CN108134680B - A kind of systematic survey node optimization configuration method based on Bayesian network - Google Patents

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

A Method for Optimal Configuration of System Measurement Nodes Based on Bayesian Network

technical field

The invention relates to the field of complex system control and fault diagnosis, in particular to a Bayesian network-based system measurement node optimization configuration method.

Background technique

Fault diagnosis is the key to ensure the reliable operation of the system. Fault diagnosis is to detect the key variables of the system through the measurement points to obtain the fault information of the variables, and determine the fault symptoms of the system according to the fault information. When the system performs fault diagnosis, it is often required to use as few measuring points as possible to obtain as much fault information as possible to meet the maximum fault diagnosis capability, that is, the optimal configuration of measuring points is the key. For a large and complex system such as the spacecraft attitude control system, in order to ensure its long-term reliable operation, it is necessary to configure measuring points to obtain fault information and maximize the fault diagnosis capabilities of the measuring points. In actual engineering, in order to obtain as much information as possible, it is often necessary to configure a lot of sensors, but such a configuration has a certain degree of blindness and will also cause a waste of resources. Under the limitation of resource costs, the optimal configuration of measuring points is particularly important. .

Contents of the invention

Aiming at the deficiencies of the prior art, the present invention provides a Bayesian network-based system measurement node optimization configuration method, which solves the problem of diagnostic capability and cost of measurement point configuration schemes during fault diagnosis of spacecraft and other complex systems.

The technical scheme that the present invention adopts for realizing the above object is:

A method for optimal configuration of system measurement nodes based on Bayesian network, comprising the following steps:

Step 1: Establish a Bayesian network model of the system;

Step 2: Calculate the mutual information matrix between the fault node and the measurement node according to the Bayesian network model;

Step 3: According to the mutual information matrix between the fault node and the measurement node, calculate the contribution of the measurement point to the diagnosis of the fault node, and determine the comprehensive diagnosis ability index;

Step 4: Describe the optimization problem according to the contribution of the measuring point to the diagnosis of the faulty node, the cost of the measuring point and the limit of the number of measuring points;

Step 5: Apply the improved discrete binary particle swarm optimization algorithm to obtain the optimal configuration results of the measuring points.

The Bayesian network model of the described establishment system comprises the following processes:

Step 1: Analyze the failure mode and rationale of the system according to the system structure and failure mode, and determine the nodes of the Bayesian network and the topology of the Bayesian network;

Step 2: On the basis of the topology of the Bayesian network, determine the prior distribution of the nodes according to the maximum entropy method;

Step 3: Determine the node parameter value, that is, the conditional probability distribution of the node according to the historical fault data and expert experience, and complete the establishment of the Bayesian network model.

The process of determining the prior distribution of nodes according to the maximum entropy method is:

H _B (a ^* ,b ^* )＝max(H _B (a,b))

a≥0,b≥0

a/(a+b)=p ₀

Among them, a is the prior distribution parameter of the maximum entropy; b is the prior step-by-step parameter of the maximum entropy; p is the probability parameter; a ^* and b ^* are the optimal values of the parameters a and b respectively; Beta() is Beta distribution; dp is the derivative of the probability parameter p; H _B is the maximum entropy symbol; p ₀ is the mean value of the probability parameter p.

The conditional probability distribution of the nodes is:

Among them, π(p) is the prior distribution; p(D|p) is the sample data; π(p|D) is the conditional probability distribution of the node; D is the sample data; dp is the derivative of the parameter p; p is probability parameter.

The mutual information matrix between the fault node and the measurement node is:

Among them, I is the mutual information matrix between the faulty node and the measuring node; I _ij is the mutual information between the faulty node i and the measuring node j; m is the number of faulty nodes; n is the number of measuring nodes; Probability value; f _i = 1 means that the faulty node i is in the fault state, f _i = 0 means that the faulty node i is in the normal state; s _j = 1 means that the measurement node j is configured, and s _j = 0 means that the measurement node is not configured j.

The contribution degree of the faulty node diagnosis is:

E _sj ＝(GG _sj )/G

G=trace(T)

T = (I ^T I) ^T

Among them, E _sj is the contribution degree of faulty node diagnosis; G _sj is the sum of the eigenvalues of the mutual information matrix after removing the jth measuring point in the measuring point group; G is the sum of all the eigenvalues of the matrix; T is the diagnosis information Matrix; I ^T I is recorded as matrix T ^T , and T ^T is a full-rank matrix of m×m.

The process of describing the optimization problem according to the degree of contribution and the cost and quantity of measuring points is:

Transform the contribution of faulty node diagnosis, the cost of measuring points and the limit of the number of measuring points into an objective function:

in, Contribution to faulty node diagnosis; is the measuring point cost; Q is a penalty factor, its value is a sufficiently large positive number; N is the limited number of measurement points; D is a row vector, and its elements are all 1; x _i is the solution of the optimization problem, That is, the configuration of measuring points; minf( _xi ) is an optimization problem.

The improved discrete binary particle swarm optimization algorithm is:

Step 1: Initialize the particle swarm, calculate the initial position and initial velocity of the particles;

Step 2: Calculate the objective function value, determine the individual optimal value and the overall optimal value, and update the particle velocity value according to the velocity update algorithm of the particle swarm optimization algorithm;

Step 3: Update the position value of the particle according to the number of iterations. If the current number of iterations is less than the preset parameter, use the particle position update algorithm with global search capability, otherwise use the particle position update algorithm with local search capability.

The initial position of the particle is:

The initial velocity of the particle is:

v _id =v _min +rand()(v _max -v _min )

The speed update algorithm of the particle swarm algorithm is:

v _id ＝ω·v _id +c ₁ ·rand()·(p _id -x _id )+c ₂ ·rand()·(p _gd -x _id )

The particle position update algorithm with global search capability is:

The particle position update algorithm with local search capability is:

When v _id ≤ 0,

When v _id >0,

Among them, v _max is the maximum limit value of speed; v _min is the minimum limit value of speed; rand() is a random number, randomly generated from the uniform distribution in the interval [0,1]; i is the number of particles in the particle swarm; d is the dimension of the particle swarm, indicating the total number of configurable measuring points in the system; w is the inertia weight, which is used to balance the global search and local search capabilities of the algorithm; c ₁ and c ₂ represent acceleration constants, which can also balance the global search of the algorithm The effect of local search ability; s(v _id ) represents the probability that the position x _id is 1; x _id is the current position of the particle; v _id is the current _velocity of the particle; p _id is the current individual optimal value of the particle; Overall optimal value; exp() is an exponential function.

The preset parameters are:

c _ys =r*M

Among them, c _ys is a preset parameter; r is a proportional parameter; M is the maximum number of iterations.

The present invention has the following beneficial effects and advantages:

1. The present invention considers the problem of optimal configuration of sensors under constraint conditions, which is more in line with practical engineering applications.

2. The present invention simultaneously considers the problem of fault diagnosis ability and measurement cost of the measurement point, and then performs optimization processing through an improved optimization algorithm, so as to find the best measurement node configuration scheme of the system.

Description of drawings

Fig. 1 is method flowchart of the present invention;

Fig. 2 is the flowchart of setting up system Bayesian network model of the present invention;

Fig. 3 is the flowchart of optimization problem description of the present invention;

Fig. 4 is a flowchart of the improved discrete binary particle swarm optimization algorithm of the present invention.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

As shown in Figure 1, it is a flow chart of the method of the present invention.

Step 1: Establish a systematic Bayesian network model, including determining the topology of the Bayesian network and determining the conditional probability distribution of the Bayesian network:

First, according to the structure and failure mode of the system, the failure mode and image analysis (FMEA) of the system is carried out to determine the nodes of the Bayesian network and the topology of the Bayesian network, that is, the directed-unconnected network that represents the connection relationship between nodes. Ring diagram.

Then, on the basis of the established Bayesian network topology, first determine the prior distribution of nodes according to the maximum entropy method, and then determine the node parameter values, that is, the conditional probability distribution of nodes, according to historical fault data and expert experience.

Step 2: Calculate the mutual information matrix between the fault node and the measurement node according to the Bayesian network:

When the system configures the measurement nodes, in order to improve the effective diagnosis ability of the fault, it is necessary to consider the fault diagnosis ability of the measurement point. In the Bayesian network, the greater the amount of information about the faulty node provided by the measuring node, the greater the degree of uncertainty of the variable of the faulty node itself will change. The greater the mutual information, the greater the amount of information that the measuring point can provide on the fault node, and the greater the ability to diagnose faults. At this time, the fault diagnosis of the system can be realized more effectively.

Iij is used to represent the diagnostic ability of the _{jth measurement node S j to} the ith faulty node F _i , and the matrix I can be used to describe the one-to-one diagnostic capability of all measurement nodes in the Bayesian network to all faulty nodes. It is called the mutual information matrix between the fault node and the measurement node, expressed as follows:

in

In the formula, P is expressed as a probability, and f _i and s _j are the specific states of the fault node and the measurement node respectively.

Step 3: Calculate the contribution of the measuring point to the fault diagnosis:

According to the mutual information matrix between the fault node and the measurement node, the comprehensive diagnosis ability index is determined, that is, the contribution degree of the measurement point to the diagnosis of the fault node is calculated.

To ensure the identifiability of faults is to require that the probabilistic influence of each fault node on the measuring point is different from each other, that is, the row vectors of the fault-measuring point mutual information matrix are required to be independent of each other. I ^T I is recorded as matrix T ^T , which is a m×m full-rank matrix, and matrix T is called a diagnostic information matrix. At this time, the fault node information and measuring point information are completely contained in the diagnostic information matrix T, so the purpose of measuring point optimization can be achieved by extracting the eigenvalues of the matrix T. The trace (T) of the diagnostic information matrix represents the sum of all eigenvalues of the matrix, that is, the sum of the diagnostic capabilities of the measuring point group for all deviation sources. Therefore, in the optimization of measurement nodes, the trace of the diagnostic information matrix is used as the evaluation index of the measurement points to be selected, which is also called the comprehensive diagnosis ability index. The contribution degree of the comprehensive diagnosis ability of the node is the comprehensive diagnosis ability index:

E _sj ＝(GG _sj )/G (3)

G=trace(T)

T = (I ^T I) ^T (4)

Among them, G _sj is the sum of the eigenvalues of the mutual information matrix after removing the jth measuring point in the measuring point group.

Step 4: Describe the optimization problem according to the contribution of measuring points and the cost and quantity of measuring points:

At the same time, the contribution and cost of the measuring points are considered, and it is transformed into the objective function to be obtained by the optimization algorithm. By selecting the best measuring point configuration scheme, the fault diagnosis ability of the measuring points is maximized, and the required measuring point configuration cost minimum.

Step 5, apply the improved discrete binary particle swarm optimization algorithm to optimize the configuration results of the measuring points:

The standard particle swarm optimization algorithm is suitable for calculation in the continuous search space, but it cannot be directly applied to the discrete search space, and the standard particle swarm optimization algorithm must be improved. That is, the discrete binary particle swarm optimization algorithm is used to optimize the discrete binary space.

As shown in FIG. 2, it is a flow chart of establishing a system Bayesian network model in the present invention.

First, according to the structure and failure mode of the system, the failure mode and image analysis (FMEA) of the system is carried out to determine the nodes of the Bayesian network and the topology of the Bayesian network, that is, the directed-unconnected network that represents the connection relationship between nodes. Ring diagram.

Then, on the basis of the established Bayesian network topology, first determine the prior distribution of nodes according to the maximum entropy method, and then determine the node parameter values, that is, the conditional probability distribution of nodes, according to historical fault data and expert experience.

Before determining the conditional probability distribution, it is necessary to determine the prior distribution of nodes, and the present invention adopts the method of maximum entropy to determine the prior distribution. In practical engineering applications, since the nodes in the network are two-state, the Beta (p; a, b) distribution is usually taken as the prior distribution of the nodes in the network. Determine the mean value p ₀ of parameter p according to expert experience, and then determine the optimal values a ^* and b ^* of parameters a and b according to the maximum entropy algorithm, so as to determine the prior distribution of nodes.

H _B (a ^* ,b ^* )＝max(H _B (a,b))

a≥0,b≥0

a/(a+b)=p ₀ (5)

in

After determining the pre-test distribution of nodes, the present invention applies the Bayesian method to combine the calculated pre-test distribution with historical fault sample information to obtain the post-test distribution of nodes. The specific operations are as follows:

Among them, π(p) represents the pre-test distribution, p(D|p) represents the sample data, and π(p|D) represents the posterior distribution.

As shown in FIG. 3, it is a flow chart of the description of the optimization problem of the present invention.

At the same time, consider the contribution and cost of the measuring points, and convert it into the objective function to be obtained by the optimization algorithm. Considering the configuration cost and contribution of d measuring points are c _sj (j=1,2,...,d) ,E _sj (j=1,2,...,d), by selecting the best measuring point configuration scheme, the fault diagnosis capability of the measuring point is maximized, and the required measuring point configuration cost is minimized. set variable

Then, considering the contribution of measuring points, the cost of measuring points and the limitation of the number of measuring points in practice, the problem of optimal allocation of measuring points can be expressed as:

The key to solving the problem of optimal allocation of measuring points by applying discrete binary particle swarm optimization algorithm is how to code. Here x _i is used to represent the value of the i-th particle, and the value x _i of each particle is represented as a solution to the optimization problem. x _i =[x _i1 , x _i2 ,..., x _id ], d represents the dimension of the particle, and here represents the total number of configurable measuring points. The value of x _ij represents the configuration of measuring point j of the i-th particle, and its value is 0 or 1. If x _ij =1, it means that point j of the i-th particle will be configured with a measuring point, otherwise, point j will not be configured with a measuring point.

The present invention transforms the above optimization model to obtain the following objective function of the optimization problem, namely the fitness function of particle update:

Among them, Q is a penalty factor whose value is a sufficiently large positive number. D is a d-dimensional row vector whose elements are all 1. N is the number of measurement points that limit the configuration in practice. Here we can find the minimum value of the objective function.

The position of the particle is initialized by:

The initial velocity v _ij of the particle is randomly initialized according to the following formula:

v _id =v _min +rand()(v _max -v _min ) (15)

Among them, v _max and v _min represent the maximum and minimum limit values of the speed. Its value determines the maximum distance particles can move in one iteration. If it is larger, the search ability is enhanced, but the particles are easy to fly over the optimal solution. When it is small, the development ability is enhanced, but it is easy to fall into local optimum, so the value should be selected according to the actual situation.

Figure 4 is a flow chart of the improved discrete binary particle swarm optimization algorithm of the present invention.

The standard particle swarm optimization algorithm is suitable for calculation in the continuous search space, but it cannot be directly applied to the discrete search space, and the standard particle swarm optimization algorithm must be improved. That is, the discrete binary particle swarm optimization algorithm is used to optimize the discrete binary space. The speed update formula of particle swarm optimization algorithm is:

v _id ＝ω·v _id +c ₁ ·rand()·(p _id -x _id )+c ₂ ·rand()·(p _gd -x _id ) (16)

Wherein, i is the number of particles of the particle swarm; d is the dimension of the particle swarm, which in the present invention represents the total number of configurable measuring points of the system. If its value is too small, it will easily lead to the local optimal solution. If it is too large, it will increase the search time and slow down the convergence speed. Generally, it is more appropriate to take 20; w is the inertia weight, which plays a role in balancing the global search and local optimization of the algorithm. The role of search capabilities. A large inertia weight favors global search, while a small inertia weight favors local search. In order to obtain a better optimization effect, its value is required to decrease linearly from 1.4 to 0.4; c ₁ and c ₂ represent acceleration constants, which can also play a role in balancing the global search and local search capabilities of the algorithm. It is generally required that c ₁ =c ₂ and the range is between 0 and 4, and it is usually taken as 2 in practical applications; rand() is a random number randomly generated from a uniform distribution in the interval [0,1].

The velocity update formula of the discrete binary PSO algorithm is the same as that of the original PSO algorithm. The particle position update formula is different. In order to indicate that the value of the speed is the probability that the binary bit takes 1, the value of the speed is mapped to the interval [0,1], expressed as:

Here s(v _id ) represents the probability that the position x _id takes 1, and the particle updates its bit value through formula (12):

And the improved particle swarm position update formula. The mapping formula for velocity is changed to:

And the bit value update formula of the particle is changed to:

When v _id ≤ 0,

When v _id >0,

The present invention uses the particle position update formulas shown in formula (17) and formula (18) in the early stage of iterative search to ensure the global search capability of the algorithm. In the later stage of iterative search, the particle position update formulas shown in formula (19), formula (20) and formula (21) are used to ensure the local search ability of the algorithm. Doing so can ensure the globality of the solution and the fast convergence of the algorithm. The invention adopts the improved discrete binary particle swarm algorithm to solve the problem of optimal configuration of measuring points.

Claims (9)

1. A system measurement node optimal configuration method based on a Bayesian network is characterized by comprising the following steps:

step 1: establishing a Bayesian network model of the system;

step 2: calculating a mutual information matrix between the fault node and the measurement node according to the Bayesian network model;

and step 3: calculating the contribution degree of the measuring points to fault node diagnosis according to a mutual information matrix between the fault nodes and the measuring nodes, and determining a comprehensive diagnosis capability index;

and 4, step 4: describing an optimization problem according to the contribution degree of the measuring points to fault node diagnosis, measuring point cost and measuring point quantity limit;

and 5: performing optimization processing by using an improved discrete binary particle swarm algorithm to obtain an optimized configuration result of a measuring point;

the mutual information matrix between the fault node and the measurement node is as follows:

wherein, I is a mutual information matrix between the fault node and the measurement node; i is_ijThe mutual information between the fault node i and the measurement node j is obtained; m is the number of fault nodes; n is the number of measurement nodes; p is the probability value of the fault node; f. of_i1 indicates that the failed node i is in a failed state, f_iWhen the failure node i is in a normal state, 0 is represented; s_jExpressed as configuration measurement node j, s ═ 1_j0 denotes that no measurement node j is configured.

2. The bayesian network based system measurement node optimal configuration method according to claim 1, wherein: the establishing of the Bayesian network model of the system comprises the following processes:

step 1: carrying out fault mode and image analysis on the system according to the structure and the fault mode of the system, and determining nodes of the Bayesian network and a topological structure of the Bayesian network;

step 2: determining the pre-test distribution of the nodes according to a maximum entropy method on the basis of the topological structure of the Bayesian network;

and step 3: and determining node parameter values, namely conditional probability distribution of the nodes according to historical fault data and expert experience, and completing the establishment of the Bayesian network model.

3. The bayesian network based system measurement node optimal configuration method according to claim 2, wherein: the process of determining the pre-test distribution of the nodes according to the maximum entropy method comprises the following steps:

H_B(a^*,b^*)＝max(H_B(a,b))

a≥0,b≥0

a/(a+b)＝p₀

wherein a is a distribution parameter before test of the maximum entropy; b is a pre-test step parameter of the maximum entropy; p is a probability parameter; a is^*And b^*Optimal values for parameters a and b, respectively; beta () is Beta distribution; dp is to make a derivation on the probability parameter p; h_BIs the maximum entropy sign; p is a radical of₀Is the mean value of the probability parameter p.

4. The Bayesian network-based system measurement node optimal configuration method according to claim 2, wherein the conditional probability distribution of the nodes is as follows:

wherein pi (p) is the pre-test distribution; p (Dp) is sample data; pi (p | D) is the conditional probability distribution of the node; d is sample data; dp is the derivation of the parameter p; p is a probability parameter.

5. The Bayesian network-based system measurement node optimal configuration method according to claim 1, wherein the contribution degree of fault node diagnosis is as follows:

E_sj＝(G-G_sj)/G

G＝trace(T)

T＝(I^TI)^T

wherein E is_sjThe contribution degree for fault node diagnosis; g_sjThe sum of the characteristic values of the mutual information matrix after the jth measuring point is removed from the measuring point group is obtained; g is the sum of all characteristic values of the matrix; t is a diagnosis information matrix; i is^TI is denoted as matrix T^T，T^TIs a full rank matrix of m x m.

6. The Bayesian network-based system measurement node optimal configuration method according to claim 1, wherein the description of the optimization problem process according to contribution degree, measurement point cost and quantity comprises:

converting the contribution degree of fault node diagnosis, the measuring point cost and the measuring point number limit into an objective function:

wherein,the contribution degree for fault node diagnosis;measuring point cost;limiting the number of the measuring points; q is a penalty factor, which takes the value of a sufficiently large positive number; n is the limited number of measuring points; d is a row vector, and the elements of the row vector are all 1; x is the number of_iThe solution of the optimization problem, namely the measurement point configuration condition is solved; min f (x)_i) To optimize the problem.

7. The Bayesian network-based system measurement node optimal configuration method according to claim 1, wherein the improved discrete binary particle swarm algorithm is:

step 1: initializing a particle swarm and calculating the initial position and the initial speed of the particle;

step 2: calculating an objective function value, determining an individual optimal value and an overall optimal value, and updating a particle speed value according to a speed updating algorithm of the particle swarm algorithm;

and step 3: and updating the position value of the particle according to the iteration times, if the current iteration times are less than a preset parameter, adopting a particle position updating algorithm with global searching capability, and otherwise, adopting a particle position updating algorithm with local searching capability.

8. The bayesian network based system measurement node optimal configuration method according to claim 7, wherein: the initial positions of the particles are:

the initial velocity of the particles is:

v_id＝v_min+rand()(v_max-v_min)

the speed updating algorithm of the particle swarm algorithm is as follows:

v_id＝ω·v_id+c₁·rand()·(p_id-x_id)+c₂·rand()·(p_gd-x_id)

the particle location updating algorithm with global search capability is as follows:

the particle location update algorithm with local search capability is:

when v is_idWhen the content is less than or equal to 0,

when v is_id>At the time of 0, the number of the first,

wherein v is_maxIs the maximum limit value of the speed; v. of_minIs the minimum limit value of the speed; rand () is a random number, from the interval [0,1]]Randomly in the uniform distribution; i is the particle number of the particle swarm; d is the dimension of the particle swarm and represents the total number of the configurable measuring points of the system; w is an inertia weight used for balancing the global search capability and the local search capability of the algorithm; c. C₁And c₂The acceleration constant is expressed, and the function of balancing the global search and local search capability of the algorithm can be achieved; s (v)_id) Represents the position x_idTaking the probability of 1; x is the number of_idIs the current position of the particle; v. of_idIs the current velocity of the particle; p is a radical of_idThe current individual optimal value of the particle is obtained; p is a radical of_gdThe current overall optimal value of the particles is obtained; exp () is an exponential function.

9. The Bayesian network-based system measurement node optimal configuration method according to claim 7, wherein the preset parameters are:

c_ys＝r*M

wherein, c_ysIs a preset parameter; r is a proportional parameter; m is the maximum number of iterations.