embodiment has 216 types (K=3×3×3×2×2×2) of potential state output performance. In principle, if state merging is not considered, a set of 216 differential equations must be established to achieve system-level state performance solution. In this case, direct analytical solution is often technically extremely difficult or even impossible to achieve. Even if numerical approximation is used, it requires huge computing resources. However, this paper relies on the generating function model to describe the state performance of the complex system, and resolves the problem of solving the 216-element differential equation set into three sets of three-element differential equations, three sets of two-element differential equations, and a series of elementary algebraic operations (×, +, min, max). Both the difficulty of solving the technical solution and the computing resource requirements are greatly reduced.

[0147] (2) Risk management resolution accuracy

[0148] Under the traditional "binary" state performance assumption, the reliability importance analysis of this energy transmission system only covers the "complete failure" unit scenario, such as "0.9→0, 0.85→0, 1→0." However, by introducing an improved generating function for "state reachability," this paper successfully maps the impact of "intermediate transition" state performance changes of units such as "0.9→0.6, 0.6→0, 1→0.8, and 0.8→0" into the reliability importance unit analysis process of the energy transmission system. It also provides a detailed explanation of the overall state performance changes at the system level induced by "intermediate transition" state changes. Compared with the traditional "binary" state reliability importance analysis, the accuracy of state performance control is significantly improved, and the ability to implement support work based on the analysis results to resist engineering risks is significantly enhanced. In fact, if the state reachability threshold parameter β in this case is set to (0.8, 0.85), the analysis content in this embodiment will degenerate into a "binary" state performance reliability importance analysis.

[0149] Aiming at the problem of reliability modeling, analysis and refined management of multi-state complex task function systems, a high-precision analysis algorithm for the reliability importance of multi-state complex systems based on the improved generating function model is discussed, and the refined management optimization strategy of different built-in units under the constraint of limited guarantee resources is given. By constructing a closed solution system for the reliability importance of the new algorithm and combining it with typical cases for engineering verification, it is shown that: (1) The new analysis algorithm based on the improved generating function model has strong versatility and a wide range of applications. Compared with the traditional "binary" state reliability analysis model, it has higher reliability importance resolution accuracy and is more convenient for realizing refined management of the inherent reliability characteristics of multi-state complex systems; (2) The analysis algorithm inherits the technical advantages of the generating function model in solving the reliability of large multi-state complex systems, successfully avoids the technical bottleneck of numerical solution of large-dimensional differential equations, and has low requirements for programmed computing resources and fast computing speed; (3) The analysis algorithm can be applied to different state performance requirements, different state reachable thresholds and different reliability requirements. The reliability measurement parameters are implemented, the technology is robust and easy to implement through computer programming, and its potential engineering application value is obvious; (4) Although the analysis algorithm uses the classic multi-state "series-parallel" hybrid system architecture as a verification case, the clear improved generation function determination method and reliability importance programmatic analysis process have important reference value for solving similar problems in other complex systems such as voting systems, redundant systems, and bridge systems; (5) Although the analysis algorithm uses the refined management of the inherent reliability characteristics of multi-state systems as the engineering foothold of important quantitative analysis, the relevant research results are also applicable to the refined management of other inherent general quality characteristics of multi-state complex systems such as maintainability, testability, safety, and security.

[0150] The research results developed the reliability importance modeling theory and analysis method of multi-state complex task function systems, enriched the technical approach to refined management of the inherent reliability characteristics of multi-state complex task function systems, and are of great significance for optimizing the allocation of support resources and improving the efficiency of preventive maintenance work in multi-state systems.

[0151] The reliability importance analysis method of a multi-state complex system provided in an embodiment of the present application improves the generating function of the units constituting the multi-state complex system by introducing state-reachable threshold parameters, and based on the improved generating function of the units, improves the traditional multi-state reliability generating function analytical algorithm to obtain reliability measurement parameters, and performs reliability importance analysis on the multi-state complex system, thereby constructing a general solution system for the reliability importance of a multi-state complex system with a wide range of applications, high resolution accuracy and computational efficiency, and ease of computer programming implementation, and adaptable to the constraints of different state-reachable threshold parameters.

[0152] The following describes the reliability importance analysis device for a multi-state complex system provided by the present application. The reliability importance analysis device for a multi-state complex system described below and the reliability importance analysis method for a multi-state complex system described above can be referenced to each other.

[0153] See also Figure 9 The embodiment of the present application provides a device for analyzing the reliability importance of a multi-state complex system, which may include: an improvement module 910, a first determination module 920, a second determination module 930 and an analysis module 940.

[0154] An improvement module 910 is configured to improve a generating function of a unit based on a state reachable threshold parameter of the unit constituting the multi-state complex system;

[0155] A first determining module 920 is configured to determine a specific operator of a reliability measurement parameter of the multi-state complex system when the unit is in a below-threshold state and an above-threshold state based on the improved generating function of the unit and the generating functions of the remaining units constituting the multi-state complex system;

[0156] A second determination module 930 is configured to determine reliability measurement parameters corresponding to a unit in a below-threshold state and an above-threshold state, respectively, based on the state performance requirements of the multi-state complex system to meet the task function requirements, the improved generating function of the unit, the generating functions of the remaining units, and a specific operator;

[0157] The analysis module 940 is used to perform reliability importance analysis on the multi-state complex system according to the reliability measurement parameters corresponding to the units in the below-threshold state and the above-threshold state.

[0158] The reliability importance analysis device for a multi-state complex system provided in an embodiment of the present application improves the generating function of the units constituting the multi-state complex system by introducing state-reachable threshold parameters, and based on the improved generating function of the units, improves the traditional multi-state reliability generating function analytical algorithm to obtain reliability measurement parameters, and performs reliability importance analysis on the multi-state complex system, thereby constructing a general solution system for the reliability importance of a multi-state complex system with a wide range of applications, high resolution accuracy and computational efficiency, and ease of computer programming implementation, and adaptable to the constraints of different state-reachable threshold parameters.

[0159] It is understandable that the detailed functional implementation of each of the above units / modules can be found in the introduction of the aforementioned method embodiment, and will not be repeated here.

[0160] It should be understood that the above-mentioned device is used to execute the method in the above-mentioned embodiment. The implementation principle and technical effect of the corresponding program module in the device are similar to those described in the above-mentioned method. The working process of the device can refer to the corresponding process in the above-mentioned method and will not be repeated here.

[0161] Based on the method in the above embodiment, the embodiment of the present application provides an electronic device, see Figure 10 The electronic device may include: a processor (Processor) 1010, a communication interface (Communications Interface) 1020, a memory (Memory) 1030 and a communication bus 1040, wherein the processor 1010, the communication interface 1020, and the memory 1030 communicate with each other via the communication bus 1040. The processor 1010 may call the logic instructions in the memory 1030 to execute the method in the above embodiment.

[0162] In addition, the logic instructions in the above-mentioned memory 1030 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or the part of the technical solution can be embodied in the form of a software product, which is stored in a storage medium and includes a number of instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present application.

[0163] Based on the method in the above embodiment, an embodiment of the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method in the above embodiment.

[0164] Based on the method in the above embodiment, an embodiment of the present application provides a computer program product. When the computer program product runs on a processor, the processor executes the method in the above embodiment.

[0165] It is understood that the processor in the embodiments of the present application may be a central processing unit (CPU), or may be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. The general-purpose processor may be a microprocessor or any conventional processor.

[0166] The method steps in the embodiments of the present application can be implemented by hardware or by a processor executing software instructions. The software instructions can be composed of corresponding software modules, and the software modules can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, mobile hard disks, CD-ROMs or any other form of storage medium well known in the art. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can be located in an ASIC.

[0167] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted via the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server or data center to another website, computer, server or data center via a wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) method. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrations. The available medium can be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive (SSD)).

[0168] It will be understood that the various numerical numbers involved in the embodiments of the present application are merely distinctions for the convenience of description and are not intended to limit the scope of the embodiments of the present application.

[0169] It is easy for those skilled in the art to understand that the above is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application should be included in the scope of protection of the present application.

Claims

1. A reliability importance analysis method for a multi-state complex system, characterized by: include: Based on the state reachable threshold parameters of the units constituting the multi-state complex system, improving the generating function of the units; The state reachable threshold parameter is a preset parameter used to divide the state of the state performance output of each unit in the multi-state complex system into a lower threshold state and an upper threshold state; Determining, based on the improved generating function of the unit and the generating functions of the remaining units constituting the multi-state complex system, a specific operator for measuring the reliability parameters of the multi-state complex system when the unit is in a below-threshold state and an above-threshold state; the specific operator is determined by solving the reliability measurement parameters of the multi-state complex system based on the generating functions of different built-in units; Determining reliability measurement parameters corresponding to when the unit is in a below-threshold state and an above-threshold state, respectively, based on the state performance requirements of the multi-state complex system that meet the task function requirements, the improved generating function of the unit, the generating functions of the remaining units, and the specific operator; A reliability importance analysis is performed on the multi-state complex system according to the reliability measurement parameters corresponding to the units being in the below-threshold state and the above-threshold state, respectively.

2. The reliability importance analysis method of a multi-state complex system according to claim 1, characterized in that: The improving of the generating function of the unit based on the state reachable threshold parameter of the unit constituting the multi-state complex system includes: Setting a state where the state performance output of the unit is less than or equal to the state reachable threshold parameter as a lower threshold state, and setting a state where the state performance output of the unit is greater than the state reachable threshold parameter as an upper threshold state; The generating function of the unit is improved based on the generating functions when the unit is in the below-threshold state and the above-threshold state.

3. The reliability importance analysis method of a multi-state complex system according to claim 1, characterized in that: The reliability importance analysis of the multi-state complex system is performed based on the reliability measurement parameters corresponding to the units being in the below-threshold state and the above-threshold state, including: Determining the Birnbaum importance and the Fussel-Vesely importance of the multi-state complex system according to the reliability measurement parameters corresponding to the unit when the unit is in a below-threshold state and an above-threshold state, respectively; According to the Birnbaum importance and / or the Fussel-Vesely importance, reliability importance analysis is performed on the multi-state complex system.

4. The reliability importance analysis method of a multi-state complex system according to claim 1, characterized in that: The reliability measurement parameters include at least the availability, expected performance output and expected performance failure of the multi-state complex system.

5. The reliability importance analysis method of a multi-state complex system according to claim 2, characterized in that: The method for obtaining the generating function when the unit is in the lower threshold state and the upper threshold state includes: The generating function of the unit when it is in the below-threshold state and the above-threshold state is determined based on the generating function of the unit, the state performance demarcation number of the unit, the cumulative probability sum of the unit being in the below-threshold state, and the cumulative probability sum of the unit being in the above-threshold state.

6. The reliability importance analysis method for a multi-state complex system according to claim 1, 2 or 5, characterized in that: The method for obtaining the generating function of the unit includes: The generating function of the unit is determined according to the probability distribution law of the performance of the unit in different states.

7. A reliability importance analysis device for a multi-state complex system, characterized in that: include: An improvement module, configured to improve a generating function of a unit based on a state reachable threshold parameter of the unit constituting the multi-state complex system; The state reachable threshold parameter is a preset parameter used to divide the state of the state performance output of each unit in the multi-state complex system into a lower threshold state and an upper threshold state; a first determination module for determining, based on the improved generating function of the unit and the generating functions of the remaining units constituting the multi-state complex system, a specific operator for determining the reliability measurement parameters of the multi-state complex system when the unit is in a below-threshold state and an above-threshold state; the specific operator is determined by solving the reliability measurement parameters of the multi-state complex system based on the generating functions of different built-in units; A second determination module is configured to determine, based on the state performance requirements of the multi-state complex system to meet the task function requirements, the improved generating function of the unit, the generating functions of the remaining units, and the specific operator, the reliability measurement parameters corresponding to the unit when the unit is in a below-threshold state and an above-threshold state, respectively; The analysis module is used to perform reliability importance analysis on the multi-state complex system according to the reliability measurement parameters corresponding to the units when they are in the below-threshold state and the above-threshold state.

8. An electronic device, characterized in that: include: at least one memory for storing a computer program; At least one processor is used to execute the program stored in the memory. When the program stored in the memory is executed, the processor is used to execute the reliability importance analysis method of a multi-state complex system as described in any one of claims 1-6.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program runs on a processor, the processor is enabled to execute the reliability importance analysis method for a multi-state complex system according to any one of claims 1 to 6.

10. A computer program product, characterized in that When the computer program product runs on a processor, the processor is enabled to execute the reliability importance analysis method for a multi-state complex system according to any one of claims 1 to 6.

Images