CN108134680B - A kind of systematic survey node optimization configuration method based on Bayesian network - Google Patents
A kind of systematic survey node optimization configuration method based on Bayesian network Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
- H04L41/14—Network analysis or design
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
- H04L41/06—Management of faults, events, alarms or notifications
- H04L41/0631—Management of faults, events, alarms or notifications using root cause analysis; using analysis of correlation between notifications, alarms or events based on decision criteria, e.g. hierarchy, tree or time analysis
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
- H04L41/08—Configuration management of networks or network elements
- H04L41/0803—Configuration setting
- H04L41/0823—Configuration setting characterised by the purposes of a change of settings, e.g. optimising configuration for enhancing reliability
Abstract
The systematic survey node optimization configuration method based on Bayesian network that the present invention relates to a kind of, establishes the Bayesian network model of system；The mutual information matrix between malfunctioning node and measuring node is calculated according to Bayesian network model；Measuring point is calculated to the contribution degree of Fault Node Diagnosis according to the mutual information matrix between malfunctioning node and measuring node, determines integral diagnostic capability index；According to measuring point to contribution degree and measuring point cost and measuring point quantity the limitation description optimization problem of Fault Node Diagnosis；The discrete binary particle swarm algorithm of application enhancements optimizes processing, and obtain measuring point distributes result rationally.The present invention considers Optimum sensor placement problem under that condition that the constraint conditions are met, more meet practical engineering application, the trouble diagnosibility and measurement cost problem of measuring point are considered simultaneously, then processing is optimized by improved optimization algorithm, to find the optimal measuring node allocation plan of system.
Description
Technical field
The present invention relates to control of complex systems and fault diagnosis fields, specifically a kind of to be based on Bayesian network
Unified test amount node optimization configuration method.
Background technique
Fault diagnosis is the key that guarantee system reliability service, fault diagnosis be by measuring point to the key variables of system into
Row detection obtains the fault message of variable, and the failure symptom of system is determined according to fault message.And system is carrying out fault diagnosis
When, it often requires that and obtains fault message as much as possible using measuring point as few as possible, meet the maximum diagnosis energy to failure
Power, i.e., distributing rationally for measuring point is crucial.For the large-scale complicated system as the spacecraft attitude control system, to guarantee
It runs reliably and with long-term, needs to configure measuring point acquisition fault message for it, maximizes the trouble diagnosibility of measuring point.In practical work
Information as much as possible in order to obtain in journey generally requires to configure many sensors, but there are certain blindnesses for such configuration
Property and also will cause the waste of resource, under resources costs limitation, distributing rationally for measuring point is just particularly important.
Summary of the invention
In view of the deficiencies of the prior art, the present invention provides a kind of systematic survey node optimization configuration based on Bayesian network
Method solves the diagnosis capability and cost problem of the complication systems such as spacecraft measuring point arrangement scheme when carrying out fault diagnosis.
Present invention technical solution used for the above purpose is:
A kind of systematic survey node optimization configuration method based on Bayesian network, comprising the following steps:
Step 1: establishing the Bayesian network model of system；
Step 2: the mutual information matrix between malfunctioning node and measuring node is calculated according to Bayesian network model；
Step 3: tribute of the measuring point to Fault Node Diagnosis is calculated according to the mutual information matrix between malfunctioning node and measuring node
Degree of offering determines integral diagnostic capability index；
Step 4: contribution degree and measuring point cost and measuring point quantity the limitation description optimization according to measuring point to Fault Node Diagnosis
Problem；
Step 5: the discrete binary particle swarm algorithm of application enhancements optimizes processing, and obtain measuring point distributes knot rationally
Fruit.
The Bayesian network model for establishing system includes following procedure:
Step 1: fault mode and reason picture analysis being carried out to system according to the structure of system and fault mode, determine Bayes
The node of network and the topological structure of Bayesian network；
Step 2: on the basis of the topological structure of Bayesian network, the prior distribation of node is determined according to maximum entropy method；
Step 3: node parameter values, the i.e. conditional probability distribution of node are determined according to historical failure data and expertise,
Bayesian network model is completed to establish.
The prior distribation process that node is determined according to maximum entropy method are as follows:
HB(a*,b*)=max (HB(a,b))
a≥0,b≥0
A/ (a+b)=p0
Wherein, a is the prior distribation parameter of Maximum Entropy；B tests preceding substep parameter for Maximum Entropy；P is probability parameter；a*With
b*The respectively optimal value of parameter a and b；Beta () is beta distribution；Dp is to carry out derivation to probability parameter p；HBFor Maximum Entropy
Symbol；p0For the mean value of probability parameter p.
The conditional probability distribution of the node are as follows:
Wherein, π (p) is prior distribation；P (D | p) it is sample data；π (p | D) is the conditional probability distribution of node；D is sample
Notebook data；Dp is to carry out derivation to parameter p；P is probability parameter.
Mutual information matrix between the malfunctioning node and measuring node are as follows:
Wherein, mutual information matrix of the I between malfunctioning node and measuring node；IijBetween malfunctioning node i and measuring node j
Mutual information；M is the quantity of malfunctioning node；N is the quantity of measuring node；P is the probability value of malfunctioning node；fi=1 is expressed as
Malfunctioning node i is in malfunction, fi=0, which is expressed as malfunctioning node i, is in normal condition；sj=1 is expressed as configuration measuring node
J, sj=0 is expressed as not configuring measuring node j.
The contribution degree of the Fault Node Diagnosis are as follows:
Esj=(G-Gsj)/G
G=trace (T)
T=(ITI)T
Wherein, EsjFor the contribution degree of Fault Node Diagnosis；GsjIt is according to removing the mutual trust after j-th of measuring point in measuring point group
Cease the sum of the characteristic value of matrix；G is the sum of all characteristic values of matrix；T is diagnostic message matrix；ITI is denoted as matrix TT, TTFor m ×
The non-singular matrix of m.
It is described that optimization problem process is described according to contribution degree and measuring point cost and quantity are as follows:
An objective function is converted by the limitation of the contribution degree of Fault Node Diagnosis, measuring point cost and measuring point quantity:
Wherein,For the contribution degree of Fault Node Diagnosis；For measuring point cost；For the limitation of measuring point quantity；Q is a penalty factor, and value is a sufficiently big positive number；N is limited
The measuring point quantity of system；D is row vector, and element is all 1；xiFor the solution of optimization problem, i.e. measuring point arrangement situation；minf(xi) be
Optimization problem.
The improved discrete binary particle swarm algorithm are as follows:
Step 1: initialization population calculates the initial position and initial velocity of particle；
Step 2: calculating target function value determines individual optimal value and all optimal values, and according to the speed of particle swarm algorithm
It spends more new algorithm and updates particle rapidity value；
Step 3: being adopted according to the positional value of the number of iterations more new particle if current iteration number is less than parameter preset
With the more new algorithm of the particle position with ability of searching optimum, is otherwise updated and calculated using the particle position with local search ability
Method.
The initial position of the particle are as follows:
The initial velocity of the particle are as follows:
vid=vmin+rand()(vmax-vmin)
The speed of particle swarm algorithm more new algorithm are as follows:
vid=ω vid+c1·rand()·(pid-xid)+c2·rand()·(pgd-xid)
Particle position with ability of searching optimum more new algorithm are as follows:
Particle position with local search ability more new algorithm are as follows:
Work as vidWhen≤0,
Work as vidWhen > 0,
Wherein, vmaxFor the KB limit of speed；vminFor the minimum limits value of speed；Rand () is a random number,
It is randomly generated from the univesral distribution of section [0,1]；I is the population of population；D is the dimension of population, indicates system
Configurable measuring point sum；W is inertia weight, is used for balanced algorithm global search and local search ability；c1And c2It indicates to accelerate normal
Number, can also play the role of balanced algorithm global search and local search ability；s(vid) indicate position xidTake 1 probability；xid
For particle current location；vidFor particle present speed；pidFor particle current individual optimal value；pgdIt is current all optimal for particle
Value；Exp () is exponential function.
The parameter preset are as follows:
cys=r*M
Wherein, cysFor parameter preset；R is scale parameter；M is maximum number of iterations.
The invention has the following beneficial effects and advantage:
1. the present invention considers Optimum sensor placement problem under that condition that the constraint conditions are met, more meets Practical Project and answer
With.
2. the present invention considers the trouble diagnosibility and measurement cost problem of measuring point simultaneously, then pass through improved optimization
Algorithm optimizes processing, to find the optimal measuring node allocation plan of system.
Detailed description of the invention
Fig. 1 is flow chart of the method for the present invention；
Fig. 2 is the flow chart for establishing system Bayesian network model of the invention；
Fig. 3 is the flow chart that optimization problem of the invention describes；
Fig. 4 is improved discrete binary version of particle swarm optimization algorithm flow chart of the invention.
Specific embodiment
The present invention is described in further detail with reference to the accompanying drawings and embodiments.
It is as shown in Figure 1 flow chart of the method for the present invention.
Step 1: the Bayesian network model of system is established, including determining the topological structure of Bayesian network and determining pattra leaves
The conditional probability distribution of this network:
Firstly, fault mode and reason picture analysis (FMEA) are carried out to system according to the structure of system and fault mode, with this
It determines the node of Bayesian network and the topological structure of Bayesian network, that is, indicates the directed acyclic graph of connection relation between nodes.
Then, on the basis of established Bayesian Network Topology Structures, node is determined according to maximum entropy method first
Prior distribation, then determine the node parameter values i.e. conditional probability of node point further according to historical failure data and expertise
Cloth.
Step 2: the mutual information matrix between malfunctioning node and measuring node is calculated according to Bayesian network:
In system configuration measuring node, in order to improve the efficient diagnosis ability to failure, need to consider measuring point to failure
Diagnosis capability.The information content about malfunctioning node that measuring node provides in Bayesian network is bigger, malfunctioning node variable
The uncertain change degree of itself is bigger.Mutual information is bigger, and the information content for the malfunctioning node that measuring point is capable of providing is also bigger, right
The diagnosis capability of failure is also bigger, at this moment can more effectively realize the fault diagnosis of system.
Use IijIndicate j-th of measuring node SjTo i-th of malfunctioning node FiDiagnosis capability, can be described with matrix I
I is known as malfunctioning node and survey to the one-to-one diagnosis capability of all malfunctioning nodes by all measuring nodes in Bayesian network
The mutual information matrix between node is measured, is expressed as follows:
Wherein
P is expressed as probability, f in formulai、sjThe respectively particular state of malfunctioning node and measuring node.
Step 3: measuring point is calculated to the contribution degree of fault diagnosis:
Integral diagnostic capability index, i.e. calculating measuring point pair are determined according to the mutual information matrix between malfunctioning node and measuring node
The contribution degree of Fault Node Diagnosis.
Guarantee failure identifiability be exactly require each malfunctioning node be to the impact probability of measuring point it is mutually different, i.e.,
It is required that the row vector of failure-measuring point mutual information matrix is mutually indepedent.By ITI is denoted as matrix TT, which is one m × m full rank
Matrix, and matrix T is referred to as diagnostic message matrix.Malfunctioning node information and measuring point information are completely contained in diagnostic message matrix at this time
In T, therefore it can achieve the purpose that measuring point optimizes by extracting the characteristic value of matrix T.The mark trace of diagnostic message matrix
(T) sum namely measuring point group for representing all characteristic values of matrix are to the diagnosis capability summations of all deviation sources.Therefore it is saved in measurement
Using the mark of diagnostic message matrix as the evaluation index of measuring point to be selected, also referred to as integral diagnostic capability index, institute in the optimization of point
It is that synthesis is examined to the contribution degree of malfunctioning node integral diagnostic capability for objective function, to define j-th of measuring point with G=trace (T)
Cutting capacity index:
Esj=(G-Gsj)/G (3)
G=trace (T)
T=(ITI)T (4)
Wherein GsjIt is the sum according to the characteristic value for removing the mutual information matrix after j-th of measuring point in measuring point group.
Step 4: optimization problem is described according to measuring point contribution degree and measuring point cost and quantity:
The contribution degree and cost for considering measuring point simultaneously, are translated into optimization algorithm objective function to be asked, pass through selection
Optimal measuring point arrangement scheme, so that measuring point is maximum to the diagnosis capability of failure, while required measuring point arrangement cost minimization.
Step 5, the discrete binary particle swarm algorithm of application enhancements optimizes processing, and obtain measuring point distributes knot rationally
Fruit:
Standard particle group's algorithm is useful in continuous search space and calculates, and for discrete search space, it cannot
It is directly applied, it is necessary to standard particle group's algorithm improvement.Optimize discrete two using discrete binary particle swarm algorithm
The problem of system space.
It is illustrated in figure 2 the flow chart for establishing system Bayesian network model of the invention.
Firstly, fault mode and reason picture analysis (FMEA) are carried out to system according to the structure of system and fault mode, with this
It determines the node of Bayesian network and the topological structure of Bayesian network, that is, indicates the directed acyclic graph of connection relation between nodes.
Then, on the basis of established Bayesian Network Topology Structures, node is determined according to maximum entropy method first
Prior distribation, then determine the node parameter values i.e. conditional probability of node point further according to historical failure data and expertise
Cloth.
It needs to be determined that the prior distribation of node, the present invention are determined using the method for Maximum Entropy before determining conditional probability distribution
Prior distribation.In practical engineering applications, since the node in network is all binary states, so usually taking Beta (p；a,b)
It is distributed the prior distribation as nodes.The mean value p of parameter p is determined according to expertise0, then according to Maximum Entropy algorithm
Determine the optimal value a of parameter a and b*And b*, so that it is determined that the prior distribation of node.
HB(a*,b*)=max (HB(a,b))
a≥0,b≥0
A/ (a+b)=p0 (5)
Wherein
After the prior distribation of node has been determined, present invention application bayes method will be computed before the testing of acquisition point
Cloth is combined with historical failure sample information, obtains the posterior distribution of node with this, concrete operations are as follows:
Wherein, π (p) expression prior distribation, and p (D | p) expression sample data, π (p | D) and indicate posterior distribution.
It is illustrated in figure 3 the flow chart of optimization problem description of the invention.
The contribution degree and cost for considering measuring point simultaneously are translated into optimization algorithm objective function to be asked, and consider d survey
The deployment cost and contribution degree of point are respectively csj(j=1,2 ..., d), Esj(j=1,2 ..., d) pass through the optimal survey of selection
Point allocation plan, so that measuring point is maximum to the diagnosis capability of failure, while required measuring point arrangement cost minimization.If variable
Then consider measuring point contribution degree, measuring point cost and in practice needed for the measuring point of measuring point quantity restrictive condition distribute rationally and ask
Topic may be expressed as:
The key that measuring point optimization allocation is solved using discrete binary particle swarm algorithm is how to encode.Here x is usedi
Indicate the value of i-th of particle, each particle value xiIt is expressed as a solution of optimization problem.xi=[xi1,xi2,...,
xid], d indicates the dimension of particle, represents configurable measuring point sum herein.xijValue indicate that the measuring point j of i-th particle matches
Situation is set, value value is 0 or 1.If xijThe j point of=1 i-th of particle of expression will configure measuring point, and otherwise j point does not configure survey
Point.
The present invention converts above-mentioned Optimized model, obtains the objective function of following optimization problem, i.e. particle updates
Fitness function:
Wherein, Q is a penalty factor, and value is a sufficiently big positive number.D is the row vector of d dimension, and element is all
It is 1.N is the quantity of the measuring point of limitation arrangement in practice.Here the minimum value of objective function is sought.
The position of particle is initialized by following formula:
The initial velocity v of particleijRandom initializtion as the following formula:
vid=vmin+rand()(vmax-vmin) (15)
Wherein vmaxAnd vminIndicate the minimax limits value of speed.Its value determines particle maximum shifting in an iteration
Dynamic distance.If larger, search capability enhancing, but particle is easy to fly over optimal solution.When smaller, development ability enhancing, but hold
Local optimum easily is fallen into, it should appropriate value according to the actual situation.
It is illustrated in figure 4 improved discrete binary version of particle swarm optimization algorithm flow chart of the invention.
Standard particle group's algorithm is useful in continuous search space and calculates, and for discrete search space, it cannot
It is directly applied, it is necessary to standard particle group's algorithm improvement.Optimize discrete two using discrete binary particle swarm algorithm
The problem of system space.The speed of particle swarm algorithm more new formula are as follows:
vid=ω vid+c1·rand()·(pid-xid)+c2·rand()·(pgd-xid) (16)
Wherein, i is the population of population；D is the dimension of population, indicates the configurable measuring point of system in the present invention
Sum.Its value obtain it is too small to be easy to cause the solution found out be local optimum, acquirement will increase greatly very much search time, lead to convergence speed
It spends slack-off, it is proper to be generally taken as 20；W is inertia weight, it plays balanced algorithm global search and local search ability
Effect.One big inertia weight is conducive to global search, and a small inertia weight is then conducive to local search.To obtain
Preferable effect of optimization, it is desirable that its value linear decrease from 1.4 to 0.4；c1And c2It indicates aceleration pulse, can also play balanced algorithm
The effect of global search and local search ability.Generally require c1=c2And range is between 0 and 4, when practical application usually all
It is taken as 2；Rand () is a random number, is randomly generated from the univesral distribution of section [0,1].
The speed of discrete binary particle swarm algorithm more new formula is identical as original particle swarm algorithm.And particle position is more
New formula is different.In order to indicate that the value of speed is the probability that binary digit takes 1, the value of speed is mapped to section [0,1], is indicated
Are as follows:
Here s (vid) indicate position xid1 probability is taken, particle updates its place value by formula (12):
And improved population location update formula.The mapping equation of speed is changed are as follows:
And the place value of particle updates reformulation are as follows:
Work as vidWhen≤0,
Work as vidWhen > 0,
The present invention, using particle position more new formula shown in formula (17) and formula (18), guarantees algorithm in iterative search early period
Ability of searching optimum.And public affairs are updated using particle position shown in formula (19), formula (20) and formula (21) in the iterative search later period
Formula guarantees the local search ability of algorithm.Doing so can guarantee to solve of overall importance and algorithm fast convergence.The present invention adopts
The optimization allocation of measuring point is solved with this improved discrete binary particle swarm algorithm.
Claims (9)
1. a kind of systematic survey node optimization configuration method based on Bayesian network, which comprises the following steps:
Step 1: establishing the Bayesian network model of system；
Step 2: the mutual information matrix between malfunctioning node and measuring node is calculated according to Bayesian network model；
Step 3: measuring point is calculated to the contribution degree of Fault Node Diagnosis according to the mutual information matrix between malfunctioning node and measuring node,
Determine integral diagnostic capability index；
Step 4: according to measuring point to contribution degree and measuring point cost and measuring point quantity the limitation description optimization problem of Fault Node Diagnosis；
Step 5: the discrete binary particle swarm algorithm of application enhancements optimizes processing, and obtain measuring point distributes result rationally；
Mutual information matrix between the malfunctioning node and measuring node are as follows:
Wherein, mutual information matrix of the I between malfunctioning node and measuring node；IijIt is mutual between malfunctioning node i and measuring node j
Information；M is the quantity of malfunctioning node；N is the quantity of measuring node；P is the probability value of malfunctioning node；fi=1 is expressed as failure
Node i is in malfunction, fi=0, which is expressed as malfunctioning node i, is in normal condition；sj=1 is expressed as configuration measuring node j, sj
=0 is expressed as not configuring measuring node j.
2. the systematic survey node optimization configuration method according to claim 1 based on Bayesian network, it is characterised in that:
The Bayesian network model for establishing system includes following procedure:
Step 1: fault mode and reason picture analysis being carried out to system according to the structure of system and fault mode, determine Bayesian network
Node and Bayesian network topological structure；
Step 2: on the basis of the topological structure of Bayesian network, the prior distribation of node is determined according to maximum entropy method；
Step 3: node parameter values, the i.e. conditional probability distribution of node being determined according to historical failure data and expertise, are completed
Bayesian network model is established.
3. the systematic survey node optimization configuration method according to claim 2 based on Bayesian network, it is characterised in that:
The prior distribation process that node is determined according to maximum entropy method are as follows:
HB(a*,b*)=max (HB(a,b))
a≥0,b≥0
A/ (a+b)=p0
Wherein, a is the prior distribation parameter of Maximum Entropy；B tests preceding substep parameter for Maximum Entropy；P is probability parameter；a*And b*Point
Not Wei parameter a and b optimal value；Beta () is beta distribution；Dp is to carry out derivation to probability parameter p；HBFor Maximum Entropy symbol；
p0For the mean value of probability parameter p.
4. the systematic survey node optimization configuration method according to claim 2 based on Bayesian network, which is characterized in that
The conditional probability distribution of the node are as follows:
Wherein, π (p) is prior distribation；P (D | p) it is sample data；π (p | D) is the conditional probability distribution of node；D is sample number
According to；Dp is to carry out derivation to parameter p；P is probability parameter.
5. the systematic survey node optimization configuration method according to claim 1 based on Bayesian network, which is characterized in that
The contribution degree of the Fault Node Diagnosis are as follows:
Esj=(G-Gsj)/G
G=trace (T)
T=(ITI)T
Wherein, EsjFor the contribution degree of Fault Node Diagnosis；GsjIt is according to removing the mutual information matrix after j-th of measuring point in measuring point group
Characteristic value sum；G is the sum of all characteristic values of matrix；T is diagnostic message matrix；ITI is denoted as matrix TT, TTFor expiring for m × m
Order matrix.
6. the systematic survey node optimization configuration method according to claim 1 based on Bayesian network, which is characterized in that
It is described that optimization problem process is described according to contribution degree and measuring point cost and quantity are as follows:
An objective function is converted by the limitation of the contribution degree of Fault Node Diagnosis, measuring point cost and measuring point quantity:
Wherein,For the contribution degree of Fault Node Diagnosis；For measuring point cost；For
The limitation of measuring point quantity；Q is a penalty factor, and value is a sufficiently big positive number；N is the measuring point quantity of limitation；D is row
Vector, element are all 1；xiFor the solution of optimization problem, i.e. measuring point arrangement situation；min f(xi) it is optimization problem.
7. the systematic survey node optimization configuration method according to claim 1 based on Bayesian network, which is characterized in that
The improved discrete binary particle swarm algorithm are as follows:
Step 1: initialization population calculates the initial position and initial velocity of particle；
Step 2: calculating target function value determines individual optimal value and all optimal values, and more according to the speed of particle swarm algorithm
New algorithm updates particle rapidity value；
Step 3: according to the positional value of the number of iterations more new particle, if current iteration number is less than parameter preset, using tool
There is the particle position more new algorithm of ability of searching optimum, otherwise using the particle position more new algorithm with local search ability.
8. the systematic survey node optimization configuration method according to claim 7 based on Bayesian network, it is characterised in that:
The initial position of the particle are as follows:
The initial velocity of the particle are as follows:
vid=vmin+rand()(vmax-vmin)
The speed of particle swarm algorithm more new algorithm are as follows:
vid=ω vid+c1·rand()·(pid-xid)+c2·rand()·(pgd-xid)
Particle position with ability of searching optimum more new algorithm are as follows:
Particle position with local search ability more new algorithm are as follows:
Work as vidWhen≤0,
Work as vidWhen > 0,
Wherein, vmaxFor the KB limit of speed；vminFor the minimum limits value of speed；Rand () is a random number, from area
Between [0,1] univesral distribution in be randomly generated；I is the population of population；D is the dimension of population, indicates matching for system
Set measuring point sum；W is inertia weight, is used for balanced algorithm global search and local search ability；c1And c2Indicate aceleration pulse,
Also it can play the role of balanced algorithm global search and local search ability；s(vid) indicate position xidTake 1 probability；xidFor grain
Sub- current location；vidFor particle present speed；pidFor particle current individual optimal value；pgdFor the current all optimal values of particle；
Exp () is exponential function.
9. the systematic survey node optimization configuration method according to claim 7 based on Bayesian network, which is characterized in that
The parameter preset are as follows:
cys=r*M
Wherein, cysFor parameter preset；R is scale parameter；M is maximum number of iterations.
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