Discrete event system fault diagnosis research method based on lambda-free Petri network

Abstract

The invention belongs to the technical field of discrete event system fault diagnosis, and particularly relates to a discrete event system fault diagnosis research method based on a lambda-free Petri net, and the research method comprises the following steps: S1, constructing a label lambda-free Petri net model for a discrete event system; s2, judging whether the occurrence of a fault can be detected through an observation sequence with a finite length, namely, whether the system has diagnosability or not; and S3, if the system is not diagnosable, constructing a verification network on the basis of the original Petri network, expanding and trimming a reachable tree by using a system structure captured in the verification network, and searching a label needing to be marked again. According to the method, the efficiency and accuracy of fault diagnosis can be improved, and the complexity of system description can be reduced by the Petri network model after the null transition is removed, so that the fault diagnosis process is simplified.

Description

Technical Field

[0001] The present invention relates to the technical field of discrete event system fault diagnosis, and in particular to a discrete event system fault diagnosis research method based on λ-free Petri net. Background Art

[0002] Discrete Event System (DES) is a dynamic system composed of discrete states and discrete events, in which the occurrence of events is random. Fault diagnosis of discrete event systems has been a research field that has received widespread attention in recent years. Faults can correspond to any discrete event. Due to the characteristics of randomness, concurrency and strong discretization, DES has a very large and complex state space 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 hierarchy of the system and analyze related problems. Petri nets take into account both strict semantics and graphical languages. They can well describe and study phenomena such as asynchrony and concurrency in discrete event systems. They are widely used in the research of DES fault diagnosis, monitor synthesis, resource optimization, and other issues.

[0003] Traditional Petri net models may introduce complex λ (empty label) transitions, which not only make the model more difficult to understand, but also have a negative impact on the accuracy and efficiency of fault diagnosis algorithms. Summary of the invention

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

[0005] The steps include:

[0006] S1: Constructing a labeled λ-free Petri net model for discrete event systems;

[0007] N is a Petri net, which is a triple N = (P, T, F), where P and T are the set of places p and the set of transitions t, respectively. It is a flow relation, connecting places and transitions, and represents the set of directed arcs between places and transitions;

[0008] Each transition in the Petri net represents a physical event in the system, and sensors may be connected to it. The transition set is divided into observable transitions and unobservable transitions. Observable transitions may share the same label, while faults that cannot be observed by the naked eye are modeled as unobservable transitions. Assuming that there are no other unobservable transitions except faults, λ-free label PNs are PNs with no transitions marked empty.

[0009] It should be noted that the so-called observable changes are those that can be observed by people through sensors or other technical means in the automatic manufacturing system. Adding a label to the change means that it can be observed through the corresponding label. Different observable changes may correspond to the same label.

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

[0011] S21. Assume that a labeled Petri net does not trigger deadlock after any fault transition occurs;

[0012] S22. If there are two emission sequences σ 1 , σ 2 Satisfies: Sequence σ 1 and σ 2 The labels are the same, where σ 1 Does not include fault transition, σ 2 Contains at least one fault transition and σ 2 If the length after the fault transition is infinite, the system is judged to be undiagnosable;

[0013] S3. If the system is not diagnosable, a verification net is constructed based on the original Petri net. The system structure captured in the verification net is used to expand and prune its reachability tree, and the labels that need to be relabeled are searched.

[0014] S31, assuming that the synchronization is carried out on the observable transition labels, the marked Petri net system and the induced subnet are combined into a verification net system in a clearly stated manner;

[0015] S32. Draw a reachability graph of the verification network. If it contains at least one loop entered after triggering the fault transition, then the (bounded) network system cannot be diagnosed.

[0016] S33. To make the system diagnosable, each path in the reachable graph of the verification network starting from the root node and including the path that enters the loop after the triggering fault transition must be disabled, and the repeated nodes encountered in the path from the root to the leaf of the reachable tree must be expanded;

[0017] S34, due to the deadlock path and the transition leading to the "duplicate" node but not containing the fault (λ, tf ) will not violate diagnosability in the reachability tree, so these paths are pruned, leaving only the paths leading to the “duplicate” node and containing the fault transition (λ, t f ) path.

[0018] It should be noted that the verification net is a specific Petri net structure, which is composed of a label Petri net system and an induced subnet in a clearly stated manner, assuming synchronization on observable transition labels. It allows the state transition path of the system to be explored and analyzed to evaluate the accessibility and behavior of the system under fault conditions, and is used to simulate the behavior of the system in different states.

[0019] S4. Propose an integer linear programming problem to find an optimal labeling function to make the system diagnosable;

[0020] S41. Define a binary variable set v t ∈{0,1}, where v t = 1 means that the transition is relabeled under the new label. A linear inequality associated with the pruned reachability graph is constructed to ensure that each undiagnosable path is properly handled, in the following form:

[0021]

[0022] Among them, t i These are all the transitions on the path that need to be relabeled, ensuring that at least one transition in each path is relabeled.

[0023] S42. Check each transition pair from the root to the leaf in the pruned reachable graph. The specific steps are as follows:

[0024] (1) For each transition pair (t i , t j ), where i≠j, if the path has transition t i and t j If they are different, add the corresponding variable v to the inequality. i and v j ;

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

[0026] (3) If the transition pair in the path is (λ, t f )(indicates fault transition), no processing is done on these transitions, but their impact on path diagnostics needs to be specially considered.

[0027] S43. Let R be the set of all linear inequalities obtained from the pruned reachable graph, and solve the inequality set R using solving tools such as linear programming or integer linear programming.

[0028] S44, determine whether there is a marking function that satisfies these constraints. If the constraint set R has a solution, then 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, re-analyze the pruning of the verification network and update the marking function.

[0029] S45. The label of the system is updated according to the linear inequality. The re-labeled system does not include a loop entered after the fault transition is triggered, and the network system can be diagnosed.

[0030] The technical effects achieved by the present invention are:

[0031] 1. The simplified λ-free Petri net model proposed in the present invention 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 present invention proposes to construct a verification net based on the original Petri net, and use the system structure captured in the verification net to guide the search for the required new labeling function, which provides necessary and sufficient conditions for diagnosability.

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

[0034] Figure 1 It is a schematic diagram of a flow chart of an embodiment of the present invention;

[0035] Figure 2 It is a schematic diagram of the structure of a λ-free Petri net constructed according to a discrete event system in an embodiment of the present invention;

[0036] Figure 3 A schematic diagram of the basic structure of a verification network constructed based on the original Petri net in an embodiment of the present invention;

[0037] Figure 4 A schematic diagram of the basic structure of a reachability graph of a verification network in an embodiment of the present invention;

[0038] Figure 5 Schematic diagram of the basic structure of a reachable graph after expansion and pruning in an embodiment of the present invention. DETAILED DESCRIPTION

[0039] In order to make the purpose and advantages of the present invention more clearly understood, the present invention is 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 invention, and does not strictly limit the scope of protection of the specific claims of the present invention.

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

[0041] S1. Construct a label λ-free Petri net model for discrete event systems and model faults as unobservable transitions.

[0042] S2, determine whether the occurrence of a fault can be detected through an observation sequence of finite length, that is, whether the system is diagnosable;

[0043] S3. If the system is not diagnosable, a verification net is constructed based on the original Petri net. The system structure captured in the verification net is used to expand and prune its reachability tree, and the labels that need to be relabeled are searched.

[0044] S4. Propose an integer linear programming problem to find an optimal labeling function to make the system diagnosable;

[0045] In an embodiment of the present invention, the specific steps of constructing a labeled λ-free Petri net model for a discrete event system in S1 are:

[0046] S11. Construct a label λ-free Petri net model based on the above description. 0 is the initial state of the system, N is a Petri net, a Petri net is a triple N = (P, T, F), P and T are the set of places p and the set of transitions t, respectively. is a flow relation, connecting places and transitions, and representing the set of directed arcs between places and transitions. 0 ={T 2 ,T 3 ,T 4}, T f =T 1 , except for failure, no other unobservable changes are included, and the initial label L init (T 2 )=L init (T 3 )=a,L init (T 4 )=b.

[0047] like Figure 1-Figure 2As shown, in the embodiment of the present invention, the specific steps of determining whether the occurrence of a fault can be detected by an observation sequence of finite length in S2, that is, whether the system is diagnosable, are:

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

[0049] S22. Determine whether the system is diagnosable: According to the embodiment, it can be obtained that the λ-free Petri net system has two emission sequences σ 1 =t f t 2 (t 4 ) k and σ 2 =t 3 (t 4 ) k , satisfying that the labels of two different sequences are the same, that is, L(σ 1 )=L(σ 2 )=ab k (k≥0). 1 Including fault transition, σ 2 Does not include fault transition and σ 2 The length after the fault transition is infinite, which determines that this system is undiagnosable.

[0050] like Figure 4-Figure 5 As shown, in the embodiment of the present invention, in S3, for the undiagnosable system, a verification net is constructed based on the original Petri net, and the reachable tree is expanded and pruned using the system structure captured in the verification net. The specific steps of searching for labels that need to be re-labeled are:

[0051] S31, assuming that the synchronization is carried out on the observable transition labels, the label Petri net system and the induced subnet are combined into a verification net system in a clearly stated manner;

[0052] S32. Draw a reachability graph of the verification network and perform a reachability tree search in the verification network. This process starts from the initial state of the system and gradually explores all possible state transition paths. The reachability mark is M. 1 =(100100) T 、M 2 =(010100) T 、M 3 =(001001) T The system contains at least one loop that is entered after triggering a fault transition, which means that this (bounded) network system is not diagnosable;

[0053] S33. To make the system diagnosable, each path in the reachable graph of the verification network starting from the root node and including the path that enters the loop after the fault transition is triggered must be disabled. If duplicate nodes are encountered in the path from the root to the leaf of the reachable tree, expand;

[0054] S34, due to the deadlock path and the transition leading to the "duplicate" node but not containing the fault (λ, t f ) will not violate diagnosability in the reachability tree, so these paths are pruned, leaving only the paths leading to the “duplicate” node and containing the fault transition (λ, t f ) path.

[0055] like Figure 3 As shown, in the embodiment of the present invention, an integer linear programming problem is proposed in S4 to find an optimal labeling function, and the specific steps of making the system diagnosable are:

[0056] S41. Define a binary variable set v t ∈{0,1}, where v t = 1 means that the transition is relabeled under the new label. A linear inequality associated with the pruned reachability graph is constructed to ensure that each undiagnosable path is properly handled, in the following form:

[0057]

[0058] Among them, t i These are all the transitions on the path that need to be relabeled, ensuring that at least one transition in each path is relabeled.

[0059] S42. Check each transition pair from the root to the 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 path has transition t i and t j If they are different, add the corresponding variable v to the inequality. i and v j ;

[0061] (2) If two transitions t in the path i and t j If they are the same, no processing will be done in the current step;

[0062] (3) If the transition pair in the path is (λ, t f )(indicates fault transition), no processing is done on these transitions, but their impact on path diagnostics needs to be specially considered.

[0063] S43, let R be the set of all linear inequalities obtained from the pruned reachable graph, solve these inequality sets, and use linear programming or integer linear programming solving tools to determine whether there is a marking function that satisfies these constraints. If the constraint set R has a solution, then 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, re-analyze the pruning of the verification network and update the marking function. Its linear inequality is:

[0064] t 2 +t 3 ≥1

[0065] S44, the change of the reachable tree path after pruning (t i , t j ) is relabeled according to the rule. According to the above linear inequality, for t 2 or 3 Re-label: L new (t 2 ) = t 2 , L new (t 3 ) = t 3 .

[0066] S45. The re-marked system does not include a loop entered after triggering the fault transition, and the network system can be diagnosed.

[0067] According to the above analysis results, by systematically checking and processing the states and paths in the verification network, it is ensured that the final model can effectively diagnose system faults, making the system diagnosable, thereby improving the reliability and maintainability of the system. Therefore, the control target can be achieved according to the present invention.

[0068] λ-free Petri net refers to a Petri net model that does not contain empty labeled transitions. This model simplifies the description of the system and helps improve the efficiency and accuracy of fault diagnosis. The Petri net model after removing empty transitions can reduce the complexity of the system description, thereby simplifying the fault diagnosis process. Secondly, for undiagnosable systems, it is necessary to obtain the optimal re-labeling information from the verification net to make it diagnosable. Through in-depth research and application of discrete event system fault diagnosis, more reliable and efficient solutions can be provided for practical engineering applications.

[0069] The definitions of the parameters and instructions in the present invention are as follows:

[0070] A Petri net is a triple N = (P, T, F), where P represents the set of places p, T represents the set of transitions t, represents the set of directed arcs between places and transitions. Let x∈P∪T be a node of the Petri net, and the set of x’s predecessors · x is defined as · x={y∈P∪T|(y,x)∈F}, the postposition set x of x · Defined as x · ={y∈P∪T|(x,y)∈F}.

[0071] The notation M:P→N is a mapping that assigns a number of tokens to each place p, where N is a set of natural numbers; M(p) represents the number of tokens in place p; (N,M 0 ) is called an initial identifier M 0 Petri net system; R(N,M 0 ) represents the set of all reachable identifiers in the Petri net;

[0072] A transition t∈T is enabled under the flag M if and only if: M(p)≥W(p,t). It is denoted as M[t>; M[σ> represents the transition sequence σ=t 1 t 2 …t k Enabled under flag M.

[0073] Given a Petri net, L(N,M 0 )={σ|M 0 [σ>} indicates that in the initial mark M 0 The set of all enabled transition sequences at L(N,M 0 ) / σ represents the set of transition sequences that can be enabled after the transition sequence σ occurs, that is, L(N,M 0 ) / σ={σ'|σσ'∈L(N,M 0 )}.

[0074] Given a Petri net, transition t in M 0 The following is alive if and only if: Transition sequence σ∈L(N,M 0 ) is deadlocked if and only if: Make M 0 [σ>M, M[t>. A Petri net is deadlock-free if and only if:

[0075] Given a Petri net N = (P, T, F), delete T from N fBy combining all transitions and directed arcs connected to them, we can obtain a fault-free subnetwork of N, which is represented by N'=(P,T',F'). f Represents a collection of fault transitions.

[0076] Definition 1: A bounded labeled Petri net (N,M 0 ,K) does not enter deadlock after a failure if: Then the system is diagnosable.

[0077] Definition 2: A verification net system is a marked Petri net system <N,M 0 ,L> and induced subnetwork <N',M' 0 ,L'> is a labelled Petri net system composed in a well-specified manner, assumed to be synchronized on observable transition labels. It is defined as and (λ is the empty transition marker).

[0078] The algorithm for building the verification network is as follows:

[0079] Input: Label Petri Net System <N,M 0 ,L>, where N = (P, T, Pre, Post), T = T 0 ∪T f And L:T→L.

[0080] Output: VN tag system in

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

[0082] 2) Order

[0083] 3) Order

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

[0085] Add a transition Defined as (λ, t f );

[0086] For all p∈P', let

[0087] For all p∈P, let

[0088] 5) For all labels l∈L,

[0089] For any pair t' 0 ,t 0 , t' 0 ∈T' 0 , t 0 ∈T 0 , L'(t' 0 )=L(t 0 )=1,

[0090] Add a transition Defined as (t' 0 ,t 0 );

[0091] For all p∈T', let Post(p,t)=Post(p,t′ 0 )

[0092] The above is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention. The structures, devices and operating methods not specifically described and explained in the present invention shall be implemented according to the conventional means in the art unless otherwise specified and limited.

Claims

1. A discrete event system fault diagnosis research method based on λ-free Petri net, characterized by: The research method comprises the following steps: S1: Constructing a labeled λ-free Petri net model for discrete event systems; S2: Determine whether the occurrence of a fault can be detected through an observation sequence of finite length, that is, whether the system is diagnosable; S3: If the system is not diagnosable, a verification net is constructed based on the original Petri net, and the reachability tree is expanded and pruned using the system structure captured in the verification net, searching for labels that need to be relabeled; S4: An integer linear programming problem is proposed to find an optimal labeling function to make the system diagnosable.

2. The discrete event system fault diagnosis research method based on λ-free Petri net according to claim 1 is characterized by: In S1, N is a Petri net, which is a triple N = (P, T, F), where P and T are respectively a set of places p and a set of transitions t. It is a flow relation, connecting places and transitions, and represents the set of directed arcs between places and transitions; Each transition in the Petri net represents a physical event in the system, and sensors are connected to it. The transition set is divided into observable transitions 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 discrete event system fault diagnosis research method based on λ-free Petri net according to claim 2 is characterized by: Except for faults, no other unobservable transitions are included. λ-free label PNs are PNs with no transitions marked by null.

4. The discrete event system fault diagnosis research method based on λ-free Petri net according to claim 1 is characterized by: In 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 occurs; S22: If there are two emission sequences σ1 and σ2, which satisfy the following conditions: the labels of sequences σ1 and σ2 are the same, σ1 does not contain any fault transition, σ2 contains at least one fault transition, and the length of σ2 after the occurrence of the fault transition is infinite, then the system is determined to be undiagnosable.

5. The discrete event system fault diagnosis research method based on λ-free Petri net according to claim 1 is characterized by: In S3, the specific steps are as follows: S31: Assuming synchronization on observable transition labels, combine the labeled Petri net system and the induced subnet into a verification net system in an explicitly stated manner; S32: Draw a reachability graph of the verification network. If it contains at least one loop entered after triggering the fault transition, the network system cannot be diagnosed; S33: To make the system diagnosable, it is necessary to disable each path in the reachable graph of the verification network that starts from the root node and contains each path that enters the loop after triggering the fault transition, and expand the reachable tree for repeated nodes encountered in the path from the root to the leaf; S34: Since the deadlock path and the path leading to the "duplicate" node but not containing the fault transition do not violate diagnosability in the reachable tree, these paths are pruned and only the path leading to the "duplicate" node and containing the fault transition is retained.

6. The discrete event system fault diagnosis research method based on λ-free Petri net according to claim 1 is characterized by: In S4, the specific steps are as follows: S41. Define a binary variable set v t ∈{0,1}, where v t = 1 means that the transition is relabeled under the new label. A linear inequality associated with the pruned reachable graph is constructed to ensure that each undiagnosable path is properly handled, in the following form: Among them, t i These are all the transitions on the path that need to be relabeled, ensuring that at least one transition in each path is relabeled; S42, check each transition pair from the root to the leaf in the pruned reachable graph; S43, let R be the set of all linear inequalities obtained from the pruned reachable graph, and the solver solves the inequality set R; S44, determine whether there is a marking function that satisfies these constraints. If the constraint set R has a solution, then 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, re-analyze the pruning of the verification network and update the marking function; S45. The label of the system is updated according to the linear inequality. The re-labeled system does not include a loop entered after the fault transition is triggered, and the network system can be diagnosed.

7. The discrete event system fault diagnosis research method based on λ-free Petri net according to claim 6 is characterized by: In S42, the following steps are used to check the pruned transition pairs: (1) For each transition pair (t i , t j ), where i≠j, if the path changes t i and t j If they are different, add the corresponding variable v to the inequality. i and v j ; (2) If two transitions t in the path i and t j If they are the same, no processing will be done in the current step; (3) If the transition pair in the path is (λ, t f ), then no processing is done on these changes, but their impact on path diagnostics needs to be considered.

8. The discrete event system fault diagnosis research method based on λ-free Petri net according to claim 6 is characterized by: In S43, the solving tool solves the inequality set R by using either linear programming or integer linear programming.

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