CN110647911A - Bearing fault diagnosis method based on principal component analysis and deep belief network - Google Patents

Bearing fault diagnosis method based on principal component analysis and deep belief network Download PDF

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CN110647911A
CN110647911A CN201910744175.6A CN201910744175A CN110647911A CN 110647911 A CN110647911 A CN 110647911A CN 201910744175 A CN201910744175 A CN 201910744175A CN 110647911 A CN110647911 A CN 110647911A
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朱静
胡天真
侯益静
张鹏
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a bearing fault diagnosis method based on principal component analysis and a deep belief network, which comprises the following steps: 1) after the bearing vibration signal is obtained through monitoring, carrying out dimensionality reduction processing on original vibration signal data by using principal component analysis; 2) carrying out [0,1] standardization on the vibration signal data of the bearing after dimensionality reduction, defining fault types, and then dividing the data into a training set and a test set in proportion; 3) initializing related parameters of the deep belief network; 4) and training the deep belief network model by using a training set, then performing parameter optimization on the deep belief network model by using a test set, and finally establishing a deep learning model for bearing fault diagnosis. The invention aims at the bearing fault diagnosis problem, develops research based on principal component analysis and deep belief network, and provides an effective tool and method for solving the bearing fault diagnosis problem in the big data era.

Description

Bearing fault diagnosis method based on principal component analysis and deep belief network
Technical Field
The invention relates to a bearing fault diagnosis method based on Principal Component Analysis (PCA) and Deep Belief Network (DBN), and belongs to the technical field of bearing fault diagnosis.
Background
Bearings are mechanical components widely used in industrial machines, the operating conditions of which greatly affect the performance and the service life of the machine. According to statistics, bearing faults account for a large proportion of annual mechanical faults in China. Failure to timely monitor bearing failure can result in damage to the machine and even loss of life. On the premise of improving productivity, the fault of the machine can affect the whole production line and bring huge economic loss to factories. Therefore, in practical production application, it is very important to monitor the working state of the bearing and perform fault diagnosis on the bearing.
The bearing can produce corresponding vibration signal in the operation process, can judge whether bearing operation is normal through monitoring the vibration signal. And the monitoring data is fully utilized to extract required characteristics from the vibration signals, and the result of characteristic extraction determines the result of vibration signal processing, namely the accuracy of bearing fault diagnosis. And the bearing is diagnosed in time and as early as possible, measures are taken in advance, and the loss caused by faults can be effectively reduced. The data in the bearing fault process is monitored and recorded, and effective data can be provided for analyzing fault reasons afterwards, so that similar faults are avoided.
With the continuous enhancement of industrial intelligence, the operation of equipment in various fields becomes more and more complex, the data obtained by monitoring becomes larger and larger, the dimensionality is higher and higher, and great challenges are brought to the monitoring and fault diagnosis of the bearing operation state. The bearing vibration signal obtained by monitoring has the characteristics of complexity, nonlinearity, non-stationarity and the like. The traditional bearing fault diagnosis technology needs a large amount of signal processing knowledge and experience of workers, and fault diagnosis is carried out after vibration signals are analyzed and processed. The traditional fault diagnosis technology is usually a shallow network model, when facing a large amount of high-dimensional bearing vibration signal data, the deep characteristics of the data cannot be obtained, the bearing fault diagnosis is difficult to be carried out timely and effectively, and the identification accuracy of the bearing fault diagnosis is also greatly influenced.
Deep learning is a method of learning features from data. The deep learning method can be classified into unsupervised learning and supervised learning. The powerful nonlinear processing capability of deep learning makes it highly distinctive in the fields of computer vision, speech recognition, handwriting recognition, and the like. Compared with a shallow network model, the deep learning can automatically learn and identify the fault type more easily according to the intrinsic characteristics of the bearing vibration signal. However, the research and application of the domestic deep learning theory in the field of fault diagnosis are still in a starting stage, and when a large number of high-dimensional samples are processed, a large amount of manual work is needed to process vibration signals and manually extract features, so that the workload and the fault diagnosis complexity are increased. In addition, the increase of the number of the neurons brings certain difficulty to the training of the deep learning model.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims at the bearing fault diagnosis problem, develops research based on principal component analysis and deep belief network, and provides an effective tool and method for solving the bearing fault diagnosis problem in the big data era.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the technical scheme that:
a bearing fault diagnosis method based on principal component analysis and a deep belief network comprises the following steps:
1) after the bearing vibration signal is obtained through monitoring, carrying out dimensionality reduction processing on original vibration signal data by using principal component analysis;
2) carrying out [0,1] standardization on the vibration signal data of the bearing after dimensionality reduction, defining fault types, and then dividing the data into a training set and a test set in proportion;
3) initializing related parameters of the deep belief network;
4) training the deep belief network model by using a training set, then performing parameter optimization on the deep belief network model by using a test set (dropout is used for reducing overfitting in the training and optimizing process), and finally establishing a deep learning model for bearing fault diagnosis.
Further, the step 1) specifically includes:
1.1, given bearing vibration signal X belongs to RN×M(i.e., X is a sample matrix of N rows and M columns, one for each column of the matrixSamples, one measurement per line), calculate the average vector value a for all samples:
Figure BDA0002165008330000021
in the formula, xiIs the ith column sample column vector of the matrix X;
1.2, calculating a covariance matrix:
it is worth pointing out that because P ∈ RN×NP has N eigenvectors, so the eigenvalue λ of P is calculatediI 1.. N and a feature vector vi,i＝1,...,N；
1.3, arranging the eigenvalues from large to small, i.e. λ1≥λ2≥…≥λNTherefore, the cumulative contribution rate α of the first r principal components is:
Figure BDA0002165008330000031
1.4, if alpha is more than or equal to 0.85, constructing a corresponding feature vector viN, E ∈ R, where i is 1N×rI.e. E ═ v1,v2,…,vr) And further maps the original data to a new sample X' by matrix E:
X′＝ETX
wherein X' is ∈ Rr×M. To this end, the new samples retain the main information while reducing the dimensionality of the data compared to the original data.
Further, the ratio of the training set to the test set in step 2) is preferably 3: 1.
further, the DBM in step 3) is formed by stacking a plurality of RBMs, and includes an input layer, a plurality of hidden layers, and an output layer, and the parameter initialization process includes:
the energy function that defines the RBM is:
Figure BDA0002165008330000032
wherein v isiAnd hjRespectively the states of the visible layer and the hidden layer, the corresponding bias is ai、bjThe number of corresponding nodes is nvAnd nh，θ＝{wij,ai,bjIs a parameter of the RBM;
the joint probability of the hidden layer and the visible layer is:
Figure BDA0002165008330000033
wherein Z (θ) is a normalization factor, in addition
Figure BDA0002165008330000035
Since v, h ∈ {0,1} and there is no connection between the layers, the activation function of a neuron is
Figure BDA0002165008330000036
Figure BDA0002165008330000037
The RBM training aim is to increase the probability distribution P (v) of input data, and the parameter updating rule is
ΔWij＝η(<vihj>data-<vihj>recon)
Δai＝η(<vi>data-<vi>recon)
Δbj＝η(<hj>data-<hj>recon)
Wherein eta is the learning rate,<·>datait is referred to the expectation of the data,<·>reconthe method is expected to reconstruct data, because the existence of Z (theta) makes the calculation of the joint probability distribution P (v, h; theta) very difficult, so that the method can be used for calculating the joint probability distribution P (v, h; theta), and in practical application, the method can obtain good effect by taking k as 1. And determining the number of the bearing fault types according to the actual situation, and determining the number of nodes of an input layer and an output layer, wherein the number of the nodes of the output layer is determined by the fault types.
Has the advantages that: compared with the prior art, the bearing fault diagnosis method based on principal component analysis and deep belief network provided by the invention has the following advantages: on one hand, a large amount of high-dimensional bearing vibration signal data are processed through principal component analysis, and the experience and knowledge of signal processing are not needed, so that the dimensionality of sample data is greatly reduced, and the training efficiency of a subsequent deep learning model is effectively improved; on the other hand, the deep belief network model used by the invention is very effective for processing a large amount of sample data of the bearing vibration signals, and is very suitable for fault diagnosis of the condition of generating a large amount of bearing vibration signals.
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FIG. 1 is a schematic overall flow diagram of the present invention;
FIG. 2 is a schematic flow chart of Principal Component Analysis (PCA) in an embodiment of the present invention;
FIG. 3 is a diagram of a deep belief network model employed in an embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the following drawings and specific embodiments.
Fig. 1 shows a bearing fault diagnosis method based on principal component analysis and deep belief network, which includes:
1) after the bearing vibration signal is obtained through monitoring, carrying out dimensionality reduction processing on original vibration signal data by using principal component analysis;
2) carrying out [0,1] standardization on the vibration signal data of the bearing after dimensionality reduction, defining fault types, and then dividing the data into a training set and a test set in proportion;
3) initializing related parameters of the deep belief network;
4) training the deep belief network model by using a training set, then performing parameter optimization on the deep belief network model by using a test set (dropout is used for reducing overfitting in the training and optimizing process), and finally establishing a deep learning model for bearing fault diagnosis.
Step 1) dimensionality reduction Using Principal Component Analysis (PCA)
As shown in fig. 2, mapping n-dimensional features of data to k-dimensions by PCA, that is, mapping original data to a new feature space specifically includes:
1.1, given bearing vibration signal X belongs to RN×M(i.e., X is a matrix of samples in N rows and M columns, with one sample per column and one measurement per row), the average vector value a for all samples is calculated:
Figure BDA0002165008330000051
in the formula, xiIs the ith column sample column vector of the matrix X;
1.2, calculating a covariance matrix:
Figure BDA0002165008330000052
it is worth pointing out that because P ∈ RN×NP has N eigenvectors, so the eigenvalue λ of P is calculatediI 1.. N and a feature vector vi,i＝1,...,N；
1.3, arranging the eigenvalues from large to small, i.e. λ1≥λ2≥…≥λNTherefore, the cumulative contribution rate α of the first r principal components is:
Figure BDA0002165008330000053
1.4, if alpha is more than or equal to 0.85, constructing a corresponding feature vector vi1, N, i ═ 1The array E is equal to RN×rI.e. E ═ v1,v2,…,vr) And further maps the original data to a new sample X' by matrix E:
X′＝ETX
wherein X' is ∈ Rr×M. To this end, the new samples retain the main information while reducing the dimensionality of the data compared to the original data.
Step 2) data normalization and sample partitioning
Carrying out [0,1] standardization treatment on the sample X' obtained in the step 1), and then dividing a training set and a test set according to specific conditions in proportion, wherein the number of the training set samples is more than that of the test set samples, so that the subsequent deep learning model can be trained conveniently.
Step 3) initializing relevant parameters of DBN
The DBM is formed by stacking a plurality of RBMs, and generally includes an input layer, a plurality of hidden layers, and an output layer.
The energy function that defines the RBM is:
Figure BDA0002165008330000061
wherein v isiAnd hjRespectively the states of the visible layer and the hidden layer, the corresponding bias is ai、bjThe number of corresponding nodes is nvAnd nh，θ＝{wij,ai,bjIs a parameter of the RBM;
the joint probability of the hidden layer and the visible layer is:
Figure BDA0002165008330000062
wherein Z (θ) is a normalization factor, in addition
Figure BDA0002165008330000063
Figure BDA0002165008330000064
Since v, h ∈ {0,1} and there is no connection between the layers, the activation function of a neuron is
Figure BDA0002165008330000065
Figure BDA0002165008330000066
The RBM training aim is to increase the probability distribution P (v) of input data, and the parameter updating rule is
ΔWij＝η(<vihj>data-<vihj>recon)
Δai＝η(<vi>data-<vi>recon)
Δbj＝η(<hj>data-<hj>recon)
Wherein eta is the learning rate,<·>datait is referred to the expectation of the data,<·>reconthe method is expected to reconstruct data, because the existence of Z (theta) makes the calculation of the joint probability distribution P (v, h; theta) very difficult, so that the method can be used for calculating the joint probability distribution P (v, h; theta), and in practical application, the method can obtain good effect by taking k as 1.
The number of the bearing fault types is determined according to actual conditions, the number of nodes of an input layer and the number of nodes of an output layer are determined, the number of the nodes of the output layer is determined by the fault types, and the number of the nodes of a hidden layer and the number of the layers are reasonably selected. An embodiment of the present invention uses a DBM model that contains two RBMs, as shown in FIG. 3.
Step 4) MATLAB simulation training
The bearing fault data of the driving end in the bearing center website of the university of western storage is taken and divided into ten conditions of normal inner ring faults with the diameters of 0.1778mm, 0.3556mm and 0.5334mm, outer ring faults with the diameters of 0.1778mm, 0.3556mm and 0.5334mm and ball faults with the diameters of 0.1778mm, 0.3556mm and 0.5334 mm.
The data contains a total of 12120 samples, each of which has dimensions of 400. And (3) carrying out dimensionality reduction on the bearing vibration signal data by using Principal Component Analysis (PCA), wherein the accumulated contribution rate is 95%, and the dimensionality of the obtained dimensionality-reduced data is 123 dimensions.
And (3) carrying out [0,1] standardization processing on the data subjected to dimensionality reduction, and then dividing a training set and a test set, wherein the training set comprises 9090 samples, and the test set comprises 303 samples.
Initializing parameters of a Deep Belief Network (DBN), wherein an input layer is 123 nodes, the number of layers of two hidden layers is 100, an output layer is 10 nodes, a forward learning rate is set to be 0.1, momentum is set to be 0.9, and a dropout parameter is set to be 0.1.
Inputting the training set into a DBN network to train a deep learning model, then using a test set to carry out parameter optimization on the model, namely parameter adjustment, and using dropout to reduce overfitting in the training and optimization processes. And (3) obtaining that the bearing fault diagnosis accuracy of the training set is 99.6% and the bearing fault diagnosis accuracy of the test set is 91.16% after MATLAB simulation.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (4)

1. A bearing fault diagnosis method based on principal component analysis and a deep belief network is characterized by comprising the following steps:
1) after the bearing vibration signal is obtained through monitoring, carrying out dimensionality reduction processing on original vibration signal data by using principal component analysis;
2) carrying out [0,1] standardization on the vibration signal data of the bearing after dimensionality reduction, defining fault types, and then dividing the data into a training set and a test set in proportion;
3) initializing related parameters of the deep belief network;
4) training the deep belief network model by using a training set, then performing parameter optimization on the deep belief network model by using a test set, reducing overfitting by using dropout in the training and optimizing processes, and finally establishing a deep learning model for bearing fault diagnosis.
2. The bearing fault diagnosis method based on principal component analysis and deep belief network as claimed in claim 1, wherein the step 1) specifically comprises:
1.1, given bearing vibration signal X belongs to RN×MThe average vector value a for all samples is calculated:
in the formula, xiIs the ith column sample column vector of the matrix X;
1.2, calculating a covariance matrix:
Figure FDA0002165008320000012
and calculating the characteristic value lambda of PiI 1.. N and a feature vector vi,i＝1,...,N；
1.3, arranging the eigenvalues from large to small, i.e. λ1≥λ2≥…≥λNTherefore, the cumulative contribution rate α of the first r principal components is:
Figure FDA0002165008320000013
1.4, if alpha is more than or equal to 0.85, constructing a corresponding feature vector viN, E ∈ R, where i is 1N×rI.e. E ═ v1,v2,…,vr) And further maps the original data to a new sample X' by matrix E:
X′＝ETX
3. the method for diagnosing the bearing fault based on the principal component analysis and the deep belief network as recited in claim 1, wherein the ratio of the training set to the testing set in the step 2) is 3: 1.
4. The method for diagnosing bearing fault based on principal component analysis and deep belief network as claimed in claim 1, wherein the DBM in the step 3) is formed by stacking a plurality of RBMs including an input layer, a plurality of hidden layers and an output layer, and the parameter initialization process comprises:
the energy function that defines the RBM is:
wherein v isiAnd hjRespectively the states of the visible layer and the hidden layer, the corresponding bias is ai、bjThe number of corresponding nodes is nvAnd nh，θ＝{wij,ai,bjIs a parameter of the RBM;
the joint probability of the hidden layer and the visible layer is:
Figure FDA0002165008320000022
wherein Z (θ) is a normalization factor, in addition
Figure FDA0002165008320000024
Since v, h ∈ {0,1} and there is no connection between the layers, the activation function of a neuron is
Figure FDA0002165008320000025
Figure FDA0002165008320000026
The RBM training aim is to increase the probability distribution P (v) of input data, and the parameter updating rule is
ΔWij＝η(<vihj>data-<vihj>recon)
Δai＝η(<vi>data-<vi>recon)
Δbj＝η(<hj>data-<hj>recon)
Wherein eta is the learning rate,<·>datait is referred to the expectation of the data,<·>reconfor the expectation of reconstructing data, a joint probability distribution P (v, h; θ) is calculated using a contrast divergence algorithm, and the number of sampling times k is taken to be 1.
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CN111678679A (en) * 2020-05-06 2020-09-18 内蒙古电力(集团)有限责任公司电力调度控制分公司 Circuit breaker fault diagnosis method based on PCA-BPNN
CN112464154A (en) * 2020-11-27 2021-03-09 中国船舶重工集团公司第七0四研究所 Method for automatically screening effective features based on unsupervised learning
CN112632466A (en) * 2020-11-26 2021-04-09 江苏科技大学 Bearing fault prediction method based on principal component analysis and deep bidirectional long-time and short-time memory network
CN113065602A (en) * 2021-04-13 2021-07-02 华中科技大学 Method and device for diagnosing valve fault of fracturing pump
CN113111752A (en) * 2021-04-01 2021-07-13 燕山大学 Rolling mill fault diagnosis method for sample imbalance enhanced extended depth confidence network
CN113405799A (en) * 2021-05-20 2021-09-17 新疆大学 Bearing early fault detection method based on health state index construction and fault early warning limit self-learning

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CN111678679A (en) * 2020-05-06 2020-09-18 内蒙古电力(集团)有限责任公司电力调度控制分公司 Circuit breaker fault diagnosis method based on PCA-BPNN
CN111539486A (en) * 2020-05-12 2020-08-14 国网四川省电力公司电力科学研究院 Transformer fault diagnosis method based on Dropout deep confidence network
CN112632466A (en) * 2020-11-26 2021-04-09 江苏科技大学 Bearing fault prediction method based on principal component analysis and deep bidirectional long-time and short-time memory network
CN112632466B (en) * 2020-11-26 2024-01-23 江苏科技大学 Bearing fault prediction method based on deep bidirectional long-short-time memory network
CN112464154A (en) * 2020-11-27 2021-03-09 中国船舶重工集团公司第七0四研究所 Method for automatically screening effective features based on unsupervised learning
CN112464154B (en) * 2020-11-27 2024-03-01 中国船舶重工集团公司第七0四研究所 Method for automatically screening effective features based on unsupervised learning
CN113111752A (en) * 2021-04-01 2021-07-13 燕山大学 Rolling mill fault diagnosis method for sample imbalance enhanced extended depth confidence network
CN113111752B (en) * 2021-04-01 2022-07-08 燕山大学 Rolling mill fault diagnosis method for sample imbalance enhanced extended depth confidence network
CN113065602A (en) * 2021-04-13 2021-07-02 华中科技大学 Method and device for diagnosing valve fault of fracturing pump
CN113405799A (en) * 2021-05-20 2021-09-17 新疆大学 Bearing early fault detection method based on health state index construction and fault early warning limit self-learning

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Application publication date: 20200103