Multi-state complex system reliability importance analysis method and device

Abstract

The invention belongs to the technical field of software systems, and particularly discloses a multi-state complex system reliability importance analysis method and device. According to the method, the generation function of the unit forming the multivariate state complex system is improved by introducing the state-oriented reachable threshold parameter, and the traditional multivariate state reliability generation function analysis algorithm is improved based on the improved generation function of the unit, so that the reliability measurement parameter is obtained; according to the method, reliability importance analysis is carried out on a multivariate state complex system, so that a general resolving system for reliability importance of the multivariate state complex system, which is wide in application range, high in resolution precision and operation efficiency, convenient to realize by depending on computer programming, capable of adapting to different states and capable of meeting threshold parameter constraint requirements, is constructed.

Description

Technical Field

[0001] The present application belongs to the technical field of software systems, and more specifically, 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 structure of industrial products has become increasingly large, the internal coupling and association have become increasingly complex, and the task function states have become increasingly diverse. The traditional reliability engineering theory based on the "binary" state assumption is far from meeting the needs of high-precision reliability modeling, analysis, and evaluation of modern large-scale complex industrial products. It is urgent to make technical 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 many built-in components and complex and changeable state transfer relationships, it is extremely difficult to achieve refined management of their task functions and state performance, which 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 task 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 use 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] Although the research results on reliability importance in related technologies are relatively rich, most of them are limited to the basic assumptions of binary state performance of complex systems. Obviously, there is still a certain gap between this and the goal of achieving refined management of the task function state of complex systems. The reliability importance analysis model of multi-state complex systems suitable for Birnbaum importance calculation constructed in related technologies is insufficient in the technical explanation of other types of reliability importance; a type of normalized analytical algorithm that can effectively distinguish the reliability importance of different built-in units in multi-state complex systems is given in related technologies, but the modeling process is too complicated and cumbersome, and the technical difficulty of relying on computer programming is relatively 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 view of the defects of the prior art, 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 application scope, low resolution accuracy and low computational efficiency in the prior art 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 reachable threshold parameters of the units constituting the multi-state complex system, the generating function of the unit 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 that meets 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 state below the threshold and the state above the threshold, the reliability importance analysis of the multi-state complex system is carried out.

[0012] In some embodiments, based on the state reachable 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 lower threshold 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 upper threshold state;

[0014] The generating function of the unit is improved based on the generating functions when the unit is in the under-threshold state and the over-threshold state.

[0015] In some embodiments, the reliability measurement parameters corresponding to the state where the unit is below the threshold and the state where the unit is above the threshold respectively include:

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

[0017] According to Birnbaum importance and / or Fussel-Vesely importance, reliability importance analysis is performed on multi-state complex systems.

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

[0019] In some embodiments, the method of obtaining the generating function when the unit is in the lower threshold state and the upper threshold state includes:

[0020] The generating function when the unit 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 being in the below-threshold state, and the cumulative probability sum of the unit being in the above-threshold state.

[0021] In some embodiments, the method of obtaining the generating function of the 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 reliability importance analysis device for a multi-state complex system, comprising:

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

[0025] A first determination module is used to determine a specific operator of a reliability measurement parameter of a multi-state complex system when the unit is in a lower threshold state and an upper 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 the lower threshold state and the upper 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 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, which stores 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. When the computer program product 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.

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

[0032] The reliability importance analysis method and device of a multi-state complex system 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 a multi-state complex system with a wide range of applications, high resolution accuracy and computational efficiency, and ease of computer programming, and adaptable to the constraints of different state-reachable threshold parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a flowchart of a reliability importance analysis method for a multi-state complex system provided in an embodiment of the present application;

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

[0035] Figure 3 is a schematic diagram of changes in 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 : is a schematic diagram of the change of the 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 the embodiment of the present application;

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

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

[0041] Fig. 9 It is a structural schematic diagram of a reliability importance analysis device for a multi-state complex system provided in an embodiment of the present application;

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

[0043] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0044] The term "and / or" in this article is a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. The symbol " / " in this article indicates that the associated objects are in an or relationship, for example, A / B means A or B.

[0045] In the embodiments of the present 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 the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary" or "for example" is intended to present related concepts in a specific way.

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

[0047] Reliability importance is used to analyze the potential technical weaknesses of large industrial systems with complex structural characteristics. After decades of technological enrichment and continuous development, many types of reliability importance concepts have gradually emerged, including Birnbaum importance, Fussel-Vesely importance, key importance, redundancy importance, cost importance, and comprehensive importance. At present, there are few research works on reliability importance analysis of complex industrial systems.

[0048] In terms of theoretical research, the relevant technology has developed a Birnbaum importance analysis algorithm for complex systems that takes into account the correlation of built-in units based on the classical reliability importance analysis theory; 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), introduced a random weight factor, and explored 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 must 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 has been carried out.

[0049] In terms of application practice, the relevant technology applies the reliability importance analysis theory to the aviation industry, and explores the impact of different failure modes on the mission reliability of aviation power supply systems; the reliability importance analysis theory is used to identify the technical weaknesses of drone clusters in performing mission functions, and the intelligent and autonomous collaborative management of drone clusters is realized; reliability importance is used as an important factor to be considered in planning the preventive maintenance guarantee strategy of industrial bearing systems, and a type of global optimization maintenance guarantee strategy is 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 is constructed; the reliability importance analysis theory is successfully applied to the coal industry, and a type of efficient operation and maintenance management strategy for coal transportation systems is 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 reliability importance analysis theory of the existing multi-state complex system at the technical level. By introducing an improved generating function for state-reachable threshold parameters, the traditional multi-state reliability generating function analytical algorithm 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 rely 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, and can more completely interpret the core components and key technical elements that affect the ability of a multi-state complex system to perform tasks, 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 raising key supply guarantee resources for the system, 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 multivariate state complex system when the unit is in a lower threshold state and an upper threshold state based on the improved generating function of the unit and the generating functions of the remaining units constituting the multivariate state complex system;

[0055] Step 130 determines the reliability measurement parameters corresponding to the unit when it is in the lower threshold state and the upper threshold state, respectively, according to 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.

[0057] In the embodiment of the present application, the so-called multi-state complex system usually refers to a special time-varying task function system with complex physical structure design, numerous built-in units (components) and multi-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 relationship 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] In the formula, is the transition strength 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), it can be seen 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] In the formula, 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 usually 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 model is a kind of engineering solution model in the form of numerical sequence. It is widely used in the reliability modeling, analysis and evaluation of large multi-state complex systems with multi-level structures due to its many technical advantages such as wide application range, convenient calculation process, low requirement for computer computing resources and fast calculation speed. Generating function model defines the generating function u(z) that can characterize the multi-state probability distribution characteristics of any unit (component) in the multi-state complex system S, and the specific generating operator Ω that can accurately transfer the state performance association between different levels such as "unit-component, component-subsystem, subsystem-system", and deduces the generating function U(z) that can directly characterize the multi-state probability distribution characteristics of the multi-state complex system S layer by layer. Then, relying on the intrinsic numerical sequence characteristics of the generating function U(z), the various reliability measurement parameters of the multi-state complex system S in a specific mission period are analyzed and solved.

[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 with embedded 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 generating operator Ω. Taking unit i and unit j as an example, we have:

[0076]

[0077] In the formula, ψ ij (·) is a logical configuration function that reflects the state performance association between unit i and unit j. It is easy to see from the polynomial numerical sequence in formula (7) that the generating operator Ω that realizes the coupling operation between unit i and unit j is ij The numerical operation properties of 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 above-mentioned unit, it is easy to know that the generating function of the multi-state system level can be determined layer by layer by 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] In the formula, 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 S (z) can be maintained in the following mathematical form after being sorted out, as shown in formula (10).

[0082]

[0083] In the formula, K, g l and p l (t) still uses the same symbol 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 only related to the generating function at the unit level and the logical definition of operators between the levels, but has nothing to do with the transition intensity between the state performances at the system level. Therefore, it can cleverly avoid the numerical solution of large-dimensional differential equations required to directly solve the multi-state performance probability distribution characteristics of the multi-state complex system S, and can quickly and easily deduce the multi-state probability distribution characteristics of the output multi-state complex system S. Compared with the traditional Markov model, the solution technology has obvious advantages.

[0085] The traditional reliability importance analysis of a complex system in a "binary" state compares the quantitative impact of the loss of task functions of different built-in units on the state output performance of the binary state system, and analyzes the corresponding importance of different built-in units in the system's 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" accordingly. 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, based on the state reachable threshold parameters of the units constituting the multi-state complex system, improving the generating function of the units 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 lower threshold 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 upper threshold state;

[0088] The generating function of the unit is improved based on the generating functions when the unit is in the under-threshold state and the over-threshold 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 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 multivariate state complex system S can be 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 lower threshold state and the upper threshold state may include:

[0091] The generating function when the unit 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 being in the below-threshold state, and the cumulative probability sum of the unit being 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] In the formula, and are the lower and upper threshold generating functions of the improved model of “state reachable threshold parameter” for unit i, respectively. 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 below-threshold state and above-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, 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] In the formula, It is a specific operator for solving the reliability measurement parameters of a multi-state complex system S based on the generating functions of different built-in units. w When the availability A is taken, formula (12) can be written as:

[0098]

[0099] Where 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 the expected performance output E is taken, equation (12) can be written as:

[0100]

[0101] When the measurement parameter O w When the expected performance failure D is taken, equation (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, performing 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, may include:

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

[0107] According to Birnbaum importance and / or Fussel-Vesely importance, reliability importance analysis is performed on multi-state complex systems.

[0108] In the embodiment of the present application, based on the reliability measurement parameters corresponding to the state below the threshold and the state above the threshold obtained above, and The 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] Exemplarily, 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 task function system consists of 6 built-in units with multi-state performance. The rated energy transmission ratio is taken 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 of each state 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 reachable threshold parameter β = 0.8, the generating function of the improved model for the "state reachable" built-in unit i of the system 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 it can be known that the improved generating function when unit 3 is in two special states: below the threshold and above the threshold is 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 lower threshold and upper threshold states is and They can be written as:

[0130]

[0131] In the formula, 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 assembly 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] In the formula, 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 respectively, 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, and 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 in the system availability A of unit 3 in the two different states of below the threshold and above the threshold is 0, and the maximum difference is 0.9125, and the minimum difference in the system expected performance failure D is 0.0311, and the maximum difference is 0.4731.

[0139] Since availability parameters are one of the most important measurement parameters that reflect the mission performance 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 a peak, which is 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 positions of different built-in units in affecting the reliable characteristics of the energy transmission system, find out the built-in units and weak working links that need to be focused on in the daily operation and maintenance of the system, and provide decision support for the refined management of the technical integrity of the system, 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 needs to be paid special attention to in the daily operation and maintenance management of the system; (2) When the state performance requirement w∈(0.8,0.9], the change to the state performance change of unit 3 dominates among the many built-in units that affect the system availability, and needs to be paid special attention to 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 needs to be paid special attention to 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 "abnormal point" of the importance analysis of unit 3. When w is less than 0.8, the impact of unit 3 on the system availability is small; when w is greater than 0.8, its impact on the system availability is large, and it jumps to the dominant position among the 6 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 order of influence 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 reachable threshold parameter β is taken as 0.8 and the reliability measurement parameter is the availability A, the solution conclusions of Birnbaum's importance and Fussel-Vesely's importance can be used to guide the daily "fine-grained" 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-grained management resolution of the Birnbaum's importance solution is slightly better than that of Fussel-Vesely's importance, but the overall fine-grained 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 216-element differential equation group needs to be established to achieve the state performance solution at the system level. In this case, direct analytical solution is often technically difficult or even impossible to achieve. Even if numerical approximate solution is adopted, huge computing resources are required. In this paper, the state performance of the complex system is described by the generating function model, and the solution problem of the 216-element differential equation group is resolved into 3 3-element differential equation groups, 3 2-element differential equation groups, and a series of primary algebraic operations (×, +, min, max). Both the difficulty of solving the technical solution and the demand for computing resources are greatly reduced.

[0147] (2) Risk management resolution accuracy

[0148] Under the traditional "binary" state performance assumption, the reliability importance analysis of the energy transmission system can only cover the "complete failure" of the unit, such as "0.9→0, 0.85→0, 1→0", and by introducing the improved generation function for "state reachability", the article successfully maps the influence of the change of the "intermediate transition" state performance of the unit such as "0.9→0.6, 0.6→0, 1→0.8, 0.8→0" to the reliability important unit analysis process of the energy transmission system, and gives a detailed revelation of the overall state performance change at the system level induced by the "intermediate transition" state change. Compared with the traditional "binary" state reliability importance analysis, the accuracy of state performance control is significantly improved, and the ability to implement security work based on the analysis results to resist engineering risks is significantly enhanced. In fact, if the state reachability threshold parameter β in the case is taken as (0.8, 0.85), the analysis content in the embodiment will degenerate into the "binary" state performance reliability importance analysis.

[0149] In order to solve 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 the 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 used for 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 method for determining the improved generation function and the programmed analysis process of reliability importance are of great 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 for 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 mission function systems, enriched the technical approach to refined management of the inherent reliability characteristics of multi-state complex mission 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 the 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, and which can adapt to the constraints of different state-reachable threshold parameters.

[0152] The reliability importance analysis device for a multi-state complex system provided in the present application is described below. 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 Fig. 9 The embodiment of the present application provides a reliability importance analysis device for 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, for improving 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 determination module 920 is used to determine a specific operator of a reliability measurement parameter of the multivariate state complex system when the unit is in a lower threshold state and an upper threshold state based on the improved generating function of the unit and the generating functions of the remaining units constituting the multivariate state complex system;

[0156] The second determination module 930 is used to determine the reliability measurement parameters corresponding to the unit when it is in the lower threshold state and the upper 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;

[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 analysis 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, and adaptable to the constraints of different state-reachable threshold parameters.

[0159] It can be understood that the detailed functional implementation of each of the above-mentioned 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, which will not be repeated here.

[0161] Based on the method in the above embodiment, the present application embodiment provides an electronic device, see Fig.10 The electronic device may include: a processor (Processor) 1010, a communication interface (CommunicationsInterface) 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 through 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 software functional units 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 a computer device (which can be a personal computer, a server, or a network device, etc.) to perform 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 understandable that the processor in the embodiment of the present application may be a central processing unit (CPU), or 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 known in the art. An exemplary storage medium is coupled to a 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 may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions may be transmitted from a website site, a computer, a server or a data center to another website site, a computer, a server or a data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium may be any available medium that a computer can access or a data storage device such as a server or a data center that includes one or more available media integrated. The available medium may be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive (SSD)), etc.

[0168] It should be understood that the various numerical numbers involved in the embodiments of the present application are only used for the convenience of description and are not used to limit the scope of the embodiments of the present application.

[0169] It will be easily understood by those skilled in the art that the above description 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 shall 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 in that: include: Based on the state reachable threshold parameters of the units constituting the multi-state complex system, the generating function of the units is improved; Determine a specific operator of reliability measurement parameters of the multivariate 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 multivariate state complex system; 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, determine the reliability measurement parameters corresponding to the unit when it is in a lower threshold state and an upper threshold state respectively; According to the reliability measurement parameters corresponding to the units in the below-threshold state and the above-threshold state, respectively, reliability importance analysis is performed on the multi-state complex system.

2. The reliability importance analysis method of a multi-state complex system according to claim 1, characterized in that: The step of improving the generating function of the unit based on the state reachable threshold parameter of the unit constituting the multi-state complex system comprises: Set the state in which the state performance output of the unit is less than or equal to the state reachable threshold parameter as a lower threshold state, and set the state in which 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 of the unit 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 according to the reliability measurement parameters corresponding to the state where the unit is in the lower threshold state and the upper threshold state, respectively, including: Determining the Birnbaum importance and the Fussel-Vesely importance of the multivariate state complex system according to the reliability measurement parameters corresponding to the unit when it is in the lower threshold state and the upper 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 of a multivariate 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, used for improving the generating function of the unit based on the state reachable threshold parameter of the unit constituting the multi-state complex system; A first determination module is used to determine a specific operator of a reliability measurement parameter of the multivariate state complex system when the unit is in a lower threshold state and an upper threshold state based on the improved generating function of the unit and the generating functions of the remaining units constituting the multivariate state complex system; A second determination module is used to determine the reliability measurement parameters corresponding to the unit when it is in a lower threshold state and an upper 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; 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 unit when it is in the lower threshold state and the upper 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 executes the reliability importance analysis method for a multi-state complex system as described in any one of claims 1-6.

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

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