CN108573282A - Target identification method based on the BN parameter learnings under small data set - Google Patents
Target identification method based on the BN parameter learnings under small data set Download PDFInfo
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Abstract
The present invention relates to the target identification methods based on the BN parameter learnings under small data set, it is organically combined using Small Sample Database collection and qualitative expertise, BN parameter learning precision is improved by convex Optimization Solution, to complete target identification BN modelings, finally reflect dbjective state using target identification BN the reasoning results.The present invention is based on learning algorithms in BN theories and ripe reasoning algorithm to complete the modeling needed for target identification and reasoning task, take full advantage of the equation and inequality constraints condition of some expertises, influence of the data deficiencies to parameter learning precision is compensated for a certain extent, it in turn avoids carrying out target identification process complicated mathematical modeling, gained identification inference pattern has many advantages, such as that characteristic parameter is few, learning ability is strong, explanatory good, is particularly suitable for noisy, uncertain, dynamic target identification system.
Description
Technical field
The present invention relates to the target identification application fields in artificial intelligence, Management Science and Engineering, and in particular to Yi Zhongji
The target identification method of BN parameter learnings under small data set.
Background technology
Bayesian network (Bayesian Network, BN) is that dependence between node is expressed in the form of conditional probability table
Directed acyclic graph, sample information is combined by it with priori, is described respectively in the form of directed edge and conditional probability table
Qualitative and quantitative dependence between variable, expression is visual in image, and theoretical foundation is solid, and inferential capability is powerful, be uncertain
Sex chromosome mosaicism models and the effective tool of reasoning, in processing audio identification, Activity recognition, recognition of face, medical diagnosis, fault diagnosis
Equal field of target recognition are all widely used.
The study BN parameters of precise and high efficiency, are the bases for efficiently using BN model solving practical problems.The parameter learning of BN
It is that the conditional probability of node variable is learnt using sample information and priori according to the structure (directed acyclic graph) for determining BN
It is distributed (conditional probability table).At present in many classical practical algorithms of the field of BN parameter learnings research and development, but this
The realization and application of a little methods are all based on large-scale dataset (complete or after supplement complete), and in practical engineering application
In, the factors such as environment, material, time are limited to, many experiments often can not be repeated several times, enabling the experiment number of acquisition
According to less, sample size very little, the information that can be expressed in such Small Sample Database collection is sufficiently complete, the BN ginsengs thus carried out
The accuracy and reliability that mathematics is practised can not ensure.Thus the BN parameter learnings based on Small Sample Database collection, i.e. BN moulds are derived
The research of type modeling problem.
After converting Problem Areas to the expression of BN models, BN theories can be utilized to complete reasoning task.Wherein, joint tree
(Junction tree) algorithm is one of the BN Accurate Reasoning algorithms that current calculating speed is fast, most widely used.BN as solution never
The effective ways of certainty and the processing of incomplete Information Problems, due to its organically combine probability theory and graph theory it is theoretical at
Fruit is the ideal tools that can be applied to target identification.
Invention content
The object of the present invention is to provide a kind of target identification method based on the BN parameter learnings under small data set, utilization is small
Sample data set is organically combined with qualitative expertise, BN parameter learning precision is improved by convex Optimization Solution, to complete
Target identification BN modelings, finally reflect dbjective state using target identification BN the reasoning results, improve the accurate of target identification
Property and validity.
The technical solution adopted in the present invention is：
Target identification method based on the BN parameter learnings under small data set, it is characterised in that：
It is organically combined using Small Sample Database collection and qualitative expertise, BN parameter learnings is improved by convex Optimization Solution
Precision finally reflects dbjective state to complete target identification BN modelings using target identification BN the reasoning results.
The target identification method based on the BN parameter learnings under small data set, it is characterised in that：
Specifically include following steps：
1st step：It is super that Dirichlet distributions in objective attribute target attribute probability threshold value Ω and the BN parameter learning of target identification are set
Parameter alphaijk；
2nd step：BN model structures G is established according to field of target recognition knowledge；
3rd step：Obtain target sample data set D；
4th step：Judge BN parameter θsijkIt is whether modeled；If parameter model, the 8th step is jumped to；If without parameter
Modeling then utilizes the 5th step to the 7th step, calculates BN model parameters θijk；
5th step：According to sample data set D statistical sample amounts Nijk, i.e., father node state is j, saves for i-th in sample data
Point takes the statistical value of k-th of state；
6th step：Expertise is formed into constraint set ξ according to following formula (2) and formula (3)；
Formula (2) is obtained according to the regression nature of BN node parameters；Related part BN node parameters are described as differing for formula (3)
Formula set, i.e.,：
Wherein, θAExpression parameter sequence, C are a constant and C >=0；
7th step：According to sample statistic Nijk, constrain set ξ, i.e., formula (2), (3) and objective function Equation (4) into
Row parameter optimization determines BN parameter θsijk；
If NijkIt is 0, then enables Nijk=0.01；θijkIt solves and is completed using convex Optimization Solution tool, be then back to the 3rd step；
8th step：In BN models, observation evidence ev to be identified is obtained by D, is made inferences using Junction tree, from
And obtain objective attribute target attribute probability Ω '；
9th step：Judge whether objective attribute target attribute probability Ω ' is more than or equal to threshold value Ω；Return to step 3 if being unsatisfactory for；If full
It is sufficient then export objective attribute target attribute, i.e. target identification result.
The present invention has the following advantages：
The modeling needed for target identification is completed the present invention is based on learning algorithm in BN theories and ripe reasoning algorithm and is pushed away
Reason task.The equation and inequality constraints condition for taking full advantage of some expertises, compensate for data not to a certain extent
Influence of the foot to parameter learning precision in turn avoids carrying out target identification process complicated mathematical modeling, and gained identifies reasoning
Model has many advantages, such as that characteristic parameter is few, learning ability is strong, explanatory good, is particularly suitable for noisy, uncertain, dynamic
Target identification system.Compared with the prior art, target identification method proposed by the present invention can be big under conditions of data set is rare
The big accuracy and speed for improving target identification, can be widely applied to the field of target recognition such as medicine, military affairs, industrial and agricultural production.
Description of the drawings
Fig. 1 is the flow of the target identification of the BN parameter learnings under a kind of small data set that the embodiment of the present invention one provides
Figure；
Fig. 2 is target identification BN model structures under the conditions of a kind of small data sample data set provided by Embodiment 2 of the present invention
Figure.
Specific implementation mode
The present invention will be described in detail With reference to embodiment.
Bayesian network can be expressed as B (G, θ), and wherein G is a directed acyclic graph with n node, the n in G
N stochastic variable of a node on behalf, the directed edge between node represent the dependence between stochastic variable；θ is and each node
Relevant conditional probability table is expressed as P (Xi|Pa(Xi)).θ quantitatively expresses nodes XiWith its father node Pa (Xi) between according to
It is the joint probability distribution of BN to rely degree, formula (1)：
Wherein, Pa(Xi) indicate X in GiFather node set conditional probability distribution, P (Xi|Pa(Xi)) indicate to be included in G
The probability that each of the variable of given father node value is worth.
P(Xi|Pa(Xi)) k-th of probability value be expressed as θijk=P (Xi=k | Pa(Xi)=j) it is nodes XiOne
Parameter, wherein θijk∈ θ, 1≤i≤n, 1≤j≤qi, 1≤k≤ri。riIndicate XiNumber of states, qiIndicate XiFather node group
Close Pa(Xi) gesture.Obviously, nodes XiOne shared ri×qiA parameter, they constitute a ri×qiThe matrix of dimension, referred to as
Nodes XiConditional probability distribution table (ConditionProbability Table, CPT).
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation describes.
Embodiment one：
BN model parameter learning methods under the conditions of a kind of Small Sample Database collection of offer of the embodiment of the present invention, as shown in Figure 1, should
Method includes：
1st step：It is super that Dirichlet distributions in objective attribute target attribute probability threshold value Ω and the BN parameter learning of target identification are set
Parameter alphaijk；
2nd step：BN model structures G is established according to field of target recognition knowledge；
3rd step：Obtain target sample data set D；
4th step：Judge BN parameter θsijkIt is whether modeled.If parameter model, the 8th step is jumped to；If without parameter
Modeling then utilizes the method that the 5th step is described to the 7th step, calculates BN model parameters θijk；
5th step：According to sample data set D statistical sample amounts Nijk, i.e., father node state is j, saves for i-th in sample data
Point takes the statistical value of k-th of state；
6th step：Expertise is formed into constraint set ξ according to following formula (2) and formula (3)；
Formula (2) can be obtained according to the regression nature of BN node parameters；Related part BN node parameters can conveniently be described as formula
(3) inequality set, i.e.,：
Wherein, θAExpression parameter sequence, C are a constant and C >=0；
7th step：According to sample statistic Nijk, constrain set ξ, i.e., formula (2), (3) and objective function Equation (4) into
Row parameter optimization determines BN parameter θsijk。
If NijkIt is 0, then enables Nijk=0.01；θijkSolving can utilize convex Optimization Solution tool to complete, and be then back to the 3rd step.
8th step：In BN models, observation evidence ev to be identified is obtained by D, using Junction tree (referring to Judea
Pearl writes《Causality:Models, Reasoning and Inference (second edition)》, Cambridge University
Press, 2009) it makes inferences, to obtain objective attribute target attribute probability Ω '；
9th step：Judge whether objective attribute target attribute probability Ω ' is more than or equal to threshold value Ω.Return to step 3 if being unsatisfactory for；If full
It is sufficient then export objective attribute target attribute, i.e. target identification result.
Embodiment two：
Based on inventive concept identical with embodiment one, BN under the conditions of a kind of Small Sample Database collection of offer of the embodiment of the present invention
Model parameter learning method is applied to bearing failure diagnosis this typical target identification problem, illustrates that the present invention is based on small datas
The specific implementation step of the target identification method of the lower BN parameter learnings of collection.
Data are derived from the rolling bearing fault data of Case Western Reserve University bearing data center of U.S. offer in this use-case.It should
Data can website http in its center://www.eecs.case.edu/laboratory/bearing/download.htm
Upper acquisition.The drive end bearing model SKF 6205-2RS JEM of experimental provision, fan end bearing designation are SKF6203-2RS
JEM.Acceleration transducer is respectively placed in fan end and drive end axle bearing to acquire vibration information.Acceleration transducer can
To acquire, rolling bearing is normal, running state information of inner ring and rolling element.Vibration acceleration signal is recorded by 16 channel datas
Instrument acquires, and it is that 2 horse-power-hour rotating speeds are 1750rpm that drive end bearing failure sample frequency, which takes 12KHz, motor load,.
Experiment is respectively that drive end bearing inner ring, outer ring and rolling element manufacture point deteriorate by way of electrical discharge machining
Wound, simulates the failure of Injured level, distinguishes (0.007 inch, 0.014 inch, 0.021 English from small to large in lesion diameter
It is very little and 0.028 inch) when tested.The data that this case selection pitting attack damage diameter minimum acquires when being 0.007 inch into
Row analysis, to emulate bearing, there is a situation where diagnosed to it when initial failure.
Characteristic acquisition methods refer to document (depths of the such as Guo Wenqiang, Zhang Baorong, Peng Cheng based on wavelet packet and BN models
Ditch ball bearing fault diagnosis [J] bearings, 2016,59 (03)：48-52.).Choose 35 in 300 groups of true fault feature samples
Group carries out BN parameter learning modeling experiments for small data set；169 groups of true fault feature samples are used for as observation evidence ev
Reasoning is tested, and object recognition task is completed.
The hardware environment used in use-case is the computer of 4G memories, Intel CPU 2.6GHz, and BN Reasoning softwars use
Bayesian Network Tool (abbreviation BNT) kit of Kevin Murphy exploitations.That convex Optimization Solution is selected is CVX
Convex optimization tool packet (http://www.cvxr.com/cvx/) it completes.Using method proposed by the invention to bearing fault into
Row identification, is as follows：
1st step：Hyper parameter α in fault diagnosis confidence threshold parameter Ω and BN study is setijk；Threshold parameter Ω herein
=0.75；Hyper parameter αijkIt can be obtained by expertise, referring specifically to the 6th step；
2nd step：BN model structure G are established according to expertise, as shown in Figure 2.Use bearing fault type as father node
X1；X1 has q=3 value event, corresponds to rolling bearing " normal ", " inner ring " and " rolling element " failure respectively, respectively use " 1 ",
" 2 ", " 3 " indicate.It is used as child node, each Xu there are 3 value events with 8 discretized features vector Xu (u=2 ... ..., 9),
Respectively " high frequency " of vibration signal, " intermediate frequency ", " low frequency " component use " 1 ", " 2 ", " 3 " to indicate respectively.Connected successively with directed edge
Connect father node and child node, i.e., successively using X1 as the arrow tail of 8 directed edges, arrow be respectively directed to X2, X3, X4, X5, X6, X7,
X8 and X9；
3rd step：Obtain target sample data set D；
4th step：Judge BN parameter θsijkIt is whether modeled.There is no parameter model then step 5 to be utilized to be described to step 7
Method calculates BN parameter θsijk；If parameter model, 8 are gone to step；
5th step：According to sample data set D statistical sample amounts Nijk, i.e., father node state is j, saves for i-th in sample data
Point takes the statistical value of k-th of state；For this sentences X4, N4jkIndicate that the third feature vector of target to be identified is high frequency division
Measure the number occurred.Small sample set (preceding 35 groups of true fault data) is chosen to test for parameter learning；
6th step：Expertise is formed into constraint set ξ according to formula (2) and formula (3)；
For this sentences X4, known by formula (2), obtains one group of equality constraint：
Rolling bearing be " normal " state when, by expertise it is found that feature vector, X 4 " low frequency " component appearance probability,
The sum of probability that the probability that " intermediate frequency " component occurs occurs with " high frequency " component is 1, i.e. θ411+θ412+θ413=1.
Hyper parameter α in step 1ijkValue need to only work as α413=-1 and α411=1, other equal values of hyper parameter are 0, C=0,
Then the inequality constraints form of the description of formula (3) is obtained：
α411θ411+α413θ413-0≤0
Optionally, when rolling bearing is " inner ring failure " state, the probability that X4 " low frequency " component occurs is less than or equal to " height
Frequently the probability that component occurs ", i.e. θ413≤θ411；
Similar, one group of constraint set ξ of the description shaped like formula (2) and formula (3) can be obtained.
7th step：According to sample statistic Nijk, constrain set ξ, i.e., formula (2), (3) and objective function Equation (4) into
Row parameter optimization determines BN parameter θsijk.It is then back to step 3, until all parameter θs of BNijkIt all solves and completes, i.e., BN is built
Mould is completed.Then, the identification process of step 8 is carried out.
Optionally, θijkSolving can utilize convex Optimization Solution kit CVX to complete；
8th step：In BN models, observation evidence to be identified is obtained by D, is made inferences using BN reasoning algorithms, to
Complete type node X1 reliabilities Ω ' updates to be identified；
Optionally, it carries out completing reasoning using the Junction tree of Pearl；
9th step：Judge whether objective attribute target attribute probability Ω ' is more than or equal to threshold value Ω=0.75.The return to step if being unsatisfactory for
3；Objective attribute target attribute, i.e. target identification result are exported if meeting.
The BN parameter learning of (35 group fault data), and pushing away in this, as target have been carried out under small data set in this use-case
Identification model is managed, the correctness and validity of learning model building method proposed by the present invention are demonstrated：
Classical MLE methods, CML methods, IRE methods and the method for the present invention are utilized respectively using small sample set (35 groups of fault datas)
It carries out parameter learning and builds reasoning identification model, then utilize Junction tree under established BN models with 169 groups of data
Make inferences verification.Reasoning recognition result is listed in table 1.
Target identification BN model based reasoning recognition results under 1 small sample of table
Contrast table 1 can be seen that：Under the conditions of small data set, with the method for the present invention right judging rate higher than MLE methods, CML methods and
IRE methods illustrate the method for the present invention correctness.Under condition of small sample, remains able to obtain relatively good recognition result, show
The method of the present invention has larger advantage in terms of the validity of target identification reasoning.
Based on the target identification method of the BN parameter learnings under small data set, it is suitable for uncertain, dynamic environment, it should
Method is greatly improved the precision of BN parameter learnings and the discrimination of target identification, is the effective way for solving the problems, such as target identification
Diameter can be widely applied to the fields such as medicine, military affairs, industrial or agricultural.
Present disclosure is not limited to cited by embodiment, and those of ordinary skill in the art are by reading description of the invention
And to any equivalent transformation that technical solution of the present invention is taken, it is that claim of the invention is covered.
Claims (2)
1. the target identification method based on the BN parameter learnings under small data set, it is characterised in that：
It is organically combined using Small Sample Database collection and qualitative expertise, BN parameter learning essences is improved by convex Optimization Solution
Degree finally reflects dbjective state to complete target identification BN modelings using target identification BN the reasoning results.
2. the target identification method according to claim 1 based on the BN parameter learnings under small data set, it is characterised in that：
Specifically include following steps：
1st step：Dirichlet in objective attribute target attribute probability threshold value Ω and the BN parameter learning of target identification is set and is distributed hyper parameter
αijk；
2nd step：BN model structures G is established according to field of target recognition knowledge；
3rd step：Obtain target sample data set D；
4th step：Judge BN parameter θsijkIt is whether modeled；If parameter model, the 8th step is jumped to；If without parameter model
The 5th step to the 7th step is then utilized, BN model parameters θ is calculatedijk；
5th step：According to sample data set D statistical sample amounts Nijk, i.e., father node state is j in sample data, i-th of node takes
The statistical value of k-th of state；
6th step：Expertise is formed into constraint set ξ according to following formula (2) and formula (3)；
Formula (2) is obtained according to the regression nature of BN node parameters；It is described as the set of inequalities of formula (3) in relation to part BN node parameters
It closes, i.e.,：
Wherein, θAExpression parameter sequence, C are a constant and C >=0；
7th step：According to sample statistic Nijk, set ξ is constrained, i.e. formula (2), (3) and objective function Equation (4) is joined
BN parameter θs are determined in number optimizationijk；
If NijkIt is 0, then enables Nijk=0.01；θijkIt solves and is completed using convex Optimization Solution tool, be then back to the 3rd step；
8th step：In BN models, observation evidence ev to be identified is obtained by D, is made inferences using Junction tree, to
To objective attribute target attribute probability Ω '；
9th step：Judge whether objective attribute target attribute probability Ω ' is more than or equal to threshold value Ω；Return to step 3 if being unsatisfactory for；If meeting
Export objective attribute target attribute, i.e. target identification result.
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Application publication date: 20180925 |