CN110231165B - Mechanical equipment fault diagnosis method based on expectation difference constraint confidence network - Google Patents

Mechanical equipment fault diagnosis method based on expectation difference constraint confidence network Download PDF

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CN110231165B
CN110231165B CN201910466135.XA CN201910466135A CN110231165B CN 110231165 B CN110231165 B CN 110231165B CN 201910466135 A CN201910466135 A CN 201910466135A CN 110231165 B CN110231165 B CN 110231165B
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雷亚国
姜鑫伟
邢赛博
李乃鹏
司小胜
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Xian Jiaotong University
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Abstract

A mechanical equipment fault diagnosis method based on an expected difference constraint confidence network comprises the steps of firstly, obtaining vibration signals of mechanical equipment in different health states, and extracting translation invariant features; taking the translation invariant feature as input, and extracting the depth feature of the vibration signal; then, taking the depth characteristic as input, and extracting fault characteristics robust to the working condition; and finally training a Softmax classifier based on the extracted fault features robust to the working conditions, and completing intelligent diagnosis of the fault of the mechanical equipment under the multiple working conditions by using the trained classifier.

Description

Mechanical equipment fault diagnosis method based on expectation difference constraint confidence network
Technical Field
The invention belongs to the technical field of mechanical equipment fault diagnosis, and particularly relates to a mechanical equipment fault diagnosis method based on an expected difference constraint confidence network.
Background knowledge
Mechanical equipment is widely applied to fields such as aerospace, petrochemical industry, precision machine tool, high-speed train, and in these fields, mechanical equipment often works in the environment that the operating mode is complicated, and the harsh operating mode environment makes mechanical equipment trouble frequent, consequently needs to carry out fault diagnosis and maintenance to mechanical equipment to guarantee mechanical equipment's safe and reliable, steady operation. The traditional fault diagnosis method generally comprises three steps of signal acquisition, feature extraction and fault identification, and with the introduction of a deep learning theory, the deep intelligent fault diagnosis method can directly extract fault features from original signals in a self-adaptive manner, so that the intelligent identification of the health state of machinery is realized, and the defects that the traditional fault diagnosis method excessively depends on diagnosis professional knowledge and has weak generalization capability in the era of mechanical big data are overcome. As a common Deep learning model, a Deep Belief Network (DBN) is commonly used in the field of intelligent fault diagnosis due to the simplicity of a model and a training algorithm. A Restricted Boltzmann Machine (RBM) serving as a basic component of the DBN can automatically extract data features for diagnosis, and a classifier is trained by combining training data labels to realize fault recognition. However, in the fault diagnosis process, only labeled training data under certain working conditions can be collected, so that the trained RBM model can only identify faults occurring under the working conditions, but under a new working condition lacking the labeled data, the extracted feature distribution changes due to the change of the working conditions, so that the fault identification precision is reduced. Therefore, aiming at the problem that labeled data are incomplete under certain operating conditions of mechanical equipment, an unsupervised feature learning method is needed to extract features robust to the operating conditions, and finally, accurate identification of faults under multiple operating conditions is achieved.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a mechanical equipment fault diagnosis method based on an expected difference constraint confidence network, which is used for extracting fault characteristics robust to working conditions from an original vibration signal and improving the reliability and accuracy of fault diagnosis of mechanical equipment under a new working condition with missing label data.
In order to achieve the purpose, the invention adopts the technical scheme that:
a mechanical equipment fault diagnosis method based on an expected difference constraint confidence network comprises the following steps:
1) obtaining vibration signals of mechanical equipment under different health states under multiple working conditions to form a vibration signal set
Figure BDA0002079449560000021
Wherein, C is the number of signal samples, and D is the number of data points contained in each vibration signal sample;
2) obtaining a vibration signal training set, and training a bureau to connect with a slip limited Boltzmann machine through a contrast divergence algorithm; then, a vibration signal sample set is taken as input, and the translation invariant feature f of the vibration signal is extracted through a local connection slip limited Boltzmann machineSIF；
3) Acquiring a translation invariant feature training set, and training a fully-connected limited Boltzmann machine by a contrast divergence algorithm; then, the translation invariant feature sample set is used as input, and the depth feature f of the vibration signal is extracted through a full-connection limited Boltzmann machineDF；
4) Acquiring a depth characteristic training set, and training a robust limited Boltzmann machine by a contrast divergence algorithm; then, a depth feature sample set is used as input, and fault features f robust to working conditions are extracted through a robust limited Boltzmann machineRF；
5) Characterizing the fault fRFInputting the fault characteristics of the vibration signals into a Softmax classifier, and training the classifier by maximizing the output probability of the labels corresponding to the vibration signals; and after the training is finished, the label with the maximum output probability is used as the health state corresponding to the vibration signal, and intelligent fault diagnosis of the mechanical equipment under multiple working conditions is finished.
The objective function in the training of the step 3) is as follows:
Figure BDA0002079449560000031
wherein v represents a visible unit, viDenotes the ith visible cell, aiDenotes viH denotes a hidden unit, hjDenotes the jth hidden unit, bjRepresents hjOffset of (d), wijRepresents a connection viAnd hjWeight of (a)iThe standard deviation of gaussian noise is indicated.
The step 4) of extracting the fault features robust to the working conditions specifically comprises the following steps:
4.1) Using the depth feature fDFThe training is completed by simultaneously minimizing the objective function in the training of step 3) and the expected Difference constraint EDC (expectation Difference constraint) which is minimized by the contrast divergence algorithm and the gradient descent algorithm, and the updating process of w, a and b of the expected Difference constraint EDC is as follows:
Figure BDA0002079449560000032
Figure BDA0002079449560000033
Figure BDA0002079449560000034
where t is the number of iterations, η is the learning rate, and the gradient values of w, a, and b for the expected variance constraint EDC are:
Figure BDA0002079449560000041
Figure BDA0002079449560000042
Figure BDA0002079449560000043
where the gradient values for the expected variance-constrained EDC are:
Figure BDA0002079449560000044
Figure BDA0002079449560000045
in the formula
Figure BDA0002079449560000046
Where the desired variance constraint EDC is designed to:
Figure BDA0002079449560000047
combining the objective function in the training of the step 3) and the expected difference constraint EDC, the objective function of the expected difference constraint limited Boltzmann machine is as follows:
Figure BDA0002079449560000048
in the formula (I), the compound is shown in the specification,
Figure BDA0002079449560000049
β is the penalty factor of EDC, P is the number of training samples, Q is the number of testing samples;
Figure BDA00020794495600000410
the output of the jth hidden layer unit when the input is the pth training sample;
Figure BDA00020794495600000411
the output of the jth hidden layer unit when the input is the Qth test sample;
4.2) extracting depth characteristic f from step 3)DFAs input, a fault feature f robust to the operating conditions is extractedRF；
fRF＝sigm(w·fDF+b)
In the formula, sigm (. cndot.) represents an activation function.
The invention has the beneficial effects that:
according to the method, the expected difference constraint confidence network is utilized, the mechanical equipment fault characteristics robust to the working conditions can be directly extracted from the original vibration signals, higher diagnosis precision can be obtained under multiple working conditions, and the fault identification robustness is better; meanwhile, the characteristic distribution difference under different working conditions is reduced, and the fault diagnosis precision under a new working condition is improved.
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FIG. 1 is a flow chart of an embodiment of the present invention.
FIG. 2 is a block diagram of a robust limited Boltzmann machine of the present invention.
FIG. 3 shows the results of the diagnosis of the method of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and examples.
Referring to fig. 1, a method for diagnosing a fault of a mechanical device based on an expected difference constraint confidence network includes the following steps:
1) obtaining vibration signals of mechanical equipment under different health states under multiple working conditions to form a vibration signal set
Figure BDA0002079449560000051
Wherein, C is the number of signal samples, and D is the number of data points contained in each vibration signal sample;
2) obtaining a vibration signal training set, and training a bureau to connect with a slip limited Boltzmann machine through a contrast divergence algorithm; then, a vibration signal sample set is taken as input, and the translation invariant feature f of the vibration signal is extracted through a local connection slip limited Boltzmann machineSIFThe method specifically comprises the following steps:
2.1) in the vibration signal set
Figure BDA0002079449560000061
Above with ItrainRespectively intercepting M data points for the step length of intercepting the sample fragment to form N ((D-M)/I)train+1) training sample sets; obtaining a preprocessed training sample set through whitening and Z-score standardization
Figure BDA0002079449560000062
Then, taking the preprocessed training sample set as input, and completing training through a contrast divergence algorithm;
the Z-score normalized operation expression is shown below:
Figure BDA0002079449560000063
in the formula, x is original data;
Figure BDA0002079449560000064
is the mean of the original data; sigma is the standard deviation of the original data; x is the number of*Data normalized for Z-score;
2.2) by step size ItestObtaining a set of local features of a vibration signal
Figure BDA0002079449560000065
Wherein K is (D-M)/Itest+ 1; by passing
Figure BDA0002079449560000066
The operation extracts each local data set
Figure BDA0002079449560000067
Local feature of (f)iWherein W isLC、bLCThe obtained local feature matrixes of all local feature composition signals are respectively weight and bias
Figure BDA0002079449560000068
2.3) taking the maximum value of each column of the local feature matrix as a vibration signal xiSignal translation invariant feature fSIF；
Figure BDA0002079449560000069
Where max (f)LC1) represents a calculation matrix fLCThe maximum value of each column in;
3) acquiring a translation invariant feature training set, and training a fully-connected limited Boltzmann machine by a contrast divergence algorithm; then taking the translation invariant feature sample set as input, and carrying out full transformationConnecting a limited Boltzmann machine, and extracting the depth characteristic f of the vibration signalDFThe method specifically comprises the following steps:
3.1) use of the translation invariant feature fSIFAnd completing training through a contrast divergence algorithm, wherein the process is as follows:
a) randomly giving an initial weight W, a visible layer bias a and a hidden layer bias b, and extracting translation invariant features from the vibration signal set to obtain a translation invariant feature training set;
b) minimizing an objective function by using a contrast divergence algorithm by using a translation invariant feature training set to complete training;
the objective function in the training is:
Figure BDA0002079449560000071
wherein v represents a visible unit, viDenotes the ith visible cell, aiDenotes viH denotes a hidden unit, hjDenotes the jth hidden unit, bjRepresents hjOffset of (d), wijRepresents a connection viAnd hjWeight of (a)iRepresents the standard deviation of gaussian noise;
the contrast divergence algorithm is as follows:
Δwij＝ε(<vihj>data-<vihj>reco)
Δai＝ε(<vi>data-<vi>reco)
Δbj＝ε(<hj>data-<hj>reco)
in the formula, epsilon is the learning rate,<·>datawhich is indicative of the expected value of the data,<·>recorepresenting an expected value of the reconstruction;
3.2) fine adjustment is carried out by combining a translation invariant feature training set through a BP algorithm;
3.3) using the translation invariant feature f extracted in step 2)SIFAs an input to the process, the process may,extracting the depth characteristic f of the vibration signal by a full-connection limited Boltzmann machineDF；
4) Referring to FIG. 2, a depth feature training set is obtained, and a robust limited Boltzmann machine is trained through a contrast divergence algorithm; then, a depth feature sample set is used as input, and fault features f robust to working conditions are extracted through a robust limited Boltzmann machineRFThe method specifically comprises the following steps:
4.1) Using the depth feature fDFThe training is completed by simultaneously minimizing the objective function in the training of step 3) and the expected Difference constraint EDC (expectation Difference constraint) which is minimized by the contrast divergence algorithm and the gradient descent algorithm, and the updating process of w, a and b of the expected Difference constraint EDC is as follows:
Figure BDA0002079449560000081
Figure BDA0002079449560000082
Figure BDA0002079449560000083
where t is the number of iterations, η is the learning rate, and the gradient values of w, a, and b for the expected variance constraint EDC are:
Figure BDA0002079449560000084
Figure BDA0002079449560000085
Figure BDA0002079449560000086
in the formula,. DELTA.wij，Δai，ΔbjHas been obtained by step 3)；
Wherein the EDC has a gradient value of:
Figure BDA0002079449560000087
Figure BDA0002079449560000088
in the formula
Figure BDA0002079449560000091
Where the desired variance constraint EDC is designed to:
Figure BDA0002079449560000092
combining the objective function in the training of the step 3) and the expected difference constraint EDC, the objective function of the expected difference constraint limited Boltzmann machine is as follows:
Figure BDA0002079449560000093
in the formula (I), the compound is shown in the specification,
Figure BDA0002079449560000094
β is the penalty factor of EDC, P is the number of training samples, Q is the number of testing samples;
Figure BDA0002079449560000095
the output of the jth hidden layer unit when the input is the pth training sample;
Figure BDA0002079449560000096
the output of the jth hidden layer unit when the input is the Qth test sample;
4.2) taking the depth feature extracted in the step 3) as fDFExtracting a fault characteristic f robust to the working condition for inputRF；
fRF＝sigm(w·fDF+b)
In the formula, sigm (-) represents an activation function;
5) characterizing the fault fRFInputting the fault characteristics of the vibration signals into a Softmax classifier, and training the classifier by maximizing the output probability of the labels corresponding to the vibration signals; and after the training is finished, the label with the maximum output probability is used as the health state corresponding to the vibration signal, and intelligent fault diagnosis of the mechanical equipment under multiple working conditions is finished.
Example (b): the present invention is further described by intelligently diagnosing gear faults in mechanical equipment under multiple operating conditions.
The data set adopted in the embodiment is a secondary planetary gearbox fault data set, which totally comprises 5 subsets, which respectively correspond to 5 health states, namely, wear of a sun gear, peeling of the sun gear, crack of a planet gear, fault and normal states of a planet gear bearing. Each health state corresponds to 4 working conditions, and data sets under different rotating speed conditions are adopted, wherein the rotating speeds are 30Hz, 35Hz, 40Hz and 45Hz respectively. The planetary gearbox collected 50 vibration signal samples at each speed for each state of health, with each vibration signal sample having a data length of 2560 data points. Therefore, a total of 200 vibration signal samples are collected for each healthy state, and the entire data set contains 1000 vibration signal samples. In order to verify the diagnostic performance of the method of the invention under different working conditions, the model is trained by using samples under a single rotating speed respectively, and the remaining samples with different rotating speeds are used as unknown new working conditions to test the diagnostic performance of the method of the invention. The method of the invention is used for diagnosing a planetary gearbox fault data set, and for the data set, expected difference constraint confidence network parameters are set as follows: selecting the number of visible layer units as 100 and the number of hidden units as 400 in the step 2), intercepting the step length of a sample segment as 60, the learning rate as 9.85E-5, stopping training after 1500 iterations, and extracting the translation invariant feature of the vibration signal; step 3) selecting the number of the hidden units to be 350, training the learning rate to be 1E-4, stopping training after 500 times of iteration, and extracting depth features, wherein the learning rate in the fine tuning process is 2.5E-3; selecting 350 hidden units, 5E-6 learning rate and 0.2 penalty coefficient of EDC item in the step 4), stopping training after 500 iterations, and extracting fault features robust to working conditions; the weight decay factor lambda of the Softmax classifier is trained to be 1E-5. The fault diagnosis precision obtained by using the method is shown in table 1, and as can be seen from table 1, the method can keep the diagnosis precision of more than 90% under each rotating speed difference value, has higher diagnosis stability, and shows that the fault identification robustness of the method is better when the rotating speed changes.
In order to verify the effectiveness of the method, the method is compared with the fault identification precision of a fault diagnosis method based on a local connection slip limited Boltzmann machine and a fault diagnosis method based on a convolutional neural network. The diagnostic result pairs are shown in fig. 3. As can be seen from the comparison result of FIG. 3, the fault identification obtained by the method of the present invention has higher precision and better robustness to the change of the rotating speed, thereby overcoming the problem of data loss of the vibration signal with the label at the new rotating speed. Through the analysis of the specific processing procedure of the fault diagnosis of the planetary gearbox and the comparison of the diagnosis results of the two methods, the invention utilizes the expected difference to constrain the confidence network, can directly extract the gear fault characteristics robust to the working conditions from the original vibration signals, can obtain higher diagnosis precision under multiple working conditions, has better fault recognition robustness, simultaneously reduces the characteristic distribution difference under different working conditions, and improves the fault diagnosis precision under new working conditions.
TABLE 1
Figure BDA0002079449560000111

Claims (1)

1. A mechanical equipment fault diagnosis method based on an expected difference constraint confidence network is characterized by comprising the following steps:
1) obtaining vibration signals of mechanical equipment under different health states under multiple working conditions to form a vibration signal set
Figure FDA0002357085650000011
Where C is the number of signal samples and D is eachThe number of data points contained in the vibration signal sample;
2) obtaining a vibration signal training set, and training a bureau to connect with a slip limited Boltzmann machine through a contrast divergence algorithm; then, a vibration signal sample set is taken as input, and the translation invariant feature f of the vibration signal is extracted through a local connection slip limited Boltzmann machineSIF；
3) Acquiring a translation invariant feature training set, and training a fully-connected limited Boltzmann machine by a contrast divergence algorithm; then, the translation invariant feature sample set is used as input, and the depth feature f of the vibration signal is extracted through a full-connection limited Boltzmann machineDF；
4) Acquiring a depth characteristic training set, and training a robust limited Boltzmann machine by a contrast divergence algorithm; then, a depth feature sample set is used as input, and fault features f robust to working conditions are extracted through a robust limited Boltzmann machineRF；
5) Characterizing the fault fRFInputting the fault characteristics of the vibration signals into a Softmax classifier, and training the classifier by maximizing the output probability of the labels corresponding to the vibration signals; after training is finished, the label with the maximum output probability is used as the health state corresponding to the vibration signal, and intelligent fault diagnosis of mechanical equipment under multiple working conditions is finished;
the objective function in the training of the step 3) is as follows:
Figure DEST_PATH_FDA0002079449550000021
wherein v represents a visible unit, viDenotes the ith visible cell, aiDenotes viH denotes a hidden unit, hjDenotes the jth hidden unit, bjRepresents hjOffset of (d), wijRepresents a connection viAnd hjWeight of (a)iRepresents the standard deviation of gaussian noise;
the step 4) of extracting the fault features robust to the working conditions specifically comprises the following steps:
4.1) Using the depth feature fDFBy simultaneous minimizationStep 3) performing training by using an objective function in the training and an expected Difference constraint EDC (expectation Difference constraint), wherein the objective function in the training of step 3) is minimized by using a contrast divergence algorithm, the expected Difference constraint EDC is minimized by using a gradient descent algorithm, and the updating process of w, a and b of the expected Difference constraint EDC is as follows:
Figure FDA0002357085650000021
Figure FDA0002357085650000022
Figure FDA0002357085650000023
where t is the number of iterations, η is the learning rate, and the gradient values of w, a, and b for the expected variance constraint EDC are:
Figure FDA0002357085650000024
Figure FDA0002357085650000025
Figure FDA0002357085650000026
where the gradient values for the expected variance-constrained EDC are:
Figure FDA0002357085650000027
Figure FDA0002357085650000031
in the formula
Figure FDA0002357085650000032
Where the desired variance constraint EDC is designed to:
Figure FDA0002357085650000033
combining the objective function in the training of the step 3) and the expected difference constraint EDC, the objective function of the expected difference constraint limited Boltzmann machine is as follows:
Figure FDA0002357085650000034
in the formula (I), the compound is shown in the specification,
Figure FDA0002357085650000035
β is the penalty factor of EDC, P is the number of training samples, Q is the number of testing samples;
Figure FDA0002357085650000036
the output of the jth hidden layer unit when the input is the pth training sample;
Figure FDA0002357085650000037
the output of the jth hidden layer unit when the input is the Qth test sample;
4.2) extracting depth characteristic f from step 3)DFAs input, a fault feature f robust to the operating conditions is extractedRF；
fRF＝sigm(w·fDF+b)
In the formula, sigm (. cndot.) represents an activation function.
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