1. A hierarchical system structure function learning method fused with an incomplete monitoring sequence is characterized by comprising the following steps:

s1, constructing a dynamic Bayesian network structure of the system based on the internal structure relationship of the hierarchical system;

s2, updating the joint state probability distribution of each node and the father node in the dynamic Bayesian network established in the step S1 by utilizing the state information monitored at the component, the subsystem and the system at different times;

and S3, estimating unknown parameters of the node condition probability table in the dynamic Bayesian network, namely system structure function parameters, based on the expectation-maximization algorithm by using the joint state probability distribution of each node and the father node thereof obtained in the step S2.

2. The method for learning a hierarchical system structure function fused with an incomplete monitoring sequence according to claim 1, wherein step S3 specifically comprises: if the obtained system structure function parameter estimation value meets the convergence condition, obtaining a final system structure function parameter estimation result; otherwise, updating the unknown parameters to be estimated in the node condition probability table of the dynamic Bayesian network by using the obtained system structure function parameter estimation value, and returning to the step S2 until the convergence condition is satisfied and then terminating.

3. The method for learning hierarchical system structure function fused with incomplete monitoring sequence according to claim 2, wherein said step S1 comprises the following sub-steps:

s11, establishing a dynamic Bayesian network structure according to the structural relationship of the system, the subsystem and the components in the hierarchical system, specifically: number of subsystems N in hierarchical system_subAnd number of parts N_unitDetermining the number of nodes in a single time slice of the dynamic Bayesian network;

number of State of component # lNumber of sub-System # m statesAnd the number of system states M_SDefine part # l node U separately_l(t) subsystem # m node S_m(t) and the value space of the system node S (t);

passing component node U between adjacent time slices in dynamic Bayesian network_l(t)→U_l(t +1) are connected to form the whole dynamic Bayesian network structure, and the node set is omega ═ U_l(t),S_m(t),S(t)}(l＝1,2,…,N_unit，m＝1,2,...,N_sub)；

S12, inputting known component # l degradation parameters into dynamic Bayesian network component node U_l(t) in the conditional probability table, the subsystem # m node S in the dynamic Bayesian network is set at random_m(t) and system node s (t) unknown parameters of the conditional probability table.

4. The method as claimed in claim 3, wherein in step S11, the time-domain invariance of the system structure function parameter is considered, and the conditional probability table parameters of the same type of node in different time slices in the dynamic bayesian network have the same value.

5. According to claimThe method for learning a hierarchical system structure function fused with an incomplete monitoring sequence, as claimed in claim 3, wherein the step S12 is implemented by randomly setting a subsystem # m node S in a dynamic bayesian network_m(t) and system node s (t) the unknown parameters of the conditional probability table specifically are:

randomly setting a subsystem # m node S in a time slice_m(t) copying the conditional probability table parameters of the system node S (t) and the system node S (t) into the conditional probability table of any time slice of the whole dynamic Bayesian network;

for the subsystem # m node, the node is randomly set at its parent node pa (S)_m(t)) parameter vector at jth combination ofAnd must satisfy

For a system node, a parameter vector of the node under the jth combination of its parent node pa (S (t)) is randomly setAnd must satisfy

After the parameters meeting the requirements are randomly generated, the parameters are input into the node S_m(t) and S (t) in the conditional probability table of each time slice of the dynamic Bayesian network, the time-domain invariance of the system structure function parameter is ensured.

6. The method for learning a hierarchical system structure function fused with an incomplete monitoring sequence according to claim 5, wherein the known degradation parameters of component # l in step S12 are specifically: to be provided withPresentation part # lThe probability of transitioning from state i to j after one unit of time, thenIts degradation parameter, i.e. one-step state transition probability matrix P^lExpressed as:

7. the method as claimed in claim 1, wherein the step S3 is implemented by integrating the monitoring information representing the same structure function parameter in different time slices, and calculating the sub-system # m node S based on the joint state probability distribution of each node and its parent node obtained in the step S2_m(t) and the expected value of the combination of the system node S (t) and the state of the father node, filling the incomplete state monitoring sequence into complete monitoring data under each time slice through the expected value; unknown parameters of the node condition probability table in the dynamic bayesian network are then estimated based on an expectation-maximization algorithm.

Background

With the increase of the industrialization requirement of intelligent manufacturing equipment and the promotion of the industrialization process, the customer requirement, the system composition, the system technology and the working environment of modern systems (such as industrial robots, numerical control machines, anti-tank missiles and remote bombers) are increasingly complex, and the reliability evaluation of the systems is increasingly difficult. The accurate grasp of the structural and functional relationships between the system and its components, and the establishment of the system structural function are the prerequisites for the reliability assessment, optimization and maintenance decision of the system.

On one hand, the system structure function in actual engineering is often not directly and accurately given by experts due to the limitations of various types and quantities of components, complex system organization structures, variable operation environments and the like. On the other hand, due to the reasons of high monitoring cost, difficult test organization, complex system technology and the like, engineers cannot perform a large number of reliability tests on the whole complex system, and the state monitoring data at the system operation stage usually has the characteristics of small sample, incompleteness and cross-hierarchy. The small sample size of the system monitoring data can lead to low learning accuracy of the system structure function due to the small subsample characteristic, and further the accuracy requirement of reliability evaluation can not be met. In addition, the cross-hierarchy and incomplete characteristics of the system monitoring data can cause strong correlation to exist in the available monitoring information, and simply neglecting the correlation can cause loss of key information contained in the system monitoring data, thereby reducing the learning precision of the system structure function. Therefore, there is a strong need in academia and industry for a reliable and accurate learning method of system structure function, which fully utilizes the existing system status monitoring data to guide the construction of system structure function.

The Bayesian network is a directed acyclic graph for describing uncertainty relations among variables, and mainly comprises two parts, namely a network structure and a conditional probability table: determining the dependency relationship among variables qualitatively by the network structure; the conditional probability table quantitatively expresses the strength of the dependency relationship between the variables. The dynamic Bayesian network is a special expression mode of the Bayesian network, can effectively reveal the complex failure process and the degradation nature of the system and the components thereof along with the change of time, and has obvious advantages in fusing incomplete state monitoring sequence data. It is worth noting that modern systems often have a distinct hierarchical relationship, and their network structure can be directly built. Therefore, the learning of the system structure function is further converted into parameter estimation of the conditional probability table. However, since the monitoring sequence data contains dynamic monitoring information of the system at different time instants and has small sub-sample, incomplete and cross-hierarchy characteristics, it has a great challenge to effectively fuse such monitoring sequence data. Up to now, a hierarchical system structure function learning technology for fusing incomplete monitoring sequences is still blank at home and abroad. The existing method, such as a random field method, can only process the problem of hierarchical system structure function learning under the condition of continuous internal variables. In engineering practice, the states of the system and the components thereof are often discrete binary values or multiple values, so that a system structure function learning method under incomplete monitoring sequence data is urgently needed to be developed, and a feasible solution is provided for the hierarchical system structure function learning problem in engineering practice.

Disclosure of Invention

In order to solve the technical problems, the invention provides a hierarchical system structure function learning method fusing an incomplete monitoring sequence, which can effectively fuse incomplete, cross-hierarchical and small sub-sample state monitoring data of a hierarchical system and accurately and effectively learn system structure parameters.

The technical scheme adopted by the invention is as follows: a hierarchical system structure function learning method fusing an incomplete monitoring sequence comprises the following steps:

s1, constructing a dynamic Bayesian network structure of the system based on the internal structure relationship of the hierarchical system;

s2, updating the joint state probability distribution of each node and the father node in the dynamic Bayesian network established in the step S1 by utilizing the state information monitored at the component, the subsystem and the system at different times;

and S3, estimating unknown parameters of the node condition probability table in the dynamic Bayesian network, namely system structure function parameters, based on the expectation-maximization algorithm by using the joint state probability distribution of each node and the father node thereof obtained in the step S2.

Step S3 specifically includes: if the obtained system structure function parameter estimation value meets the convergence condition, obtaining a final system structure function parameter estimation result; otherwise, updating the unknown parameters to be estimated in the node condition probability table of the dynamic Bayesian network by using the obtained system structure function parameter estimation value, and returning to the step S2 until the convergence condition is satisfied and then terminating.

The step S1 includes the following sub-steps:

s11, establishing a dynamic Bayesian network structure according to the structural relationship of the system, the subsystem and the components in the hierarchical system, specifically: number of subsystems N in hierarchical system_subAnd number of parts N_unitDetermining the number of nodes in a single time slice of the dynamic Bayesian network;

number of State of component # lNumber of sub-System # m statesAnd the number of system states M_SDefine part # l node U separately_l(t) subsystem # m node S_m(t) and the value space of the system node S (t);

passing component node U between adjacent time slices in dynamic Bayesian network_l(t)→U_l(t +1) are connected to form the whole dynamic Bayesian network structure, and the node set is omega ═ U_l(t),S_m(t),S(t)}(l＝1,2,…,N_unit，m＝1,2,...,N_sub)；

S12, inputting the known degradation parameters of the part # l into the dynamic Bayesian networkNetwork element node U_l(t) in the conditional probability table, the subsystem # m node S in the dynamic Bayesian network is set at random_m(t) and system node s (t) unknown parameters of the conditional probability table.

In step S11, considering the time-domain invariance of the system structure function parameters, the conditional probability table parameters of different time slices in the dynamic bayesian network of the same type of node have the same value.

In step S12, the random setting of the subsystem # m node S in the dynamic bayesian network_m(t) and system node s (t) the unknown parameters of the conditional probability table specifically are:

randomly setting a subsystem # m node S in a time slice_m(t) copying the conditional probability table parameters of the system node S (t) and the system node S (t) into the conditional probability table of any time slice of the whole dynamic Bayesian network;

for the subsystem # m node, the node is randomly set at its parent node pa (S)_m(t)) parameter vector at jth combination ofAnd must satisfy

For a system node, a parameter vector of the node under the jth combination of its parent node pa (S (t)) is randomly setAnd must satisfy

After the parameters meeting the requirements are randomly generated, the parameters are input into the node S_m(t) and S (t) in the conditional probability table of each time slice of the dynamic Bayesian network, the time-domain invariance of the system structure function parameter is ensured.

The known degradation parameters of the component # l in the step S12 are specifically: to be provided withRepresenting the probability that component # l transitions from state i to j after one unit time, then there isIts degradation parameter, i.e. one-step state transition probability matrix P^lExpressed as:

step S3 is to integrate the monitoring information representing the same structure function parameter in different time slices, and to calculate the subsystem # m node S based on the joint state probability distribution of each node and its father node obtained in step S2_m(t) and the expected value of the combination of the system node S (t) and the state of the father node, filling the incomplete state monitoring sequence into complete monitoring data under each time slice through the expected value; unknown parameters of the node condition probability table in the dynamic bayesian network are then estimated based on an expectation-maximization algorithm.

The invention has the beneficial effects that: according to the invention, a dynamic Bayesian network is used for representing a structural function of a hierarchical system, and a network structure can be directly constructed according to the structural relationship of the hierarchical system; the dynamic Bayesian network with different time slices can fuse incomplete state monitoring information of the system and the components thereof at different moments and effectively perform probabilistic reasoning; finally, learning the conditional probability table parameters of the dynamic Bayesian network nodes through an expectation-maximization algorithm, and ensuring the time domain invariance of the system structure function parameters by using the parameter modularization idea; the method can effectively fuse incomplete, cross-level and small subsample state monitoring data of a hierarchical system, and accurately and effectively learn the structural parameters of the system; the accuracy of the hierarchical system reliability evaluation of the incomplete state monitoring sequence is improved.

Drawings

FIG. 1 is a flow chart of the method of the present invention;

FIG. 2 is a block diagram of the reliability of an electromechanical actuator system to which embodiments of the present invention are directed;

fig. 3 is a dynamic bayesian network structure of an electromechanical actuator system to which an embodiment of the present invention is directed.

Detailed Description

In order to facilitate the understanding of the technical contents of the present invention by those skilled in the art, the present invention will be further explained with reference to the accompanying drawings.

As shown in FIG. 1, the present invention is embodied in an electromechanical actuator system, comprising the steps of:

s1: constructing a dynamic Bayesian network structure based on the internal structure relationship of the electronic mechanical actuator system, and converting system structure function learning into conditional probability table parameter learning of nodes in the network; known component degradation parameters are filled in a conditional probability table of a component node, and initial values are randomly set for unknown parameters in the conditional probability table.

The electromechanical actuator system in this embodiment is composed of 5 components including 2 pulse width modulation controllers of the same type, 2 dc motors of the same type, and 1 power supply. The pulse width modulation controller #1 and the direct current motor #1 jointly form an actuating mechanism servo drive subsystem # 1. Similarly, the pwm controller #2 and the dc motor #2 together form an actuator servo drive subsystem # 2. Two actuator servo drive subsystems with the same function together with power supply #1 constitute the entire electromechanical actuator system, the reliability block diagram of which is shown in fig. 2.

In fig. 2, the component includes: the pwm controller #1, the dc motor #1, the pwm controller #2, the dc motor #2, and the power supply #1 are denoted as U, respectively₁(t)、U₂(t)、U₃(t)、U₄(t) and U₅(t); the subsystem includes: actuator servo drive subsystems #1 and #2 are denoted S, respectively₁(t)、S₂(t), a subsystem node S₃(t) is represented by S₁(t) and S₂(t) the subsystems together, and then S₃(t) and U₅(t) together make up the entire system S (t).

Electronic structure constructed according to the above system structure relationshipThe dynamic Bayesian network structure of the mechanical driver system is shown in FIG. 3, and has N_unit5 and N_sub3. Wherein the arrow containing a "1" indicates the connection of the component node on the adjacent time slice, i.e. U_l(t)→U_l(t + 1). As can be seen from FIG. 3, S₁Parent node pa (S) of (t) node₁(t))＝{U₁(t),U₂(t)}，S₃Parent node pa (S) of (t) node₃(t))＝{U₅(t),S₃(t), S (t) node parent pa (S (t) ═ S (t) } S₁(t),S₂(t)}。

The number of the states of the components, the subsystems and the system is 4, and the one-step state transition probability matrix corresponding to the 5 components is as follows:

the above-mentioned one-step state transition probability matrix P¹、P²、P³、P⁴And P⁵The internal parameter information is directly input into a conditional probability table of each component node in the dynamic Bayesian network, and for any one of l 1,2, 5, m 1,2When each component node is in the best state when t is equal to 0, the state 1 represents the best state, the state 4 represents the worst state, and the state probability distribution is [1,0,0,0]. Due to the subsystem S₃(t) by two subsystems S of the same type₁(t) and S₂(t) are of the same composition and function, thus S₃(t) State is determined by the subsystem S₁(t) and S₂Optimum state determination in (t), i.e. parameter takingValues were obtained directly as shown in table 1. As can be seen from Table 1, S₃And (t) the conditional probability table parameters of the nodes are independent of t, namely the conditional probability table parameters of the same type of nodes on any time slice are the same and accord with the time-domain invariant characteristic of the system structure function parameters.

TABLE 1S₃(t) conditional probability table parameters of nodes

In this embodiment, the subsystem #1 and the subsystem #2 are composed of the same type of components and have the same function, so the node S₁(t) and S₂The conditional probability table parameters of (t) are the same. Thus, learning the electromechanical actuator system structure function is equivalent to learning node S₁(t) and conditional probability table parameters of node S (t), i.e.Andand the parameters have a time-domain invariant characteristic. For any j e {1, 2.,. 16}, there is a subsystem #1 node S₁(t) and system node S (t) are respectively the unknown parameter vectors under the status combination of the jth father nodeAndin satisfyingAndunder the condition (S), the node (S) is randomly set₁The initial values of the unknown parameters in the conditional probability tables of (t) and s (t) are shown in tables 2 and 3. Inputting the initial parameter values in Table 2 into node S₁(t) and S₂(t) inputting the initial parameter values in table 3 into the node s (t) in the conditional probability table for each time slice of the dynamic bayesian network.

TABLE 2 input node S₁(t) and S₂(t) de initial parameter values in conditional probability table for each time slice of dynamic Bayesian network

Table 3 initial parameter values of input nodes s (t) in conditional probability tables for each time slice of a dynamic bayesian network

S2: existing N_sample100 electromechanical actuator systems of the same type are available for monitoring, at T₀At 30 months, the monitoring intervals and monitoring time series for the components, subsystems and systems are shown in table 4. The monitoring scheme can obtain the state monitoring information of the system at different moments and different levels, so that the available state monitoring sequence data has the characteristics of incompleteness and cross-level.

TABLE 4 at T₀Monitoring intervals and monitoring time series for components, subsystems and systems at 30 months

Monitoring hierarchy	Numbering	Monitoring interval (moon)	Monitoring time series (moon)
				Component part	#1,#2,#3,#4,#5	3	{0,3,6,...,30}
Sub-system	#1,#2	2	{0,2,4,...,30}
				System for controlling a power supply	-	2	{0,2,4,...,30}

Monitoring sequence data D ═ D based on states of the system at different times and different levels₁,d₂,...,d₁₀₀And respectively calculating a node S in the dynamic Bayesian network built in the S1 step for any n element {1, 2.,. 100} and t element {0, 1.,. 30}, wherein the node S is in the dynamic Bayesian network built in the S1 step₁(t)、S₂(t) and S (t) Joint State probability distributions with their respective parent nodes, i.e., Pr { S₁(t),pa(S₁(t))|d_n}、Pr{S₂(t),pa(S₂(t))|d_nAnd Pr { S (t), pa (S (t)) | d_n}。

S3: the system structure function parameter reflects the state mapping relation between the system and the components thereof, and has the characteristic of time-domain invariance, namely for any te {0, 1., 30}, node S₁(t)、S₂The parameters of both (t) and s (t) conditional probability tables remain unchanged. By utilizing the thought of parameter modularization, information representing the same structure function parameters in different time slices is integrated, and the structure function parameters of the system are learned more accurately and effectively. There is | sp (pa (S)₁(t)))|＝|sp(pa(S₂(t)) | sp (pa (S (t))) | 16, so S is calculated for each of arbitrary k ∈ {1,2,3,4} and j ∈ {1,2₁(t)、S₂(t) and S (t) expected values for their respective parent nodes:

after the incomplete state monitoring sequence is filled into the complete monitoring data under each time slice through the expected value, estimating the system structure function parameter based on the maximum likelihood estimation method, namely the dynamic Bayesian network node S₁(t)、S₂(t) and S (t) unknown parameters in the conditional probability table. It is noted that actuator servo drive subsystems #1 and #2 have the same components and functions, and the system architecture function parameters are the same. Therefore, the node S is modularized by using parameters₁(t) and S₂And (t) integrating the monitoring information, and jointly learning the same conditional probability table parameters. For any k ∈ {1,2,3,4}, j ∈ {1,2,. 16}, useAndunknown parameters respectively representing that the subsystem #1 and the subsystem #2 are in the state k when the parent node is in the jth state combinationAndthe estimation result of (2) is:

and then has node S₁(t) unknown parameter vector estimation value of conditional probability table under jth father node state combinationGet node S₁(t) estimated values of all unknown parameters in the conditional probability tableConsidering node S₁(t) and S₂(t) have the same conditional probability table parameters, so

For system node S (t), any k ∈ {1,2,3,4} and j ∈ {1,2Unknown parameter representing that a system node is in state k when its parent node is in the jth state combinationThe estimation result of (2) is:

further, there is a node S (t) condition probability table with unknown parameter vector estimation value under the jth father node state combinationObtaining the estimated values of all unknown parameters in the node S (t) conditional probability table

Two adjacent iterations in a decision expectation maximization algorithmWhether the log likelihood difference of the monitoring data is less than a specific threshold value epsilon is 2 multiplied by 10^-3. Let theta^knownIs a known parameter in the dynamic Bayesian network, namely a one-step state transition probability matrix of the component, an initial state distribution of the component and a node S₃(t) conditional probability table parameters; theta^unknown,oldAnd Θ^unknown,newRespectively, the estimated values of the unknown parameters under two adjacent iterations are estimated by the subsystem parametersAnd system parameter estimationTogether, then the termination conditions are equivalent to:

|ln(Pr{D|Θ^unknown,new,Θ^known})-ln(Pr{D|Θ^unknown,old,Θ^known})|≤ε (6)

if the termination condition is met, estimating the parameter in the last iterationFilling node S₁(t) and S₂(t) in a conditional probability table in each time slice of the dynamic bayesian network; estimating the parameter under the last iterationFilling the node S (t) in the conditional probability table of each time slice of the dynamic Bayesian network, and regarding the node S (t) as a final system structure function parameter estimation value; otherwise, using the parameter estimation value in the last iterationUpdating the parameter theta to be estimated in the dynamic Bayesian network^unknown,oldAnd continuing to step S2 to perform the next joint probability distribution calculation and parameter estimation, and iterating until the convergence condition is satisfied and then terminating.

The dynamic Bayesian network in this embodiment is used to characterize electro-mechanical transmissionThe structural function of the actuator system, the system structural function parameters of which are further converted into a subsystem S₁(t) node, S₂(t) conditional probability table parameters for the node and the system S (t) node. Each node has 16 father node state combinations, each combination contains 4 unknown parameters, and the parameter sum is 1. To characterize the accuracy of the estimation result of the unknown parameters, S is defined₁(t)、S₂The absolute value differences between the estimated parameters and the real parameters of the (t) node and the S (t) node under the jth father node state combination are respectively as follows:

due to node S₁(t) and S₂Since the conditional probability tables of (t) have the same parameters and the results of the accuracy of parameter estimation are the same, only S is shown in table 5₁And (t) and S (t) nodes respectively obtain parameter estimation accuracy results under 16 parent node state combinations.

TABLE 5S₁(t) and S (t) nodes respectively have parameter estimation accuracy results under respective 16 parent node state combinations

The results of the above embodiments show that the difference between the system structure function parameter estimation value obtained by the method of the present invention and the real parameter value is very small, and is close to 0, which indicates that the method of the present invention can effectively fuse the incomplete state monitoring sequence to perform the hierarchical system structure function learning, and well process the small subsample, incomplete and cross-hierarchical characteristics of the existing state monitoring data. In the process of learning the system structure function, the time domain invariant characteristic of the structure function parameter is considered by the method, and the whole structure function learning process is more in line with the engineering practice.

It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.