A research method of fault diagnosis for discrete event systems based on lambda-free petri nets

Abstract

The application belongs to the technical field of fault diagnosis of discrete event systems, and particularly relates to a research method of fault diagnosis of discrete event systems based on a lambda-free Petri net, which comprises the following steps: S1: constructing a labeled lambda-free Petri net model for a discrete event system; S2: judging whether a fault can be detected through an observation sequence with a limited length, that is, whether the system is diagnosable; S3: if the system is not diagnosable, then a verification net is constructed on the basis of the original Petri net, the reachable tree thereof is unfolded and pruned by using the system structure captured in the verification net, and labels that need to be relabeled are searched. The application can help to improve the efficiency and accuracy of fault diagnosis, and the Petri net model after removing empty transitions can reduce the complexity of system description, thereby simplifying the fault diagnosis process.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of fault diagnosis of discrete event systems, and in particular to a research method for fault diagnosis of a discrete event system based on a lambda-free Petri net. BACKGROUND

[0002] A discrete event system (DES) is a dynamic system composed of discrete states and discrete events, wherein the occurrence of events is random. Fault diagnosis of a discrete event system is a research field that has attracted widespread attention in recent years, and a fault can correspond to any discrete event. Due to the randomness, concurrency and strong discretization of a DES, the state space thereof is very large and complex, and cannot be simply described by traditional mathematical methods. Usually, mathematical models such as automata, Petri nets and queuing theory are used to describe the logical levels of a system and analyze related problems. A Petri net can well describe and research asynchronous and concurrent phenomena of a discrete event system, and is widely used in research on problems such as fault diagnosis, monitor synthesis and resource optimization of a DES.

[0003] Traditional Petri net models can introduce complex lambda (empty token) transitions, which not only make the models more difficult to understand, but also have a negative impact on the accuracy and efficiency of a fault diagnosis algorithm. SUMMARY

[0004] The application aims to provide a research method for fault diagnosis of a discrete event system based on a lambda-free Petri net, which can help improve the efficiency and accuracy of fault diagnosis, and a Petri net model after removing empty transitions can reduce the complexity of system description, thereby simplifying the fault diagnosis process.

[0005] The method comprises the following steps:

[0006] S1: constructing a labeled lambda-free Petri net model for a discrete event system;

[0007] N is a Petri net, and the Petri net is a three-tuple N=(P,T,F), P and T are a place set and a transition set respectively, is a flow relation, connecting a place and a transition, and representing a set of directed arcs between a place and a transition;

[0008] Each transition in a Petri net represents a physical event in the system, which can be connected to a sensor. The set of transitions is divided into observable and unobservable transitions. Observable transitions can share the same label. A failure can not be modeled as an unobservable transition. A λ-free labeled Petri net is a Petri net in which no transition is labeled with λ.

[0009] It should be noted that: the so-called observable transition, that is, in an automatic manufacturing system, people can observe the corresponding transition through sensors or other technical means, etc. Giving a transition a label means that it can be observed through the corresponding label. Different observable transitions can correspond to the same label.

[0010] S2, determine whether the occurrence of the failure can be detected through a finite length observation sequence, that is, whether the system is diagnosable;

[0011] S21, assume that a labeled Petri net does not trigger deadlock after any failure transition occurs;

[0012] S22, if there are two firing sequences σ1 and σ2 that satisfy: the labels of sequences σ1 and σ2 are the same, σ1 does not contain a failure transition, σ2 contains at least one failure transition, and the length of σ2 after the occurrence of the failure transition is infinite, then the system is determined to be non-diagnosable;

[0013] S3, if the system is non-diagnosable, then a verification net is constructed on the basis of the original Petri net, the reachable tree of the system structure captured in the verification net is expanded and pruned, and the labels that need to be relabeled are searched;

[0014] S31, assume that synchronization is performed on the observable transition labels, and combine the marked Petri net system and the induced subnets into a verification net system in the manner specified;

[0015] S32, draw the reachability graph of the verification net. If it contains at least one cycle that enters after triggering a failure transition, the (bounded) network system is non-diagnosable;

[0016] S33, in order to make the system diagnosable, each path in the reachable graph of the verification net that starts from the root node and contains a cycle that enters after triggering a failure transition must be disabled, and the repeated nodes encountered in the path from the root to the leaf of the reachable tree are expanded;

[0017] S34, since the deadlock path and the path leading to the "repeated" node but not containing the failure transition (λ, t f ) do not violate the diagnosability in the reachable tree, these paths are pruned, and only the path leading to the "repeated" node and containing the failure transition (λ, t f ) is retained.

[0018] Note that the verification net is a specific Petri net structure, which is composed of the labeled Petri net system and the induced subnets in a specified way, assuming that the observable transition labels are synchronized. It allows the state transition paths of the system to be explored and analyzed to evaluate the reachability and behavior of the system under fault conditions, which is used to simulate the behavior of the system under different states.

[0019] S4, an integer linear programming problem is proposed to find an optimal marking function to make the system diagnosable;

[0020] S41, a binary variable set v t ∈{0,1} is defined, where v t =1 indicates that the transition is re-marked under the new marking. Linear inequalities related to the pruned reachability graph are constructed to ensure that each non-diagnosable path is properly handled, which is in the form as follows:

[0021]

[0022] where t i is all the transitions on the path that need to be re-marked, ensuring that at least one transition in each path is re-marked.

[0023] S42, check each transition pair from root to leaf in the pruned reachability graph, the specific steps are as follows:

[0024] (1) For each transition pair (t i , t j ), where i≠j, if the transitions t i and t j in the path are different, then the corresponding variables v i and v j are added to the inequality;

[0025] (2) If the two transitions t i and t j in the path are the same, then no processing is done in the current step;

[0026] (3) If the transition pair in the path is (λ, t f ) (indicating a fault transition), then no processing is done for these transitions, but special consideration is given to its impact on path diagnosability.

[0027] S43, let R be the set of all linear inequalities obtained from the pruned reachability graph, and solve the inequality set R by linear programming or integer linear programming solving tools.

[0028] S44, judge whether there is a marking function that satisfies these constraints. If the constraint set R has a solution, the marking function will make the system diagnosable; if there is no solution, it means that the system is still not diagnosable under the current marking, and it is necessary to return to step S34 to reanalyze the pruning of the verification net and update the marking function.

[0029] S45, update the label of the system according to the linear inequality, and the system after relabeling does not contain a cycle entered after triggering the fault transition, and the network system is diagnosable.

[0030] The technical effects obtained by the present application are:

[0031] 1. The simplified lambda-free Petri net model proposed by the present application can reduce the amount of calculation, speed up the fault diagnosis process, and make it more suitable for large-scale systems in practical applications.

[0032] 2. The verification net constructed on the basis of the original Petri net proposed by the present application uses the system structure captured in the verification net to guide the search for the required new marking function, and provides necessary and sufficient conditions for diagnosability.

[0033] 3. The present application can more accurately locate the fault source through optimization tools such as integer linear programming, thereby improving the reliability and maintenance efficiency of the system. DETAILED DESCRIPTION

[0034] Figure 1 is a flowchart of an embodiment of the present application;

[0035] Figure 2 is a structural diagram of a lambda-free Petri net constructed according to a discrete event system in an embodiment of the present application;

[0036] Figure 3 is a basic structural diagram of a verification net constructed on the basis of an original Petri net in an embodiment of the present application;

[0037] Figure 4 is a basic structural diagram of the reachability graph of the verification net in an embodiment of the present application;

[0038] Figure 5 is a basic structural diagram of the expanded and pruned reachability graph in an embodiment of the present application. DETAILED DESCRIPTION

[0039] In order to make the purpose and advantages of the present application clearer and more apparent, the present application will be specifically described below in conjunction with embodiments. It should be understood that the following text is only used to describe one or several specific embodiments of the present application, and does not strictly limit the specific protection scope requested by the present application.

[0040] As Figures 1-5As shown, a kind of discrete event system fault diagnosis research method based on λ-free Petri net, research method includes the following steps:

[0041] S1, for discrete event system, build label λ-free Petri net model, model fault as unobservable transition;

[0042] S2, judge whether the occurrence of fault can be detected by finite length observation sequence, i.e. whether the system is diagnosable;

[0043] S3, if the system is not diagnosable, then build a verification net on the basis of original Petri net, use the system structure captured in the verification net to expand and prune its reachability tree, search the label that needs to be relabeled;

[0044] S4, propose an integer linear programming problem to find an optimal marking function, so that the system has diagnosability;

[0045] In the embodiment of the application, the specific steps of constructing a label λ-free Petri net model for a discrete event system in S1 are as follows:

[0046] S11, according to the above description, build a label λ-free Petri net model, M0 is the initial state of the system, N is a Petri net, and the Petri net is a three-tuple N=(P,T,F), P and T are the set of places p and the set of transitions t respectively, is the flow relation, connecting places and transitions, indicating the set of directed arcs between places and transitions. Wherein observable transition T0={T2,T3,T4}, T f =T1, except fault, does not contain other unobservable transition, initial label L init (T2)=L init (T3)=a, L init (T4)=b.

[0047] As Figures 1-2 shown, in the embodiment of the application, the specific steps of judging whether the occurrence of fault can be detected by finite length observation sequence, i.e. whether the system is diagnosable in S2 are as follows:

[0048] S21, suppose that the above label Petri net does not trigger deadlock after any fault transition occurs;

[0049] S22, judge whether the system is diagnosable: according to the embodiment, it can be obtained that λ-free Petri net system exists two emission sequences σ1=t f t2(t4) k And σ2=t3(t4) k, meet the same label of two different sequences, that is, L(σ1) = L(σ2) = ab k (k≥0). Where σ1 contains fault transitions, σ2 does not contain fault transitions and the length of σ2 after the fault transition is infinite, thus determining that the system is not diagnosable.

[0050] As shown in Figures 4-5 , in the embodiment of the present application, for the non-diagnosable system in S3, a verification net is constructed on the basis of the original Petri net, and the reachable tree is expanded and pruned using the system structure captured in the verification net, and the specific steps of searching for the specific label that needs to be relabeled are as follows:

[0051] S31, assuming that the synchronization is performed on the observable transition label, the label Petri net system and the induced sub-net are combined into a verification net system in the manner as specified;

[0052] S32, draw the reachability graph of the verification net, and perform reachable tree expansion search in the verification net. This process starts from the initial state of the system, and gradually explores all possible state transition paths, and the reachable identification is M1 = (100100) T , M2 = (010100) T , M3 = (001001) T . The system contains at least one cycle entered after triggering the fault transition, thus determining that the (bounded) network system is not diagnosable;

[0053] S33, in order to make the system diagnosable, each path starting from the root node and containing the cycle entered after triggering the fault transition in the reachable graph of the verification net must be disabled. The repeated nodes encountered in the path from the root to the leaf of the reachable tree are expanded;

[0054] S34, since the deadlock path and the path leading to the "repeated" node but not containing the fault transition (λ, t f ) will not violate the diagnosability in the reachable tree, these paths are pruned, and only the path leading to the "repeated" node and containing the fault transition (λ, t f ) is retained.

[0055] As shown in Figure 3 , in the embodiment of the present application, the specific steps of proposing an integer linear programming problem in S4 to find an optimal marking function to make the system diagnosable are as follows:

[0056] S41, define a binary variable set v t ∈{0,1}, where v t =1 indicates that the transition is relabeled under the new marking. Linear inequalities related to the pruned reachable graph are constructed to ensure that each non-diagnosable path is properly handled, and the form is as follows:

[0057]

[0058] where t i is the path of all transitions that need to be relabeled, ensuring that at least one transition in each path is relabeled.

[0059] S42, check each transition pair from root to leaf in the pruned reachable graph, the specific steps are as follows:

[0060] (1) for each transition pair (t i , t j ), where i≠j, if the transitions t i and t j in the path are different, then the corresponding variables v i and v j are added in the inequality;

[0061] (2) if the two transitions t i and t j in the path are the same, then no processing is done in the current step;

[0062] (3) if the transition pair in the path is (λ, t f ) (indicating a fault transition), then no processing is done for these transitions, but special consideration is given to its impact on the diagnosability of the path.

[0063] S43, let R be the set of all linear inequalities obtained from the pruned reachable graph, solve the inequality set, and determine whether there is a marking function that satisfies the constraints by using a linear programming or integer linear programming solving tool. If the constraint set R has a solution, the marking function will make the system diagnosable; if there is no solution, it means that the system is still not diagnosable under the current marking, and it needs to return to step S34 to reanalyze the pruning of the verification net and update the marking function. Its linear inequalities are:

[0064] t2+t3≥1

[0065] S44, the possible relabeling options for the transitions (t i , t j ) of the pruned reachable tree path are relabeled according to the rules, and according to the above linear inequalities, relabel t2 or t3: L new (t2) = t2, L new (t3) = t3.

[0066] S45, the relabeled system does not contain a cycle entered after triggering a fault transition, and the network system is diagnosable.

[0067] According to the analysis result, by systematically checking and processing the state and path in the verification net, it is ensured that the final model can effectively diagnose system faults, the system is diagnosable, and the reliability and maintainability of the system are improved.

[0068] The free Petri net refers to a Petri net model without empty marking transition, which simplifies the description of the system and helps to improve the efficiency and accuracy of fault diagnosis.

[0069] The definitions of various parameters and descriptions in the application are as follows:

[0070] The Petri net is a three-tuple N=(P, T, F), wherein P represents a place set, T represents a transition set, F represents a set of directed arcs between the places and the transitions. Let x be a node of the Petri net, the pre-set of x is defined as · x · ={y e P U T | (y, x) e F}, and the post-set of x is defined as · x · ={y e P U T | (x, y) e F}.

[0071] The marking M: P -> N is a mapping that allocates a number of tokens to each place p, wherein N represents a natural number set; M(p) represents the number of tokens in the place p; (N, M0) is referred to as a Petri net system with an initial marking M0; and R(N, M0) represents a set of all reachable markings in the Petri net.

[0072] A transition t e T is enabled under the marking M if and only if: M(p) >= W(p, t). Denoted as M[t >; M[σ > represents that the transition sequence sigma = t1t2…t k is enabled under the marking M.

[0073] Given a Petri net, L(N, M0) = {sigma | M0[sigma > represents a set of all enabled transition sequences at the initial marking M0; and L(N, M0) / sigma represents a set of enabled transition sequences after the occurrence of the transition sequence sigma, i.e., L(N, M0) / sigma = {sigma'| sigma sigma' e L(N, M0)}.

[0074] Given a Petri net, a transition t is lived under M0 if and only if: A transition sequence σ∈L(N,M0) is deadlock if and only if: such that M0[σ>M, M[t>. A Petri net is deadlock-free if and only if:

[0075] Given a Petri net N=(P,T,F), delete all transitions in T f and the directed arcs connected to them from N, and get a subnet of N, denoted as N'=(P,T',F'). T f denotes the set of faulty transitions.

[0076] Definition 1: A bounded labeled Petri net (N,M0,K) is deadlock-free after failure if: then the system is diagnosable.

[0077] Definition 2: A verification net system is a labeled Petri net system composed of a marked Petri net system <N,M0,L> and an induced subnet <N',M'0,L'> in a specified way, assuming that it is synchronized on observable transition labels. It is defined as and (λ is the empty transition label).

[0078] The algorithm for constructing a verification net is as follows:

[0079] Input: Labeled Petri net system <N,M0,L>, where N=(P,T,Pre,Post), T=T0∪T f and L:T→L.

[0080] Output: VN labeled system where

[0081] 1) Let <N',M'0,L'> be the T' induced subnet of N, T'=T\T f =T0;

[0082] 2) Let

[0083] 3) Let

[0084] 4) For all transitions t f ∈T f ,

[0085] • add a transition defined as (λ, t f );

[0086] • for all p e P', let

[0087] • for all p e T, let

[0088] 5) for all labels l e L,

[0089] • for any pair t'0, t0, t'0 e T'0, t0 e T, L'(t'0) = L(t0) = 1,

[0090] • add a transition defined as (t'0, t0);

[0091] • for all p e T', let Post(p, t) = Post(p, t'0)

[0092] The above only describes the preferred embodiments of the present application, it should be noted that for those skilled in the art, without departing from the principles of the present application, can make several improvements and refinements, these improvements and refinements should also be considered as the protection scope of the present application. The structure, device and operation method not specifically described and explained in the present application, if no special description and limitation, are implemented according to the conventional means in the art.

Claims

1. A research method for fault diagnosis of discrete event systems based on λ-free Petri nets, characterized in that: The research method includes the following steps: S1: Construct a labeled λ-free Petri net model for discrete event systems; S2: Determine whether the occurrence of a fault can be detected through a finite-length observation sequence, i.e., whether the system is diagnosable; S3: If the system is not diagnosable, then build a verification network on the basis of the original Petri net, expand and prune its reachability tree using the system structure captured in the verification network, and search for labels that need to be relabeled. S4: Propose an integer linear programming problem to find an optimal labeling function that makes the system diagnosable.

2. The method for fault diagnosis of discrete event systems based on λ-free Petri nets according to claim 1, characterized in that: In S1, N is a Petri net, which is a triple N = (P, T, F), where P and T are the sets of places p and transitions t, respectively. It is a flow relationship, connecting places and changes, representing the set of directed arcs between places and changes; Each transition in a Petri net represents a physical event in the system. Sensors are connected to the transitions, which are divided into observable and unobservable transitions. Observable transitions share the same label, while faults that cannot be observed by the naked eye are modeled as unobservable transitions.

3. The method for fault diagnosis of discrete event systems based on λ-free Petri nets according to claim 2, characterized in that: Aside from faults, λ-free labeled PNs contain no other unobservable transitions; that is, PNs without transitions are empty-labeled.

4. The method for fault diagnosis of discrete event systems based on λ-free Petri nets according to claim 1, characterized in that: In step S2, the following steps are used to determine whether the system is diagnosable: S21: Assume that a labeled Petri net does not trigger deadlock after any fault transition; S22: If there are two transmission sequences σ1 and σ2 that satisfy the following conditions: σ1 does not contain a fault transition, σ2 contains at least one fault transition, and the length of σ2 after the fault transition is infinite, then the system is determined to be undiagnosable.

5. The method for fault diagnosis of discrete event systems based on λ-free Petri nets according to claim 1, characterized in that: In step S3, the specific steps are as follows: S31: Assuming that the process is synchronized on observable transition labels, the labeled Petri net system and the induced subnet are combined into a verification net system in an explicitly described manner; S32: Draw the reachability graph of the verification network. If it contains at least one loop that is entered after a fault transition, the network system is not diagnosable. S33: To make the system diagnosable, it is necessary to disable the verification network reachability graph from the root node and contain every path that enters a loop after triggering a fault transition, and expand the duplicate nodes encountered in the path from the root to the leaf of the reachability tree. S34: Since deadlock paths and paths leading to "repeating" nodes but without fault transitions do not violate diagnosability in the reachability tree, prune these paths and keep only the paths leading to "repeating" nodes and containing fault transitions.

6. The method for fault diagnosis of discrete event systems based on λ-free Petri nets according to claim 1, characterized in that: In step S4, the specific steps are as follows: S41. Define a binary variable set v t ∈{0,1}, where v t =1 indicates that the transition is relabeled under the new label. A linear inequality related to the pruned reachable graph is constructed to ensure that each undiagnosable path is properly handled, in the following form: Among them, t i It refers to all transitions on the path that need to be remarked, ensuring that at least one transition in each path is remarked; S42. Examine each transition pair from root to leaf in the accessibility graph after pruning; S43. Let R be the set of all linear inequalities obtained from the trimmed reachable graph. Use a solver to solve for the inequality set R. S44. Determine whether there exists a labeling function that satisfies these constraints. If the constraint set R has a solution, the labeling function will make the system diagnosable. If there is no solution, it means that the system is still not diagnosable under the current labeling. It is necessary to return to step S34, re-analyze the pruning of the verification network, and update the labeling function. S45. Update the system's label according to the linear inequality. The relabeled system does not contain loops entered after triggering fault transitions, and the network system can be diagnosed.

7. The method for fault diagnosis of discrete event systems based on λ-free Petri nets according to claim 6, characterized in that: In step S42, the following steps are used to check the transition pairs after pruning: (1) For each transition pair (t) i , t j ), where i≠j, if transition t in the path i and t j If they are different, add the corresponding variable v to the inequality. i and v j ; (2) If there are two transitions t in the path i and t j If they are the same, no action is taken in the current step; (3) If the transition pair in the path is (λ, t) f If these changes are not processed, their impact on path diagnostics needs to be considered.

8. The method for fault diagnosis of discrete event systems based on λ-free Petri nets according to claim 6, characterized in that: In S43, the solution tool solves the inequality set R using either linear programming or integer linear programming.

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