CN107450517A - A kind of safe diagnosability determination method of Stochastic discrete event systems and system - Google Patents

A kind of safe diagnosability determination method of Stochastic discrete event systems and system Download PDF

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CN107450517A
CN107450517A CN201710671203.7A CN201710671203A CN107450517A CN 107450517 A CN107450517 A CN 107450517A CN 201710671203 A CN201710671203 A CN 201710671203A CN 107450517 A CN107450517 A CN 107450517A
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event
state
msub
discrete event
systems
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刘富春
杨鹏飚
赵锐
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Guangdong University of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B23/00—Testing or monitoring of control systems or parts thereof
    • G05B23/02—Electric testing or monitoring
    • G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults

Abstract

This application discloses a kind of safe diagnosability determination method of Stochastic discrete event systems and system, in this method, after probabilistic automata corresponding with Stochastic discrete event systems is determined, the error-free automatic machine of the specification normative language for representing Stochastic discrete event systems will be created, it is then based on error-free automatic machine, create the illegal speech recognizer for being used for differentiation and forbidding event string on illegal language set, it is next based on illegal speech recognizer, create safety verification device, and determine for judging the whether safe diagnosable necessary and sufficient condition of Stochastic discrete event systems, finally according to safety verification device and above-mentioned necessary and sufficient condition, may determine that Stochastic discrete event systems, whether safety is diagnosable.Time complexity corresponding to the process of above-mentioned establishment safety verification device and the time complexity of the diagnosable deterministic process of the safety based on above-mentioned safety verification device are polynomial time, the complexity thus, it is possible to further reduce Stochastic discrete event systems security diagnostics.

Description

A kind of safe diagnosability determination method of Stochastic discrete event systems and system
Technical field
The present invention relates to Stochastic discrete event systems security diagnostics technical field, more particularly to a kind of Random Discrete event system Unite safe diagnosability determination method and system.
Background technology
Discrete event system (Discrete Event System, be abbreviated as DES) is the one kind proposed the 1980s Interacted by discrete event according to certain operation rule and cause the dynamical system of state evolution, it was both used directly for Modeling to discrete system, it can be used for again to the system modelling after discrete model construction.At present, the own warp of discrete event system It is widely applied to computer integrated manufacturing system, traffic control, computer network, communication network, flexible production line, military affairs refer to The field such as wave.Particularly Stochastic discrete event systems, it is that a probability is with the addition of on the basis of classical discrete event system Structure, the stochastic behaviour of the probability size that each event occurs in real application systems more can be accurately described, has been widely used To fields such as pattern-recognition, language identification, weather forecasting, robot controls.In the 14th world of International Federation of Automatic Control In conference, former Chinese Academy of Engineering president Song Jian academician is in plenary lecture by discrete event system and nonlinear system, distribution Formula parameter system, robust control, faults-tolerant control and adaptive, self-correcting, self-organizing system etc. are classified as " having great expectations " Research direction；Famous cybernetist, Peking University professor, Chinese Academy of Sciences Huang beautiful jade academician et al. then claim " discrete event system System is the research direction that domestic and international control theory circle is paid attention to extensively, in the series of engineering technical problem such as high-tech man-made system With important research meaning " (Zheng great Zhong, Zhao Qian river discrete event dynamic system Beijing:Publishing house of Tsing-Hua University, 2001).
With the fast development of modern science and technology, commercial production scale expands day by day, and automation equipment maximizes increasingly, system Structure also becomes to become increasingly complex, once system or equipment breaks down, not only influences system normal operation, or even be also possible to make Into life and the massive losses of property.Especially in industrial control field, system operation is monitored in real time, timely and accurately Fault detect is carried out to system core equipment, to prevent the generation of serious even catastrophic failure, for an industrial system It is particularly important.Therefore, the Research on Fault Diagnosis Technology for being widely used in the discrete event system of modern industry receives research people The great attention of member, turned into the world automatically control etc. one of the study hotspot in field (J.Zaytoon, S.Lafortune.Overview of Fault Diagnosis Methods for Discrete Event Systems.Annual Reviews in Control,37(2):308-320,2013)。
One Stochastic discrete event systems can be modeled as probabilistic automata G=(X, Σ, a ηG,x0), wherein X is that have Limit state set, original state x0, Σ is definite event collection, and Σ is typically divided into observable event set Σ hereoNot observable Event set Σuo, i.e. Σ=Σ0∪Σuo, wherein event of failure collection ΣfIn event belong to inconsiderable event；ηG：X×Σ× X → [0,1] represents partial status transition function：For x, x ' ∈ X and σ ∈ Σ, ηG(x, σ, x ') represents system in state x Event σ occurs and is transferred to state x ' probability.
In Stochastic discrete event systems G=(X, Σ, ηG,x0) on the basis of, a part transfer function δ can be definedG:X × Σ → X is as follows：δG(x, σ)=x ' and if only if ηG(x, σ, x ') ＞ 0, wherein x, x ' ∈ X, σ ∈ Σ.When system G is in state During x, it is by the probability recursive definition that an event string occurs after system：If ηG(x, σ, x ') ＞ 0, then and Pr (σ | x)=ηG (x, σ), and Pr (s σ | x)=Pr (s | x) ηG(x ', σ), wherein δG(x, s)=x ', s ∈ ∑s*, ∑*Representing all on event set ∑ has The set of limit event string.
As described above, fault diagnosis is intended to identify and determine in time the event that can not be observed directly in system by sensor The generation of barrier event, but the security of system can not be ensured during fault diagnosis, because fault diagnosis needs the regular hour, Certain delay be present in fault diagnosis, and during the delay of fault diagnosis, system may continue executing with some dangerous behaviour Make, therefore, the fault diagnosis of system has potential safety hazard.And the safety failure diagnosis of system is considered as then discrete event system First steps necessary of fault-tolerant monitoring.The safety failure diagnosis of Stochastic discrete event systems can ensure that system occurs in failure Afterwards, all it is diagnosed before uneasy full operation performs by institute is faulty.
Stochastic discrete event systems G=(X, ∑, ηG,x0) safe diagnosticability can formalize it is as follows：If probabilistic automata G generation language is L, if meeting condition：
And the following at least one establishment of condition：
(1) D (sv)=1, that is,
(2) to any t ∈ L/s, | | t | | >=n0There are Pr (t:D (sv)=0) ＜ ε, to all v ∈ pre (t), diagnose letter Number D:Σ*→ { 0,1 } is defined as follows：
It is that safety is diagnosable then to claim G.
Intuitively, G is the diagnosable any one occurrence string meaned after the event of failure fi of the i-th type occurs of safety T, t prefix v be present so that do not include any non-syntax language in v, and for it is all withsvThere is identical observed result Event string ω, otherwise directly the fault diagnosis in ω can be come out, otherwise although directly the fault diagnosis in ω can not be gone out Come, (i.e. can be with sufficiently large probability by ω but the probability that can ensure that the fault diagnosis in ω can not be come out is sufficiently small In fault diagnosis come out).That is, nearly all failure can before system is not carried out any uneasy full operation quilt It is diagnosed.
For to being proposed before Stochastic discrete event systems fault diagnosis with high safety, inventor herein's Liu Fu spring et al. A kind of safety failure diagnostic method (Fuchun Liu (Liu Fuchun), Daowen Qiu.Safe based on security diagnostics device diagnosability of stochastic discrete event systems.IEEETransactions on Automatic Control,vol.53,no.5,pp:1291-1296,2008), its step is：
(1) an illegal speech recognizer G for being used for non-syntax language in identifying system G is builtr；
(2) in illegal speech recognizer GrOn the basis of, build a security diagnostics device Gd=(Qd,Σo,δd,Φ,q0), To Stochastic discrete event systems G fault diagnosises with high safety；
(3) it is right according to the sufficient and necessary condition of safe diagnosticability of the system based on security diagnostics deviceGCarrying out safety can examine The judgement of disconnected property.
It is illustrated below by an example.
Example 1：Consider the Stochastic discrete event systems G in Fig. 11=(X, Σ, ηG,x0), wherein, X=(0,1,2,3), Σ= (a,b,σf,σuo), Σ0={ a, b },And forbid event set of strings Γi={ b }.
According to (1) step of the above method, construction system G1Illegal speech recognizer Gr, as shown in Figure 2.Further according to (2) step, the security diagnostics device G of system is constructedd, as shown in Figure 3.
In figure 3, due to security diagnostics device GdAsynchronously meet following two conditions：
1) in QdIn be not present the nondeterministic statement of part often returned containing F；
2)GdIn following transfer is not present：q1For nondeterministic statement, q2For containing BiThe state of tag component, q3To contain BiOften The state of part is returned, and meets δd(q1, σ) and=q2, δd(q2, α) and=q3Wherein σ ∈ Σo,
Therefore, Stochastic discrete event systems G1The sufficient and necessary condition of safe diagnosticability is unsatisfactory for, so as to obtain system G1 It is not the diagnosable conclusion of safety.
But.The safety failure diagnostic method of above-mentioned Stochastic discrete event systems is although can be by constructing security diagnostics device To the diagnosis with high safety of Stochastic discrete event systems failure, still, the complexity of security diagnostics device and diagnosis with high safety are constructed The complexity of algorithm is all referring to several times：With increasing for system mode and event number, the complexity of system safety failure diagnosis Property will be sharply increased exponentially, have a strong impact on the applicability and service efficiency of safety failure diagnostic method.
In summary as can be seen that the complexity of Stochastic discrete event systems security diagnostics how is further reduced, to carry High safety fault diagnosis efficiency is that also have the problem of to be solved at present.
The content of the invention
In view of this, it is an object of the invention to provide a kind of safe diagnosability determination method of Stochastic discrete event systems And system, the complexity of Stochastic discrete event systems security diagnostics can be further reduced, is diagnosed so as to improve safety failure Efficiency.Its concrete scheme is as follows：
A kind of safe diagnosability determination method of Stochastic discrete event systems, including：
It is determined that automatic machine corresponding with Stochastic discrete event systems, obtains probabilistic automata；
Create oneself of the specification normative language for being used to represent the Stochastic discrete event systems corresponding with the probabilistic automata Motivation, obtain error-free automatic machine；Wherein, the specification normative language is corresponding with non-faulting event in the Stochastic discrete event systems Language；
Based on the error-free automatic machine, the taboo for being used to distinguish the Stochastic discrete event systems on illegal language set is created The only identifier of event string, obtain illegal speech recognizer；
Based on the illegal speech recognizer, create corresponding validator, obtain safety verification device, and determine with it is described It is used to judge the whether safe diagnosable necessary and sufficient condition of the Stochastic discrete event systems corresponding to safety verification device；
According to the safety verification device and the necessary and sufficient condition, judge whether the Stochastic discrete event systems safely may be used Diagnosis, obtains corresponding result of determination.
Optionally, the expression formula of the probabilistic automata, it is specially：
G=(X, Σ, ηG,x0)；
In formula, X represents the finite state collection of the Stochastic discrete event systems, and x0 represents the Stochastic discrete event systems Original state, what Σ represented the Stochastic discrete event systems includes observable event set ΣoNot observable event set Σuo Definite event collection, ηG：X × Σ × X → [0,1] represents the partial status transition probability letter of the Stochastic discrete event systems Number：For x, x ' ∈ X and σ ∈ Σ, ηG(x, σ, x ') represents that the Stochastic discrete event systems occur in the event σ that state is x And it is transferred to state x ' probability.
Optionally, the expression formula of the error-free automatic machine, it is specially：
H=(X ', Σ ', ηH,δH,x0)；
In formula,For finite state collection,For definite event collection, ΣfRepresent event of failure Collection, the event that the event of failure is concentrated are not observable event；ηH:X ' × Σ ' × X ' → [0,1] is state transition probability Function：To x, x ' ∈ X ' and σ ∈ Σ ', if ηG(x, σ, x ') ＞ 0, then ηH(x, σ, x ')=ηG(x,σ,x′)；δH:X′×∑′ → X ' is state transition function：To x, x ' ∈ X ' and σ ∈ ∑ ', δH(x, σ)=x ' and if only if ηH(x, σ, x ') ＞ 0；To any X ' ∈ X, if ω ∈ ∑s be present*So thatAnd ηG(x0, ω, x ') and ＞ 0, then x ' ∈ X ', wherein, Σ*Represent definite event collection The set of all definite event strings on ∑.
Optionally, the expression formula of the illegal speech recognizer, it is specially：
Gr=(Qr,Σ,ηr,δr,p0)；
In formula,Finite state collection is represented, LB={ N, F, B } represents to forbid event string ΓiOn label Collection, i=1,2 ... m, wherein, N tag representations are not carried out event of failure；F tag representations have been carried out event of failure, but Event of failure is also not carried out Γ after occurringiIn forbid event string；B tag representations have been carried out event of failure, and in failure Event performs Γ again after occurringiIn forbid event string；Original state p0=(x0,N)∈Qr；ηr:Qr×Σ×Qr→[0,1] For partial status transition function, and ηr(pi,σ,pj)=ηG(xi,σ,xj), wherein, pi=(xi,lbi), pj=(xj,lbj) ∈Qr, σ ∈ Σ；δr:Qr×Σ→QrFor partial status transfer function, it is assumed that pi=(xi,lbi)∈Qr, lbi∈ LB, σ ∈ Σ and δG(xi,σ,xj) be defined, then：
Also, δr(pi, s σ) and=δr(δr(pi, s), σ), s ∈ Σ*。
Optionally, the expression formula of the safety verification device, it is specially：
Gv=(Qv,Σo,δv,ηv,q0)；
In formula, q0=(x0,N,y0) represent original state；ΣoRepresent observable event set；QvFinite state collection is represented, andWherein, Y=X ' ∪ { E }, E is expressed as sky；ηv:Qv×Σo×Qv→[0,1]2It is partial status transition probability Function, it is rightq2=(x2,lb2,y2)∈Qv, σ ∈ ∑so, ηv(q1,σ,q2)=(θ, θ ') ＞ 0, wherein,
δv:Qv×∑o→QvFor partial status transfer function；
In formula, q1=(x1,lb1,y1)∈Qv, σ ∈ ∑so, s ∈ Lσ(G,x1), p1=(x1,lb1)∈Qr, state E represent exist In the error-free automatic machine H, state y1Do not shifted by considerable event σ；
In the safety verification device GvIn, for a reachable state qi=(xi,lbi,yi)∈QvIf lbi=N, then claim State qiFor normal condition, it is designated asIf lbi=B, then claim state qiFor B state, it is designated asIf lbi=F, and yi≠ E, then claim state qiFor malfunction, it is designated asIf in safety verification device GvIn, existence qk,qk+1,qk+2,...ql∈ Qv, event σk,σk+1,σk+2,...σl∈∑o, 0≤k≤l so that：
Then claim status switch qk,qk+1,qk+2,...ql∈QvA ring is formd, is denoted as cl=(qk,qk+1,qk+2, ...ql)；By event string scl=σkσk+1...σl, from state qkTo state qlTransition probability be ring cl transition probability, Specially：
The set of state is designated as in ring：Cl '={ qk,qk+1,qk+2,...ql}；Assuming that cl=(qk,qk+1,qk+2,...ql) For random security validator GvIn a ring, its transition probabilityIfAndThen state ring cl is often to return B state ring
Optionally, the necessary and sufficient condition, it is specially：
The safety verification device GvIn be not presentSo that δv(q1, σ) and=q2, δv(q2, α) and=q3, wherein σ ∈ ∑so, α ∈ ∑s*。
Optionally, it is described according to the safety verification device and the necessary and sufficient condition, judge the Random Discrete event system Whether safety is diagnosable for system, obtains the process of corresponding result of determination, including：
A1：Construct the safety verification device GvDigraph D G=(VDG,EDG)；Wherein, vertex set VDGWith side collection EDGRespectively It is defined as follows：
VDG={ (xi,lbi,yi)∈Qv}；
EDG={ (v, w, θ):v,w∈Qv, andSo that θ=ηv(v, σ, w) ＞ 0 }；
A2：Travel through the digraph D G, find the ring that B labels are contained on all summits, and in ring between summit side θ=1, If the ring is not present, judge that the Stochastic discrete event systems are diagnosable safely, and terminate；Otherwise the collection that will be obtained after traversal Close VBIn first summit be defined as current summit to be verified；
A3：From the set VBCurrent summit to be verified set out, recurrence finds a summit thereon, until finding first Untill label is not B representative points, the representative points are designated as m=(x, lb, y) ∈ VDGIf label lb in the representative points =N or lb=F and y ≠ E, then it is not that safety is diagnosable to judge the Stochastic discrete event systems, and is terminated；Otherwise enter Enter step A4；
Step A4：By the set VBIn next summit be defined as current summit to be verified, reenter step A3, such as Label lb=N or lb=F and y ≠ E representative points are not present in fruit, then judge that the Stochastic discrete event systems can examine safely It is disconnected, and terminate.
The present invention further discloses a kind of safe diagnosticability of Stochastic discrete event systems to determine system, including：
Probabilistic automata determining module, for determining corresponding with Stochastic discrete event systems automatic machine, obtain it is random oneself Motivation；
Error-free automatic machine creation module, it is corresponding with the probabilistic automata for representing the Random Discrete for creating The automatic machine of the specification normative language of event system, obtain error-free automatic machine；Wherein, the specification normative language is the Random Discrete event Language corresponding with non-faulting event in system；
Identifier creation module, for based on the error-free automatic machine, creating described for distinguishing on illegal language set The identifier for forbidding event string of Stochastic discrete event systems, obtains illegal speech recognizer；
Safety verification device creation module, for based on the illegal speech recognizer, creating corresponding validator, being pacified Full validator；
Necessary and sufficient condition determining module, it is corresponding with the safety verification device for judging the Random Discrete for determining The whether safe diagnosable necessary and sufficient condition of event system；
The diagnosable judge module of safety, for according to the safety verification device and the necessary and sufficient condition, judge it is described with Whether safety is diagnosable for machine discrete event system, obtains corresponding result of determination.
Optionally, the expression formula of the probabilistic automata, it is specially：
G=(X, ∑, ηG,x0)；
In formula, X represents the finite state collection of the Stochastic discrete event systems, x0Represent the Stochastic discrete event systems Original state, what ∑ represented the Stochastic discrete event systems includes observable event set ∑oNot observable event set ∑uo Definite event collection, ηG：X × ∑ × X → [0,1] represents the partial status transition probability letter of the Stochastic discrete event systems Number：For x, x ' ∈ X and σ ∈ ∑s, ηG(x, σ, x ') represents that the Stochastic discrete event systems occur in the event σ that state is x And it is transferred to state x ' probability；
The expression formula of the error-free automatic machine, it is specially：
H=(X ', ∑ ', ηH,δH,x0)；
In formula,For finite state collection,For definite event collection, ∑fRepresent event of failure Collection, the event that the event of failure is concentrated are not observable event；ηH:X ' × ∑ ' × X ' → [0,1] is state transition probability Function：To x, x ' ∈ X ' and σ ∈ Σ ', if ηG(x, σ, x ') ＞ 0, then ηH(x, σ, x ')=ηG(x,σ,x′)；δH:X′×Σ′ → X ' is state transition function：To x, x ' ∈ X ' and σ ∈ Σ ', δH(x, σ)=x ' and if only if ηH(x, σ, x ') ＞ 0；To any X ' ∈ X, if ω ∈ Σ be present*So thatAnd ηG(x0, ω, x ') and ＞ 0, then x ' ∈ X ', wherein, Σ*Represent definite event collection The set of the upper all definite event strings of Σ；
The expression formula of the illegal speech recognizer, it is specially：
Gr=(Qr,Σ,ηr,δr,p0)；
In formula,Finite state collection is represented, LB={ N, F, B } represents to forbid event string ΓiOn label Collection, i=1,2 ... m, wherein, N tag representations are not carried out event of failure；F tag representations have been carried out event of failure, but Event of failure is also not carried out Γ after occurringiIn forbid event string；B tag representations have been carried out event of failure, and in failure Event performs Γ again after occurringiIn forbid event string；Original state p0=(x0,N)∈Qr；ηr:Qr×Σ×Qr→[0,1] For partial status transition function, and ηr(pi,σ,pj)=ηG(xi,σ,xj), wherein, pi=(xi,lbi), pj=(xj,lbj) ∈Qr, σ ∈ Σ；δr:Qr×Σ→QrFor partial status transfer function, it is assumed that pi=(xi,lbi)∈Qr, lbi∈ LB, σ ∈ Σ and δG(xi,σ,xj) be defined, then：
Also, δr(pi, s σ) and=δr(δr(pi, s), σ), s ∈ Σ*；
The expression formula of the safety verification device, it is specially：
Gv=(Qv,Σo,δv,ηv,q0)；
In formula, q0=(x0,N,y0) represent original state；ΣoRepresent observable event set；QvFinite state collection is represented, andWherein, Y=X ' ∪ { E }, E is expressed as sky；ηv:Qv×Σo×Qv→[0,1]2It is partial status transition probability Function, it is rightq2=(x2,lb2,y2)∈Qv, σ ∈ Σo, ηv(q1,σ,q2)=(θ, θ ') ＞ 0, wherein,
δv:Qv×Σo→QvFor partial status transfer function；
In formula, q1=(x1,lb1,y1)∈Qv, σ ∈ Σo, s ∈ Lσ(G,x1), p1=(x1,lb1)∈Qr, state E represent exist In the error-free automatic machine H, state y1Do not shifted by considerable event σ；
In the safety verification device GvIn, for a reachable state qi=(xi,lbi,yi)∈QvIf lbi=N, then claim State qiFor normal condition, it is designated asIf lbi=B, then claim state qiFor B state, it is designated asIf lbi=F, and yi≠ E, then claim state qiFor malfunction, it is designated asIf in safety verification device GvIn, existence qk,qk+1,qk+2,...ql∈ Qv, event σk,σk+1,σk+2,...σl∈Σo, 0≤k≤l so that：
Then claim status switch qk,qk+1,qk+2,...ql∈QvA ring is formd, is denoted as cl=(qk,qk+1,qk+2, ...ql)；By event string scl=σkσk+1...σl, from state qkTo state qlTransition probability be ring cl transition probability, Specially：
The set of state is designated as in ring：Cl '={ qk,qk+1,qk+2,...ql}；Assuming that cl=(qk,qk+1,qk+2,...ql) For random security validator GvIn a ring, its transition probabilityIfAndThen state ring cl is often to return B state ring
The necessary and sufficient condition, it is specially：
The safety verification device GvIn be not presentSo that δv(q1, σ) and=q2, δv(q2, α) and=q3, wherein σ ∈ Σo, α ∈ Σ*。
Optionally, the diagnosable judge module of the safety, including digraph structural unit, digraph Traversal Unit, recurrence Find unit and recurrence finds cycling element；Wherein：
The digraph structural unit, for constructing the safety verification device GvDigraph D G=(VDG,EDG)；Wherein, Vertex set VDGWith side collection EDGIt is defined respectively as：
VDG={ (xi,lbi,yi)∈Qv}；
EDG={ (v, w, θ):v,w∈Qv, andSo that θ=ηv(v, σ, w) ＞ 0 }；
The digraph Traversal Unit, for traveling through the digraph D G, the ring that B labels are contained on all summits is found, and In ring between summit side θ=1, if the ring is not present, judge that the Stochastic discrete event systems are diagnosable safely, and tie Beam；Otherwise the set V that will be obtained after traversalBIn first summit be defined as current summit to be verified；
The recurrence finds unit, for from the set VBCurrent summit to be verified set out, recurrence finds thereon one Summit, untill finding the representative points that first label is not B, the representative points are designated as m=(x, lb, y) ∈ VDGIf Label lb=N or lb=F and y ≠ E in the representative points, then it is not that safety can examine to judge the Stochastic discrete event systems Disconnected, and terminate；Otherwise start the recurrence and find cycling element；
The recurrence finds cycling element, for by the set VBIn next summit be defined as current top to be verified Point, restart the recurrence and find unit, if there is no label lb=N or lb=F and y ≠ E representative points, then sentence The fixed Stochastic discrete event systems are diagnosable safely, and terminate.
In the present invention, after probabilistic automata corresponding with Stochastic discrete event systems is determined, it will create and be used for The error-free automatic machine of the specification normative language of Stochastic discrete event systems is represented, error-free automatic machine is then based on, creates illegal language set On be used to distinguish and forbid the illegal speech recognizer of event string, be next based on illegal speech recognizer, create corresponding safety Validator, and determine corresponding with safety verification device for judging Stochastic discrete event systems whether want by diagnosable the filling of safety Condition, finally according to safety verification device and above-mentioned necessary and sufficient condition, it can be determined that go out whether Stochastic discrete event systems safely may be used Diagnosis, so as to obtain corresponding result of determination.Due to time complexity corresponding to the process of above-mentioned establishment safety verification device and The time complexity of the diagnosable deterministic process of safety based on above-mentioned safety verification device is polynomial time, so of the invention In the time complexity of safe diagnosticability determination process be also polynomial time, and the time complexity of prior art It it is then the exponential time, it is seen then that the present invention can further reduce the complexity of Stochastic discrete event systems security diagnostics, so as to carry High safety failure diagnosis efficiency.
Brief description of the drawings
In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing There is the required accompanying drawing used in technology description to be briefly described, it should be apparent that, drawings in the following description are only this The embodiment of invention, for those of ordinary skill in the art, on the premise of not paying creative work, can also basis The accompanying drawing of offer obtains other accompanying drawings.
Fig. 1 is a kind of specific Stochastic discrete event systems schematic diagram；
Fig. 2 is that the non-syntax language corresponding with the Stochastic discrete event systems in Fig. 1 based on prior art structure is known Other device schematic diagram；
Fig. 3 is that the security diagnostics device corresponding with the illegal speech recognizer in Fig. 2 based on prior art structure shows It is intended to；
Fig. 4 is a kind of safe diagnosability determination method flow of Stochastic discrete event systems disclosed in the embodiment of the present invention Figure；
Fig. 5 is the safe diagnosability determination method of a kind of specific Stochastic discrete event systems disclosed in the embodiment of the present invention Flow chart；
Fig. 6 is the error-free automatic machine schematic diagram corresponding with the Stochastic discrete event systems in Fig. 1 built based on the present invention；
Fig. 7 is the illegal speech recognizer schematic diagram corresponding with the error-free automatic machine in Fig. 6 built based on the present invention；
Fig. 8 is the safety verification device schematic diagram corresponding with the illegal speech recognizer in Fig. 7 built based on the present invention；
Fig. 9 is another specific Stochastic discrete event systems schematic diagram；
Figure 10 is the error-free automatic machine signal corresponding with the Stochastic discrete event systems in Fig. 9 built based on the present invention Figure；
Figure 11 is the illegal speech recognizer schematic diagram corresponding with the error-free automatic machine in Figure 10 built based on the present invention；
Figure 12 is the safety verification device schematic diagram corresponding with the illegal speech recognizer in 11 built based on the present invention；
Figure 13 is that a kind of safe diagnosticability of Stochastic discrete event systems disclosed in the embodiment of the present invention determines system architecture Schematic diagram.
Embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete Site preparation describes, it is clear that described embodiment is only part of the embodiment of the present invention, rather than whole embodiments.It is based on Embodiment in the present invention, those of ordinary skill in the art are obtained every other under the premise of creative work is not made Embodiment, belong to the scope of protection of the invention.
The embodiment of the invention discloses a kind of safe diagnosability determination method of Stochastic discrete event systems, referring to Fig. 4 institutes Show, this method includes：
Step S11：It is determined that automatic machine corresponding with Stochastic discrete event systems, obtains probabilistic automata；
Step S12：Create oneself of the specification normative language for being used to represent Stochastic discrete event systems corresponding with probabilistic automata Motivation, obtain error-free automatic machine；Wherein, specification normative language is language corresponding with non-faulting event in Stochastic discrete event systems；
Step S13：Based on error-free automatic machine, the taboo for being used to distinguish Stochastic discrete event systems on illegal language set is created The only identifier of event string, obtain illegal speech recognizer；
Step S14：Based on illegal speech recognizer, create corresponding validator, obtain safety verification device, and determine with It is used to judge the whether safe diagnosable necessary and sufficient condition of Stochastic discrete event systems corresponding to safety verification device；
Step S15：According to safety verification device and necessary and sufficient condition, judge whether Stochastic discrete event systems can examine safely It is disconnected, obtain corresponding result of determination.
In the embodiment of the present invention, after probabilistic automata corresponding with Stochastic discrete event systems is determined, it will wound The error-free automatic machine of the specification normative language for representing Stochastic discrete event systems is built, is then based on error-free automatic machine, is created illegal The illegal speech recognizer for being used for differentiation and forbidding event string on language set, is next based on illegal speech recognizer, creates corresponding Safety verification device, and determine it is corresponding with safety verification device be used for judge Stochastic discrete event systems whether safety it is diagnosable Necessary and sufficient condition, finally according to safety verification device and above-mentioned necessary and sufficient condition, it can be determined that whether go out Stochastic discrete event systems Safety is diagnosable, so as to obtain corresponding result of determination.Because the time corresponding to the process of above-mentioned establishment safety verification device is complicated Degree and the time complexity of the diagnosable deterministic process of safety based on above-mentioned safety verification device are polynomial time, so The time complexity of safe diagnosticability determination process in the present invention is also polynomial time, and the time of prior art Complexity is then the exponential time, it is seen then that the embodiment of the present invention can further reduce Stochastic discrete event systems security diagnostics Complexity, so as to improve safety failure diagnosis efficiency.
The embodiment of the invention discloses a kind of specific safe diagnosability determination method of Stochastic discrete event systems, referring to Shown in Fig. 5, including：
Step S21：It is determined that automatic machine corresponding with Stochastic discrete event systems, obtains probabilistic automata；
Wherein, the expression formula of above-mentioned probabilistic automata, it is specially：
G=(X, Σ, ηG,x0)；
In formula, X represents the finite state collection of Stochastic discrete event systems, x0Represent the initial shape of Stochastic discrete event systems State, Σ expression Stochastic discrete event systems include observable event set ΣoNot observable event set ΣuoDefinite event Collection, ηG：X × Σ × X → [0,1] represents the partial status transition function of Stochastic discrete event systems：For x, x ' ∈ X and σ ∈ Σ, ηG(x, σ, x ') represents that Stochastic discrete event systems occur in the event σ that state is x and are transferred to state x ' probability.
Step S22：Create oneself of the specification normative language for being used to represent Stochastic discrete event systems corresponding with probabilistic automata Motivation, obtain error-free automatic machine；Wherein, specification normative language is language corresponding with non-faulting event in Stochastic discrete event systems；
Wherein, the expression formula of above-mentioned error-free automatic machine, it is specially：
H=(X ', Σ ', ηH,δH,x0)；
In formula,For finite state collection,For definite event collection, ΣfRepresent event of failure Collection, the event that event of failure is concentrated are not observable event；ηH:X ' × Σ ' × X ' → [0,1] is state transition probability letter Number：To x, x ' ∈ X ' and σ ∈ Σ ', if ηG(x, σ, x ') ＞ 0, then ηH(x, σ, x ')=ηG(x,σ,x′)；δH:X′×Σ′→ X ' is state transition function：To x, x ' ∈ X ' and σ ∈ Σ ', δH(x, σ)=x ' and if only if ηH(x, σ, x ') ＞ 0；To any x ' ∈ X, if ω ∈ Σ be present*So thatAnd ηG(x0, ω, x ') and ＞ 0, then x ' ∈ X ', wherein, Σ*Represent definite event collection Σ The set of upper all definite event strings.
Obviously, language caused by error-free automatic machine H is the language for not including event of failure in system G.
Step S23：Based on error-free automatic machine, the taboo for being used to distinguish Stochastic discrete event systems on illegal language set is created The only identifier of event string, obtain illegal speech recognizer；
In the present embodiment, above-mentioned illegal language set can be expressed as
Wherein, the expression formula of above-mentioned illegal speech recognizer, it is specially：
Gr=(Qr,Σ,ηr,δr,p0)；
In formula,Finite state collection is represented, LB={ N, F, B } represents to forbid event string ΓiOn label Collection, i=1,2 ... m, wherein, N tag representation Stochastic discrete event systems are also not carried out event of failure；F tag representations at random from Scattered event system has been carried out event of failure, but is also not carried out Γ after event of failure generationiIn forbid event string；B is marked Label represent that Stochastic discrete event systems have been carried out event of failure, and perform Γ again after event of failure generationiIn taboo Only event string；Original state p0=(x0,N)∈Qr；ηr:Qr×Σ×Qr→ [0,1] is partial status transition function, and ηr (pi, σ, pj)=ηG(xi,σ,xj), wherein, pi=(xi,lbi), pj=(xj,lbj)∈Qr, σ ∈ Σ；δr:Qr×Σ→QrFor portion Isloation state transfer function, it is assumed that pi=(xi,lbi)∈Qr, lbi∈ LB, σ ∈ Σ and δG(xi,σ,xj) be defined, then：
Also, δr(pi, s σ) and=δr(δr(pi, s), σ), s ∈ Σ*。
Step S24：Based on illegal speech recognizer, create corresponding validator, obtain safety verification device, and determine with It is used to judge the whether safe diagnosable necessary and sufficient condition of Stochastic discrete event systems corresponding to safety verification device；
Wherein, the expression formula of above-mentioned safety verification device, it is specially：
Gv=(Qv,Σo,δv,ηv,q0)；
In formula, q0=(x0,N,y0) represent original state；ΣoRepresent observable event set；QvFinite state collection is represented, andWherein, Y=X ' ∪ { E }, E is expressed as sky；ηv:Qv×Σo×Qv→[0,1]2It is partial status transition probability Function, it is rightq2=(x2,lb2,y2)∈Qv, σ ∈ Σo, ηv(q1,σ,q2)=(θ, θ ') ＞ 0, wherein,
δv:Qv×Σo→QvFor partial status transfer function；
In formula, q1=(x1,lb1,y1)∈Qv, σ ∈ Σo, s ∈ Lσ(G,x1), p1=(x1,lb1)∈Qr, state E represent exist In error-free automatic machine H, state y1Do not shifted by considerable event σ；
In safety verification device GvIn, for a reachable state qi=(xi,lbi,yi)∈QvIf lbi=N, then claim the shape State qiFor normal condition, it is designated asIf lbi=B, then claim state qiFor B state, it is designated asIf lbi=F, and yi≠ E, then Claim state qiFor malfunction, it is designated asIf in safety verification device GvIn, existence qk,qk+1,qk+2,...ql∈Qv, thing Part σk,σk+1,σk+2,...σl∈Σo, 0≤k≤l so that：
Then claim status switch qk,qk+1,qk+2,...ql∈QvA ring is formd, is denoted as cl=(qk,qk+1,qk+2, ...ql)；By event string scl=σkσk+1...σl, from state qkTo state qlTransition probability be ring cl transition probability, Specially：
The set of state is designated as in ring：Cl '={ qk,qk+1,qk+2,...ql}；Assuming that cl=(qk,qk+1,qk+2,...ql) For random security validator GvIn a ring, its transition probabilityIfAndThen state ring cl is often to return B state ring
In addition, above-mentioned necessary and sufficient condition, is specially：
Safety verification device GvIn be not presentSo that δv(q1, σ) and=q2, δv (q2, α) and=q3, wherein σ ∈ ∑so, α ∈ Σ*。
Step S25：Construct safety verification device GvDigraph D G=(VDG,EDG)；Wherein, vertex set VDGWith side collection EDGPoint It is not defined as follows：
VDG={ (xi,lbi,yi)∈Qv}；
EDG={ (v, w, θ):v,w∈Qv, andSo that θ=ηv(v, σ, w) ＞ 0 }；
Step S26：Travel through digraph D G, find the ring that B labels are contained on all summits, and in ring between summit side θ= 1, if the ring is not present, judge that Stochastic discrete event systems are diagnosable safely, and terminate；Otherwise the set that will be obtained after traversal VBIn first summit be defined as current summit to be verified；
Step S27：From set VBCurrent summit to be verified set out, recurrence finds a summit thereon, until finding first Untill individual label is not B representative points, the representative points are designated as m=(x, lb, y) ∈ VDGIf label in the representative points Lb=N or lb=F and y ≠ E, then it is not that safety is diagnosable to judge Stochastic discrete event systems, and is terminated；Otherwise enter Step S28；
Step S28：Will set VBIn next summit be defined as current summit to be verified, reenter step S27, if In the absence of label lb=N or lb=F and y ≠ E representative points, then judge that Stochastic discrete event systems are diagnosable safely, and Terminate.
Next, the time complexity of the technical scheme disclosed in the embodiment of the present invention is analyzed.Specifically：
If Stochastic discrete event systems G=(X, Σ, ηG,x0) safety verification device be Gv=(Qv,Σo,δv,ηv,q0), then The complexity T of Stochastic discrete event systems safety failure diagnosis is divided to for two aspects：Construct safety verification device GvTime it is complicated Spend and judge whether G is the diagnosable time complexity of safety, i.e.,
T=T1+T2；
In formula, T1To construct safety verification device GvTime complexity, T2For according to GvJudge whether G is that safety is diagnosable Time complexity.
Conclusion 1：If probabilistic automata G=(X, Σ, ηG,x0) it is a Stochastic discrete event systems, order | X |=n1Represent G The number of middle state, | ∑ |=n2Represent the number of event in G.Then construct safety verification device GvTime complexity be
Conclusion 2：If finite-state automata Gv=(Qv,Σo,δv,ηv,q0) be Stochastic discrete event systems G=(X, Σ, ηG,x0) safety verification device, DG=(VDG,EDG) it is GvDigraph, | X |=n1The number of state in G is represented, | Σ |=n2Table Show the number of event in G, judge whether system G is that the diagnosable time complexity of safety is according to algorithm 1
Conclusion 3：If G=(X, Σ, ηG,x0) it is a Stochastic discrete event systems, | X |=n1Represent of state in G Number, | Σ |=n2Represent the number of event in G.Finite-state automata Gv=(Qv,Σo,δv,ηv,q0) be G safety verification Device, then the total time complexity of Stochastic discrete event systems G fault diagnosises with high safety is
It can be seen that in the embodiment of the present invention, time complexity corresponding to the process of above-mentioned establishment safety verification device and it is based on The time complexity of the diagnosable deterministic process of the safety of above-mentioned safety verification device is polynomial time, so in the present invention The time complexity of safe diagnosticability determination process is also polynomial time, and the time complexity of prior art is then Exponential time, it is seen then that the embodiment of the present invention can further reduce the complexity of Stochastic discrete event systems security diagnostics, so as to Improve safety failure diagnosis efficiency.
It is illustrated below by several examples.
Example 2：For convenience of contrast, below still with the Stochastic discrete event systems G in example 11=(X, Σ, ηG,x0) (such as Fig. 1 institutes Show) exemplified by.In example 1, system G has been obtained with the method for security diagnostics device1It is not the diagnosable conclusion of safety.Use below Itd is proposed in the embodiment of the present invention based on the safe diagnosability determination method of safety verification device come to system G1Verified.
According to above-mentioned steps S22, construction system G1Error-free automatic machine H1, as shown in Figure 6.Further according to step S23, construction Illegal speech recognizer Gr1, as shown in Figure 7.
Then, according to step S24, construction system G1Safety verification device Gv1, as shown in Figure 8, it can be seen that, in Gv1In deposit In following transfer：
δv((0, N, 0), b)=(3, B, E), δv((3, B, E), b)=(3, B, E)),
Also, δv((2, F, 1), b)=(3, B, E)), δv((3, B, E), b)=(3, B, E)), wherein According to Stochastic discrete event systems, diagnosable necessary and sufficient condition obtains safely Go out, system G1It is not the diagnosable conclusion of safety, this conclusion drawn with example 1 matches.
Example 3：Consider Stochastic discrete event systems G2=(X, Σ, ηG,x0), as shown in figure 9, wherein X={ 0,1,2 }, Σ= {a,b,c,σf, Σ0={ a, b, c },And it is Γ to forbid event traili={ c }.
Below with the safe diagnosability determination method based on safety verification device that proposes in the present invention, to system G2Implement Safety failure diagnoses.G is constructed according to above-mentioned steps S222Error-free automatic machine H2, as shown in Figure 10.Further according to above-mentioned steps S23 Construct illegal speech recognizer Gr2, as shown in figure 11.
Then, system G is constructed according to step S242Safety verification device Gv2, as shown in figure 12.Due to the safety in Figure 12 Validator Gv2In can not find transfer in the sufficient and necessary condition for meeting above-mentioned steps S24, it can thus be concluded that, Random Discrete event system Unite G2It is that safety is diagnosable.
Accordingly, the embodiment of the present invention further discloses a kind of safe diagnosticability of Stochastic discrete event systems and determined System, it is shown in Figure 13, including：
Probabilistic automata determining module 11, for determining automatic machine corresponding with Stochastic discrete event systems, obtain random Automatic machine；
Error-free automatic machine creation module 12, it is corresponding with probabilistic automata for representing Random Discrete event system for creating The automatic machine of the specification normative language of system, obtain error-free automatic machine；Wherein, specification normative language be Stochastic discrete event systems in non-faulting Language corresponding to event；
Identifier creation module 13, for based on error-free automatic machine, create on illegal language set be used to distinguish at random from The identifier for forbidding event string of event system is dissipated, obtains illegal speech recognizer；
Safety verification device creation module 14, for based on illegal speech recognizer, creating corresponding validator, obtaining safety Validator；
Necessary and sufficient condition determining module 15, it is corresponding with safety verification device for judging Random Discrete event system for determining The whether safe diagnosable necessary and sufficient condition of system；
The diagnosable judge module 16 of safety, for according to safety verification device and necessary and sufficient condition, judging Random Discrete event Whether safety is diagnosable for system, obtains corresponding result of determination.
Wherein, the expression formula of above-mentioned probabilistic automata, it is specially：
G=(X, Σ, ηG,x0)；
In formula, X represents the finite state collection of Stochastic discrete event systems, x0Represent the initial shape of Stochastic discrete event systems State, Σ expression Stochastic discrete event systems include observable event set ΣoNot observable event set ΣuoDefinite event Collection, ηG：X × Σ × X → [0,1] represents the partial status transition function of Stochastic discrete event systems：For x, x ' ∈ X and σ ∈ Σ, ηG(x, σ, x ') represents that Stochastic discrete event systems occur in the event σ that state is x and are transferred to state x ' probability；
In addition, the expression formula of above-mentioned error-free automatic machine, is specially：
H=(X ', Σ ', ηH,δH,x0)；
In formula,For finite state collection,For definite event collection, ΣfRepresent event of failure Collection, the event that event of failure is concentrated are not observable event；ηH:X ' × Σ ' × X ' → [0,1] is state transition probability letter Number：To x, x ' ∈ X ' and σ ∈ Σ ', if ηG(x, σ, x ') ＞ 0, then ηH(x, σ, x ')=ηG(x,σ,x′)；δH:X′×Σ′→ X ' is state transition function：To x, x ' ∈ X ' and σ ∈ Σ ', δH(x, σ)=x ' and if only if ηH(x, σ, x ') ＞ 0；To any x ' ∈ X, if ω ∈ Σ be present*So thatAnd ηG(x0, ω, x ') and ＞ 0, then x ' ∈ X ', wherein, Σ*Represent definite event collection Σ The set of upper all definite event strings；
Secondly, the expression formula of above-mentioned illegal speech recognizer, it is specially：
Gr=(Qr,Σ,ηr,δr,p0)；
In formula,Finite state collection is represented, LB={ N, F, B } represents to forbid event string ΓiOn label Collection, i=1,2 ... m, wherein, N tag representations are not carried out event of failure；F tag representations have been carried out event of failure, but Event of failure is also not carried out Γ after occurringiIn forbid event string；B tag representations have been carried out event of failure, and in failure Event performs Γ again after occurringiIn forbid event string；Original state p0=(x0,N)∈Qr；ηr:Qr×Σ×Qr→[0,1] For partial status transition function, and ηr(pi,σ,pj)=ηG(xi,σ,xj), wherein, pi=(xi,lbi), pj=(xj,lbj) ∈Qr, σ ∈ Σ；δr:Qr×Σ→QrFor partial status transfer function, it is assumed that pi=(xi,lbi)∈Qr, lbi∈ LB, σ ∈ Σ and δG(xi,σ,xj) be defined, then：
Also, δr(pi, s σ) and=δr(δr(pi, s), σ), s ∈ Σ*；
Further, the expression formula of above-mentioned safety verification device, it is specially：
Gv=(Qv,Σo,δv,ηv,q0)；
In formula, q0=(x0,N,y0) represent original state；ΣoRepresent observable event set；QvFinite state collection is represented, andWherein, Y=X ' ∪ { E }, E is expressed as sky；ηv:Qv×Σo×Qv→[0,1]2It is partial status transition probability Function, it is rightq2=(x2,lb2,y2)∈Qv, σ ∈ Σo, ηv(q1,σ,q2)=(θ, θ ') ＞ 0, wherein,
δv:Qv×Σo→QvFor partial status transfer function；
In formula, q1=(x1,lb1,y1)∈Qv, σ ∈ Σo, s ∈ Lσ(G,x1), p1=(x1,lb1)∈Qr, state E represent exist In error-free automatic machine H, state y1Do not shifted by considerable event σ；
In safety verification device GvIn, for a reachable state qi=(xi,lbi,yi)∈QvIf lbi=N, then claim the shape State qiFor normal condition, it is designated asIf lbi=B, then claim state qiFor B state, it is designated asIf lbi=F, and yi≠ E, then Claim state qiFor malfunction, it is designated asIf in safety verification device GvIn, existence qk,qk+1,qk+2,...ql∈Qv, thing Part σk,σk+1,σk+2,...σl∈Σo, 0≤k≤l so that：
Then claim status switch qk,qk+1,qk+2,...ql∈QvA ring is formd, is denoted as cl=(qk,qk+1,qk+2, ...ql)；By event string scl=σkσk+1...σl, from state qkTo state qlTransition probability be ring cl transition probability, Specially：
The set of state is designated as in ring：Cl '={ qk,qk+1,qk+2,...ql}；Assuming that cl=(qk,qk+1,qk+2,...ql) For random security validator GvIn a ring, its transition probabilityIfAndThen state ring cl is often to return B state ring
In the present embodiment, above-mentioned necessary and sufficient condition, it is specially：
Safety verification device GvIn be not presentSo that δv(q1, σ) and=q2, δv (q2, α) and=q3, wherein σ ∈ ∑so, α ∈ ∑s*。
More specifically, the diagnosable judge module of above-mentioned safety, it is single that digraph structural unit, digraph traversal can be included Member, recurrence find unit and recurrence finds cycling element；Wherein：
Digraph structural unit, for constructing safety verification device GvDigraph D G=(VDG,EDG)；Wherein, vertex set VDG With side collection EDGIt is defined respectively as：
VDG={ (xi,lbi,yi)∈Qv}；
EDG={ (v, w, θ):v,w∈Qv, andSo that θ=ηv(v, σ, w) ＞ 0 }；
Digraph Traversal Unit, for traveling through digraph D G, find the ring that B labels are contained on all summits, and summit in ring Between side θ=1, if the ring is not present, judges that Stochastic discrete event systems are diagnosable safely, and terminate；Otherwise will traversal The set V obtained afterwardsBIn first summit be defined as current summit to be verified；
Recurrence finds unit, for from set VBCurrent summit to be verified set out, recurrence finds a summit thereon, until Untill finding the representative points that first label is not B, the representative points are designated as m=(x, lb, y) ∈ VDGIf the target top Label lb=N or lb=F and y ≠ E in point, then it is not that safety is diagnosable to judge Stochastic discrete event systems, and is terminated； Otherwise start recurrence and find cycling element；
Recurrence finds cycling element, for will set VBIn next summit be defined as current summit to be verified, open again Dynamic recurrence finds unit, if there is no label lb=N or lb=F and y ≠ E representative points, then judges Random Discrete thing Part system is diagnosable safely, and terminates.
It can be seen that in the embodiment of the present invention, time complexity corresponding to the process of above-mentioned establishment safety verification device and it is based on The time complexity of the diagnosable deterministic process of the safety of above-mentioned safety verification device is polynomial time, so in the present invention The time complexity of safe diagnosticability determination process is also polynomial time, and the time complexity of prior art is then Exponential time, it is seen then that the embodiment of the present invention can further reduce the complexity of Stochastic discrete event systems security diagnostics, so as to Improve safety failure diagnosis efficiency.
Finally, it is to be noted that, herein, such as first and second or the like relational terms be used merely to by One entity or operation make a distinction with another entity or operation, and not necessarily require or imply these entities or operation Between any this actual relation or order be present.Moreover, term " comprising ", "comprising" or its any other variant meaning Covering including for nonexcludability, so that process, method, article or equipment including a series of elements not only include that A little key elements, but also the other element including being not expressly set out, or also include for this process, method, article or The intrinsic key element of equipment.In the absence of more restrictions, the key element limited by sentence "including a ...", is not arranged Except other identical element in the process including the key element, method, article or equipment being also present.
A kind of safe diagnosability determination method of Stochastic discrete event systems provided by the present invention and system are entered above Go and be discussed in detail, specific case used herein is set forth to the principle and embodiment of the present invention, and the above is implemented The explanation of example is only intended to help the method and its core concept for understanding the present invention；Meanwhile for the general technology people of this area Member, according to the thought of the present invention, there will be changes in specific embodiments and applications, in summary, this explanation Book content should not be construed as limiting the invention.

Claims (10)

  1. A kind of 1. safe diagnosability determination method of Stochastic discrete event systems, it is characterised in that including：
    It is determined that automatic machine corresponding with Stochastic discrete event systems, obtains probabilistic automata；
    The automatic machine for being used to represent the specification normative language of the Stochastic discrete event systems corresponding with the probabilistic automata is created, Obtain error-free automatic machine；Wherein, the specification normative language is language corresponding with non-faulting event in the Stochastic discrete event systems Speech；
    Based on the error-free automatic machine, create on illegal language set be used to distinguish the Stochastic discrete event systems forbid thing The identifier of part string, obtain illegal speech recognizer；
    Based on the illegal speech recognizer, corresponding validator is created, obtains safety verification device, and is determined and the safety It is used to judge the whether safe diagnosable necessary and sufficient condition of the Stochastic discrete event systems corresponding to validator；
    According to the safety verification device and the necessary and sufficient condition, judge whether the Stochastic discrete event systems can examine safely It is disconnected, obtain corresponding result of determination.
  2. 2. the safe diagnosability determination method of Stochastic discrete event systems according to claim 1, it is characterised in that described The expression formula of probabilistic automata, it is specially：
    G=(X, ∑, ηG,x0)；
    In formula, X represents the finite state collection of the Stochastic discrete event systems, x0Represent the first of the Stochastic discrete event systems Beginning state, the ∑ expression Stochastic discrete event systems include observable event set ∑oNot observable event set ∑uoHave Limit event set, ηG：X × ∑ × X → [0,1] represents the partial status transition function of the Stochastic discrete event systems：It is right In x, x ' ∈ X and σ ∈ ∑s, ηG(x, σ, x ') represents that the Stochastic discrete event systems occur and shifted in the event σ that state is x To state x ' probability.
  3. 3. the safe diagnosability determination method of Stochastic discrete event systems according to claim 2, it is characterised in that described The expression formula of error-free automatic machine, it is specially：
    H=(X ', ∑ ', ηH,δH,x0)；
    In formula,For finite state collection,For definite event collection, ∑fEvent of failure collection is represented, it is described The event that event of failure is concentrated is not observable event；ηH:X ' × ∑ ' × X ' → [0,1] is state transition probability function：It is right X, x ' ∈ X ' and σ ∈ ∑s ', if ηG(x, σ, x ') ＞ 0, then ηH(x, σ, x ')=ηG(x,σ,x′)；δH:X ' × ∑ ' → X ' are shape State transfer function：To x, x ' ∈ X ' and σ ∈ ∑ ', δH(x, σ)=x ' and if only if ηH(x, σ, x ') ＞ 0；To any x ' ∈ X, if ω ∈ ∑s be present*So thatAnd ηG(x0, ω, x ') and ＞ 0, then x ' ∈ X ', wherein, ∑*Represent own on definite event collection ∑ The set of definite event string.
  4. 4. the safe diagnosability determination method of Stochastic discrete event systems according to claim 3, it is characterised in that described The expression formula of illegal speech recognizer, it is specially：
    Gr=(Qr,∑,ηr,δr,p0)；
    In formula,Finite state collection is represented, LB={ N, F, B } represents to forbid event string ΓiOn tally set, i= 1,2 ... m, wherein, N tag representations are not carried out event of failure；F tag representations have been carried out event of failure, but in failure thing Part is also not carried out Γ after occurringiIn forbid event string；B tag representations have been carried out event of failure, and are sent out in event of failure Γ is performed after life againiIn forbid event string；Original state p0=(x0,N)∈Qr；ηr:Qr×Σ×Qr→ [0,1] is part State transition probability function, and ηr(pi,σ,pj)=ηG(xi,σ,xj), wherein, pi=(xi,lbi), pj=(xj,lbj)∈Qr, σ ∈Σ；δr:Qr×Σ→QrFor partial status transfer function, it is assumed that pi=(xi,lbi)∈Qr, lbi∈ LB, σ ∈ Σ and δG(xi, σ,xj) be defined, then：
    Also, δr(pi, s σ) and=δr(δr(pi, s), σ), s ∈ Σ*。
  5. 5. the safe diagnosability determination method of Stochastic discrete event systems according to claim 4, it is characterised in that described The expression formula of safety verification device, it is specially：
    Gv=(Qv,Σo,δv,ηv,q0)；
    In formula, q0=(x0,N,y0) represent original state；ΣoRepresent observable event set；QvFinite state collection is represented, andWherein, Y=X ' ∪ { E }, E is expressed as sky；ηv:Qv×Σo×Qv→[0,1]2It is partial status transition probability Function, it is rightq2=(x2,lb2,y2)∈Qv, σ ∈ Σo, ηv(q1,σ,q2)=(θ, θ ') ＞ 0, wherein,
    <mrow> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>s</mi> <mo>&amp;Element;</mo> <msub> <mi>L</mi> <mi>&amp;sigma;</mi> </msub> <mrow> <mo>(</mo> <mi>H</mi> <mo>,</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </munder> <msub> <mi>&amp;eta;</mi> <mi>H</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>s</mi> <mo>,</mo> <msub> <mi>y</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>&amp;theta;</mi> <mo>=</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>s</mi> <mo>&amp;Element;</mo> <msub> <mi>L</mi> <mi>&amp;sigma;</mi> </msub> <mrow> <mo>(</mo> <mi>G</mi> <mo>,</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </munder> <msub> <mi>&amp;eta;</mi> <mi>G</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>s</mi> <mo>,</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
    δv:Qv×Σo→QvFor partial status transfer function；
    In formula, q1=(x1,lb1,y1)∈Qv, σ ∈ Σo, s ∈ Lσ(G,x1), p1=(x1,lb1)∈Qr, state E expressions are described In error-free automatic machine H, state y1Do not shifted by considerable event σ；
    In the safety verification device GvIn, for a reachable state qi=(xi,lbi,yi)∈QvIf lbi=N, then claim the state qiFor normal condition, it is designated asIf lbi=B, then claim state qiFor B state, it is designated asIf lbi=F, and yi≠ E, then claim State qiFor malfunction, it is designated asIf in safety verification device GvIn, existence qk,qk+1,qk+2,...ql∈Qv, event σk,σk+1,σk+2,...σl∈Σo, 0≤k≤l so that：
    Then claim status switch qk,qk+1,qk+2,...ql∈QvA ring is formd, is denoted as cl=(qk,qk+1,qk+2,...ql)； By event string scl=σkσk+1...σl, from state qkTo state qlTransition probability be ring cl transition probability, be specially：
    The set of state is designated as in ring：Cl '={ qk,qk+1,qk+2,...ql}；Assuming that cl=(qk,qk+1,qk+2,...ql) it is random Safety verification device GvIn a ring, its transition probabilityIf(k≤i≤l) andThen state ring cl is often to return B state ring
  6. 6. the safe diagnosability determination method of Stochastic discrete event systems according to claim 5, it is characterised in that described Necessary and sufficient condition, it is specially：
    The safety verification device GvIn be not presentSo that δv(q1, σ) and=q2, δv(q2, α)=q3, wherein σ ∈ ∑so, α ∈ ∑s*。
  7. 7. the safe diagnosability determination method of Stochastic discrete event systems according to claim 6, it is characterised in that described According to the safety verification device and the necessary and sufficient condition, judging the Stochastic discrete event systems, whether safety is diagnosable, obtains To the process of corresponding result of determination, including：
    A1：Construct the safety verification device GvDigraph D G=(VDG,EDG)；Wherein, vertex set VDGWith side collection EDGDefine respectively It is as follows：
    VDG={ (xi,lbi,yi)∈Qv}；
    EDG={ (v, w, θ):v,w∈Qv, andSo that θ=ηv(v, σ, w) ＞ 0 }；
    A2：Travel through the digraph D G, find the ring that B labels are contained on all summits, and in ring between summit side θ=1, if should Ring is not present, then judges that the Stochastic discrete event systems are diagnosable safely, and terminate；Otherwise the set V that will be obtained after traversalB In first summit be defined as current summit to be verified；
    A3：From the set VBCurrent summit to be verified set out, recurrence finds a summit thereon, until finding first label Untill for B representative points, the representative points are designated as m=(x, lb, y) ∈ VDGIf in the representative points label lb=N or Person lb=F and y ≠ E, then it is not that safety is diagnosable to judge the Stochastic discrete event systems, and is terminated；Otherwise step is entered Rapid A4；
    Step A4：By the set VBIn next summit be defined as current summit to be verified, step A3 is reentered, if not Label lb=N or lb=F and y ≠ E representative points be present, then judge that the Stochastic discrete event systems are diagnosable safely, And terminate.
  8. 8. a kind of safe diagnosticability of Stochastic discrete event systems determines system, it is characterised in that including：
    Probabilistic automata determining module, for determining automatic machine corresponding with Stochastic discrete event systems, obtain probabilistic automata；
    Error-free automatic machine creation module, it is corresponding with the probabilistic automata for representing the Random Discrete event for creating The automatic machine of the specification normative language of system, obtain error-free automatic machine；Wherein, the specification normative language is the Stochastic discrete event systems In language corresponding with non-faulting event；
    Identifier creation module, for based on the error-free automatic machine, creating described random for distinguishing on illegal language set The identifier for forbidding event string of discrete event system, obtains illegal speech recognizer；
    Safety verification device creation module, for based on the illegal speech recognizer, creating corresponding validator, being tested safely Demonstrate,prove device；
    Necessary and sufficient condition determining module, it is corresponding with the safety verification device for judging the Random Discrete event for determining The whether safe diagnosable necessary and sufficient condition of system；
    The diagnosable judge module of safety, for according to the safety verification device and the necessary and sufficient condition, judge it is described at random from Whether safety is diagnosable for scattered event system, obtains corresponding result of determination.
  9. 9. the safe diagnosticability of Stochastic discrete event systems according to claim 8 determines system, it is characterised in that
    The expression formula of the probabilistic automata, it is specially：
    G=(X, ∑, ηG,x0)；
    In formula, X represents the finite state collection of the Stochastic discrete event systems, x0Represent the first of the Stochastic discrete event systems Beginning state, the ∑ expression Stochastic discrete event systems include observable event set ΣoNot observable event set ΣuoHave Limit event set, ηG：X × Σ × X → [0,1] represents the partial status transition function of the Stochastic discrete event systems：It is right In x, x ' ∈ X and σ ∈ Σ, ηG(x, σ, x ') represents that the Stochastic discrete event systems occur and shifted in the event σ that state is x To state x ' probability；
    The expression formula of the error-free automatic machine, it is specially：
    H=(X ', Σ ', ηH,δH,x0)；
    In formula,For finite state collection,For definite event collection, ΣfEvent of failure collection is represented, it is described The event that event of failure is concentrated is not observable event；ηH:X ' × Σ ' × X ' → [0,1] is state transition probability function：It is right X, x ' ∈ X ' and σ ∈ Σ ', if ηG(x, σ, x ') ＞ 0, then ηH(x, σ, x ')=ηG(x,σ,x′)；δH:X ' × Σ ' → X ' is shape State transfer function：To x, x ' ∈ X ' and σ ∈ Σ ', δH(x, σ)=x ' and if only if ηH(x, σ, x ') ＞ 0；To any x ' ∈ X, if ω ∈ Σ be present*So thatAnd ηG(x0, ω, x ') and ＞ 0, then x ' ∈ X ', wherein, Σ*Represent own on definite event collection Σ The set of definite event string；
    The expression formula of the illegal speech recognizer, it is specially：
    Gr=(Qr,Σ,ηr,δr,p0)；
    In formula,Finite state collection is represented, LB={ N, F, B } represents to forbid event string ΓiOn tally set, i= 1,2 ... m, wherein, N tag representations are not carried out event of failure；F tag representations have been carried out event of failure, but in failure thing Part is also not carried out Γ after occurringiIn forbid event string；B tag representations have been carried out event of failure, and are sent out in event of failure Γ is performed after life againiIn forbid event string；Original state p0=(x0,N)∈Qr；ηr:Qr×Σ×Qr→ [0,1] is part State transition probability function, and ηr(pi,σ,pj)=ηG(xi,σ,xj), wherein, pi=(xi,lbi), pj=(xj,lbj)∈Qr, σ ∈∑；δr:Qr×∑→QrFor partial status transfer function, it is assumed that pi=(xi,lbi)∈Qr, lbi∈ LB, σ ∈ Σ and δG(xi, σ,xj) be defined, then：
    Also, δr(pi, s σ) and=δr(δr(pi, s), σ), s ∈ Σ*；
    The expression formula of the safety verification device, it is specially：
    Gv=(Qv,Σo,δv,ηv,q0)；
    In formula, q0=(x0,N,y0) represent original state；ΣoRepresent observable event set；QvFinite state collection is represented, andWherein, Y=X ' ∪ { E }, E is expressed as sky；ηv:Qv×Σo×Qv→[0,1]2It is partial status transition probability Function, it is rightq2=(x2,lb2,y2)∈Qv, σ ∈ Σo, ηv(q1,σ,q2)=(θ, θ ') ＞ 0, wherein,
    <mrow> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>s</mi> <mo>&amp;Element;</mo> <msub> <mi>L</mi> <mi>&amp;sigma;</mi> </msub> <mrow> <mo>(</mo> <mi>H</mi> <mo>,</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </munder> <msub> <mi>&amp;eta;</mi> <mi>H</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>s</mi> <mo>,</mo> <msub> <mi>y</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>&amp;theta;</mi> <mo>=</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>s</mi> <mo>&amp;Element;</mo> <msub> <mi>L</mi> <mi>&amp;sigma;</mi> </msub> <mrow> <mo>(</mo> <mi>G</mi> <mo>,</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </munder> <msub> <mi>&amp;eta;</mi> <mi>G</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>s</mi> <mo>,</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
    δv:Qv×Σo→QvFor partial status transfer function；
    In formula, q1=(x1,lb1,y1)∈Qv, σ ∈ Σo, s ∈ Lσ(G,x1), p1=(x1,lb1)∈Qr, state E expressions are described In error-free automatic machine H, state y1Do not shifted by considerable event σ；
    In the safety verification device GvIn, for a reachable state qi=(xi,lbi,yi)∈QvIf lbi=N, then claim the state qiFor normal condition, it is designated asIf lbi=B, then claim state qiFor B state, it is designated asIf lbi=F, and yi≠ E, then claim State qiFor malfunction, it is designated asIf in safety verification device GvIn, existence qk,qk+1,qk+2,...ql∈Qv, event σk,σk+1,σk+2,...σl∈Σo, 0≤k≤l so that：
    Then claim status switch qk,qk+1,qk+2,...ql∈QvA ring is formd, is denoted as cl=(qk,qk+1,qk+2,...ql)； By event string scl=σkσk+1...σl, from state qkTo state qlTransition probability be ring cl transition probability, be specially：
    The set of state is designated as in ring：Cl '={ qk,qk+1,qk+2,...ql}；Assuming that cl=(qk,qk+1,qk+2,...ql) it is random Safety verification device GvIn a ring, its transition probabilityIf(k≤i≤l) andThen state ring cl is often to return B state ring
    The necessary and sufficient condition, it is specially：
    The safety verification device GvIn be not presentSo that δv(q1, σ) and=q2, δv(q2, α)=q3, wherein σ ∈ ∑so, α ∈ Σ*。
  10. 10. the safe diagnosticability of Stochastic discrete event systems according to claim 9 determines system, it is characterised in that institute The diagnosable judge module of safety is stated, including digraph structural unit, digraph Traversal Unit, recurrence find unit and recurrence is found Cycling element；Wherein：
    The digraph structural unit, for constructing the safety verification device GvDigraph D G=(VDG,EDG)；Wherein, summit Collect VDGWith side collection EDGIt is defined respectively as：
    VDG={ (xi,lbi,yi)∈Qv}；
    EDG={ (v, w, θ):v,w∈Qv, andSo that θ=ηv(v, σ, w) ＞ 0 }；
    The digraph Traversal Unit, for traveling through the digraph D G, the ring that B labels are contained on all summits is found, and in ring θ=1 on side between summit, if the ring is not present, judge that the Stochastic discrete event systems are diagnosable safely, and terminate；It is no The set V that will then be obtained after traversalBIn first summit be defined as current summit to be verified；
    The recurrence finds unit, for from the set VBCurrent summit to be verified set out, recurrence finds a summit thereon, Untill finding the representative points that first label is not B, the representative points are designated as m=(x, lb, y) ∈ VDGIf the mesh Label lb=N or lb=F and y ≠ E in summit are marked, then it is not that safety is diagnosable to judge the Stochastic discrete event systems , and terminate；Otherwise start the recurrence and find cycling element；
    The recurrence finds cycling element, for by the set VBIn next summit be defined as current summit to be verified, again Start the recurrence and find unit, if there is no label lb=N or lb=F and y ≠ E representative points, then judge described in Stochastic discrete event systems are diagnosable safely, and terminate.
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Cited By (5)

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Publication number Priority date Publication date Assignee Title
CN108804771A (en) * 2018-05-22 2018-11-13 同济大学 Discrete event system method for analyzing and designing human-computer interaction logic
CN109725528A (en) * 2018-11-13 2019-05-07 广东工业大学 The failure predictability detection method and failure predictor of discrete event system
CN109977581A (en) * 2019-04-04 2019-07-05 长春理工大学 A kind of Stochastic discrete event systems mode diagnosticability determination method
CN111209516A (en) * 2020-01-06 2020-05-29 广东工业大学 Discrete event system mode fault online diagnosis method based on Petri network diagnoser
CN113098871A (en) * 2021-04-02 2021-07-09 西安电子科技大学 Method for guaranteeing system security

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108804771A (en) * 2018-05-22 2018-11-13 同济大学 Discrete event system method for analyzing and designing human-computer interaction logic
CN108804771B (en) * 2018-05-22 2022-05-13 同济大学 Discrete event system method for analyzing and designing human-computer interaction logic
CN109725528A (en) * 2018-11-13 2019-05-07 广东工业大学 The failure predictability detection method and failure predictor of discrete event system
CN109977581A (en) * 2019-04-04 2019-07-05 长春理工大学 A kind of Stochastic discrete event systems mode diagnosticability determination method
CN111209516A (en) * 2020-01-06 2020-05-29 广东工业大学 Discrete event system mode fault online diagnosis method based on Petri network diagnoser
CN111209516B (en) * 2020-01-06 2023-04-28 广东工业大学 Discrete event system mode fault online diagnosis method based on Petri network diagnostor
CN113098871A (en) * 2021-04-02 2021-07-09 西安电子科技大学 Method for guaranteeing system security

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