CN103699762B - A kind of CPS attribute verification method based on statistical model detection - Google Patents
A kind of CPS attribute verification method based on statistical model detection Download PDFInfo
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Abstract
A kind of CPS attribute verification method based on statistical model detection, comprises the following steps.S1, COM1 is set expands to hybrid automata extend hybrid automata, and obtain the track that CPS model is run by described extension hybrid automata.S2, it is configured to produce the monitor of the track sample of described CPS model running, and the track sample generated by described monitor is as the input in SMC statistical testing of business cycles stage.S3, use statistical estimation technology are collected described CPS model and are met the evidence of particular community, and use the second algorithm preset to judge whether CPS model meets described particular community.
Description
Technical field
The invention belongs to Internet of Things and CPS field, be specifically related to model inspection technology and statistical estimation technology, especially one
Plant CPS attribute verification method based on statistical model detection.
Background technology
Along with the development of embedded technology, computer technology and network technology, and hardware product performance and data
The continuous lifting of disposal ability, computer system gradually tends to information-based, intelligent.Under this demand, information physical melts
Assembly system (Cyber-Physical Systems, CPS) arises at the historic moment as a kind of novel intelligent system, and causes various countries
The great attention of government, academia and industrial quarters.
CPS is the complicated Embedded network system having merged calculating and physics process, and it passes through embedded system and network
Physical equipment it is monitored and controls, and being influenced each other by feedback mechanism.In future, CPS is important by being widely used in
The numerous areas such as the monitoring of infrastructure and control, Defense Weapon System, health care and intelligent transportation, thus it is guaranteed that CPS
Safe and reliable extremely important.Owing to uncertainty and the physical equipment itself of physical environment may be out of order, so ensureing whole
The vigorousness of individual CPS and safety are important challenges.
There are some methods that CPS system is verified, such as software test etc. at present.Although software test can be necessarily
Ensure the reliability of system in degree, but the most obvious mistake can only be found, and can only be in the later stage of software development
Just can carry out, there is certain limitation.
Just can be able to find in design in the design phase of system it practice, use formal method that system carries out checking
Mistake, thus later stage be effectively ensured everything goes well with your work and carry out, greatly reduce the cost of software development.Model inspection technology is
A kind of the more commonly used formalization method, it has supermatic feature, and it is tested by the state space of Ergodic Theory
Whether model of a syndrome meets specific attitude layer.Model inspection typically requires three steps, i.e. modeling, stipulations and checking: system modelling
(Modeling) it is by system is carried out abstract, sets up the formalized model of system, be generally modeled as state transition system, M=
<L,T,S>.Requirements specification (Specification) is demand temporal logic formula formalization representation system must being fulfilled for
Become φ.Modelling verification (Verification) is to given system model M, system property stipulations φ, is calculated by certain checking
Method comes whether judgment models M meets attribute φ, i.e. M ' φ.
At present, to be that the state space by Ergodic Theory verifies whether system meets specific for common model inspection technology
Attribute, thus limited by the size of system state space, i.e. faced State-explosion problem.And CPS in reality
System state space is the biggest, and uncertainty and the equipment itself of adding physical environment may be out of order, thus traditional
CPS is verified and just seems and be pale and weak by model inspection technology.
Statistical model detection (Statistical Model Checking, SMC) is that the one checking being recently proposed is large-scale
Complication system new technique.The core concept of SMC is the emulation that structure system performs, and is then sentenced by the method for statistical estimation technology
Determine whether system meets specific attribute with a certain confidence level.
Although CPS has caused extensive concern both domestic and external, but the research being because being correlated with is at the early-stage, is taken at present
The achievement in research obtained is fairly limited, presently, there are following CPS attribute verification methods.
The Ptolemy engineering of California, USA university Edward professor A.Lee leader, studies system concurrent, real-time, embedded
System modeling, emulate and design.Its main focus is the combination of concurrent assembly, and cardinal principle is: by multiple computation model
Carry out stratification combination, to solve the problem that Heterogeneous Computing model is used in mixed way.But these work focus primarily upon building of CPS
Mould and emulation, the checking to the attribute of CPS relates to less.Additionally, Li Lihang etc. are with Timed Automata as instrument, will supervise respectively
The physical entity surveyed and control and different types of service Independent modeling, and time attribute is verified.Owing to CPS is soft
Part and the closely-coupled feature of hardware, the restriction of the ability to express of Timed Automata, it is therefore desirable to the model that ability to express is higher.
SMC is initially to be proposed by Younes and utilize acceptance sampling to verify the attribute of discrete event system, and opens
Send out statistical model detection model detector, discussed the error control in statistical model detection, have studied about unbounded until
The statistical testing of business cycles problem of operator attribute.In these work, the model used is CTMC, DTMC and MDP, due to CPS originally
The feature of body, uses these models the most difficult to CPS modeling.
Bayesian statistic student movement is used in the statistical model detection of stochastic system by Paolo Zuliani etc., utilizes coupling
It is quick-fried that theoretical (Coupling) and importance sampling technical research statistical model detects the calculating time caused due to rare event
Fried problem.Importance sampling and mutual entropy technique are applied to solve statistical model detection calculating time blast by the researcheres such as Clarke
Problem, has carried out extension and has made it support uncertain sight, and be applied to partial order yojan comprise pseudo-probabilistic mould SMC
Type.
In the middle of research in terms of above-mentioned various CPS attribute checkings, all make significant headway, but there is also
Not enough: first, there is part work to be primarily upon the modeling and simulation of CPS, and the verification of correctness of CPS attribute is studied less；
Secondly, in current statistical model detection algorithm, the model of employing is CTMC, DTMC and MDP mostly, due to CPS's itself
Feature, these models can not well be expressed.
In view of the foregoing, the present invention provides a kind of CPS attribute verification method based on statistical model detection, mainly uses
CPS is modeled by the hybrid automata network of extension, reconstructs the sample that model inspection needs, and designs one and blend together automatically
The statistical model detection algorithm of machine network, in order to verify the correctness of CPS attribute.
Summary of the invention
The present invention provides a kind of CPS attribute verification method based on statistical model detection, comprises the following steps:
S1, COM1 is set hybrid automata expands to extend hybrid automata, and obtain CPS model by described
The track that extension hybrid automata runs；
S2, it is configured to produce the monitor of the track sample of described CPS model running, and described monitor is generated
Track sample is as the input in SMC statistical testing of business cycles stage；
S3, use statistical estimation technology are collected described CPS model and are met the evidence of particular community, and use second preset
Algorithm judges whether CPS model meets described particular community.
Preferably, in step sl, described COM1 is tuple Port=<pid,value,dom,options>, its
In, pid is the unique identifier of port, and value is the data of port, and dom is the data type of message communicating, and options is
Port is allowed the set of the operation carried out.
Preferably, in step sl, described extension hybrid automata is expressed as EHA=<HA, P>, wherein, HA is for blending together certainly
Motivation and described HA=<Loc, Var, Lab, E, Act, Inv>, P={p1,p2,…,pnIt it is the collection of all ports associated with HA
Close.
Preferably, in step s 2, the first algorithm that described monitor is arranged according to self generates track sample, and described
Discrete event all of in CPS system is monitored by monitor.
Preferably, the particular community that the CPS model described in step S3 need to meet, use probability linear time temporal logic to retouch
State.
Preferably, described step S3 uses Bayesian statistical model detection method to carry out CPS attribute checking.
Preferably, in step s3, if CPS model is M, σ is arbitrary execution track of M, φ is CPS attribute to be verified
Formula, θ ∈ (0,1) is probability threshold value, and p represents that the track that performs of M meets the probability of equation φ, then when meeting M ' P≥θ(φ), i.e.
During p >=θ, complete attribute checking.
The CPS attribute verification method based on statistical model detection provided according to the present invention, will by arranging COM1
After hybrid automata expands to extend hybrid automata, obtain the track that CPS model is run by extension hybrid automata, right
CPS has made and having described more accurately.Meanwhile, construct the monitor track sample with generation CPS model running, in this, as
The input in SMC statistical testing of business cycles stage, and use statistical estimation technology collection CPS model to meet the evidence of particular community, to judge
Whether CPS model meets particular community.So, effectively prevent the bottleneck of conventional model detection technique, and the system brought
State-explosion problem.
Accompanying drawing explanation
In order to be illustrated more clearly that the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing
In having technology to describe, the required accompanying drawing used is briefly described, it should be apparent that, the accompanying drawing in describing below is only this
Some embodiments of invention, for those of ordinary skill in the art, on the premise of not paying creative work, it is also possible to
Other accompanying drawing is obtained according to these accompanying drawings.
Fig. 1 is the CPS attribute verification method flow chart based on statistical model detection that present pre-ferred embodiments provides；
Fig. 2 is the hybrid automata model schematic of the thermostat that present pre-ferred embodiments provides；
Fig. 3 is the CPS software attributes validation framework schematic diagram that present pre-ferred embodiments provides.
Detailed description of the invention
Below with reference to accompanying drawing and describe the present invention in detail in conjunction with the embodiments.It should be noted that do not conflicting
In the case of, the embodiment in the application and the feature in embodiment can be mutually combined.
Fig. 1 is the CPS attribute verification method flow chart based on statistical model detection that present pre-ferred embodiments provides.As
Shown in Fig. 1, present pre-ferred embodiments provide based on statistical model detection CPS attribute verification method include step S1～
S3。
Step S1: COM1 is set and expands to hybrid automata extend hybrid automata, and obtain CPS model and pass through
The track that described extension hybrid automata runs.
Specifically, hybrid automata is a kind of to be described discrete and continuous dynamic system shape by what Alur proposed simultaneously
Formula model.Hybrid automata adds the extension of one group of variable on the basis of finite automata, its position
(location) representing the successional evolution of system, its conversion (transition) represents the discrete transition of system mode.
Fig. 2 is the hybrid automata model schematic of the thermostat that present pre-ferred embodiments provides.As in figure 2 it is shown, generally with oriented
Figure represents hybrid automata, uses vertex representation position, represents discrete migration with limit.
Generally, hybrid automata HA is a hexa-atomic group of HA=<Loc, Var, Lab, E, Act, Inv>, wherein: Loc is top
The set of point, is called position (location)；Var is the set of real-valued variable, and variable x is entered as function v (x): Var → R,
By variable mappings to real number value, representing the set of all assignment with V, the state of hybrid automata is<l, v>, wherein l ∈ Loc, v
∈ V, represents the set of all states with ∑；Lab is the set of sync tag；E is the set on limit, limit e=<l, a, μ, l'>comprise
Source position l ∈ Loc and target location l' ∈ Loc, sync tag a ∈ Lab, transformational relation μ ∈ V × V；Labeling function Act is every
Individual position l ∈ Loc labelling a series of activity (activity) function Act (l): R≥0→ V, is mapped to the function of V by time t；Mark
Note function Inv give each position one invariant Inv (l) ∈ V of l ∈ Loc labelling2。
In CPS, each assembly also non-fully isolates, and they are the unified entirety connected each other.Therefore, can be more accurately
Describe CPS, need classical hybrid automata is extended.The concept that the present embodiment is provided with COM1 is different by CPS
Part connects, and is described in detail below.
Described COM1 is tuple Port=<pid,value,dom,options>, wherein, pid is unique mark of port
Knowing symbol, value is the data of port, and dom is the data type of message communicating, and options is allowed the operation carried out by port
Set.
Described COM1 only allows to carry out two kinds of operation Read and Write.For example, sensor COM1 and biography
That one end that sensor is connected can carry out Read and Write operation, and this one end being connected with computing unit then can only be carried out
Read operates.Its operation format is such as shown in table 1:
Table 1
In the present embodiment, described extension hybrid automata is expressed as EHA=<HA, P>, wherein, HA is hybrid automata, and
Described HA=<Loc, Var, Lab, E, Act, Inv>, P={p1,p2,…,pnIt it is the set of all ports associated with HA.Generally,
The track that once performs of hybrid automata is a limited or unlimited sequenceWherein σi=<li,ti>,
li∈ Loc, ti>=0 represents at position liResidence time.
Step S2: be configured to produce the monitor of the track sample of described CPS model running, and described monitor is raw
The track sample become is as the input in SMC statistical testing of business cycles stage.
Specifically, the core concept of SMC is by emulating system to obtain the execution sample of system, then utilizing
The execution sample collected is analyzed by statistical estimation technology, whether meets specific genus with a certain confidence level with decision-making system
Property.The sample that execution to the hybrid automata that the present invention uses, i.e. system perform below produces process and makes an explanation.
Wherein, the validation problem of stochastic system M and logical formula φ seeks to calculate the probability of M ' φ.Solve this kind of at present
The method of problem mainly has two classes: numerical method and statistical method (such as SMC).The method of numerical value is generally of very pinpoint accuracy,
But limited by state space size.SMC regards statistical inference problem as this validation problem, and utilizes the emulation to model
Path is made reasonably sampling and is solved.Effectively avoid the restriction of system state space size.Fig. 3 is that the present invention is preferable
The CPS software attributes validation framework schematic diagram that embodiment provides.
In SMC, generally use probability linear time temporal logic (Probabilistic Bounded Linear
Temporal Logic, PBLTL) attribute is described by formula, and wherein PBLTL is the extension to LTL.Such as, to model M and
The set Var of real-valued variable, the Boolean-predicate of definition shape such as y～v on Var, wherein y ∈ Var ,～∈≤, >=,=, v ∈
R。
In this, the syntactic definition of BLTL attribute equation φ is:Described
The semanteme of BLTL formula defines on the execution track of M, represents that with σ ' φ the execution track of M meets attribute φ.The present embodiment is used
σiRepresent the suffix of the track σ started from the i-th step, especially, σ0Original track σ can be represented.Variable y is the value of the i-th step in σ
Be expressed as V (σ, i, y).The semanteme of BLTL formula may be interpreted as: σk' y～v, and if only if V (σ, k, y)～v；σk‘φ1∨φ2,
And if only if σk‘φ1Or σk‘φ2；σk‘φ1∧φ2, and if only if σk‘φ1And σk‘φ2；And if only if σk
‘φ1It is false (i.e. σk‘/φ1)；σk‘φ1Utφ2, and if only if exists i ∈ N and makes (1) Σ0≤l≤itk+1≤ t, (2) σk+i
‘φ2, (3) 0≤j≤i, σk+j‘φ1。
Owing to the sample of unlimited execution can not be obtained, and have turned out the limited prefix having only at an execution track
On just can determine that whether track meets attribute equation φ.The length of track prefix is to be determined by the boundary # (φ) of attribute formula.
The boundary # (φ) of BLTL equation φ is defined as follows: # (y～v) :=0；#(φ1∨φ2):=max(#
(φ1),#(φ2))；#(φ1∧φ2):=max(#(φ1),#(φ2))；#(φ1Utφ2):=t+max(#(φ1),#(φ2))。
The definition of above-mentioned PBLTL formula is: it is a kind of P≥θ(φ) formula of form, wherein φ is BLTL formula, and θ
∈ (0,1) is referred to as probability threshold value.Model M meets PBLTL attribute P≥θ(φ) M ' P it is represented by≥θ(φ)。M‘P≥θ(φ) setting up ought
And if only if M's once performs the probability meeting attribute φ more than or equal to θ.The present embodiment only discuss more than or equal to relation (>=), phase
That answers can be by P less than relation<θ(φ)=1-P≥θ(φ) obtain.
The track that SMC uses system model to perform is used as the input in statistical testing of business cycles stage, the most how to obtain model
Performing sample is a critical problem in SMC.The execution sample form for example, (s of CPS model0,t0),(s1,t1),
(s2,t2) ..., wherein si=<li,vi> it is the state of CPS model, tiFor system in state siResidence time.
The present embodiment produces, by design monitor, the track sample that model performs, and described monitor is arranged according to self
The first algorithm generate track sample, and discrete event all of in CPS system monitors, in order to record by described monitor
The change of the state of system.Described first algorithm is as shown in table 2.
Table 2
Step S3: use statistical estimation technology to collect described CPS model and meet the evidence of particular community, and use and preset
Second algorithm judges whether CPS model meets described particular community.
Specifically, as it was previously stated, the particular community that in the present invention, CPS model need to meet, probability linear temporal is used to patrol
Collect and be described.
SMC attempts arbitrary execution track of calculating automaton and meets the Probability p of PBLTL attribute φ.Clarke proposes two kinds
The bayes method of core: interval estimation and hypothesis testing.Two kinds of methods are with the difference of traditional model inspection technology: no
The track meeting φ is not the counter-example of model, but the evidence of p < 1.In this step, use Bayesian statistical model detection method
Carry out CPS attribute checking.
If CPS model is M, σ is arbitrary execution track of M, φ is CPS attribute formula to be verified, and θ ∈ (0,1) is general
Rate threshold value, p represents that the track that performs of M meets the probability of equation φ, then when meeting M ' P≥θ(φ), i.e. during p >=θ, complete attribute and test
Card.Specific explanations is: M ' P≥θ(φ), i.e. want to obtain p >=θ, M ' P≥θ(φ) set up, otherwise M ' P≥θ(φ) it is false.
Assume H respectively0: p >=θ and H1: p < θ, CPS model is performed a sample d={ σ of track1,σ2,σ3... }, with
Machine variable XiRepresent track σiMeeting the result of attribute φ, its value takes 0 or 1, thenOwing to these perform track
It both is from same model, then can obtain one group of independent identically distributed observation { x1,x2,x3,…,xn}.Due to H0With H1Mutual exclusion,
Assume that prior probability has P (H0)+P(H1)=1.According to bayesian theory posterior probability it is:i∈
0,1}, then to each sample d, P (d)=P (d | H0)+P(d|H1) > 0 always set up.
In the present embodiment, define sample d, H0And H1Bayesian Factor beWherein, Bayesian Factor β
Regard support H as0Evidence, it is reciprocalFor supporting H1Evidence.The evidence accepting to assume needs is represented by threshold value T.At present
There is a kind of efficient β computing formulaWherein x is d={x1,x2,…,xnSuccess in }
Sample number, F(s,t)() is the Beta distribution function with s and t as parameter.
In this step, the second algorithm that the statistical model for CPS model detects is as shown in table 3, and σ ' φ therein is permissible
Verify easily.
Table 3
In sum, the CPS attribute verification method based on statistical model detection provided according to present pre-ferred embodiments,
Expand to hybrid automata extend after hybrid automata by arranging COM1, obtain CPS model and blend together oneself by extension
The track that motivation is run, has made CPS and having described more accurately.Meanwhile, structure monitor is to produce the rail of CPS model running
Mark sample, in this, as the input in SMC statistical testing of business cycles stage, and uses statistical estimation technology collection CPS model to meet specified genus
The evidence of property, to judge whether CPS model meets particular community.So, effectively prevent the bottleneck of conventional model detection technique,
And the system state space explosion issues brought.
Described above to the disclosed embodiments, makes professional and technical personnel in the field be capable of or uses the present invention.
Multiple amendment to these embodiments will be apparent from for those skilled in the art, as defined herein
General Principle can realize without departing from the spirit or scope of the present invention in other embodiments.Therefore, the present invention
It is not intended to be limited to embodiment illustrated herein, and is to fit to consistent with principles disclosed herein and features of novelty
The widest scope.Described above to the disclosed embodiments, makes professional and technical personnel in the field be capable of or uses this
Bright.Multiple amendment to these embodiments will be apparent from for those skilled in the art, is determined herein
The General Principle of justice can realize without departing from the spirit or scope of the present invention in other embodiments.Therefore, originally
Invention is not intended to be limited to embodiment illustrated herein, and is to fit to and principles disclosed herein and features of novelty phase one
The widest scope caused.
Claims (7)
1. a CPS attribute verification method based on statistical model detection, it is characterised in that comprise the following steps:
S1, COM1 is set expands to hybrid automata extend hybrid automata, and obtain CPS model by described extension
The track that hybrid automata runs；
S2, it is configured to produce the monitor of the track sample of described CPS model running, and the track generated by described monitor
Sample is as the input in SMC statistical testing of business cycles stage；
S3, use statistical estimation technology are collected described CPS model and are met the evidence of particular community, and use Bayesian statistical model
Detection method judges whether CPS model meets described particular community.
Method the most according to claim 1, it is characterised in that in step sl, described COM1 is tuple Port=
＜ pid, value, dom, options >, wherein, pid is the unique identifier of port, and value is the data of port, and dom is for disappearing
The data type of message communication, options is allowed the set of the operation carried out by port.
Method the most according to claim 1, it is characterised in that in step sl, described extension hybrid automata is expressed as
EHA=＜ HA, P >, wherein, HA is hybrid automata and described HA=＜ Loc, Var, Lab, E, Act, Inv >, P={p1,
p2,…,pnIt it is the set of all ports associated with HA.
Method the most according to claim 1, it is characterised in that in step s 2, described monitor is arranged according to self
First algorithm generates track sample, and discrete event all of in CPS system is monitored by described monitor.
Method the most according to claim 1, it is characterised in that the particular community that the CPS model described in step S3 need to meet,
Probability linear time temporal logic is used to be described.
Method the most according to claim 1, it is characterised in that described step S3 uses Bayesian statistical model detection method
Carry out CPS attribute checking.
Method the most according to claim 1, it is characterised in that in step s3, if CPS model is M, σ is that the arbitrary of M holds
Row track, φ is CPS attribute formula to be verified, and θ ∈ (0,1) is probability threshold value, and P represents that the execution track of M meets equation φ
Probability, then when meeting M ' P >=θ (φ), i.e. during P >=θ, complete attribute checking.
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| CN104951618A (en) * | 2015-07-06 | 2015-09-30 | 广东轻工职业技术学院 | Possibility measurement calculating tree logic detection model optimization method |
| CN109961172B (en) * | 2018-12-28 | 2023-11-03 | 东南大学 | CPS rare event probability prediction method based on statistical model test |
| CN110062009A (en) * | 2019-05-21 | 2019-07-26 | 杭州逍邦网络科技有限公司 | A kind of formalization detection method of information physical emerging system defence |
| CN115801460B (en) * | 2023-01-16 | 2023-04-11 | 四川大学 | Power distribution information physical system security risk assessment method considering network attack vulnerability |
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| CN102426521A (en) * | 2011-10-28 | 2012-04-25 | 东南大学 | CPS (Cyber Physical Systems) adaptability verification method based on Hybrid UML (Unified Modeling Language) and theorem proving |
| CN102436375A (en) * | 2011-10-28 | 2012-05-02 | 东南大学 | Characters per second (CPS) Modeling and verification method based on model transformation |
| CN102722593A (en) * | 2011-10-28 | 2012-10-10 | 东南大学 | Cyber physical system (CPS) attribute verification method based on differential algebra timing sequence dynamic logic (DATL) |
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| CN102426521A (en) * | 2011-10-28 | 2012-04-25 | 东南大学 | CPS (Cyber Physical Systems) adaptability verification method based on Hybrid UML (Unified Modeling Language) and theorem proving |
| CN102436375A (en) * | 2011-10-28 | 2012-05-02 | 东南大学 | Characters per second (CPS) Modeling and verification method based on model transformation |
| CN102722593A (en) * | 2011-10-28 | 2012-10-10 | 东南大学 | Cyber physical system (CPS) attribute verification method based on differential algebra timing sequence dynamic logic (DATL) |
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| US10262143B2 (en) | 2016-09-13 | 2019-04-16 | The Mitre Corporation | System and method for modeling and analyzing the impact of cyber-security events on cyber-physical systems |
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