Manufacturing system networking importance evaluation method

Abstract

A manufacturing system networking importance assessment method belongs to the importance measure analysis field, and comprises the following steps: constructing a manufacturing system networking topology model according to a network theory; analyzing influence factors of the manufacturing system; and carrying out importance measure calculation based on an improved Leader Rank algorithm on the constructed manufacturing system networked topology model, comparing importance measures influenced by different centrality degrees, and carrying out sensitivity analysis on the equipment load busy rate. According to the method, a topological structure between equipment of the manufacturing system is mapped into a networked model, main system characteristics such as equipment criticality, reliability, centrality and fault chain risk coefficients are investigated, and importance measurement evaluation of the manufacturing system is realized. The method can be effectively expanded and applied to a manufacturing system with networked characteristics, can consider multiple influence factors to identify the key of the system, makes a targeted scheme, and provides a reference for further improving the reliability of the system.

Description

Technical Field

[0001] The invention belongs to the technical field of importance measurement analysis, and in particular relates to a manufacturing system network importance evaluation method. Background Art

[0002] As the complexity of products increases, the structure of manufacturing systems becomes more and more complex, and the factors that affect their importance measurement are increasing and the degree of influence is increasing, so the requirements for their reliability are also increasing. How to consider multiple factors to analyze the importance measurement of manufacturing systems based on the existing data in the example system is the first problem to be solved.

[0003] In reliability theory, importance measurement is an effective tool to evaluate the relative importance of equipment and identify system weaknesses. In order to ensure consistent system performance while reducing system maintenance costs, Zhang et al. [+] An importance-based maintenance priority (IBMP) model is proposed to guide the selection of maintenance components (Zhang C, Zhang Y, Dui H, Wang S, Tomovic MM. Importance measure-based maintenance strategy considering maintenance costs. Eksploatacja i –Maintenance and Reliability.2022;24(1):15-24.doi:10.17531 / ein.2022.1.3.). Sakurahara et al. proposed a global importance measure method and applied it to the integrated probabilistic risk assessment framework (Tatsuya Sakurahara, Seyed Reihani, Global importance measure methodology for integrated probabilistic risk assessment[J].Proceedings of the Institution of Mechanical Engineers, Part O:Journal of Risk and Reliability,2019). Lyu and Si used the theory of sequential statistics to propose an importance measure for the K-out-of-n:G system under repeated random load (Dong Lyu, Shubin Si. Dynamic importance measure for the K-out-of-n:G system under repeated random load[J].Reliability Engineering and System Safety,2020,195). Aggarwal introduced an important measure that considers the minimum path set of the system, which helps to optimize the identification of important equipment in any complex system and solve the constrained redundant optimization problem (Aggarwal S. Minimal path set importance in complex systems. Proceedings of the Institution of Mechanical Engineers [J], Part O: Journal of Risk and Reliability. 2021; 235 (2): 201-208.).Dui and Yang et al. proposed a system-level comprehensive support rate method based on importance measurement in response to the problems that the development of society has put forward higher requirements for the supply of spare parts and the existing support indicators are not enough to comprehensively evaluate the capabilities of the system (Hongyan Dui, Xingju Yang & Meng Liu (2022) Importance measure-based maintenance analysis and spare parts storage configuration in two-echelon maintenance and supply support system, International Journal of Production Research, DOI: 10.1080 / 00207543.2022.2142312.). Wen et al. proposed a resilience-based structural importance measure, a resilience-based redundancy importance measure and a resilience-based reinforcement importance measure from the three perspectives of topology, cold backup and component elasticity limit for systems suffering from different degrees of failure (Wen M, Chen Y, Yang Y, et al. Resilience-based component importance measures [J]. International Journal of Robust and Nonlinear Control, 2020, 30 (11): 4244-4254.). Ahme and Liu proposed a production volume importance measure and a maintenance effect importance measure to address the long-term impact of the criticality of different components and successful maintenance activities on the production volume of the production system over a certain period of time (Ahmed Awil Abdrahman Ahmed, Yiliu Liu. Throughput-based importance measures of multistate production systems[J]. International Journal of Production Research, 2019, 57(2).).In order to effectively solve the multi-objective model, Zhao et al. proposed a harmonious search multi-objective particle swarm optimization algorithm based on importance measure based on the harmonious search and multi-objective particle swarm optimization algorithms (Zhao J, Si S, Cai Z, et al. Multiobjective optimization of reliability-redundancy allocation problems for serial parallel-series systems based on importance measure[J]. Proceedings of the Institution of Mechanical Engineers Part O Journal of Risk and Reliability, 2019, 233.). Xu et al. introduced the Birnbaum importance measurement algorithm to effectively quantify the impact of operational dependency on the importance of each equipment system task in SoS (Xu T, Chen Y, Lu C, et al. Importance Measure of Equipment Task Based on Operational Dependency of SoS[J]. IEEE Access, 2021, PP(99):1-1.). Vishnu et al. proposed a risk-based component importance measure (RCIM) to identify critical components of bridges under earthquake action (Vishnu N, Padgett JE,. -Osorio L.Risk-based bridge component importance measures under seismic loads.Earthquake Spectra.2022;38(3):1683-1704.doi:10.1177 / 87552930211073815.). Huseby et al. proposed four new importance measures for repairable multistate systems based on the classic Birnbaum measure, taking into account the periodic component life cycle and general semi-Markov process (Huseby, A., Kalinowska, M., & Abrahamsen, T. (2022). BIRNBAUM CRITICALITY AND IMPORTANCE MEASURES FOR MULTISTATE SYSTEMS WITH REPAIRABLE COMPONENTS. Probability in the Engineering and Informational Sciences, 36(1), 66-86.doi:10.1017 / S0269964820000340.). Lyu et al. proposed a new computational method for Birnbaum importance measure of the k-out-n system based on the system-level stress-strength interference model (Lyu D, Si S, Cai Z, et al. Computational method for importance measure of the k-out-of-n system based on stress-strength interference[J]. Journal of Risk and Reliability, 2020, 234.). Do et al. proposed a new time-varying importance measure for multiple non-repairable devices composed of a system, which improves the system reliability capability during the mission given the current state (state or degradation level) of the components (Do P, Berenguer C. Conditional reliability-based importance measures[J]. Reliability Engineering & System Safety, 2020, 193(1): 106633.1-106633.10.).Chen et al. used integrated importance measure and Griffith importance measure to analyze component importance (Chen L, Gao Y, H Dui, et al. Importance measure-based maintenance optimization strategy for pod slewing system [J]. Reliability Engineering and System Safety, 2021, 216.). Song et al. used variable importance measure (VIM) to sort or select important variables, effectively reducing the variable dimension and shortening the calculation time (Song, S., He, R., Shi, Z., Zhang, W.. Variable Importance Measure System Based on Advanced Random Forest [J]. CMES-Computer Modeling in Engineering & Sciences, 2021; 128 (1), 65–85.). Manríquez proposed a method for ranking the importance of undirected edge weighted nodes and generalized the line importance measurement method based on centrality (Manríquez R, Guerrero-Nancuante CA Generalization of the Importance of Vertices for an Undirected Weighted Graph [J]. Symmetry. 2021; 13(5): 902.). The above literature is based on the assumption of component independence for measuring the importance of equipment, and does not take into account the impact of functional dependencies between components.

[0004] Mi et al. [+] An extended Birnbaum importance is defined to identify key common cause failure events and coupling influencing factors (Mi J, Li Y, Beer M, Broggi M, Cheng Y. Importance measure of probabilistic common cause failures under system hybrid uncertainty based on bayesian network. Eksploatacja i –Maintenance and Reliability.2020;22(1):111-120.doi:10.17531 / ein.2020.1.13.). Gu et al. considered the reliability importance measure of failure correlation, which is an effective measure to identify the importance of CNC lathe. Based on Copula function, a connection reliability model of each subsystem of CNC lathe was established (Gu, D, Zhong, Y, Xu, Z, Chen, B, Wang, Z. An importance measure of a CNC lathe considering failure correlations [J]. Quality and Reliability Engineering International.2021;1-13.). Based on the consideration of component strength, Yu [+] et al. ranked the importance of components considering common cause failure based on the stress-strength interference (SSI) model. (Yu G, Du Y, Yan L, Ren F. Stress-strength interference-based importance for series systems considering common cause failure. Eksploatacja i –Maintenance and Reliability.2020;22(2):241-252.doi:10.17531 / ein.2020.2.7.) Zhang et al. assumed that fault propagation follows a Markov process and adopted an improved LeaderRank algorithm to evaluate the importance of components by introducing background nodes and calculating the failure influence of components (Zhang Y, Liang S, Liu J, Cao P, Luan L. Evaluation for machine tool components importance based on improved LeaderRank. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability.2021;235(3):331-337.). Wang et al. established a reliability optimization model and used a genetic algorithm based on importance measure to effectively solve the reliability optimization problem (Wang N, Zhao JB, Jiang ZY, et al. Reliability optimization of systems with component improvement cost based on importance measure [J]. Advances in Mechanical Engineering, 2018, 10 (11): 168781401880978.). Dui et al. proposed a new method for resilience management of multi-node systems after multi-node failures caused by natural disasters or man-made accidents based on importance measure, and applied it to analyze the recovery order of faulty nodes in wind power generation systems (WPGS) with multi-node failures (Dui HY, Zheng XQ, Guo JJ, et al. Importance measure-based resilience analysis of a wind power generation system [J]. Proceedings of the Institution of Mechanical Engineers Part O: Journal of Risk and Reliability, 2021.).Yao proposed a genetic local search (BIGLS) algorithm based on Birnbaum importance measure, which embeds the local search using Birnbaum importance into the genetic algorithm (Yao Q, Zhu X, Kuo W. A Birnbaum-importance based genetic local search algorithm for component assignment problems [J]. Annals of Operations Research, 2014, 212 (jan.): 185-200.). Zhai proposed a general statement of moment-independent importance measure and unified several commonly used importance measures based on Minkowski distance (MD) (Zhai Q, Yang J, Xie M, et al. Generalized moment-independent importance measures based on Minkowski distance [J]. European Journal of Operational Research, 2014, 239 (2): 449-455.). The importance measure research in the above literature mainly analyzes the single influencing factors of equipment or systems, and rarely conducts in-depth research on manufacturing systems with "networked" topological characteristics. Summary of the invention

[0005] In order to solve the problems existing in the prior art, the present invention provides a manufacturing system networking importance evaluation method.

[0006] The present invention constructs a network topology model of the manufacturing system based on the topological characteristics of the manufacturing system; comprehensively considers multiple factors such as the reliability, hazard degree, directional centrality and the failure cascading risk coefficient based on weighted entropy of the equipment, and performs importance measurement analysis of the manufacturing system by improving the importance measurement of the LeaderRank algorithm.

[0007] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0008] The present invention provides a manufacturing system network importance evaluation method, which mainly includes the following steps:

[0009] Step S1: construct a network topology model of the manufacturing system based on network theory;

[0010] Step S2: Analyze factors affecting the manufacturing system;

[0011] Step S3: Calculate the importance measure of the constructed manufacturing system network topology model based on the improved LeaderRank algorithm, compare the importance measures of different centralities, and perform sensitivity analysis on the equipment load busy rate.

[0012] Furthermore, the specific implementation process of step S1 is as follows:

[0013] Step S1.1: Overview of network theory;

[0014] Let G = (X, K) represent a complex network, X = {x1, x2, ..., x n} is a set of nodes; K = {k1, k2, ..., k m} represents the set of connecting edges between nodes; there are four different types of complex networks, depending on whether there is a direction and the strength of the connection relationship between nodes: undirected unweighted network, undirected weighted network, directed unweighted network and directed weighted network; manufacturing system equipment has both link relationships and production and processing sequences; therefore, manufacturing system equipment is usually similar to a directed unweighted network to fully reflect its system structure layout;

[0015] Step S1.2: construct a networked topology model of the manufacturing system;

[0016] Assume there are n devices x1, x2, ..., x n ,i,j∈[x1,x2,...,x n ], these different types of equipment constitute the manufacturing system X = {x1, x2, …, x n}; According to the system production process, it is mapped into a network topology model to build a network topology diagram of the directed manufacturing system; Equipment x m (m=1, 2, 3, 4, 5) is the input device, device x 13 to x 15 It is the output device; the transmission path and direction of the manufacturing system product are from device i to device j.

[0017] Furthermore, the specific implementation process of step S2 is as follows:

[0018] Step S2.1: Analysis and calculation of system equipment reliability;

[0019] Step S2.2: Analysis and calculation of system criticality;

[0020] Step S2.3: Analysis and calculation of system equipment centrality considering production direction;

[0021] Step S2.4: Analysis and calculation of failure cascading risk coefficient based on weighted entropy.

[0022] Furthermore, the specific implementation process of step S2.1 is as follows:

[0023] Firstly, according to the Weibull distribution model, the Monte Carlo method is used to randomly generate sample data of the failure interval time with a sample size of 500 for each device; then the Bayesian and EM methods are combined to estimate the parameters; finally, the KS test method is used to determine the number of heterogeneous populations.

[0024] Furthermore, the specific implementation process of step S2.2 is as follows:

[0025] The risk priority number method is used to analyze the criticality of the system.

[0026] Furthermore, the specific implementation process of step S2.3 is as follows:

[0027] (1) Degree centrality;

[0028] The degree centrality of node i in a complex network is defined as:

[0029]

[0030] Among them, k i is the total number of nodes connected to node i, a ij is the element in the i-th row and j-th column of the network adjacency matrix G, which represents the connection relationship between node i and node j, and N is the total number of network nodes;

[0031] (2) semi-local centrality;

[0032] The two-layer neighbor degree of network node j is represented by M j , which means the total number of neighboring nodes that can be reached by node j as the initial node in two steps. SLC is used to represent local centrality, and the SLC of node i is defined as:

[0033]

[0034] Among them, Γ i is a set representing all first-layer neighbor nodes of node j;

[0035] (3) Betweenness centrality;

[0036] In the process of network information flow transmission, the control of nodes over it is described by betweenness centrality; betweenness centrality is defined as:

[0037]

[0038] Among them, g wj represents the number of all shortest paths between nodes w and j, g wj(i) represents the number of shortest paths between nodes w and j that pass through node i;

[0039] (4) Directional centrality;

[0040] The directional centrality of node i is:

[0041]

[0042] Where A represents the set of paths from node i to other nodes, and p∈A.

[0043] Furthermore, the specific implementation process of step S2.4 is as follows:

[0044] The number of products that pass through the manufacturing system equipment in a given unit time is called the equipment load busy rate u; input equipment load busy rate u m According to a certain allocation principle, it is allocated to the next device, and the next device is also allocated to the next device, and this process continues until the output device; devices x7, x 10 Equal to the number of products that pass through the input device x1 per unit time, that is, u1=u7=u 10 ; Device x 13 The load busy rate is determined by the input devices x1 to x4 and is finally obtained through a certain distribution method; given the constant series U = [U1, U2, ..., U k ,U k+1 ,...U n ], The equipment load busy rate is in the range (U k ,U k+1 ], the device load busy rate is (U k ,U k+1 ]The probability P of the interval k for:

[0045]

[0046] Where N k The load busy rate u is (U k ,U k+1 ]; considering the impact of equipment failure on the production progress of other equipment, the chain reaction degree of system equipment failure is reflected by weighted entropy; the weighted entropy H of system equipment, that is, the failure chain risk coefficient, is:

[0047]

[0048] Furthermore, in step S3, the specific implementation process of importance measurement calculation is as follows:

[0049] (1) A system with n nodes transmits products according to the system production process. If node i is directly connected to node j and the transmission direction is from node i to node j, then the element a of the adjacency matrix is ij =1, otherwise, a ij =0; When the system introduces the background node of the LeaderRank algorithm, it is connected to each node through a bidirectional link and represented by an adjacency matrix G of (n+1)×(n+1); Assume that the initial value of the background node ILR g is 0, and the initial value of ILR of nodes other than background nodes is 1; then the improved algorithm ILR i The (t+1) value is shown in formula (7), where t represents the number of iterations:

[0050]

[0051] (2) Combined with the directional centrality, the state transfer matrix Q is established as shown in formula (8), that is, the ILR value of each node is assigned to the node it points to through weights, and this is used as the allocation probability to establish the state transfer matrix Q; the elements in Q can be intuitively regarded as the association strength between nodes; the matrix Q is continuously iterated:

[0052] Q=DTC i a ij (8)

[0053] (3) During the iteration, when all nodes reach the critical value The iteration stops when the node values ​​are approximate steady-state values ​​ILR. (stable) ; The background node value ILR obtained after iteration g(stable) Distributed to all other nodes in the system through step (4);

[0054] (4) Obtained ILR i The (t+1) value takes into account the impact of the device's directional centrality on the system; first, the obtained ILR (stable) The value is combined with the reliability R(t) and FRPN as shown in formula (9); finally, the fault settings are performed for each system device one by one, and the fault cascading risk coefficient H of the i-th device is calculated i , which reflects the severity of the chain reaction caused by the failure of device i; by combining the H i ILR g(stable) Assigned to

[0055]

[0056] In the formula, ILR i is the final ILR value of node i, and is used as an important measurement value of the system node.

[0057] Furthermore, in step S3, the specific implementation process of comparing the importance measures under the influence of different centralities is as follows:

[0058] In the importance measurement based on the improved LeaderRank algorithm under the influence of DC, when t = 0h, the top 5 devices are x6, x9, x 12 、x 11 and x4;x 12 The importance measurement value shows an upward trend with time. When t = 487h, x 12 The importance measurement rises to the second place; in the importance measurement under the influence of SLC, when t = 0h, the top 5 devices are x6, x9, x 11 , x8 and x 12 ; When t = 237h, the importance measure of x9 rises to the first place, and the importance measures of other devices also change with the change of t; in the importance measure under the influence of BC, when t = 0h, the top 5 devices are x6, x8, x 11 , x9 and x 14 ; In the importance measure under the influence of directional centrality, when t=0h, the top 5 devices are x6, x4, x5, x3 and x9 respectively; from 712h onwards, the importance measure of x4 gradually begins to decrease; in the time domain t∈[0,1200], the importance measures of devices x6 and x9 are both ranked at the top; therefore, the importance measure under the influence of directional centrality can maintain a certain consistency with other importance measures, and can also analyze important devices from the perspective of direction.

[0059] Furthermore, in step S3, the specific implementation process of the equipment load busy rate sensitivity analysis is as follows:

[0060] Taking input devices x1, x4, and x5 as an example, given that the load busy rate of x1, x4, and x5 is u m =1, 4, 8, and then the load busy rate of each device is obtained.

[0061] The beneficial effects of the present invention are:

[0062] The present invention aims at the problem that the "networked" topological structure layout of equipment in the manufacturing system is difficult to evaluate and identify key equipment due to the influence of multiple factors during the production operation. The topological structure between the equipment in the manufacturing system is mapped into a networked model, and an importance measurement analysis method based on the improved LeaderRank algorithm is proposed. The topological structure between the equipment in the manufacturing system is mapped into a networked model, and the main system characteristics such as the equipment hazard, reliability, centrality and fault chain risk coefficient are investigated to realize the importance measurement evaluation of the manufacturing system. In order to further analyze the practicality of the importance measurement evaluation method, the importance measurement analysis method of the improved LeaderRank algorithm is applied to the lithium battery pole piece production line system. By comparing the structural importance measurement with the B importance measurement, the results are consistent on the whole, which verifies the effectiveness and advantages of the method proposed in this article. The method in this article can be effectively expanded and applied to manufacturing systems with networked characteristics, and can consider multiple influencing factors to identify the key of the system, make targeted solutions, and provide a reference for further improving the reliability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 There are four types of complex networks.

[0064] Figure 2 It is a directed network topology diagram of the manufacturing system based on the production process.

[0065] Figure 3 is the centrality evaluation result.

[0066] Figure 4 It is an evaluation process based on the importance measurement of the improved LeaderRank algorithm.

[0067] Figure 5 is the importance measure based on the LeaderRank algorithm.

[0068] Figure 6 It is an importance measure based on the improved LeaderRank algorithm.

[0069] Figure 7 It is the importance measure of the improved LeaderRank algorithm under the influence of different centralities.

[0070] Figure 8 Figure 2 is a sensitivity analysis diagram of load busy rate. (a) Importance measure and cumulative change of importance measure value when the load busy rate of device x1 is 1, 4 and 8 respectively; (b) Importance measure and cumulative change of importance measure value when the load busy rate of device x4 is 1, 4 and 8 respectively; (c) Importance measure and cumulative change of importance measure value when the load busy rate of device x5 is 1, 4 and 8 respectively.

[0071] Fig. 9 It is a directed network topology diagram of the lithium battery pole piece production line system based on the production process.

[0072] Fig.10 Probability distribution plot for Blender x1.

[0073] Fig.11 It is an importance measure based on the improved LeaderRank algorithm.

[0074] Fig.12 Comparison of electrode importance measurements for lithium battery electrode production lines. DETAILED DESCRIPTION

[0075] The present invention is further described in detail below in conjunction with the accompanying drawings.

[0076] The present invention maps the manufacturing system into a network topology structure based on its topological characteristics. Considering the influence of multiple factors, an analysis method based on the importance measurement of the improved LeaderRank algorithm is proposed to solve the problem of difficulty in identifying key equipment under the influence of multiple factors.

[0077] The present invention provides a manufacturing system network importance evaluation method, which mainly includes:

[0078] Step S1: construct a network topology model of the manufacturing system based on network theory;

[0079] Step S2: Analyze factors affecting the manufacturing system;

[0080] Step S3: Calculate the importance measure of the constructed manufacturing system network topology model based on the improved LeaderRank algorithm, compare the importance measures of different centralities, and perform sensitivity analysis on the equipment load busy rate.

[0081] A manufacturing system network importance evaluation method of the present invention has the following specific implementation process:

[0082] Step S1: construct a network topology model of the manufacturing system based on network theory;

[0083] Step S1.1: Overview of network theory;

[0084] At present, driven by many researchers, complex network theory has been widely used in various complex systems such as the Internet, power grid, financial network, neural network, etc. There is no doubt that most systems in reality can be described by complex network models. For example, the Internet is a complex composed of websites. The network brain is a complex neural network. Engineering products can also be a complex network, in which components are represented by nodes, and the relationship between connected components is represented by links between corresponding nodes.

[0085] Complex networks are networks with meaningful topological features, which means that the generation pattern of connections in complex networks is neither purely random nor purely regular. Figure 1 As shown, a complex network can be represented by G = (X, K), where X = {x1, x2, ..., x n} is a set of nodes; K = {k1, k2, ..., k m} is the set of edges connecting nodes. In fact, there are four different types of complex networks, depending on whether there are directions and strengths of connections between nodes. Figure 1 As shown, they are undirected unweighted networks ( Figure 1 -a), undirected weighted network ( Figure 1 -b), directed unweighted network ( Figure 1 -c) and directed weighted networks ( Figure 1 -d). The manufacturing system equipment has both link relationships and production and processing sequences. Therefore, the manufacturing system equipment is usually similar to a directed unweighted network ( Figure 1 -c), so as to fully reflect its system structure layout.

[0086] As the number of devices in today's manufacturing systems increases, their layout becomes relatively complex. Therefore, in this case, the manufacturing system structure can be mapped to a network structure and analyzed by using the research method of network theory.

[0087] Step S1.2: construct a networked topology model of the manufacturing system;

[0088] Through the study of network theory, suppose there are n devices x1, x2, ..., x n ,i,j∈[x1,x2,...,x n ], which contains some different types of equipment, which constitute the manufacturing system X = {x1, x2, ..., x n According to the system production process mapped into a network topology model, the network topology diagram of the directed manufacturing system is constructed, such as Figure 2 Device x m (m=1, 2, 3, 4, 5) is the input device, device x 13 to x 15 The solid line and direction in the figure represent the transmission path and transmission direction of the manufacturing system products, that is, from device i to device j.

[0089] Step S2: Analyze factors affecting the manufacturing system;

[0090] In order to analyze the manufacturing system more comprehensively, it is assumed that Figure 2Taking a relatively complex manufacturing system as an example, the reliability, hazard, directional centrality and failure cascading risk coefficient of the equipment based on weighted entropy are analyzed and calculated.

[0091] Step S2.1: System equipment reliability analysis and calculation;

[0092] Under the combined effect of multiple failure mechanisms, the use of the assumption of a homogeneous population for single Weibull distribution modeling will result in large errors. Considering heterogeneous populations for modeling can effectively describe complex production systems and make the model distribution more accurate (Lin K, Chen Y, Xu D. Reliability assessment model considering heterogeneous population in a multiple stresses accelerated test [J]. Reliability Engineering and System Safety, 2017, 165: 134-143.). Therefore, the present invention will consider heterogeneous populations and use mixed Weibull as the model distribution. In order to obtain Figure 2 The reliability of the equipment shown is based on the Weibull distribution model. The Monte Carlo method is used to randomly generate sample data of the failure interval time with a sample size of 500 for each equipment. The Bayesian and EM methods are combined for parameter estimation. Finally, the KS test method is used to determine the number of heterogeneous populations, and the solution results are shown in Table 1.

[0093] Table 1 Mixed Weibull distribution parameters

[0094]

[0095] Step S2.2: System criticality analysis and calculation;

[0096] Paying attention to the failure modes and mechanisms of manufacturing systems and completing failure analysis can not only improve the reliability level of manufacturing systems in the design phase, but also reduce the inspection errors of manufacturing systems in the use phase. The risk priority number method (RPN) is the most commonly used method for criticality analysis of systems. In order to avoid inaccurate equipment criticality values ​​caused by expert misjudgment, the criticality based on the fuzzy risk priority number (FRPN) is calculated according to the literature (Testik, OM, Unlu, ET. Fuzzy FMEA in risk assessment for test and calibration laboratories. Qual Reliab Eng Int. 2023; 39: 575–589. https: / / doi.org / 10.1002 / qre.3198). The criticality values ​​obtained are shown in Table 2.

[0097] Table 2 FRPN values ​​of various equipment in the manufacturing system

[0098] equipment FRPN equipment FRPN 1 34.2 9 40.6 2 27.8 10 22.6 3 39.7 11 30.3 4 20.3 12 26.0 5 56.1 13 31.4 6 33.5 14 35.5 7 27.3 15 46.7 8 54.4

[0099] Step S2.3: Analysis and calculation of system equipment centrality considering production direction;

[0100] The basic goal of studying complex networks is to conduct a deeper study of the original systems they represent. In particular, it is to understand how the failure of a single device affects the overall behavior or performance of the original system of the network (L. Costa, F. da, et al., Characterization of complex networks: A survey of measurements, Adv. Phys. 56 (1) (2007) 167–242.). Undoubtedly, it is usually most important to identify those components that have the greatest impact on the performance of the entire complex network. It is also important to maintain the high reliability of those key components to ensure the stability and security of the entire complex network. For complex networks, various node centralities have emerged, such as DC, SLC, and EC.

[0101] (1) Degree Centrality (DC)

[0102] The degree centrality (DC) of a node in a complex network represents the total number of neighbors of a node. The most intuitive assumption is that the more nodes a given vertex is connected to, the more important it is (Krackhardt D. Assessing the political landscape: Structure, cognition, and power in organizations [J]. Administrative Science Quarterly, 1990, 35 (1): 342-369.). In different networks, the degree is further subdivided. For example, in a directed network, there are out-degree and in-degree. For a weighted network, the degree of a node refers to the sum of the weights of the edges of the node. The degree centrality of node i in a complex network is defined as:

[0103]

[0104] Among them, k i is the total number of nodes connected to node i, a ij is the element in the i-th row and j-th column of the network adjacency matrix G, which represents the connection relationship between node i and node j. N is the total number of network nodes.

[0105] (2) Semilocal centrality (SLC)

[0106] Chen et al., considering the multi-order neighbor information of network nodes, proposed semi-local centrality (SLC) as an identification method for node importance measurement, and the scope of node neighbor information involves fourth-order neighbors (Chen DB, Lv LY, Shang MS, Zhang YC, Zhou T. Identifying influential nodes in complex networks [J]. Physica A-statistical mechanics and its applications, 2012, 391 (4): 1777-1787.). In this method, the two-layer neighbor degree of network node j is represented as M j , which means the total number of neighboring nodes that can be reached by spreading outward from node j as the initial node in two steps. If SLC is used to represent local centrality, the SLC of node i can be defined as:

[0107]

[0108] Among them, Γ i is a set representing all first-layer neighbor nodes of node j.

[0109] (3) Betweenness Centrality (BC)

[0110] Betweenness centrality (BC) The importance of a node is related to the shortest path through the node. Because information flow is generally transmitted through the shortest path, if the shortest path of any node passes through a certain node at the same time, then this node is an important node (Girvan M, Newma ME J. Community structure in social and biological networks [J]. Proceedings of the National Academy of Sciences, 2002, 99 (12): 7821–7826.). In the process of network information flow transmission, the control of the node over it can be described by the betweenness centrality. The betweenness centrality is defined as:

[0111]

[0112] Among them, g wj represents the number of all shortest paths between nodes w and j, g wj (i) represents the number of shortest paths between nodes w and j that pass through node i.

[0113] (4) Directional centrality

[0114] In order to better reflect the directionality of the production process of the manufacturing system, a centrality that covers directional characteristics, namely directional centrality, is proposed to quantify the importance of equipment in a directed network system. Directional centrality can be used to measure the link relationship of the product transmission path from device i in the system, which can be expressed by the in-degree and out-degree of the device. The equipment in the manufacturing system is called a node. The sum of the paths pointing to node i is called the in-degree of node i. The sum of the paths from node i to other nodes is called the out-degree of node i. like Figure 2 The sum of the paths pointing to node x8 is The sum of the paths from node x8 to other nodes is The directional centrality of node i is shown in formula (4).

[0115]

[0116] Where A represents the set of paths from node i to other nodes, and p∈A.

[0117] The centrality evaluation results of DC, SLC, BC and directional centrality are as follows Figure 3As shown in Figure 2. Direction centrality is very different from other centrality indicators.

[0118] Step S2.4: Analysis and calculation of failure cascading risk coefficient based on weighted entropy;

[0119] Consider the phenomenon of fault chaining in the manufacturing system, that is, the process in which the failure of a certain device in the system causes other devices in the network manufacturing system to fail to work properly one after another. Therefore, it is necessary to accurately identify the important devices in the process - devices that are likely to cause a larger range of the system to fail to work properly after failure. The present invention uses a weighted entropy method to identify devices with a high risk of fault chaining. According to the calculation needs of the weighted entropy method, the following parameters are introduced, and finally the fault chain risk coefficient based on weighted entropy is obtained.

[0120] The number of products that pass through the manufacturing system equipment in a given unit time is called the equipment's load busy rate u. Enter the equipment's load busy rate u m According to a certain allocation principle, it is allocated to the next device, and the next device is also allocated to the next device, and this process continues until the output device. Figure 2 In the device x7, x 10 Equal to the number of products that pass through the input device x1 per unit time, that is, u1=u7=u 10 ; Device x 13 The load busy rate of is determined by the input devices x1 to x4 and is finally obtained through a certain distribution method. Given a constant series U = [U1, U2, ..., U k ,U k+1 ,…U n ], The equipment load busy rate is in the range (U k ,U k+1 ], the device load busy rate is (U k ,U k+1 ]The probability P of the interval k for:

[0121]

[0122] Where N k The load busy rate u is (U k ,U k+1 ] Considering the impact of equipment failure on the production progress of other equipment, the chain reaction degree of system equipment failure is reflected by weighted entropy. This can better assess the degree of danger to the system after equipment failure. Therefore, the weighted entropy H of the system equipment, that is, the failure chain risk coefficient, is:

[0123]

[0124] Step S3: Calculate the importance measure of the constructed manufacturing system network topology model based on the improved LeaderRank algorithm, compare the importance measures of different centralities, and perform sensitivity analysis on the equipment load busy rate;

[0125] Step S3.1: importance measure calculation;

[0126] The LeaderRank algorithm has strong anti-interference and robustness, and can quickly identify the most influential nodes in the network system. However, because the LeaderRank algorithm is too simple, its state transfer matrix is ​​only constructed through the out-degree of each node, and the background nodes are iteratively calculated in a uniformly distributed manner. The algorithm ignores the impact of the node's in-degree on the system, and also ignores the impact of the node on other nodes, which sometimes causes large errors. The present invention uses an improved LeaderRank algorithm to reconstruct the state transfer matrix and assign weights to background nodes, thereby avoiding the problems of a single state transfer matrix structure and uniform distribution of background nodes, making the analysis results more reasonable. The importance evaluation flow chart based on the improved LeaderRank algorithm is shown in the figure. Figure 4 As shown, the specific steps are as follows:

[0127] (1) A system with n nodes transmits products according to the system production process. If node i is directly connected to node j and the transmission direction is from node i to node j, then the element a of the adjacency matrix is ij =1, otherwise, a ij = 0. When the system introduces the background node of the LeaderRank algorithm, it is connected to each node through a bidirectional link, which can be represented by an (n+1)×(n+1) adjacency matrix G. Assume that the initial value ILR of the background node is g is 0, and the initial value of ILR for nodes other than background nodes is 1. Then the improved algorithm ILR i The (t+1) value is shown in formula (7), where t represents the number of iterations.

[0128]

[0129] (2) Combined with the directional centrality, the state transfer matrix Q is established as shown in formula (8). That is, the ILR value of each node is assigned to the node it points to through weights, and this is used as the allocation probability to establish the state transfer matrix Q. The elements in Q can be intuitively regarded as the strength of the association between nodes. This matrix Q is continuously iterated.

[0130] Q=DTC i a ij (8)

[0131] (3) During the iteration, when all nodes reach the critical value The iteration stops when the node values ​​are approximate steady-state values ​​ILR. (stable) The background node value ILR obtained after iteration g(stable) Distributed to all other nodes in the system through step (4).

[0132] (4) Obtained ILR i The (t+1) value takes into account the impact of the device's directional centrality on the system. First, in order to consider the impact of the device reliability and hazard index, the obtained ILR (stable) The value is combined with the reliability R(t) and FRPN as shown in formula (9). Finally, the fault settings are performed for each system device one by one, and the fault cascading risk coefficient H of the i-th device is calculated. i , which reflects the severity of the chain reaction caused by the failure of device i. i ILR g(stable) Assigned to As shown below.

[0133]

[0134] In the formula: ILR i is the final ILR value of node i, and is used as an important measurement value of the system node.

[0135] like Figure 2 As shown, the manufacturing system X={x1,x2,…,x 15} consists of 15 devices. Given the input device load busy rate u m The load busy rate of the input device is evenly distributed to the subsequent devices, thereby obtaining the load busy rate of each device in the system. The load busy rate of each device is given in Table 3.

[0136] Table 3 System equipment load busy rate

[0137] equipment <![CDATA[u i ]]> equipment <![CDATA[u i ]]> 1 1 9 8.5 2 2 10 1 3 3 11 5.5 4 4 12 8.5 5 5 13 3.25 6 7 14 7 7 1 15 4.25 8 5.5

[0138] According to equations (7) to (9) and Figure 4 The importance measurement evaluation process of system equipment is shown in Figure 1, and the ILR value of each equipment is calculated. The importance measurement based on the LeaderRank algorithm and the importance measurement based on the improved LeaderRank algorithm are respectively as follows: Figure 5 and Figure 6 shown.

[0139] like Figure 5 As shown in the figure, based on the importance measurement of the LeaderRank algorithm, the more important equipment in the manufacturing system are x6, x 13 and x 14The importance measurement values ​​of x1=x2=x3=x4=x5 are the same, and x8=x9, x 11 =x 12 , which makes it impossible to clearly distinguish the device importance measure.

[0140] like Figure 6 As shown in the figure, the importance measure based on the improved LeaderRank algorithm is time-varying. When t=0h, the devices with higher importance measures are x6>x4>x5>x3>x9; when t=170h and t=443h, the importance measures of x5 and x3 have changed; from t=717h, the importance measure of x4 gradually began to decrease. It is worth noting that the importance measure of x6 is the same as the importance measure based on the LeaderRank algorithm. The importance measure of x6 has always remained in the first place with the change of t, indicating that it has a relatively large impact on the system and needs to be given sufficient attention by the designer.

[0141] Step S3.2: Comparison of importance measures under different centrality influences;

[0142] The present invention takes the reliability, directional centrality and cascading failure risk coefficient of the equipment as the main influencing factors of the manufacturing system, and establishes an evaluation model based on the improved LeaderRank importance measure. In order to better identify the importance of equipment in the manufacturing system, based on different centralities, without changing other conditions, the importance measures based on the improved LeaderRank algorithm under the influence of DC, SLC, BC centrality and directional centrality are constructed respectively. Figure 7 shown.

[0143] from Figure 7 It can be observed that in the importance measurement based on the improved LeaderRank algorithm under the influence of DC, when t = 0h, the top 5 devices are x6, x9, x 12 、x 11 and x4. x 12 The importance measurement value shows an upward trend with time. When t = 487h, x 12 The importance measurement rises to the second place. In the importance measurement under the influence of SLC, when t = 0h, the top 5 devices are x6, x9, x 11 , x8 and x 12 When t = 237h, x9's importance measure rises to the first place, and the importance measures of other devices also change with the change of t. In the importance measure under the influence of BC, when t = 0h, the top 5 devices are x6, x8, x 11 , x9 and x 14In the importance measure under the influence of directional centrality, when t = 0h, the top 5 devices are x6, x4, x5, x3 and x9. From 712h onwards, the importance measure of x4 gradually begins to decrease. Overall, Figure 7 , in the time domain t∈[0,1200], the importance measures of devices x6 and x9 are both ranked at the top. Therefore, the importance measure under the influence of directional centrality can not only maintain a certain consistency with other importance measures, but also analyze important devices from the perspective of direction.

[0144] Step S3.3: equipment load busy rate sensitivity analysis;

[0145] From the perspective of experiment, in order to verify the impact of device load busy rate on the importance of system devices, taking input devices x1, x4, and x5 as examples, given that the load busy rate of x1, x4, and x5 is u m =1, 4, 8, and then the load busy rate of each device can be obtained. The importance measure based on the improved LeaderRank algorithm and the cumulative change of the importance measure value obtained by changing the load busy rate are as follows: Figure 8 shown.

[0146] Depend on Figure 8 It can be seen that, taking t=0h as an example, it can be observed that as the load busy rate of the same input device increases, the impact of the device on the system also increases. For example, as the load busy rate of x1 increases, its importance measure ranking changes from 10th to 4th; as the load busy rate of x5 increases, its importance measure ranking changes from 9th to 3rd. It can also be observed from the figure that the increase in the load busy rate of the input device leads to a significant increase in the importance measure of the devices subsequently connected to it. For example, the increase in the load busy rate of x1 makes the subsequent connected devices x1, x7, and x5 of x1 more important. 10 and x 13 The cumulative change of the importance measurement value of is large, which has a greater impact on their importance measurement. It can be seen that in the evaluation of manufacturing system importance measurement, input devices also participate in determining the importance measurement of subsequent devices. Therefore, while paying attention to the ranking of the importance measurement of all equipment, we should also focus on the input devices with higher rankings.

[0147] Example Analysis

[0148] Taking the lithium battery pole piece production line as an example, the importance measurement based on the improved LeaderRank algorithm will be compared with the structural importance measurement and B importance measurement to verify the effectiveness and advantages of the importance measurement based on the improved LeaderRank algorithm.

[0149] The lithium battery pole piece production line is a comprehensive manufacturing system that integrates machinery, electricity, control and management. Fig. 9As shown in the figure, the lithium battery pole piece production line is a system consisting of a mixer, a coating machine, a roller press, a die cutter and a slitting machine. Among them, x1 and x2 are mixers; x3 and x4 are coating machines; x5 is a roller press; x6 and x7 are die cutters; x8 and x9 are slitting machines. And its annual production of products is 6,000 pieces.

[0150] A one-year field reliability test was conducted on the lithium battery pole piece production line, and a total of 122 pieces of on-site production failure data of the lithium battery pole piece production line were collected. The failure time observation values ​​of each device were obtained by analyzing them, as shown in Table 4.

[0151] Table 4 Equipment failure interval of lithium battery electrode production line

[0152]

[0153] In order to verify the advantages of the importance measure based on the improved LeaderRank algorithm for the lithium battery pole piece production line system, it is compared with the structural importance measure and the B importance measure.

[0154] (1) Importance measurement based on improved LeaderRank algorithm

[0155] In order to obtain the optimal fitting distribution of the equipment failure interval of the lithium battery pole piece production line system, taking the lithium battery pole piece production line mixer x1 as an example, the probability distribution diagram of the production line equipment is obtained by Minitab as shown below Fig.10 As shown, it can be seen that the failure data of mixer x1 is more consistent with the Weibull distribution. Therefore, the Weibull distribution is used when modeling the failure data of the lithium battery pole piece production line.

[0156] The parameter estimates of the mixed Weibull model were calculated by combining the Bayesian and EM algorithms. After verification, the heterogeneous populations of the lithium battery pole piece production line system equipment were confirmed and separated. Table 5 shows the mixed Weibull distribution parameters and heterogeneous populations of the lithium battery pole piece production line equipment.

[0157] Table 5 Equipment parameters and heterogeneous population number of lithium battery pole piece production line

[0158]

[0159]

[0160] According to the annual production volume of 6,000 products, the load busy rate of each device in the lithium battery pole piece production line can be calculated. The centrality of the production line is calculated according to the production process. The hazard value is calculated based on the fuzzy risk priority number method. The directional centrality, load busy rate and hazard value of the equipment are shown in Table 6. Based on the improved LeaderRank algorithm, the importance measurement is as follows Fig.11shown.

[0161] Table 6 Directional centrality, load busy rate and FRPN value of lithium battery pole piece production line system equipment

[0162]

[0163] like Fig.11 As shown in the figure, when t = 0h, the importance measurement of the lithium battery pole piece production line system equipment is ranked as x5>x3>x2>x1>x7>x6>x4>x8>x9. Fig. 9 As shown, only from the perspective of the lithium battery pole piece production line system structure, x5 is connected in series with other devices, and its importance measure is the highest. However, based on the importance measure calculation based on the improved LeaderRank algorithm, it can be seen that when t>1276h, due to the influence of factors such as reliability, the importance measures of devices x3 and x5 change, and device x3 has the highest importance measure. It can be seen that the importance measure based on the improved LeaderRank algorithm can obtain the importance measure that changes over time. Therefore, this method can provide a reference for the importance measure evaluation of the lithium battery pole piece production line system for a long time.

[0164] (2) Structural Importance Measure (SIM)

[0165] The structural importance measure reflects the importance of a component in the system. It analyzes the role of each component in the entire system from the topological structure of the system. The structural importance measure of a component has nothing to do with its own reliability, but only considers its position in the system. For a system with n components, excluding the component i being studied, there are n-1 components left, and each component has 2 states. So the remaining state space has 2 n-1 possible combinations. i The measure that represents the contribution of component i to system failure is as follows:

[0166]

[0167] Wherein, L represents the state set of the remaining n-1 components after removing component i.

[0168] Normalize the structural importance measure so that it is ≤1, then the structural importance measure of component i can be expressed as:

[0169]

[0170] Converting the above formula into probability form, the expression of structural importance measurement can be obtained as follows:

[0171]

[0172] Its physical meaning is: when component i fails, the system is 1, that is, the system fails, and the number of state combinations of the remaining n-1 components. When component i does not fail, the system is 1, that is, the system still fails, and the number of state combinations of the remaining n-1 components. The ratio of the number of two state sets to the total number of state combinations after subtracting them is the structural importance measure of each component.

[0173] (3) BIM

[0174] In reliability system analysis, the B importance measure describes the impact of changes in component reliability on changes in the reliability of the entire system. The B importance measure is as follows:

[0175]

[0176] Among them, R represents the system reliability, p i represents the working probability of component i. The probability distribution of production line equipment obtained by Minitab is as follows: Fig.10 As shown, the lithium battery pole piece production line system conforms to the Weibull distribution.

[0177] Therefore, the Weibull distribution obeyed by the lithium battery manufacturing system equipment is shown in formula (14).

[0178]

[0179] In summary, according to Fig.11 It can be seen that there are two main importance measurement rankings before and after t = 1276h. Therefore, in order to compare the importance measurements more intuitively, the importance measurements at t = 0h and t = 1500h are used as the main importance measurements before and after t = 1276h. The comparison of the importance measurement based on the improved LeaderRank algorithm and the structural importance measurement and B importance measurement at t = 0h and t = 1500h is shown in Tables 7 and Fig.12 shown.

[0180] Table 7 Comparison of importance measurements of lithium battery electrode production lines

[0181]

[0182]

[0183] As shown in Table 7, in the lithium battery pole piece production line system, the SIM value of the equipment is x5>x1=x2=x3=x4=x6=x7=x8=x9. In the results of the calculation of the structural importance measure, the importance measure of x5 in the lithium battery pole piece production line equipment is the highest, but the importance measure of the remaining equipment cannot be identified. According to the calculation of the B importance measure, the B importance measure value of the equipment is x5>x7>x4>x6>x3>x2>x9>x1>x8. Through the importance measure analysis based on the improved LeaderRank algorithm, taking t=0h as an example, the equipment importance measure is ranked as x5>x3>x2>x1>x7>x6>x4>x8>x9. Among them, the equipment x5 ranks first in all importance measure analysis methods, which further shows the importance of x5. Compared with the importance measure of B, x3, x2 and x1 of the improved LeaderRank algorithm importance measure become more important under the influence of factors such as reliability, ranking second, third and fourth respectively. As time increases to 1500h, the importance measure based on the improved LeaderRank algorithm will also change over time.

[0184] In summary, by comparing the importance measure of B, the effectiveness of the importance measure based on the improved LeaderRank algorithm can be verified. In addition, the structural importance measure only analyzes the importance measure of system equipment from the perspective of structure, and cannot clearly distinguish the importance of the equipment. This is enough to prove the advantage of the importance measure based on the improved LeaderRank algorithm.

[0185] The present invention uses case analysis to compare the importance measure of the LeaderRank algorithm. The importance measure of the improved LeaderRank algorithm can obtain the change of the importance measure over time, which has obvious advantages. By comparing the importance measures under the influence of different centralities, the importance measure of directional centrality can analyze the importance from the perspective of direction, which can more specifically analyze the importance measure of the manufacturing system. Through the sensitivity analysis of the equipment load busy rate, the equipment load busy rate has a greater impact on the system. Therefore, when analyzing the importance measure of the manufacturing system, the factor of load busy rate should be considered. The present invention takes the lithium battery pole piece production line as an example to perform importance measure analysis, and verifies the effectiveness of the importance measure based on the improved LeaderRank algorithm by comparing and analyzing with the structural importance measure and the B importance measure. At the same time, it is determined that equipment x5, x3 and x2 are the most important, which provides a direction for further improving the lithium battery pole piece production line.

[0186] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A manufacturing system networking importance evaluation method, characterized in that: The following steps are involved: Step S1: construct a network topology model of the manufacturing system based on network theory; Step S2: Analyze factors affecting the manufacturing system; Step S3: Calculate the importance measure of the constructed manufacturing system network topology model based on the improved LeaderRank algorithm, compare the importance measures of different centralities, and perform sensitivity analysis on the equipment load busy rate.

2. A manufacturing system networking importance evaluation method according to claim 1, characterized in that: The specific implementation process of step S1 is as follows: Step S1.1: Overview of network theory; Let G = (X, K) represent a complex network, X = {x1, x2, ..., x n } is a set of nodes; K = {k1, k2, ..., k m } represents the set of connecting edges between nodes; there are four different types of complex networks, depending on whether there is a direction and the strength of the connection relationship between nodes: undirected unweighted network, undirected weighted network, directed unweighted network and directed weighted network; manufacturing system equipment has both link relationships and production and processing sequences; therefore, manufacturing system equipment is usually similar to a directed unweighted network to fully reflect its system structure layout; Step S1.2: construct a networked topology model of the manufacturing system; Assume there are n devices x1, x2, ..., x n ,i,j∈[x1,x2,...,x n ], these different types of equipment constitute the manufacturing system X = {x1, x2, …, x n }; According to the system production process, it is mapped into a network topology model to build a network topology diagram of the directed manufacturing system; Equipment x m (m=1, 2, 3, 4, 5) is the input device, device x 13 to x 15 It is the output device; the transmission path and direction of the manufacturing system product are from device i to device j.

3. A manufacturing system networking importance evaluation method according to claim 1, characterized in that: The specific implementation process of step S2 is as follows: Step S2.1: Analysis and calculation of system equipment reliability; Step S2.2: Analysis and calculation of system criticality; Step S2.3: Analysis and calculation of system equipment centrality considering production direction; Step S2.4: Analysis and calculation of failure cascading risk coefficient based on weighted entropy.

4. A manufacturing system networking importance evaluation method according to claim 3, characterized in that: The specific implementation process of step S2.1 is as follows: Firstly, according to the Weibull distribution model, the Monte Carlo method is used to randomly generate sample data of the failure interval time with a sample size of 500 for each device; then the Bayesian and EM methods are combined to estimate the parameters; finally, the KS test method is used to determine the number of heterogeneous populations.

5. A manufacturing system networking importance evaluation method according to claim 3, characterized in that: The specific implementation process of step S2.2 is as follows: The risk priority number method is used to analyze the criticality of the system.

6. A manufacturing system networking importance evaluation method according to claim 3, characterized in that: The specific implementation process of step S2.3 is as follows: (1) Degree centrality; The degree centrality of node i in a complex network is defined as: Among them, k i is the total number of nodes connected to node i, a ij is the element in the i-th row and j-th column of the network adjacency matrix G, which represents the connection relationship between node i and node j, and N is the total number of network nodes; (2) semi-local centrality; The two-layer neighbor degree of network node j is represented by M j , which means the total number of neighboring nodes that can be reached by node j as the initial node in two steps. SLC is used to represent local centrality, and the SLC of node i is defined as: Among them, Γ i is a set representing all first-layer neighbor nodes of node j; (3) Betweenness centrality; In the process of network information flow transmission, the control of nodes over it is described by betweenness centrality; betweenness centrality is defined as: Among them, g wj represents the number of all shortest paths between nodes w and j, g wj (i) represents the number of shortest paths between nodes w and j that pass through node i; (4) Directional centrality; The directional centrality of node i is: Where A represents the set of paths from node i to other nodes, and p∈A.

7. A manufacturing system networking importance evaluation method according to claim 3, characterized in that: The specific implementation process of step S2.4 is as follows: The number of products that pass through the manufacturing system equipment in a given unit time is called the equipment load busy rate u; input equipment load busy rate u m According to a certain allocation principle, it is allocated to the next device, and the next device is also allocated to the next device, and this process continues until the output device; devices x7, x 10 Equal to the number of products that pass through the input device x1 per unit time, that is, u1=u7=u 10 ; Device x 13 The load busy rate is determined by the input devices x1 to x4 and is finally obtained through a certain distribution method; Given a constant series U = [U1, U2, ..., U k ,U k+1 ,...U n ], The equipment load busy rate is in the range (U k ,U k+1 ], the device load busy rate is (U k ,U k+1 ]The probability P of the interval k for: Where N k The load busy rate u is (U k ,U k+1 ]; considering the impact of equipment failure on the production progress of other equipment, the chain reaction degree of system equipment failure is reflected by weighted entropy; the weighted entropy H of system equipment, that is, the failure chain risk coefficient, is:

8. A manufacturing system networking importance evaluation method according to claim 1, characterized in that: In step S3, the specific implementation process of importance measurement calculation is as follows: (1) A system with n nodes transmits products according to the system production process. If node i is directly connected to node j and the transmission direction is from node i to node j, then the element a of the adjacency matrix is ij =1, otherwise, a ij =0; When the system introduces the background node of the LeaderRank algorithm, it is connected to each node through a bidirectional link and represented by an (n+1)×(n+1) adjacency matrix G; Assume that the initial value of the background node is ILR g is 0, and the initial ILR value of nodes other than background nodes is 1; then the improved algorithm ILR i The (t+1) value is shown in formula (7), where t represents the number of iterations: (2) Combined with the directional centrality, the state transfer matrix Q is established as shown in formula (8), that is, the ILR value of each node is assigned to the node it points to through weights, and this is used as the allocation probability to establish the state transfer matrix Q; the elements in Q can be intuitively regarded as the association strength between nodes; the matrix Q is continuously iterated: Q=DTC i a ij (8) (3) During the iteration, when all nodes reach the critical value The iteration stops when the node values ​​are approximate steady-state values ​​ILR. (stable) ; The background node value ILR obtained after iteration g(stable) Distributed to all other nodes in the system through step (4); (4) Obtained ILR i The (t+1) value takes into account the impact of the device's directional centrality on the system; first, the obtained ILR (stable) The value is combined with the reliability R(t) and FRPN as shown in formula (9); finally, the fault settings are performed for each system device one by one, and the fault cascading risk coefficient H of the i-th device is calculated i , which reflects the severity of the chain reaction caused by the failure of device i; by combining the H i ILR g(stable) Assigned to In the formula, ILR i is the final ILR value of node i, and is used as an important measurement value of the system node.

9. A manufacturing system networking importance evaluation method according to claim 1, characterized in that: In step S3, the specific implementation process of comparing importance measures under different centrality influences is as follows: In the importance measurement based on the improved LeaderRank algorithm under the influence of DC, when t = 0h, the top 5 devices are x6, x9, x 12 、x 11 and x4;x 12 The importance measurement value shows an upward trend with time. When t = 487h, x 12 The importance measurement rises to the second place; in the importance measurement under the influence of SLC, when t = 0h, the top 5 devices are x6, x9, x 11 , x8 and x 12 ; When t = 237h, the importance measure of x9 rises to the first place, and the importance measures of other devices also change with the change of t; in the importance measure under the influence of BC, when t = 0h, the top 5 devices are x6, x8, x 11 , x9 and x 14 ; In the importance measure under the influence of directional centrality, when t=0h, the top 5 devices are x6, x4, x5, x3 and x9 respectively; from 712h onwards, the importance measure of x4 gradually begins to decrease; in the time domain t∈[0,1200], the importance measures of devices x6 and x9 are both ranked at the top; therefore, the importance measure under the influence of directional centrality can maintain a certain consistency with other importance measures, and can also analyze important devices from the perspective of direction.

10. A manufacturing system networking importance evaluation method according to claim 1, characterized in that: In step S3, the specific implementation process of the equipment load busy rate sensitivity analysis is as follows: Taking input devices x1, x4, and x5 as an example, given that the load busy rate of x1, x4, and x5 is u m =1, 4, 8, and then the load busy rate of each device is obtained.

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