Uncertain CPS modeling and analysis method based on GSOPN

Abstract

The present invention discloses an uncertain CPS modeling and analysis method based on GSOPN. The present invention constructs a generalized random object Petri net GSOPN according to an actual industrial information-physical system CPS; uses an object net ablation algorithm to convert the embedded object net structure of the generalized random object Petri net GSOPN into a traditional GSPN; uses normal membership function, inverse cloud algorithm, and forward cloud algorithm methods to process the uncertainty of GSPN; regards GSPN as an embedded Markov chain EMC and performs performance analysis on it. The present invention proposes that GSOPN has a strong description capability for the dynamic production process of the CPS system, and uses an object net ablation algorithm to enable it to have the efficiency and accuracy of GSPN, and can make faster and more accurate analysis of more complex CPS systems with more uncertainties based on traditional GSPN.

Description

Technical Field

[0001] The present invention belongs to the technical field of CPS modeling, and relates to an uncertain CPS modeling and analysis method based on GSOPN, and specifically to an uncertain industrial information-physical system modeling and analysis method based on generalized random object Petri nets. Background Art

[0002] Cyber-Physical System (CPS) is a real-time complex system that embeds computing, communication, and control into multiple physical devices based on environmental perception. It achieves deep integration and real-time interaction between the information world and the physical world through feedback loops between computing processes representing embedded computers and network monitoring and physical processes representing the physical world. In recent years, CPS has become one of the most attractive fields in academia, and has been widely used in industrial manufacturing, aerospace, medical care, transportation and other fields. In our daily lives at this stage, CPS has played an irreplaceable role, processing data through computers, influencing and changing the way the physical world interacts.

[0003] With the advancement of science and technology in recent years, the availability and affordability of computers, sensors and other equipment have become higher. Due to the competitiveness between industries, more and more factories have moved from the original "manufacturing" to modern "intelligent manufacturing". The information physical system in the field of industrial manufacturing is called industrial CPS. Industrial CPS can be processed by robots and other types of equipment to achieve intelligent manufacturing and automated production, turning factories into industrial 4.0 factories with huge economic potential. Industrial CPS is at the core of the fourth industrial revolution. Germany's "Industry 4.0" and the United States' "Industrial Internet" have made great contributions to the establishment of its important position.

[0004] In order to better design and operate industrial CPS, it is crucial to establish an abstract model and analyze it. A good formal model can not only standardize and verify the system and its properties, but also ensure the correctness and reliability of the system, providing guarantee for its normal operation. Existing CPS research has taken into account the properties of each component and the interaction between them, but in industrial intelligent manufacturing, industrial CPS modeling still has the following problems: (1) From a macro perspective, CPS-related research can well represent the production process of industrial CPS, but from a micro perspective, the production status of the workpiece in the production process has hardly been paid attention to, and the intuitiveness of the production process is insufficient; (2) The models established by these methods are too abstract and difficult to understand for industrial production lines, and their complexity is also high; (3) Industrial intelligent manufacturing production lines require quantitative analysis of productivity and equipment utilization over a period of time, data statistics, and process optimization, but most existing CPS modeling methods ignore the uncertainty of the time of event occurrence in the actual production process, making the analysis results inaccurate.

[0005] Based on the above analysis, in view of the problems of existing methods in terms of insufficient intuitive modeling and insufficient analysis capabilities, the present invention focuses on the workflow, interaction between equipment and production status of workpieces in industrial CPS, and proposes a generalized stochastic object Petri Net (GSOPN). In order to facilitate the analysis of performance indicators such as productivity and equipment utilization of industrial CPS, an object net ablation algorithm is further proposed to convert the embedded object net structure of GSOPN into a traditional generalized stochastic Petri Net (GSPN) to simplify the performance analysis process. The Markov chain related method is introduced to perform performance analysis on GSPN to improve the accuracy of the analysis results. Summary of the invention

[0006] An object of the present invention is to address the deficiencies of the prior art and to propose a modeling and analysis method for uncertain industrial cyber-physical systems based on generalized random object Petri nets.

[0007] The general idea of ​​the method of the present invention is:

[0008] In the modeling stage of CPS, in order to intuitively represent the actual production process, the interaction between multiple types of equipment and the processing status of the workpiece during the production process, a generalized random object Petri net is proposed. GSOPN contains system nets and object nets. The system net is used to describe the specific workflow of industrial CPS and the interaction between equipment, while the object net is a special type of token in the system net, which is used to describe the production status of the workpiece. In order to simplify the performance analysis process of GSOPN, an object net ablation algorithm is proposed to convert GSOPN into GSPN. In view of the uncertainty of complex systems such as industrial CPS, the normal membership function is applied to improve the rationality and accuracy of the analysis results.

[0009] The steps of the method adopted by the present invention to solve the technical problem are as follows:

[0010] Step (1), constructing a generalized stochastic object Petri Net (GSOPN) based on an actual industrial cyber-physical system (CPS);

[0011] The generalized random object Petri net GSOPN is composed of a quaternion S = (SN, ON, ρ, σ), which is an embedded object network structure. The system network SN and the object network ON are used to form a two-layer separation model of the entire GSOPN network system. The system network and the object network are combined through the synchronous interaction relationship ρ of the changes in the system network and the object network and a corresponding relationship σ of the library. The details are as follows:

[0012] 1) Object network ON

[0013] The object network ON is an abstract modeling of the workpiece processing flow in the actual industrial cyber-physical system CPS, which is used to reflect the relationship between the processing state of the workpiece, the processing state between workpieces and the factors causing the change of the workpiece processing state; the object network is denoted as The state of the workpiece before and after processing in the current processing flow is used as the library set of ON The factors that cause the change of the library in the current processing flow are used as the transition set of ON The factors that cause the library to change include instantaneous actions such as starting processing, ending processing, and state judgment, and time-consuming actions such as punching and bending. The instantaneous actions are reflected in ON as instantaneous transition sets. The time-consuming action is reflected as the time change set Construct a directed arc set of ON based on the state transitions between places and transitions and in is the set of directed arcs from place to transition, is the set of directed arcs that transition to places;

[0014] 2) System Network SN

[0015] The system network SN is an abstract modeling of the overall workflow in the actual industrial CPS, which is used to reflect the relationship between the resource status of workpiece processing, the workpiece processing status and the factors that cause the change of the workpiece processing status; the workpiece processing status and the factors that cause the change of the workpiece processing status in SN are simplified versions in the object network, because ON should provide SN with the workpiece it needs, and the specific processing details are shielded from SN; the system network is recorded as SN = (P, T, I, O), and the status of the workpiece before and after processing and the status of the resources required for workpiece processing in the current processing flow are taken as the library set P of SN; the factors that cause the change of the library in the current processing flow are taken as the transition set T of SN, and the factors that cause the change of the library are instantaneous actions such as starting processing, ending processing, and state judgment, and time-consuming actions such as punching and bending. Instantaneous actions are reflected in SN as instantaneous transition set p i , and the time-consuming action is reflected in the time transition set T t ; Construct the directed arc sets I and O of SN according to the state transitions between places and transitions, where is the set of directed arcs from place to transition, is the set of directed arcs that transition to places;

[0016] 3) Correspondence set σ

[0017] The correspondence relationship set σ represents a correspondence relationship between the system network and the object network, specifically, the correspondence relationship between different locations of a certain state in the object network and the system network during implementation; therefore, the steps for establishing the correspondence relationship set are as follows:

[0018] Arbitrarily take all the places P in the object network o and all places P of the system network s ;

[0019] If P o and P s have the same real meaning, then add the two to the corresponding relationship set;

[0020] If P o and P s If they do not have the same real meaning, they will not be added to the corresponding relationship set;

[0021] Repeat the above steps until the object network and system network are traversed;

[0022] 4) Interaction relationship set ρ

[0023] The interactive relationship set ρ represents a corresponding relationship between the system network and the object network. The interactive relationship set is established as follows:

[0024] According to all the places P in the corresponding relationship set σ o and P s , find out the subsequent changes of these two places in the object network and system network respectively, add the changes with the same practical significance and type to the interaction relationship set and repeat the above steps until the corresponding relationship set is traversed;

[0025] Step (2) uses the object net ablation algorithm to transform the embedded object net structure of the generalized random object Petri net GSOPN into a traditional GSPN for performance analysis. Specifically:

[0026] 2-1 In order to eliminate the embedded object network structure, firstly, it is necessary to delete all transitions belonging to the interactive relationship set ρ on the object network; after deleting the above transitions, there will be many isolated places in the object network. Traverse all the places in the object network. If there is no directed arc between the place and other transitions, delete the current place; otherwise, keep the place;

[0027] 2-2 Define the network structure obtained in step 2-1 as If a library and Library is the starting place, where Indicates the change of input in the library; if and Library To terminate the library, Indicates that there is a transition of output in this place; the starting place set S is the set containing all starting places, denoted as The termination place set E is the set of all termination places, denoted by

[0028] Traverse all remaining places in the object network and add the places that meet the definition of the starting place or the ending place to the corresponding set S or E;

[0029] 2-3 If the conditions are met: and in For any element in S, σ(s) represents the relationship corresponding to s in the corresponding relationship set σ, then s is directly added to the system network using the corresponding relationship set, otherwise is an element of the input set of the starting place s in the initial object network. According to the interaction relationship set ρ, find the transition t in the system network that interacts with the transition in the input set. s , create transition t s The directed arc pointing to place s is added to the system network SN together with place s;

[0030] 2-4 If the conditions are met: and in For any element in E, σ(e) represents the relationship corresponding to e in the corresponding relationship set σ. Then e is added to the system network directly using the corresponding relationship set. Otherwise, To terminate an element of the output set of place e in the initial object network, find the transition t in the system network that interacts with the transition in the input set according to the interaction relationship set ρ e , create a library place e pointing to transition t e The directed arc of is added to the system network SN together with the library place e;

[0031] Step (3), in order to improve the actual availability of the GSPN network system, the normal membership function, the reverse cloud algorithm, and the forward cloud algorithm are used to process the uncertainty in the GSPN to determine the specific occurrence rate of each time transition in the GSPN;

[0032] 3-1 Use normal membership function to solve the uncertainty of time change rate;

[0033] The normal membership function uses three numerical features, Ex (Expected Value), En (Entropy), and He (HyperEntropy), to represent the uncertainty of things, combining randomness and fuzziness to construct a model that obeys the pan-normal distribution.

[0034] Assume that U is a quantitative domain represented by exact numerical values, and that qualitative concept C(Ex, En, He) is a qualitative concept on the quantitative domain U. If x∈U is a random realization of concept C, it follows the normal distribution N(Ex, En′ 2 ), En′ obeys the normal distribution N(En,He 2 ), the certainty of x to C μ(x)∈[0,1] is a random number with a stable tendency, satisfying:

[0035]

[0036] Then the distribution of random variables X constituted by all models on the domain U obeys the pan-normal distribution. The membership function in the above formula is called the normal membership function. The quantitative value x reflects the randomness of the quantitative value representing the concept, and μ(x) reflects the degree of certainty that the quantitative value x belongs to the qualitative concept C.

[0037] Ex is the mathematical expectation of the distribution of the model in the domain space, that is, the point that best represents the qualitative concept; En can represent the discreteness of the model on the one hand, and on the other hand, it determines the certainty of the model that can be accepted by the concept in the domain space. The larger En is, the wider the distribution range of the model is; He represents the general acceptance of common sense concepts. The smaller He is, the greater the acceptance is.

[0038] 3-2 In order to deal with the uncertainty of the time change rate, the collected time change rate is firstly transformed into three digital features Ex, En and He through the Multiple Backward Cloud Transformation based on Sampling with Replacement (MBCT-SR) algorithm;

[0039] 3-3 After using the multi-step reverse cloud transformation algorithm to obtain the Ex, En, and He of each transition, the forward cloud transformation algorithm can be used to obtain an estimate of the rate at which the time transition occurs;

[0040] Step (4), treating GSPN as an embedded Markov Chain (EMC) to analyze its performance and improve the accuracy of the analysis results;

[0041] The state space set of GSPN consists of two parts: the existing state set and the disappearing state set. Let X be the GSPN reachable identifier set S r For an element in M, if at least one time transition is in the enabled state under the label X, then M is called an existing state, otherwise it is called a vanishing state. Let the state space set of GSPN be S g , the number of state space sets |S g |=k s ; Existing state set S t ,|S t |=k t ; Disappearing state set S v ,|S v |=k v , where S = S t ∪S v , k s =k t +k v ; Ignoring the time factor, we only focus on the GSPN state and the transition between states. The GSPN can be regarded as an embedded Markov Chain (EMC). The transfer matrix M of the EMC is shown in the following formula:

[0042]

[0043] The elements in the matrix A are composed of the transition probability matrix C from the disappearing state to the disappearing state and the transition probability matrix D from the disappearing state to the real state. The elements in the matrix B are composed of the transition probability matrix E from the real state to the disappearing state and the transition probability matrix F from the real state to the real state set. The transition from the real state to other states is determined by the occurrence rate of time transition. The occurrence rate of time transition generated by the forward cloud transformation algorithm will determine the values ​​of the elements in the matrices E and F.

[0044] Remove all the vanishing states in EMC and keep the existing states to get a reduced EMC (REMC). Then calculate the transition probability matrix M' of REMC. The element m' of M' ij The calculation method of is as follows (6):

[0045]

[0046] Where i, j represent the real state in EMC, that is, i, j∈S t , f ij is the transition probability from the existing state i to the existing state j, e ir is the transition probability from the existing state i to the disappearing state r, where r represents the disappearing state of EMC, i.e. r∈S v , P r The elements of [r→j] are the probabilities of going from the vanishing state r to the existing state j for the first time after any number of steps; the matrix G ∞ The elements in G represent the probability of going from the disappearing state to the existing state for the first time. ∞ The calculation is as follows (7):

[0047]

[0048] Among them, k0 satisfies the following conditions

[0049]

[0050] Therefore, M' can be expressed as follows:

[0051] M'=F+EG ∞ (8)

[0052] REMC is solved by the linear equation system of formula (9), where Y = (y1, y2, ..., y c ), c=k t , element y i represents the stable probability distribution of REMC's existing state;

[0053]

[0054] At this time, considering the time factor, the steady-state probability of GSPN can be obtained, and the average residence time in the actual state i can be calculated by formula (10), where E(i) = {the set of transitions that can be implemented in the actual state i}, λ k represents the rate of occurrence of transitions in the set of transitions that can be implemented under the existing state i;

[0055]

[0056] The steady-state probability of GSPN can be expressed by the following formula (11):

[0057]

[0058] Each time the forward cloud transformation algorithm generates a set of occurrence rates of time transitions, the steady-state probability of the existing state obtained will be different; based on the steady-state probability of GSPN, the throughput rate of each transition can be calculated, and the production capacity of the entire CPS system can be evaluated based on this throughput rate.

[0059] Another object of the present invention is to provide an electronic device, characterized in that it includes a processor and a memory, the memory stores machine executable instructions that can be executed by the processor, and the processor executes the machine executable instructions to implement the described method.

[0060] Another object of the present invention is to provide a machine-readable storage medium, characterized in that the machine-readable storage medium stores machine-executable instructions, and when the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the described method.

[0061] Beneficial effects of the present invention:

[0062] The present invention innovatively proposes GSOPN, which has a strong ability to describe the dynamic production process of the CPS system. The object net ablation algorithm enables it to have the efficiency and accuracy of GSPN. Therefore, the present invention can make faster and more accurate analysis of more complex CPS systems with more uncertainties based on traditional GSPN. This also makes it applicable to the production and manufacturing process of high-precision equipment, such as the production process of high-precision equipment in aerospace, medical and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 Partial equipment diagram of punching, folding and welding production line;

[0064] Figure 2 Workflow of punching, folding and welding production line;

[0065] Figure 3GSOPN model of punching, folding and welding production line; (a) is the system network, (b) is the object network;

[0066] Figure 4 The structure diagram after deleting some places and changes in the object network;

[0067] Figure 5 GSPN model after GSOPN conversion;

[0068] Figure 6 Model diagrams under different digital features; (a) Ex = 0, En = 20, He = 1; (b) Ex = 20, En = 20, He = 1; (c) Ex = 0, En = 10, He = 1; (d) Ex = 0, En = 10, He = 5;

[0069] Figure 7 Reachability graph of GSPN;

[0070] Figure 8 Production situation;

[0071] Fig. 9 Change throughput rate;

[0072] Fig.10 Equipment utilization. DETAILED DESCRIPTION

[0073] The specific implementation details of the present invention will be introduced below in conjunction with a specific implementation case.

[0074] The punching, folding and welding production line of Hangzhou Xio Elevator Co., Ltd. (www.xiolift.com, XIOLIFT) is an industrial CPS system with complex processes and high reliability requirements. The components of this production line include Omron length measuring sensors, two MAGNUM-5000 punching machines and two ABB (Asea Brown Boveri) robots, an LLVDPEB320 / 20 bending machine and an ABB robot, an ABB palletizing robot, an ABB welding robot, and a Junwei nut spot welder. Some of the equipment in the punching, folding and welding production line include Figure 1 shown.

[0075] This punching, folding and welding production line is used to process raw material type A plates and raw material type B plates to produce finished metal plates. The specific process is as follows:

[0076] (1) The ABB robot cooperates with the MAGNU-5000 punch press to punch holes in the A-type plate.

[0077] (2) After the A-type plate is punched, the ABB robot cooperates with the LVD PPEB bending machine to bend the A-type plate.

[0078] (3) The Omron length sensor will detect the bent A-type plate to see if the length meets the specification and send the test result to the OPC server. If it meets the specification, the following steps will be continued; if it does not meet the specification, the system will take another A-type plate and perform steps (1), (2), and (3).

[0079] (4) The Junwei nut spot welding machine performs spot welding of nuts on the bent A-type plate.

[0080] (5) During steps (1), (2), (3), and (4), another MAGNU-5000 punching machine and an ABB-type robot punch holes in the B-type plate.

[0081] (6) The ABB robot welds the A-type plate that meets the specifications and the B-type plate that has been punched together.

[0082] (7) The ABB robot stacks and stores the finished metal plates after welding, and then repeats the above steps to continue producing finished metal plates.

[0083] The above steps are as follows Figure 2 As shown, the processing route of type A plate is represented by gray, the processing route of type B plate is represented by blue, and the processing of the two into a metal plate and the subsequent operations are represented by green.

[0084] Before using the GSOPN network proposed in the present invention to model and analyze the above CPS system, the relevant concepts are defined. The meanings and symbols are as follows:

[0085] (1) The GSOPN network system is a four-tuple S = (SN, ON, ρ, σ), where: SN represents the system network; ON represents the object network; ρ represents the interaction relationship set; σ represents the corresponding relationship set.

[0086] (2) In order to describe the overall process and structure in CPS, the system network SN is defined as a four-tuple SN = (P, T, I, O).

[0087] P is a finite set of state places in SN;

[0088] T is a finite set of activity transitions in SN, which is divided into time transition set T t and the instantaneous transition set T i , that is, T = T t ∪T i ,

[0089] I is a finite set of input mapping functions from places to transitions in SN;

[0090] O is a finite set of output mapping functions from transitions to places in SN;

[0091] (3) In order to describe the status and resource conditions of the production process in CPS in detail, the object network ON is defined as a four-tuple in:

[0092] is a finite set of state places in ON;

[0093] is a finite set of activity transitions in ON;

[0094] is a finite set of input mapping functions from places to transitions in ON;

[0095] is a finite set of functions that map the outputs of ON from transitions to places;

[0096] (4) In order to describe the correspondence between the places in the system network and the object network, the correspondence set σ is the correspondence between different places in the object network and the system network for a certain state in the implementation;

[0097] (5) In order to describe the synchronous interaction between the system network and the object network, the interaction relationship set ρ is the correspondence relationship composed of the previous and next transitions of the library places in the corresponding relationship set σ.

[0098] (6) In order to deal with the uncertainty of the rate of time change, the normal membership function is used to solve the uncertainty of the rate of time change. The normal membership function uses three numerical features: expected value Ex (Expected Value), entropy En (Entropy), and hyper entropy He (Hyper Entropy) to represent the uncertainty of things, where:

[0099] Ex is the mathematical expectation of the distribution of the model in the domain space, that is, the point that best represents the qualitative concept;

[0100] On the one hand, En can represent the discreteness of the model, and on the other hand, it determines the certainty of the model that can be accepted by the concept in the domain space. The larger En is, the wider the distribution range of the model is.

[0101] He represents the general acceptance of common sense concepts. The smaller He is, the greater the acceptance is.

[0102] (7) Markov chain related concepts:

[0103] Let X be the set of GSPN reachable identifiers S r For an element in M, if at least one time transition under the symbol X is in the enabled state, then M is called an existential state, otherwise it is called a vanishing state.

[0104] S g : The state space set of GSPN, the number of state space sets |S g |=k s ; Existing state set S t ,|S t |=k t ; Disappearing state set S v ,|S v |=k v , where S = S t ∪S v , k s =k t +k v ;

[0105] M: transition probability matrix of the homogeneous Markov chain (EMC) of GSPN;

[0106] A: The probability matrix of transition from the vanishing state to the vanishing state and the existing state in EMC. This matrix is ​​composed of the transition probability matrix C from the vanishing state to the vanishing state and the transition probability matrix D from the vanishing state to the existing state.

[0107] B: The probability matrix of transition from the existing state to the disappearing state and from the existing state in EMC, which is composed of the transition probability matrix E from the existing state to the disappearing state and the transition probability matrix F from the existing state to the disappearing state set;

[0108] M': remove all vanishing states in the EMC, leaving only the real states, and obtain the reduced EMC (REMC). M' is the REMC transition probability matrix;

[0109] r means S v The vanishing state of EMC, that is, r∈S v ;

[0110] i, j represent the real existence state in EMC; that is, i, j∈S t ;

[0111] f ij is the transition probability from the existing state i to the existing state j;

[0112] e ir is the transition probability from the existing state i to the disappearing state r;

[0113] P r The element of [r→j] is the probability of going from the vanishing state r to the existing state j for the first time after any number of steps;

[0114] Matrix G ∞ The elements in represent the probability of going from the disappearing state to the existing state for the first time;

[0115] Y: a vector, Y = (y1, y2, ..., y c ), c=k t , element y i represents the stable probability distribution of REMC's existing state;

[0116] t i : The average residence time in the existing state i;

[0117] E(i): the set of transitions that can be implemented in the existing state i;

[0118] λ k : the rate of occurrence of transitions in the set of transitions that can be implemented under the existing state i;

[0119] π i : Steady-state probability of GSPN.

[0120] The specific implementation steps of the present invention are as follows:

[0121] Step (1) Based on the specific workflow of the modeled CPS, abstract modeling of the workpiece processing flow in the CPS is performed. The specific process is as follows:

[0122] (1.1) The status of the workpiece before and after processing in the current processing flow is used as the library set of ON

[0123] (1.2) The factors that cause the change of the library in the current processing flow are taken as the transition set of ON The factors that cause the library to change include instantaneous actions such as starting processing, ending processing, and state judgment, and time-consuming actions such as punching and bending. The instantaneous actions are taken as the instantaneous transition set. The time-consuming action is represented as a time transition set

[0124] (1.3) Construct the directed arc set of ON based on the state transitions between places and transitions and Treat the state transition from place to transition as a set of directed arcs Transitions to places are treated as directed arc sets.

[0125] After completing the above steps, the object network model is obtained as follows Figure 3 (a), and its location and transition meanings are shown in Table 1.

[0126] Table 1 Object network locations and changes of GSOPN and their meanings

[0127]

[0128] Step (2) Based on the specific workflow of the modeled CPS, abstract modeling of the overall workflow in the CPS is performed. The specific process is as follows:

[0129] (2.1) The status of the workpiece before and after processing and the status of the resources required for processing the workpiece in the current processing flow are taken as the library set P of SN;

[0130] (2.2) The factors that cause the change of the library in the current processing flow are taken as the transition set T of SN. The factors that cause the change of the library include instantaneous actions such as starting processing, ending processing, and state judgment, and time-consuming actions such as punching and bending. The instantaneous actions are taken as the instantaneous transition set p i , and the time-consuming actions are taken as the time transition set T t ;

[0131] (2.3) Construct the directed arc sets I and O of SN according to the state transitions between places and transitions, where the state transitions from places to transitions are the directed arc set I, and the state transitions from transitions to places are the directed arc set O;

[0132] After completing the above steps, the system network model is obtained as follows Figure 3 (b), and its location and transition meanings are shown in Table 2.

[0133] Table 2 GSOPN system network location and changes and their meanings

[0134]

[0135] Step (3) Create the corresponding relationship between each library place, that is, the corresponding relationship set σ, based on the ON and SN established above. The specific process is as follows:

[0136] (3.1) Take any location P in the object network o and all places P of the system network s ;

[0137] (3.2) If P o and P s have the same real meaning, then add the two to the corresponding relationship set;

[0138] (3.3) If P o and P s If they do not have the same real meaning, they will not be added to the corresponding relationship set;

[0139] (3.4) Repeat the above steps until the object network and system network are traversed;

[0140] After completing the above steps, the corresponding relationship set σ between ON and SN is obtained as shown in Table 3.

[0141] Table 3 GSOPN correspondence set

[0142]

[0143] Step (4) Create the corresponding relationship between each transition, that is, the interaction relationship set ρ, based on the ON and SN established above. The specific process is as follows:

[0144] According to all the places P in the corresponding relationship set σ o and P s , find the subsequent changes of these two places in the object network and system network respectively, and add the changes with the same practical significance and type to the interaction relationship set. Repeat the above steps until the corresponding relationship set is traversed;

[0145] After completing the above steps, the corresponding relationship set ρ between ON and SN is obtained as shown in Table 4.

[0146] Table 4 GSOPN interaction relationship set

[0147]

[0148] Step (4) converts the embedded object network structure of GSOPN into traditional GSPN to facilitate performance analysis.

[0149] (4.1) In order to eliminate the embedded object network structure, we first need to delete all transitions that belong to the interactive relationship set ρ. After deleting some transitions, there will be many isolated places in the object network. We traverse all the places in the object network. If there is no directed arc between the place and other transitions, we delete the current place; otherwise, we keep the place.

[0150] For example, delete Figure 3 (a) Time transition of ρ in the object network and At this time, there is no other transition pointing to the library There is no directed arc in the library. Directed arcs pointing to other transitions directly Delete it. The resulting structure is as follows Figure 4 shown.

[0151] (4.2) Define the network structure obtained in step 2-1 as If a library and Library is the starting place, where Indicates the change of input in the library; if and Library To terminate the library, Indicates that there is a transition of output in this place; the starting place set S is the set containing all starting places, denoted as The termination place set E is the set of all termination places, denoted by

[0152] Traverse all remaining places in the object network and add the places that meet the definition of the starting place or the ending place to the corresponding set S or E. The final place relationship is shown in Table 5;

[0153] Table 5. Relationship between libraries after classification

[0154]

[0155] (4.3) If the conditions are met: and in For any element in S, σ(s) represents the relationship corresponding to s in the corresponding relationship set σ, then s is directly added to the system network using the corresponding relationship set, otherwise is an element of the input set of the starting place s in the initial object network. According to the interaction relationship set ρ, find the transition t in the system network that interacts with the transition in the input set. s , create transition t s The directed arc pointing to place s is added to the system network SN together with place s.

[0156] (4.4) If the conditions are met: and in For any element in E, σ(e) represents the relationship corresponding to e in the corresponding relationship set σ. Then e is added to the system network directly using the corresponding relationship set. Otherwise, To terminate an element of the output set of place e in the initial object network, find the transition t in the system network that interacts with the transition in the input set according to the interaction relationship set ρ e , create a library place e pointing to transition t e The directed arc of is added to the system network SN together with the library place e.

[0157] After using the object network ablation algorithm to transform the GSOPN, the obtained GSPN is as follows Figure 5 As shown, it includes 22 places, 9 instantaneous transitions (including a set of random switches) and 7 time transitions.

[0158] Step (5) To improve the actual availability of the GSPN network system, the normal membership function, reverse cloud algorithm, and forward cloud algorithm are used to process the uncertainty in the GSPN to determine the specific occurrence rate λ of each time transition in the GSPN. i, where λ i Used to represent the corresponding time transition T i ∈T the occurrence rate.

[0159] (5.1) We use the normal membership function to resolve the uncertainty of the rate of time change. The normal membership function uses three numerical features, Ex (Expected Value), En (Entropy), and He (HyperEntropy), to represent the uncertainty of things, combining randomness and fuzziness to construct a model that obeys the pan-normal distribution.

[0160] Assume that U is a quantitative domain represented by exact numerical values, and that qualitative concept C(Ex, En, He) is a qualitative concept on the quantitative domain U. If x∈U is a random realization of concept C, it follows the normal distribution N(Ex, En' 2 ), En' follows the normal distribution N(En,He 2 ), the certainty of x to C μ(x)∈[0,1] is a random number with a stable tendency, satisfying:

[0161]

[0162] Then the distribution of the random variable X constituted by all models on the domain U obeys the pan-normal distribution. The above membership function is called the normal membership function. The quantitative value x reflects the randomness of the quantitative value representing the concept, and μ(x) reflects the degree of certainty that the quantitative value x belongs to the qualitative concept C. Figure 6 The model plots under different numerical features are shown.

[0163] (5.2) In order to handle the uncertainty of the time-varying rate, the collected time-varying rate is first transformed into three digital features: Ex, En, and He through the Multiple Backward Cloud Transformation based on Sampling with Replacement (MBCT-SR) algorithm. The MRCT-SR algorithm generates the three digital features Ex, En, and He from the given cloud droplets x1, x2, …, x n The mean is calculated as the estimated value of Ex, that is,

[0164]

[0165] The models are divided into m groups, each group has r models, and the r models are from x1,x2,…,x n There is a sample randomly drawn with replacement. Suppose the sample drawn from the kth group is x k1 ,x k2 ,…,x kr , calculate the mean variance for

[0166]

[0167] make According to Y 2 Get En 2 , He 2 The estimated value of

[0168]

[0169] (5.3) After using the multi-step reverse cloud transformation algorithm to obtain Ex, En, and He for each transition, the forward cloud transformation algorithm can be used to obtain an estimate of the rate at which time transitions occur.

[0170] We obtained the production data of a manufacturing company’s punching, folding and welding production line from May 2021 to July 2021, and obtained the time evolution of the converted GSPN {T2, T4, T6, T7, T 11 ,T 13 ,T 15 As for the actual occurrence rate, since the occurrence rate λ7 of T7 obtained has almost no change and its value is 2.73, we will not consider it here. The occurrence rates of the remaining time transitions Ex, En, and He are obtained through a multi-step inverse cloud transformation algorithm, as shown in Table 6.

[0171] Table 6 Numerical features corresponding to the occurrence rate of time transition

[0172]

[0173] Step (6) GSPN is considered as an embedded Markov Chain (EMC) to analyze its performance and improve the accuracy of the analysis results;

[0174] Figure 7 The reachable graph of GSPN is given. The red ellipse represents the existing state, the blue ellipse represents the disappearing state, and the blue rectangle represents the disappearing state at the beginning. The states are connected by transitions, which represent the transition from one state to another. Table 7 shows the state space set of the transformed GSPN.

[0175] Table 7 GSPN state space set

[0176]

[0177]

[0178] The state space set of GSPN consists of two parts: the existing state set and the disappearing state set. Let X be the GSPN reachable identifier set S r For an element in M, if at least one time transition is in the enabled state under the label X, then M is called an existing state, otherwise it is called a vanishing state. Let the state space set of GSPN be S g , the number of state space sets |S g |=k s ; Existing state set S t ,|S t |=k t ; Disappearing state set S v ,|S v |=k v , where S = S t ∪S v , k s =k t +k v ; Ignoring the time factor, we only focus on the GSPN state and the transition between states. The GSPN can be regarded as an embedded Markov Chain (EMC). The transfer matrix M of the EMC is shown in the following formula:

[0179]

[0180] The elements in the matrix A are composed of the transition probability matrix C from the disappearing state to the disappearing state and the transition probability matrix D from the disappearing state to the real state. The elements in the matrix B are composed of the transition probability matrix E from the real state to the disappearing state and the transition probability matrix F from the real state to the real state set. The transition from the real state to other states is determined by the occurrence rate of time transition. The occurrence rate of time transition generated by the forward cloud transformation algorithm will determine the values ​​of the elements in the matrices E and F.

[0181] Remove all vanishing states from EMC and keep the existing states to get a reduced EMC (REMC). Then calculate the transition probability matrix M' of REMC. ij The calculation method of is as follows (6):

[0182]

[0183] Where i, j represent the real state in EMC, that is, i, j∈S t , f ij is the transition probability from the existing state i to the existing state j, e ir is the transition probability from the existing state i to the disappearing state r, where r represents the disappearing state of EMC, i.e. r∈Sv , P r The elements of [r→j] are the probabilities of going from the vanishing state r to the existing state j for the first time after any number of steps; the matrix G ∞ The elements in G represent the probability of going from the disappearing state to the existing state for the first time. ∞ The calculation is as follows (7):

[0184]

[0185] Among them, k0 satisfies the following conditions

[0186]

[0187] Therefore, M' can be expressed as follows:

[0188] M′=F+EG ∞ (8)

[0189] REMC is solved by the linear equation system of formula (9), where Y = (y1, y2, ..., y c ), c=k t , element y i represents the stable probability distribution of REMC's existing state;

[0190]

[0191] At this time, considering the time factor, the steady-state probability of GSPN can be obtained, and the average residence time in the actual state i can be calculated by formula (10), where E(i) = {the set of transitions that can be implemented in the actual state i}, λ k represents the rate of occurrence of transitions in the set of transitions that can be implemented under the existing state i;

[0192]

[0193] The steady-state probability of GSPN can be expressed by the following formula (11):

[0194]

[0195] Each time the forward cloud transformation algorithm generates a set of occurrence rates of time transitions, the steady-state probability of the existing state obtained will be different; based on the steady-state probability of GSPN, the throughput rate of each transition can be calculated, and the production capacity of the entire CPS system can be evaluated based on this throughput rate.

[0196] We collected the company's actual production data and theoretical calculation data for comparison to verify the effectiveness of our proposed model. The company's working hours in July 2021 were 8 hours a day, the number of working days was 27 days, and the total working hours were 216 hours. In order to calculate the company's production situation in July, we used the forward cloud transformation algorithm to generate 5 groups of time transition occurrence rates with credibility in (8.9, 9.0) to calculate the production situation. Each group of time transition occurrence rates is divided into two categories, A and B. The occurrence rates of all transitions in category A are less than their corresponding Ex, while the occurrence rates of all transitions in category B are greater than their corresponding Ex. T and B are calculated respectively. 15 The throughput rate is calculated to solve the production situation of 216 hours. The time transition occurrence rate is added as the corresponding Ex for comparison. The occurrence rate λ7 of the above time transition T7 has always been a fixed value of 2.73. The maximum value of the output calculated by Class A (hereinafter referred to as Class A output) is the minimum value estimated by the model, the output calculated by the time transition occurrence rate as the corresponding Ex (hereinafter referred to as the expected output) is the expected value estimated by the model, and the maximum value of the output calculated by Class B (hereinafter referred to as Class B output) is the maximum value estimated by the model. The estimated production situation is as follows Figure 8 As shown in the figure, the transition throughput and equipment utilization under the minimum, expected and maximum values ​​estimated by the model are as follows: Fig. 9 , Fig.10 shown.

[0197] from Figure 8 It can be seen that the output of Class A is significantly lower than the expected output, and the output of Class B is significantly higher than the expected output. The calculated 5 groups of Class A output and Class B output have almost no fluctuations, so the actual output should be between the output calculated by Class A transition and Class B transition. The expected output of 4772 blocks is the expected value estimated by the model, the maximum value of Class A output is 4611 blocks, which is the minimum value estimated by the model, and the minimum value of Class B output is 4932 blocks, which is the maximum value estimated by the model. That is, the most likely output estimated by the model is 4772, and the output range of the punching, folding and welding production line is [4611, 4932] based on a credibility of 9. The company's production line actually produced 4673 finished metal plates in July. Various unexpected downtimes may occur during the production process, which may be the reason why the actual monthly output is less than the expected output, and the actual monthly output is also within the range of the output calculated by Class A transition and the output calculated by Class B transition. This also indirectly reflects the effectiveness of the modeling method proposed in the present invention, and the analysis results after model conversion are not much different from the actual production situation. Fig. 9 and Fig.10 It can be seen that as the model-estimated output increases, the throughput of the transition will increase accordingly, but only the equipment utilization of the punch press and robot that process the A-type plate increases. The reason may be that the speed at which the punch press punches the A-type plate has a greater impact on productivity.

Claims

1. Uncertain CPS modeling and analysis method based on GSOPN, characterized by include: Step (1), constructing a generalized random object Petri net GSOPN based on the actual industrial cyber-physical system CPS; The generalized random object Petri net GSOPN is composed of a quaternion S = (SN, ON, ρ, σ), which is an embedded object network structure. The system network SN and the object network ON are used to form a double-layer separation model of the entire GSOPN network system. The system network and the object network are combined through a synchronous interaction relationship ρ of the changes in the system network and the object network and a corresponding relationship σ of the library. The object network ON is an abstract modeling of the workpiece processing flow in the actual industrial cyber-physical system CPS, which is used to reflect the processing state of the workpiece, the processing state between workpieces and the relationship between the factors causing the change of the workpiece processing state; The system network SN is an abstract modeling of the overall workflow in the actual industrial CPS, which is used to reflect the relationship between the resource status of workpiece processing, the workpiece processing status and the factors causing the change of the workpiece processing status; The correspondence set σ represents a correspondence between the places in the system network and the object network, specifically, the correspondence between different places in the object network and the system network for a certain state in the implementation; The interaction relationship set ρ represents a correspondence relationship between the system network and the object network; Step (2) uses the object net ablation algorithm to transform the embedded object net structure of the generalized random object Petri net GSOPN into a traditional GSPN; specifically: 2-1 In order to eliminate the embedded object network structure, firstly, it is necessary to delete all transitions belonging to the interactive relationship set ρ on the object network; after deleting the above transitions, there will be many isolated places in the object network. Traverse all the places in the object network. If there is no directed arc between the place and other transitions, delete the current place; otherwise, keep the place; 2-2 Define the network structure obtained in step 2-1 as If a library and It is believed that the library is the starting place, where Indicates the change of input in the library; if and It is believed that the library To terminate the library, Indicates that there is a transition of output in this place; the starting place set S is the set containing all starting places, denoted as The termination place set E is the set of all termination places, denoted by Traverse all remaining places in the object network and add the places that meet the definition of the starting place or the ending place to the corresponding set S or E; 2-3 If the conditions are met: and in For any element in S, σ(s) represents the relationship corresponding to s in the corresponding relationship set σ, then s is directly added to the system network using the corresponding relationship set, otherwise is an element of the input set of the starting place s in the initial object network. According to the interaction relationship set ρ, find the transition t in the system network that interacts with the transition in the input set. s , create transition t s The directed arc pointing to place s is added to the system network SN together with place s; 2-4 If the conditions are met: and in For any element in E, σ(e) represents the relationship corresponding to e in the corresponding relationship set σ. Then e is added to the system network directly using the corresponding relationship set. Otherwise, To terminate an element of the output set of place e in the initial object network, find the transition t in the system network that interacts with the transition in the input set according to the interaction relationship set ρ e , create a library place e pointing to transition t e The directed arc of is added to the system network SN together with the library place e; Step (3), in order to improve the actual availability of the GSPN network system, the normal membership function, the reverse cloud algorithm, and the forward cloud algorithm are used to process the uncertainty in the GSPN to determine the specific occurrence rate of each time transition in the GSPN; specifically: 3-1 Use normal membership function to solve the uncertainty of time change rate; The normal membership function uses expectation Ex, entropy En, and hyperentropy He to represent the uncertainty of things, combining randomness and fuzziness to construct a model that obeys the pan-normal distribution. Assume that U is a quantitative domain represented by exact numerical values, and that qualitative concept C(Ex, En, He) is a qualitative concept on the quantitative domain U. If x∈U is a random realization of concept C, it follows the normal distribution N(Ex, En' 2 ), En' follows the normal distribution N(En,He 2 ), the certainty of x to C μ(x)∈[0,1] is a random number with a stable tendency, satisfying: Then the distribution of random variables X constituted by all models on the domain U obeys the pan-normal distribution. The membership function in the above formula is called the normal membership function. The quantitative value x reflects the randomness of the quantitative value representing the concept, and μ(x) reflects the degree of certainty that the quantitative value x belongs to the qualitative concept C. 3-2 In order to deal with the uncertainty of the time change rate, the collected time change rate is firstly transformed into Ex, En, He digital features through the multi-step reverse cloud transformation algorithm MBCT-SR; 3-3 After using the multi-step reverse cloud transformation algorithm to obtain the Ex, En, and He of each transition, use the forward cloud transformation algorithm to obtain the estimated value of the time transition occurrence rate; Step (4), consider GSPN as an embedded Markov chain EMC and analyze its performance.

2. The uncertain CPS modeling and analysis method based on GSOPN as claimed in claim 1 is characterized in that Step (4) is specifically: The state space set of GSPN consists of two parts: the existing state set and the disappearing state set. Let X be the GSPN reachable identifier set S r If an element in M ​​is in the enabled state under the label X, then M is called an existing state, otherwise it is called a vanishing state. Let the state space set of GSPN be S g , the number of state space sets |S g |=k s ; Existing state set S t ,|S t |=k t ; Disappearing state set S v ,|S v |=k v , where S = S t ∪S v , k s =k t +k v ; Ignoring the time factor for now, we only focus on the GSPN state and the transition between states. The GSPN can be regarded as an embedded Markov chain EMC, and the transfer matrix M of the EMC is shown in the following formula: The elements in the matrix A are composed of the transition probability matrix C from the disappearing state to the disappearing state and the transition probability matrix D from the disappearing state to the real state. The elements in the matrix B are composed of the transition probability matrix E from the real state to the disappearing state and the transition probability matrix F from the real state to the real state set. The transition from the real state to other states is determined by the occurrence rate of time transition. The occurrence rate of time transition generated by the forward cloud transformation algorithm will determine the values ​​of the elements in the matrices E and F. Remove all vanishing states from EMC and keep the existing states to obtain a compressed EMC, denoted as REMC; then calculate the transition probability matrix M' of REMC, the element m' of M' ij The calculation method of is as follows (6): Where i, j represent the real state in EMC, that is, i, j∈S t , f ij is the transition probability from the existing state i to the existing state j, e ir is the transition probability from the existing state i to the disappearing state r, where r represents the disappearing state of EMC, i.e. r∈S v , P r The elements of [r→j] are the probabilities of going from the vanishing state r to the existing state j for the first time after any number of steps; the matrix G ∞ The elements in G represent the probability of going from the disappearing state to the existing state for the first time. ∞ The calculation is as follows (7): Among them, k0 satisfies the following conditions C k ＝0, Therefore, M' is expressed as follows: M'=F+EG ∞ (8) REMC is solved by the linear equation system of formula (9), where Y = (y1, y2, ..., y c ), c=k t , element y i represents the stable probability distribution of REMC's existing state; At this time, the steady-state probability of GSPN can be obtained by considering the time factor, and the average residence time in the actual state i is calculated by formula (10), where E(i) = {the set of transitions that can be implemented in the actual state i}, λ k represents the rate of occurrence of transitions in the set of transitions that can be implemented under the existing state i; The steady-state probability of GSPN is expressed as follows: Every time the forward cloud transformation algorithm generates a set of occurrence rates of time transitions, the steady-state probability of the existing state obtained will be different; based on the steady-state probability of GSPN, the throughput rate of each transition can be calculated, and the production capacity of the actual industrial information-physical system CPS can be evaluated based on the current throughput rate.

3. The uncertain CPS modeling and analysis method based on GSOPN as claimed in claim 1 is characterized in that Object Network The state of the workpiece before and after processing in the current processing flow is used as the library set of ON The factors that cause the change of the library in the current processing flow are used as the transition set of ON The factors that cause the library to change include instantaneous actions and time-consuming actions. The instantaneous actions include starting processing, ending processing and state judgment, and the time-consuming actions include punching and bending. The instantaneous actions are reflected in ON as instantaneous transition sets. The time-consuming action is reflected as the time change set Construct a directed arc set of ON based on the state transitions between places and transitions and in is the set of directed arcs from place to transition, is the set of directed arcs that transition to places.

4. The uncertain CPS modeling and analysis method based on GSOPN as claimed in claim 1 is characterized in that The workpiece processing status and the factors that cause the change of the workpiece processing status in SN are simplified versions in the object network, because ON should provide the workpiece it needs to SN, and the specific processing details are shielded from SN; the system network is recorded as SN = (P, T, I, O), and the status of the workpiece before and after processing and the status of the resources required for workpiece processing in the current processing flow are taken as the library set P of SN; the factors that cause the change of the library in the current processing flow are taken as the transition set T of SN, and the factors that cause the change of the library include instantaneous actions and time-consuming actions. The instantaneous actions include starting processing, ending processing and state judgment, and the time-consuming actions include punching and bending. The instantaneous actions are reflected in SN as the instantaneous transition set p i , and the time-consuming action is reflected in the time transition set T t ; Construct the directed arc sets I and O of SN according to the state transitions between places and transitions, where is the set of directed arcs from place to transition, is the set of directed arcs that transition to places.

5. The uncertain CPS modeling and analysis method based on GSOPN as claimed in claim 1 is characterized in that The steps to establish the corresponding relationship set σ are as follows: Take any object network from all its locations P o and all places P of the system network s ; If P o and P s have the same real meaning, then add the two to the corresponding relationship set; If P o and P s If they do not have the same real meaning, they will not be added to the corresponding relationship set; Repeat the above steps until the object network and system network are traversed.

6. The uncertain CPS modeling and analysis method based on GSOPN as claimed in claim 1, characterized in that The interactive relationship set is established as follows: According to all the places P in the corresponding relationship set σ o and P s , find out the subsequent changes of these two libraries in the object network and system network respectively, add the changes with the same practical significance and type to the interaction relationship set and repeat the above steps until the corresponding relationship set is traversed.

7. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the memory stores machine executable instructions that can be executed by the processor, and the processor executes the machine executable instructions to implement the method according to any one of claims 1 to 6.

8. A machine-readable storage medium, characterized in that: The machine-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the method described in any one of claims 1 to 6.

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