CN112906893A - BN parameter learning algorithm based on self-adaptive variable weight and application thereof - Google Patents
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Abstract
The invention provides a BN parameter learning algorithm based on self-adaptive variable weight, which is characterized in that firstly, according to the change of small sample data volume, weight coefficients for adjusting sample data and qualitative constraint extension parameters are designed, then self-adaptive weighting fusion calculation is carried out to obtain a BN parameter learning result, and the problem of Bayesian network parameter learning under the condition of small data sets is solved. When the BN parameter learning algorithm based on the self-adaptive variable weight is used for learning BN parameters under a small data set, the weights of the sample size and the qualitative constraint parameters can be adjusted in a self-adaptive mode along with the change of the data size, so that the parameter learning result is optimized, the learning precision is improved, and the algorithm also shows excellent feasibility and practicability when being applied to bearing fault diagnosis.
Description
Technical Field
The invention belongs to the technical field of artificial intelligence algorithms, and particularly relates to a BN parameter learning algorithm based on self-adaptive variable weight and application thereof.
Background
With the continuous and deep research of Bayesian Network (BN) theory, the application range of the BN theory is more and more extensive, for example, the diagnosis of faults, the prediction in the economic field, and the medical diagnosis can be performed through the BN, but many times, the more accurate result cannot be learned due to insufficient data.
When the sample data set is sufficient, the Maximum Likelihood Estimation (MLE) can well realize the BN parameter estimation, but when the sample data is less, the method cannot Estimate the parameters more accurately; the Qualitative maximum posterior probability (QMAP) method performs virtual sampling on a parameter set meeting Qualitative constraints through a rejection-acceptance algorithm, real data and virtual data are combined to estimate BN parameters, but the rejection-acceptance algorithm is based on probability distribution function estimation, the probability distribution function of the BN parameters in practical problems is difficult to estimate, and the application of the method is limited. Dingjianhua and Zhangzhao propose a monotonous constraint estimation algorithm (MCE), which utilizes a monotonous constraint model to learn parameters, introduces domain knowledge into the parameter learning process when training data is insufficient, but the assumption of monotonous constraint in practical application is not easy to be given (see Bernstein polynomial estimation (English) of a part of linear model under the conditions of Tjianhua and Zhangzhao in the application probability statistics, 201, 30 (04): 381-. In addition, the scholars provide a constrained parameter evolution learning algorithm (CPEL) based on qualitative knowledge and an evolution strategy, wherein the qualitative knowledge is introduced in the BN parameter learning process to reduce the parameter search space, and then the evolution strategy is introduced to avoid the result from falling into local optimization, but the algorithm has the defect of unstable convergence result in the parameter optimization problem. The method for qualitatively constraining and expanding the BN parameters can convert qualitative expert experience into inequality constraint, and utilizes a Bootstrap algorithm to generate a group of BN parameter candidate sets meeting the constraint (see details: Guo Wen Jiang, Liran, Houyan and Gao Wen Jiang. BN parameter maximum entropy model expansion learning algorithm [ J ] under the constraint condition, computer application research, 2019,36(2): 132) 137.), but the BN parameters obtained by the method depend on the expert experience excessively, and the weight coefficients of each learning data set in parameter estimation can not be automatically adjusted according to the change condition of the size of the data set, so that the accuracy of final parameter estimation is influenced.
Disclosure of Invention
In order to overcome the defects of the method, better solve the problem of parameter learning when the sample data is less, simultaneously estimate the parameters more conveniently in practical application and obtain a stable parameter learning result, the invention combines the sample data and the field qualitative knowledge to estimate the parameters by introducing the variable weight thought, so that the BN parameter learning precision can be effectively improved under the condition of less sample data.
Based on the purpose, the invention provides a BN parameter learning algorithm based on self-adaptive variable weight, which adaptively adjusts the weight coefficients of sample data and qualitative constraint expansion parameters according to the change of the data volume of a small sample, performs variable weight fusion calculation to obtain a BN parameter learning result, and solves the problem of Bayesian network parameter learning under the condition of a small data set.
Specifically, the BN parameter learning algorithm based on the adaptive variable weight comprises,
establishing a parameter learning model structure;
acquiring a minimum sample data set threshold value required by calculating a parameter learning model;
determining inequality constraint conditions of the parameter learning model;
calculating an initial parameter set;
performing parameter expansion to obtain a candidate parameter set meeting constraint conditions;
adaptively determining a proper variable weight factor according to a designed variable weight factor function;
and substituting the initial parameter set of the sample data, the qualitative constraint expansion candidate parameter set, the variable weight factor and the number of the parameter learning total alternative data sets into a calculation to obtain a final parameter learning result.
As known to those skilled in the art, Bayesian Network (BN) parameter learning is a process of determining conditional probability distribution among related variables in a model by using expert prior knowledge and training sample data on the premise of knowing the topology of the bayesian network. The BN parameter learning is carried out by combining two or more data sets, so that the defect of insufficient utilization of data information caused by only using a single data set can be avoided, and the parameter learning precision can be improved. However, when the parameter weighting estimation is performed by combining multiple data sets, the weight occupied by each data set is considered to influence the result, and the weight can be divided into two types, namely fixed weight and variable weight. In the Parameter estimation process, the Weight coefficient of each data set is changed according to a certain rule, and is called a variable Weight method (referred to as Adaptive variable Weight, Adaptive Weight Parameter Learning, AWPL), otherwise, the Weight coefficient is a fixed Weight method (referred to as fixed Weight, FWPL).
The invention selects an adaptive variable weight frame as an estimation model of a target fusion field (BN constraint knowledge and sample data) and a target evaluation field (BN parameter learning), and is mainly based on the following considerations: the information fusion has certain fault tolerance, the adopted sample data and the constraint information are subjected to weighted combination, and the weight is adjusted without destroying the correctness of the whole estimation model; meanwhile, the method naturally solves the problem of parameter adaptability in the statistical model, namely, the weight is adjusted according to the sample data size, and the fusion of constraint knowledge and the sample data is met. The basic idea of parameter learning based on adaptive variable weight is to continuously adjust the weight coefficient of each learning data set in parameter estimation according to the change condition of data quantity, and then to determine the final parameter estimation result through weighting and fusion.
In the invention, the minimum sample data set threshold value M required by the calculation parameter learning model is obtained by the calculation of formula (1),
wherein M represents the required minimum number of data sets; λ represents a skewness coefficient that measures the probability distribution of variables in the network structure; d represents the maximum number of parent nodes; ε represents the KL error; n represents the number of network nodes; k represents the maximum state number of the network nodes; δ represents the network confidence.
In the present invention, the initial parameter set
Calculated according to the formula (2),
where η is a small constant close to zero, c ═ qi·ri，qiRepresenting the value of the parent node variable, riAnd representing the value number of the variable of the child node.
In the invention, the BN variable weight parameter is obtained by calculation and evaluation according to the formula (3),
wherein, thetadataRepresenting a sample data parameter set, thetaconstraintextensionRepresenting a qualitatively constrained extended parameter set, thetaestimateLearning results for the final parameters.
In the present invention, the designed variable weight factor ω is calculated according to equation (4),
wherein D is the sample size,
the meaning is that the size of the sample data size is reflected by the ratio of the sample size to the minimum sample data set threshold.
In the present invention, the BN variable weight parameter calculation model is the same as equation (3), and it can be found by analysis that: in the formula (4), if the data amount D tends to + ∞, ω is approximately equal to 1, and at this time, the result of the parameter estimation by the formula (3) depends on the data amount of the sample data itself, and the result tends to the result of the estimation by the MLE method. If the amount of data is close to 0, ω is approximately equal to 0, where the parameter estimation result tends to be obtained by a qualitatively constrained extended parameter set, i.e. relying on a priori knowledge. With the gradual change of the total number of the learning parameter sets, the weight factor proportion occupied by each of the qualitative constraint expansion parameter set and the sample data set can be adjusted. In summary, estimating the parameters by the BN parameter learning algorithm formula (3) based on the adaptive variable weight can effectively improve the accuracy of parameter estimation.
The invention also provides application of the BN parameter learning algorithm based on the self-adaptive variable weight in bearing fault detection. Specifically, a bearing diagnosis BN model is built according to the BN parameter learning algorithm based on the self-adaptive variable weight, and a diagnosis attribute probability threshold value is set. The bearing fault detection specifically comprises the steps of,
collecting signal data of a bearing;
inputting the signal data into a bearing diagnosis BN model, and obtaining target attribute probability by using an AWPL algorithm;
and judging whether the target attribute probability is greater than or equal to the diagnostic attribute probability threshold, and if so, outputting a target attribute result.
Compared with the prior art, the invention has the following beneficial effects or advantages:
when the BN parameter learning algorithm based on the self-adaptive variable weight is used for learning the BN parameters under a small data set, the weights of the sample amount and the qualitative constraint parameters can be continuously adjusted along with the change of the data amount, so that the parameter learning result is optimized, and the learning precision is improved. Through the intensive experimental research of the inventor, the algorithm also shows excellent feasibility and practicability when being applied to bearing fault diagnosis, and the algorithm provides an effective way for modeling and reasoning in an intelligent decision-making system, especially under the condition of a small data set.
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FIG. 1 is a flow chart of a BN parameter learning algorithm based on adaptive variable weight according to the present invention
FIG. 2 is a schematic diagram of an adaptive variable weight framework
FIG. 3 is a diagram illustrating BN parameter learning
Detailed Description
The technical aspects of the present invention will be further explained below with reference to the drawings, but the present invention is not limited to the following embodiments.
The Bayesian Network (BN) parameter learning is a process of determining conditional probability distribution among related variables in a model by utilizing expert priori knowledge and training sample data on the premise of knowing a topological structure of the Bayesian network.
Fig. 3 shows a basic procedure of BN parameter learning. The solid-line box (r) is represented by the BN1 model (where G1Denotes BN structure, θ1Representing parameters) may obtain an observation sample data set { D11,D12,…D1h,Dp}; in the same way, from model BN2(wherein G is2Indicating structure, theta2Representing a parameter) can be derived an observed data set { D21,D22,…D2f,Dp}. When the sample data set is small, the BN1 and the BN2 model have certain probability of obtaining the same data set Dp. Dashed box (B) indicates BN when sufficient data set is obtained1Model will get sample data set { D11,D12,… D1h,DpUsing a parameter learning method (e.g. MLE method) to learn the parameter theta1'; by analogy, by means of the model BN2Resulting data set { D21,D22,…D2f,DpThe parameter theta can also be estimated by using a parameter learning algorithm2'. With the increasing of the sample data amount, the corresponding parameters learned through the sample data set are closer to the real parameters, and when the sample data amount for learning is sufficient, the learned BN parameters converge to the real parameters.
As shown in fig. 2, which is a schematic diagram of an adaptive variable weight framework, the invention selects the adaptive variable weight framework as an estimation model in a target fusion domain (BN constraint knowledge and sample data) and a target evaluation domain (BN parameter learning), so as to optimize a parameter learning result and improve learning accuracy.
Specifically, the flow diagram of the BN parameter learning algorithm based on adaptive variable weight provided by the present invention is shown in fig. 1, and includes the following steps:
step 1: and establishing a parameter learning model structure (comprising nodes and directed edges of the Bayesian network model).
Step 2: obtaining a minimum sample data set threshold value M required for calculating the parameter learning model by formula (1),
formula (1):
wherein M represents the required minimum number of data sets; λ represents a skewness coefficient that measures the probability distribution of variables in the network structure; d represents the maximum number of parent nodes; ε represents the KL error; n represents the number of network nodes; k represents the maximum state number of the network nodes; δ represents the network confidence.
And step 3: and determining an inequality constraint condition omega of the parameter learning model according to expert prior knowledge.
And 4, step 4: calculating an initial parameter set theta according to formula (2) from the initial small sample setijk；
Formula (2):
where η is a small constant close to zero, c ═ qi·ri，qiRepresenting the value of the parent node variable, riAnd representing the value number of the variable of the child node.
And 5: performing parameter extension by using a Bootstrap method to obtain Q groups of candidate parameter sets theta meeting the constraint condition omegaijk(Ω)。
Step 6: the Bayesian network parameter calculation based on the self-adaptive variable weight can be conveniently described as a formula (3), and then appropriate variable weight factors omega and 1-omega are determined to distribute indexes of the confidence level of the sample data set and the qualitative constraint extended parameter set on the learning result of the parameter learning method,
formula (3):
wherein, thetadataRepresenting a sample data parameter set, thetaconstraintextensionRepresenting a qualitatively constrained extended parameter set, thetaestimateLearning results for the final parameters.
And 7: a variable weight factor omega is calculated according to equation (4),
formula (4):
wherein D is the sample size,
the meaning is that the size of the sample data size is reflected by the ratio of the sample size to the minimum sample data set threshold.
And 8: obtaining an initial parameter set theta of sample dataijkQualitatively constraining the extended candidate parameter set θijkAnd (omega), substituting the weight factors omega, 1-omega and the number of the parameter learning total alternative data sets into the formula (3) to perform weighted fusion calculation to obtain a final parameter learning result.
In the following, the technical solution of the present invention is further described by using specific embodiments and combining the above algorithm, but the present invention is not limited to the following embodiments.
Examples
The BN parameter learning algorithm based on the self-adaptive variable weight is applied to a bearing fault diagnosis experiment, the experiment program is completed through MATLAB R2014a programming, a simulation experiment platform is a Windows7 system, and a processor is Intel (R) Celeron (R) CPU 1.60 GHz.
The data in this example were taken from rolling bearing failure data provided by the bearing data center of the university of Kaiser Sichu, USA. This data may be obtained at its central website. The characteristic data acquisition method is the same as the literature (see Guwenqiang, Zhangrong, Peng journey and the like, deep groove ball bearing fault diagnosis based on wavelet packet and BN model [ J ]. bearing, 2016, 59 (03): 48-52.).
The bearing diagnosis BN model of the embodiment has nine nodes including a father node and eight child nodes, the probability confidence coefficient for diagnosing each fault type is 0.7, the number of parameter learning total alternative data sets is 500, and 8 parameter constraint conditions can be obtained according to expert experience. The experimental process of fault diagnosis includes the steps of firstly realizing structural modeling of a BN model according to field expert experience, then utilizing the algorithm to conduct parameter learning under the condition of two groups of experimental data, namely a small data set (45 groups of sample sizes) and a relatively sufficient data set (200 groups of sample sizes), and after a fault diagnosis reasoning model is built, utilizing 269 groups of data to select a classical effective joint tree algorithm to conduct various typical fault reasoning and diagnosis experiments of a bearing under the built model to verify the feasibility of the algorithm.
Tables 1 and 2 are the results of the diagnostic reasoning using 45 and 200 sets of profile data for modeling, respectively, and then 269 sets of profile data.
Table 1, 45 groups of data lower variable weight method modeling reasoning accuracy result
Table 2, modeling reasoning accuracy result of variable weight method under 200 groups of data
The experimental results in tables 1 and 2 show that when the algorithm is used for modeling reasoning under a small data set, the diagnosis effect of the fault state of the rolling body and the fault state of the outer ring is slightly worse than that of the modeling reasoning under a relatively sufficient data set. The diagnosis accuracy is high on the whole, and feasibility and effectiveness of parameter learning of the algorithm under the condition of a small data set are shown.
As described above, the BN parameter learning algorithm based on the self-adaptive variable weight in the invention better solves the problem of Bayesian network parameter learning when the sample data is less, and effectively improves the accuracy of BN parameter learning.
The above-mentioned embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various changes and modifications of the technical solution of the present invention by those skilled in the art should fall within the determined protective scope of the present invention without departing from the design spirit of the present invention.
Claims (10)
1. The BN parameter learning algorithm based on the self-adaptive variable weight is characterized in that weight coefficients of the adjusted sample data and the qualitative constraint expansion parameters are designed according to the change of the data volume of the small sample, and variable weighting fusion calculation is carried out to obtain a BN parameter learning result.
2. The adaptive variable weight-based BN parameter learning algorithm according to claim 1, wherein the adaptive variable weight-based BN parameter learning algorithm specifically comprises,
establishing a parameter learning model structure;
acquiring a minimum sample data set threshold value required by calculating a parameter learning model;
determining inequality constraint conditions of the parameter learning model;
calculating an initial parameter set;
performing parameter expansion to obtain a candidate parameter set meeting constraint conditions;
determining a proper variable weight factor according to a designed variable weight factor function;
and calculating the initial parameter set of the sample data, the constraint expansion candidate parameter set, the variable weight factor and the number of the parameter learning total candidate data sets to obtain a final parameter learning result.
3. The adaptive variable weight-based BN parameter learning algorithm according to claim 2, wherein the minimum sample data set threshold required for calculating the parameter learning model is obtained by calculation of equation (1),
formula (1):
wherein M represents the required minimum number of data sets; λ represents a skewness coefficient that measures the probability distribution of variables in the network structure; d represents the maximum number of parent nodes; ε represents the KL error; n represents the number of network nodes; k represents the maximum state number of the network nodes; δ represents the network confidence.
4. The adaptive variable weight-based BN parameter learning algorithm according to claim 2, wherein the initial parameter set is calculated according to equation (2), wherein equation (2):
where η is a small constant close to zero, c ═ qi·ri，qiRepresenting the value of the parent node variable, riAnd representing the value number of the variable of the child node.
5. The adaptive variable weight-based BN parameter learning algorithm of claim 2 wherein the variable weight parameter is determined according to equation (3),
formula (3):
wherein, thetadataRepresenting a sample data parameter set, thetaconstraintextensionRepresenting a constrained extended parameter set, thetaestimateLearning results for the final parameters.
6. The adaptive variable weight-based BN parameter learning algorithm according to claim 2 wherein the design variable weight factor is calculated according to equation (4),
formula (4):
wherein D is the sample size,
the meaning is that the size of the sample data size is reflected by the ratio of the sample size to the minimum sample data set threshold.
7. The adaptive variable weight-based BN parameter learning algorithm according to claim 2, wherein the final parameter learning result is calculated according to equation (3).
8. Use of the adaptive variable weight-based BN parameter learning algorithm of any one of claims 1 to 7 in bearing fault diagnosis.
9. The application of claim 8, wherein a bearing diagnosis BN model is constructed according to the adaptive variable weight-based BN parameter learning algorithm, and a diagnosis attribute probability threshold is set.
10. The use according to claim 8, wherein the bearing fault diagnosis comprises,
collecting signal data of a bearing;
inputting the signal data into a bearing diagnosis BN model, and obtaining target attribute probability by using an AWPL algorithm;
and judging whether the target attribute probability is greater than or equal to the diagnostic attribute probability threshold, and if so, outputting a target attribute result.
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