CN109961172A - A kind of CPS rare event probability forecasting method examined based on statistical model - Google Patents
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Abstract
The invention discloses a kind of CPS rare event probability forecasting methods examined based on statistical model.The invention is based on the statistical model method of inspection, is made of three sampling monitor, specification verification device and probability predictor modules.Specific implementation step includes: sampling monitor using importance random sampling algorithm, carries out random sampling to the CPS system mode characteristic sequence described based on hybrid automata, generates；Specification verification device based on linear temporal can generate the verification result of system visible features status switch and its corresponding specification satisfaction property, and validator can be using verification result as the training sample set of the probability predictor based on HMM hidden markov model；On the basis of by the study of enough sample sets, probability predictor calculates system succeeding state is rare event shape probability of state, and furthermore result output the present invention or is first utilized the function of probabilistic forecasting modified result fallout predictor predictive ability.
Description
Technical field
The invention belongs to information physical system control fields, and in particular to a kind of CPS examined based on statistical model is rare
Probability of happening prediction technique
Background technique
With the gradually development of " industry 4.0 " and " made in China 2025 ", supply, manufacture, sales process in production are all
By information physical system, digitization, informationization quickly, are effectively applied to realize.Information physical system (Cyber-
Physical System) closed-loop path that realizes physical space and information space, being substantially exactly will be various in physical space
Data are transported to information space, and using the information space analysis processing capacity powerful to huge data, searching out be can be realized pair
Distribute the best decision of physical space resource rationally, and by the process of Decision-making Function to physical space in a manner of data.Information
Physical system as novel multi-crossed disciplines research field and there is large-scale, complicated, distributed, time-sensitive etc.
The system of feature, academia and industry remain many challenges to its research.In the research of information physical system
It in the process, is always the key points and difficulties of research to the verifying of safety.
CPS technology needs strong verifying to ensure security of system demand in the application in criticality safety field.It is logical
Often, there are two ways to CPS security verification: non-formalization and formalization method.Informal method according to experimental evidence and
Experience verifies security of system, and emphasis is to be carried out according to specific coverage criterion to system operation to be verified
Sampling, and the agenda of program is compared with expected behavior specified in program specification.Even if but by thoroughly test
Software, wherein still may include mistake；
Formalization method be based on some mathematical theories, such as logic, automatic machine and graph theory, can accurately, without two
Free burial ground for the destitute describes the security attributes of system, and carries out strictly reasoning, guarantees the safety of system.Formal Verification Techniques are main
Including two kinds of technologies: theorem proving (Theorem Proving) and model testing (Model Checking).Theorem proving passes through
Define a series of formalized description principles and specification come to system security requirement or constraint be described, and require each
It individually proves that step can carry out deducting by the original rule of definition to be proven.Although theorem process proves every
One step is all stringent, but the decision of each proof procedure depends on the experience of researcher, intuition and insight, and is difficult to reality
Now automate reasoning；Model testing is that system establishes formalized model appropriate, and since original state, calculating does not violate constant
The possibility valuation of the state vector of amount, and new state and transfer are added for each of these valuations, it by time
The state space of system is gone through to verify whether system meets specific safety specification.Since model testing needs to be traversed for system
State space can encounter State-explosion problem when systematic comparison is big.To solve the above-mentioned problems, mould is approximately predicted
Type inspection technology, if statistical model inspection (Statistical Model Checking, SMC) is using more and more extensive.System
Meter model testing be sampled by the execution state to model, and using statistical measurement come forecasting system whether meet it is given
The expectation confidence level and error of attribute.Another considerable advantage that statistical model is examined is that sampling can benefit from multicore and GPU
Technology parallelization carries out.
CPS is as a kind of open system, and uncertainty is the inherent characteristics of this kind of open systems, and CPS is not
Certainty may result in security of system problem, and safety issue once occurs that catastrophic consequence, serious prestige will be generated
Coerce life, the property safety of people.Therefore, in CPS verifying, can be realized influences security of system
Verifying is a huge challenge.Uncertain rare event (Rare Events) occurs general in the safe system that concerns of prediction
Rate, the safety for improving system are of great significance.Statistical model inspection is sampled the operating status of system, generates
The simulaed path of system is constrained by judging whether each simulaed path meets given system property, uses hypothesis testing
Method is for statistical analysis to the sample space of system simulaed path, and the probability interval that assessment system meets attribute constraint avoids
State-explosion problem is suitable for large-scale and complex system.Therefore, safety is verified using statistical model inspection technology to concern
Uncertain rare event (Rare Events) provides outstanding technical support in system.
Summary of the invention
In order to overcome above-mentioned deficiency, a kind of CPS rare event probability forecasting method examined based on statistical model, technology
Scheme is as follows:
A kind of CPS rare event probability forecasting method examined based on statistical model, including sampling monitor, specification verification
Three modules of device and probability predictor specifically adjust four steps comprising random sampling, specification verification, probabilistic forecasting and parameter；
Wherein, random sampling realizes and obtains visible state sequence to the CPS of the model description sampling for carrying out system mode
V(v1, v2, v3..., vn)；
Specification verification is realized to not verified visible state sequence V (v1, v2, v3..., vn) safety specification test
Card, and obtain visible state sequence the V ' (v having verified that1', v2', v3' ..., vn') and its whether meet the verifying knot of specification
Fruit；
Probabilistic forecasting realizes and predicts that next state is rare event using estimation algorithm in determining prediction model
Probability, and export result；
Parameter adjustment realizes pre- using learning algorithm amendment probability using probabilistic forecasting result and its virtual condition result
The parameter of model is surveyed, to improve the accuracy to rare event probabilistic forecasting.
As a kind of further preferred side for the CPS rare event probability forecasting method examined based on statistical model of the present invention
Case, the sampling monitor, the specific execution of three modules of specification verification device and probability predictor are as follows:
Wherein, the sampling monitor module includes: the foundation of CPS system model, the construction of sample sampling monitor；
The foundation of CPS system model considers the influence that environment runs CPS, is extended to CPS software model, passes through hybrid automata
Model foundation CPS software extensions model；Sample sampling monitor construction based on importance random sampling algorithm, to simulaed path
It carries out random sampling and generates system mode characteristic sequence, run sample information required for CPS system dynamic authentication to obtain；
The specification verification device module provides the verifying to system mode specification, including two-part verifying: first
It is instructed in the verification result for establishing visible features status switch and its corresponding specification satisfaction property as probability predictor model part
The verifying of system mode when experienced sample set；Second part utilizes probabilistic forecasting result and its virtual condition verification result to correct
The verifying of system mode when probability predictor parameter；
The probability predictor module is model generation and the probabilistic forecasting based on hidden markov model.
As a kind of further preferred side for the CPS rare event probability forecasting method examined based on statistical model of the present invention
Case, the step random sampling specifically include:
The selection of step 1.1) CPS descriptive model, use can describe discrete network attribute and the continuous object of description
The hybrid automata model of attribute is managed CPS to be described, then the system described by hybrid automata model can be easy to find
Transformation relation between its state and state:
H=(Q, X, Init, f, Inv, E, G, R)
Wherein:
Q is the set of limited discrete state variable；X is the set of n continuous variable；Init is the collection of original state
It closes,F is the continuous dynamical equation set under QXU → X various discrete state q ∈ Q, and U is input variable set；
Inv is Q → 2XEach mono- invariant set of discrete state q ∈ Q is assigned, when continuous path of the system at a certain discrete state q is de-
When from invariant set, then discrete migration occurs；E is the set of discrete state migration,G is to each e=(q, q ')
∈ E assigns protection collection, and when system continuous path reaches state (q, x) ∈ G (e), discrete migration will occur；R is each time
Assignment again is carried out to continuous state and discrete state when migrating e=(q, q ') ∈ E；
The selection of step 1.2) random sampling algorithm, the purpose of sampling are expectation E [f (x)] in order to obtain, x~p, i.e. E [f
(x)]=∫xf(x)p(x)dx；If directly being sampled from p, and the actually corresponding f (x) of these samples all very littles, hits
Measuring probably can not all obtain the biggish sample of f (x) value in limited situation, be realized using importance random sampling algorithm
Under the premise of guaranteeing that the precision of systematic error and random error is met the requirements, the speed of sampling is improved as far as possible to increase list
The sample size obtained in the time of position, if the sample for meeting p (x) distribution poorly generates, importance random sampling introduces another
It is distributed q (x), and then generates sample:
Convert problem to the expectation for seeking g (x) under q (x) distribution, whereinIt is called importance weight；
If we find a q distribution, enables it to collect sample in the biggish place f (x) p (x), then can preferably approach E [f
(x)], because making a difference its specific gravity of control of right, result will not be caused too great deviations occur.
As a kind of further preferred side for the CPS rare event probability forecasting method examined based on statistical model of the present invention
Case, the step specification verification use the linear temporal based on LTL: using linear temporal and designing system safety
Specification φ, to visible state sequence V (v1, v2, v3..., vn) specification verified, thus the visible state being had verified that
Sequence V ' (v1', v2', v3' ..., vn') and its whether meet the verification result of specification.
As a kind of further preferred side for the CPS rare event probability forecasting method examined based on statistical model of the present invention
Case, the step probabilistic forecasting include:
The selection of step 3.1) Probabilistic Prediction Model, it is pre- as CPS rare event probability using hidden markov model
The model of survey, hidden Markov model μ=(A, B, π) is by hidden state transition probability matrix A (aij), hidden state is transferred to
Probability matrix B (the b of visible statej(k)) and tri- parameters of original state π determine；
The selection of step 3.2) estimation algorithm, valuation be in order to calculate given hidden markov model μ=(A, B,
π) and visible state sequence V (v1, v2, v3..., vn) under conditions of, the probability of visible state sequence V appearance is calculated, is chosen
Solve the problems, such as that the most common forwards algorithms algorithm of valuation is the general of rare event to next state in hidden Markov model
Rate is predicted.
As a kind of further preferred side for the CPS rare event probability forecasting method examined based on statistical model of the present invention
Case, the forwards algorithms specific implementation are as follows:
Input: hidden Markov model μ, it is seen that status switch V；
Output: visible state sequence probability P (V | μ)
Initial value: α1(i)=πibi(v1), i=1,2 ..., N
Recursion: to t=1,2 ..., T-1,
It terminates:
As a kind of further preferred side for the CPS rare event probability forecasting method examined based on statistical model of the present invention
Case, step parameter adjustment are realized using learning algorithm: the study of hidden Markov model according to training data whether include
Visible state sequence and corresponding status switch still only have visible state sequence, can distinguish supervised learning and non-supervisory
It practises and realizing；Using the Baum-Welch algorithm of unsupervised learning, probabilistic forecasting result and its virtual condition verification result benefit are utilized
With the parameter of learning algorithm amendment Probabilistic Prediction Model.
As a kind of further preferred side for the CPS rare event probability forecasting method examined based on statistical model of the present invention
Case, the Baum-Welch algorithm specific implementation are as follows:
Input: visible state sequence V (v1, v2, v3..., vn)；
Output: Hidden Markov Model parameter
Initialization: to n=0, α is chosenij (0), bj(k)(0), πi (0), obtain model μ(0)=(A(0), B(0), π(0))
Recursion: to n=1,2 ...,
πi(n+1)=γ1(i)
Wherein:
ξt(i, j)=P (it=qi, it+1=qj| V, μ)
It terminates: obtaining model parameter μ(n+1)=(A(n+1), B(n+1), π(n+1))。
The invention adopts the above technical scheme compared with prior art, has following technical effect that
1, the present invention proposes in the present invention through the method for rare event probability of happening in prediction CPS and verifies CPS
Safety issue, in a large amount of CPS application problem especially safety issue, it is often necessary to estimate that some event occurs general
Rate, in safety issue, index of interest is usually to be determined by rare event；
2, it when being applied to solve rare event prediction in statistical model inspection for importance sampling method in the present invention, takes out
Sample needs the problem of sizable sample size, importance sampling, thus it is possible to vary the probabilistic law that driving model develops increases rare
The probability that event occurs, then by estimator multiplied by likelihood ratio appropriate, so that it has correctly expectation；
3, the present invention predicts rare event probability of happening in CPS using hidden markov model.Random sampling obtains
Sample and its verification result by the input as hidden markov model, obtain rare event in CPS by forwards algorithms
Probability of happening；Meanwhile can use the parameter of training data amendment hidden markov model, this method is improved to rare event
The precision of prediction probability；
4, a kind of CPS rare event probability forecasting method examined based on statistical model of the present invention has systematicness, integrates
The advantages that property, adaptivity；It has the advantages that above-mentioned many and use value, and has no in similar CPS security verification
There is similar design to publish or use and really belong to innovation, has well solved security of system validation problem in CPS；Together
When, the present invention can predict to concern safely the probability that uncertain rare event in system occurs, for improving the safety of system
Property is of great significance；Three present invention sampling monitor, specification verification device and probability predictor modules become one, and realize
Random sampling, specification verification, probabilistic forecasting and parameter adjust four steps, either theoretically still technically all have
Have biggish novelty, and produce handy and practical effect, the extensive utility value with industry, really for it is one novel, into
Step, practical new design theory method.
Detailed description of the invention
Fig. 1 rare event probability adaptation prediction technique work flow diagram；
Fig. 2 rare event probability adaptation prediction framework figure.
Specific embodiment
The invention will be further described below in conjunction with the accompanying drawings.Following embodiment is only used for clearly illustrating the present invention
Technical solution, and not intended to limit the protection scope of the present invention.
As shown in Figure 1, a kind of CPS rare event probability forecasting method examined based on statistical model includes: sampling monitoring
Device, three modules of specification verification device and probability predictor and random sampling, specification verification, probabilistic forecasting and parameter adjust four steps
Suddenly.Sampling monitor module includes: the construction of the foundation of CPS system model and sample sampling monitor.CPS system model
Foundation consider the influence that runs to CPS of environment, CPS software model is extended, hybrid automata model foundation CPS is passed through
Software extensions model；Sample sampling monitor construction based on importance random sampling algorithm, takes out simulaed path at random
Sample generates system mode characteristic sequence, runs sample information required for CPS system dynamic authentication to obtain.Specification verification device mould
Block provides the verifying to system mode specification, including two-part verifying: first part is establishing visible features state
System mode tests when sample set of the verification result of sequence and its corresponding specification satisfaction property as probability predictor model training
Card；System mode when second part utilizes probabilistic forecasting result and its virtual condition verification result to correct probability predictor parameter
Verifying.Probability predictor module is model generation and the probabilistic forecasting based on hidden markov model.
A kind of CPS rare event probability forecasting method examined based on statistical model includes random sampling, specification verification, general
Rate prediction and parameter adjust four steps, and random sampling, which realizes, obtains the CPS of the model description sampling for carrying out system mode
Visible state sequence V (v1,v2,v3,…,vn)；Specification verification is realized to not verified visible state sequence V (v1,v2,
v3,…,vn) safety specification verification, and obtain visible state sequence the V ' (v that has verified that1', v2', v3' ..., vn') and its
Whether the verification result of specification is met；Probabilistic forecasting, which is realized, predicts next shape using estimation algorithm in determining prediction model
State is the probability of rare event, and exports result；Parameter adjustment, which realizes, utilizes probabilistic forecasting result and its virtual condition result
Using the parameter of learning algorithm amendment Probabilistic Prediction Model, to improve the accuracy to rare event probabilistic forecasting.
Random sampling is realized full in the precision for guaranteeing systematic error and random error using importance random sampling algorithm
Under the premise of foot requires, the speed of sampling is improved as far as possible to increase the sample size obtained in the unit time；Meanwhile using both
Discrete network attribute can be described, and the hybrid automata model of continuous physical attribute can be described CPS to be described.Rule
About verifying uses the linear temporal based on LTL: using linear temporal and designing system safety specification φ, to visible
Status switch V (v1, v2, v3..., vn) specification verified, thus visible state sequence the V ' (v being had verified that1',
v2', v3' ..., vn') and its whether meet the verification result of specification.Probabilistic forecasting is using hidden markov model as CPS
The model of rare event probabilistic forecasting, hidden Markov model μ=(A, B, π) is by hidden state transition probability matrix A (aij),
Hidden state is transferred to the probability matrix B (b of visible statej(k)) and tri- parameters of original state π determine；And choose solution
The most common forwards algorithms of valuation problem carry out the probability that next state is rare event pre- in hidden Markov model
It surveys.Parameter adjustment, which is chosen, solves the most common Baum-Welch algorithm of problem concerning study in hidden Markov model, utilizes probability
Prediction result and its virtual condition verification result correct the parameter of Probabilistic Prediction Model using learning algorithm.
As shown in Fig. 2, being the entirety for the CPS rare event probability adaptation forecasting system method examined based on statistical model
Frame diagram, learning-oriented model detector mainly include 5 component parts, leading portion emulator, and Trace feature extractor is based on
Rare event probability predictor, back segment emulator and the LTL model detector of HMM.Its workflow is as follows:
(1) Trace pre-segmentation device is according to input modelWith LTL formulaThe characteristics of determine suitable Trace leading portion with
The ration of division of back segment, the selection of ratio will have a direct impact on the accuracy of the learning efficiency of HMM probability predictor；
(2) leading portion emulator executes leading portion and emulates and obtain corresponding Trace information, then by Trace feature extractor
After extracting feature according to leading portion Trace and do some pretreatments, it is pre- that sampling samples are input to the rare event probability based on HMM
Device is surveyed, the selection of this feature has a great impact to the study and prediction of HMM；
(3) the rare event probability predictor based on HMM is by learning previously given sample set, to have one
Fixed ability predicts the status information of back segment Trace, and the Trace being unlikely to occur to prediction rare event directly determines to tie
Fruit is 0, and the quality and quantity of training sample has large effect to prediction process；
(4) back segment emulator and the inspection of LTL model can be just only executed when rare event occurs when probability predictor predicts
Device is tested, process is similar with traditional model testing based on LTL, after obtaining complete Trace by back segment emulator, then by
LTL model detector judges whether Trace meets judgement specificationAnd it will determine that result returns to statistical analyzer.
Term used in described above, symbol, formula and example are not construed as limiting the application of the invention, are only
Convenient for their explanation.
The above is only a preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, without departing from the technical principles of the invention, several improvement and deformations can also be made, these improvement and deformations
Also it should be regarded as protection scope of the present invention.
Claims (8)
1. a kind of CPS rare event probability forecasting method examined based on statistical model, it is characterised in that: monitored including sampling
Three device, specification verification device and probability predictor modules specifically include random sampling, specification verification, probabilistic forecasting and parameter tune
Whole four steps；
Wherein, random sampling realizes and obtains visible state sequence V (v to the CPS of the model description sampling for carrying out system mode1,
v2, v3..., vn)；
Specification verification is realized to not verified visible state sequence V (v1, v2, v3..., vn) safety specification verification, and
Obtain visible state sequence the V ' (v having verified that1', v2', v3' ..., vn') and its whether meet the verification result of specification；
Probabilistic forecasting realizes and predicts that next state is the general of rare event using estimation algorithm in determining prediction model
Rate, and export result；
Parameter adjustment realizes and corrects probabilistic forecasting mould using learning algorithm using probabilistic forecasting result and its virtual condition result
The parameter of type, to improve the accuracy to rare event probabilistic forecasting.
2. a kind of CPS rare event probability forecasting method examined based on statistical model according to claim 1, feature
Be: the sampling monitor, the specific execution of three modules of specification verification device and probability predictor are as follows:
Wherein, the sampling monitor module includes: the foundation of CPS system model, the construction of sample sampling monitor；CPS system
The foundation of system model considers the influence that environment runs CPS, is extended to CPS software model, passes through hybrid automata model
Establish CPS software extensions model；Sample sampling monitor construction based on importance random sampling algorithm, carries out simulaed path
Random sampling generates system mode characteristic sequence, runs sample information required for CPS system dynamic authentication to obtain；
The specification verification device module provides the verifying to system mode specification, including two-part verifying: first part
The verification result of visible features status switch and its corresponding specification satisfaction property is being established as probability predictor model training
The verifying of system mode when sample set；Second part utilizes probabilistic forecasting result and its virtual condition verification result to correct probability
The verifying of system mode when predictor parameter；
The probability predictor module is model generation and the probabilistic forecasting based on hidden markov model.
3. a kind of CPS rare event probability forecasting method examined based on statistical model according to claim 1, feature
Be: the step random sampling specifically includes:
The selection of step 1.1) CPS descriptive model, use can describe discrete network attribute and the continuous physics category of description
CPS is described in the hybrid automata model of property, then easy to find can arrive it by the system that hybrid automata model describes
Transformation relation between state and state:
H=(Q, X, Init, f, Inv, E, G, R)
Wherein:
Q is the set of limited discrete state variable；X is the set of n continuous variable；Init is the set of original state,F is the continuous dynamical equation set under QXU → X various discrete state q ∈ Q, and U is input variable set；Inv
For Q → 2XEach mono- invariant set of discrete state q ∈ Q is assigned, when continuous path of the system at a certain discrete state q is detached from not
When becoming collection, then discrete migration occurs；E is the set of discrete state migration,G is to each e=(q, q ') ∈ E
Protection collection is assigned, when system continuous path reaches state (q, x) ∈ G (e), discrete migration will occur；R is to migrate each time
Assignment again is carried out to continuous state and discrete state when e=(q, q ') ∈ E；
The selection of step 1.2) random sampling algorithm, the purpose of sampling are expectation E [f (x)] in order to obtain, x~p, i.e. E [f (x)]
=∫xf(x)p(x)dx；If directly being sampled from p, and the actually corresponding f (x) of these samples all very littles, number of samples have
The biggish sample of f (x) value can not be all probably obtained in the case where limit, is realized and is being protected using importance random sampling algorithm
Under the premise of the precision of card systematic error and random error is met the requirements, when improving the speed of sampling as far as possible to increase unit
The sample size of interior acquisition, if the sample for meeting p (x) distribution poorly generates, importance random sampling introduces another distribution q
(x), and then sample is generated:
Convert problem to the expectation for seeking g (x) under q (x) distribution, whereinIt is called importance weight；If we
A q distribution is found, enables it to collect sample in the biggish place f (x) p (x), then can preferably approach E [f (x)], because
For its specific gravity of control of right of making a difference, so result will not be caused too great deviations occur.
4. a kind of CPS rare event probability forecasting method examined based on statistical model according to claim 1, feature
Be: the step specification verification uses the linear temporal based on LTL: using linear temporal and designing system safety
Property specification φ, to visible state sequence V (v1, v2, v3..., vn) specification verified, so that is had verified that sees this
State sequence V ' (v1', v2', v3' ..., vn') and its whether meet the verification result of specification.
5. a kind of CPS rare event probability forecasting method examined based on statistical model according to claim 3, feature
Be: the step probabilistic forecasting includes:
The selection of step 3.1) Probabilistic Prediction Model, using hidden markov model as CPS rare event probabilistic forecasting
Model, hidden Markov model μ=(A, B, π) is by hidden state transition probability matrix A (aij), hidden state is transferred to visible
Probability matrix B (the b of statej(k)) and tri- parameters of original state π determine；
The selection of step 3.2) estimation algorithm, valuation be in order to calculate in given hidden markov model μ=(A, B, π) and
Visible state sequence V (v1, v2, v3..., vn) under conditions of, the probability of visible state sequence V appearance is calculated, it is hidden to choose solution
The most common forwards algorithms of valuation problem predict the probability that next state is rare event in formula Markov model.
6. a kind of CPS rare event probability forecasting method examined based on statistical model according to claim 5, feature
It is: the forwards algorithms specific implementation are as follows:
Input: hidden Markov model μ, it is seen that status switch V；
Output: visible state sequence probability P (V | μ)
Initial value: α1(i)=πibi(v1), i=1,2 ..., N
Recursion: to t=1,2 ..., T-1,
It terminates:
7. a kind of CPS rare event probability forecasting method examined based on statistical model according to claim 2, feature
Be: the step parameter adjustment is realized using learning algorithm: whether the study of hidden Markov model wraps according to training data
Sequence containing visible state and corresponding status switch still only have visible state sequence, can distinguish supervised learning and non-supervisory
Study is realized；Using the Baum-Welch algorithm of unsupervised learning, probabilistic forecasting result and its virtual condition verification result are utilized
Utilize the parameter of learning algorithm amendment Probabilistic Prediction Model.
8. a kind of CPS rare event probability forecasting method examined based on statistical model according to claim 7, feature
It is: the Baum-Welch algorithm specific implementation are as follows:
Input: visible state sequence V (v1, v2, v3..., vn)；
Output: Hidden Markov Model parameter
Initialization: to n=0, α is chosenij (0), bj(k)(0), πi (0), obtain model μ(0)=(A(0), B(0), π(0))
Recursion: to n=1,2 ...,
πi (n+1)=γ1(i)
Wherein:
ξt(i, j)=P (it=qi, it+1=qj| V, μ)
It terminates: obtaining model parameter μ(n+1)=(A(n+1), B(n+1), π(n+1))。
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