CN104616033A - Fault diagnosis method for rolling bearing based on deep learning and SVM (Support Vector Machine) - Google Patents
Fault diagnosis method for rolling bearing based on deep learning and SVM (Support Vector Machine) Download PDFInfo
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Abstract
The invention provides a fault diagnosis method for a rolling bearing based on a deep learning and SVM (Support Vector Machine). The method comprises using a manure learning algorithm in a deep belief network theory to complete a characteristic extraction task needed by fault diagnosis; automatically extracting the substantive characteristics of data input independent of manual selection from simple to complicate, from low to high, and automatically digging abundant information concealed in known data; in addition, classifying and identifying a test sample by adopting an SVM classification method, seeking and finding a global minimum of a target function through an effective method previously designed, so as to solve the problem that a deep belief network may be trapped into a locally optimal solution. According to the fault diagnosis method for the rolling bearing based on the deep learning and SVM provided by the invention, the accuracy and effectiveness of the fault diagnosis method for a rolling bearing can be improved, and a new effective way can be provided to solve the accuracy and effectiveness of the fault diagnosis method, therefore the fault diagnosis method can be extensively applied complex systems in chemistry, metallurgy, electric power, aviation fields and the like.
Description
Technical Field
The invention belongs to the technical field of mechanical fault diagnosis and computer artificial intelligence, and particularly relates to a rolling bearing fault diagnosis method based on deep learning and a support vector machine.
Background
The rolling bearing is one of the most important mechanical parts in rotary machinery, is widely applied to various important departments of chemical industry, metallurgy, electric power, aviation and the like, and is one of the most vulnerable elements. The performance of the bearing and the working condition directly affect the performance of the shaft associated with the bearing and the gear arranged on the rotating shaft and even the performance of the whole machine equipment, and the defects can cause abnormal vibration and noise of the equipment and even cause the damage of the equipment. Therefore, diagnosing the rolling bearing fault, especially analyzing the early fault, and avoiding the accident is particularly important in the practical production.
Currently, the commonly used mechanical fault feature extraction methods mainly include Fast Fourier Transform (FFT), wavelet transform and Empirical Mode Decomposition (EMD), artificial intelligence, and the like. The FFT method cannot simultaneously take into account the global and localized problems of the signal in the time domain and the frequency domain. During wavelet transformation, wavelet bases are different, decomposition results are different, and the wavelet bases are difficult to select. The EMD method can decompose a signal into a plurality of IMF (intrinsic mode functions) components, and Hilbert transform is performed on all the IMF components to obtain time-frequency distribution of the signal, but theoretically, problems such as mode confusion, under-envelope, over-envelope, endpoint effect and the like in the EMD method are still in research. In the fault diagnosis method based on artificial intelligence, currently, an artificial neural network is mainly used for finishing classification of diagnosis targets through continuous learning and information feedback on a system; however, the method has the disadvantages that the reasoning process is poor in interpretability, and when a sample to be diagnosed is incomplete (data is missing), the neural network cannot carry out effective reasoning work, and the bearing cannot be correspondingly diagnosed by utilizing early characteristics of faults.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a rolling bearing fault diagnosis method based on deep learning and a support vector machine.
In order to achieve the purpose, the invention adopts the following technical means:
the rolling bearing fault diagnosis method based on deep learning and a support vector machine comprises the following steps:
1) when the rolling bearings under four different working conditions work in a rotating mode, vibration acceleration signals of the rolling bearings under each working condition working at different rotating speeds are collected through the acceleration sensors respectively, denoising pretreatment is carried out, working condition labels are added, and vibration acceleration signal data under various working conditions after pretreatment and working condition labels are added are used as training samples; the four working conditions are normal operation, bearing inner ring fault operation, bearing rolling element fault operation and bearing outer ring fault operation respectively;
2) establishing a deep belief network model, training the deep belief network model by adopting a training sample, inputting the training sample into the deep belief network model, and performing layer-by-layer training and optimization by adopting an unsupervised greedy layer-by-layer training method to obtain a connection weight and an offset parameter of the deep belief network model;
3) respectively taking training samples under various working conditions as input of a deep belief network model for determining a connection weight and a bias parameter, carrying out deep learning on the training samples, and respectively reconstructing each training sample under each working condition by adopting the deep belief network model for determining the connection weight and the bias parameter to obtain a training sample reconstruction signal corresponding to each training sample under each working condition;
4) acquiring vibration acceleration signal data of a rolling bearing to be tested during rotation work through an acceleration sensor, and performing denoising pretreatment to obtain a test sample;
5) taking the test sample as the input of a depth belief network model for determining a connection weight and a bias parameter, carrying out depth learning on the test sample, and reconstructing the test sample by adopting the depth belief network model for determining the connection weight and the bias parameter to obtain a test sample reconstruction signal;
6) and taking the test sample reconstruction signal as the matching characteristic of the test sample, taking the training sample reconstruction signal corresponding to each training sample under each working condition as the matching reference, matching the test sample with the training sample by adopting a support vector machine classification method, and judging the working condition class to which the training sample most matched with the test sample belongs as the working condition class of the test sample, thereby obtaining the fault diagnosis result of the rolling bearing to be tested.
In the rolling bearing fault diagnosis method based on deep learning and support vector machine, specifically, the joint distribution function of the deep belief network model established in the step 2) is:
wherein θ ═ wij,ai,bj) For deep belief network model parameters, wijVisible layer ith node v representing deep belief networkiWith the jth node h of the hidden layerjThe connection weight value between aiAnd bjRespectively represent ith nodes v of visible layeriBias parameters and the jth node h of the hidden layerjThe bias parameter of (2);
an unsupervised greedy layer-by-layer training method is adopted to carry out layer-by-layer training and optimization on the deep belief network model, and the specific mode is as follows:
21) training the limited Boltzmann machines in each layer of the deep belief network model in a layer-by-layer training mode, wherein the hidden layer output of the limited Boltzmann machine at the lower layer is used as the visible layer input of the limited Boltzmann machine at the upper layer until the output of the last hidden layer of the deep belief network model is obtained; the method specifically comprises the following steps:
the joint probability distribution probability p (v, h | θ) of the visible layer node and the hidden layer node is:
p(v,h|θ)＝e-E(v,h|θ)/Z(θ)； (2)
wherein, <math>
<mrow>
<mi>Z</mi>
<mrow>
<mo>(</mo>
<mi>θ</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munder>
<mi>Σ</mi>
<mi>v</mi>
</munder>
<munder>
<mi>Σ</mi>
<mi>h</mi>
</munder>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mi>E</mi>
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<mo>(</mo>
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</math> is a distribution function;
when the state of the visible layer node is given, the jth node h of the hidden layerjThe activation probability of (c) is:
given the state of the hidden layer node, the ith node v of the visible layeriThe activation probability of (c) is:
wherein σ (x) is 1/(1+ e)-x) Is sigmoid function;
according to the activation probability, when a given training sample is input to the visible layer node, after all nodes of the hidden layer are excited by adopting a joint distribution function of a deep belief network model, the nodes of the next hidden layer are excited, so that the visible layer node is obtained again; then, calculating the condition distribution of the visible layer data by adopting a contrast divergence algorithm to obtain hidden layer data, calculating the visible layer data by calculating the condition distribution of the hidden layer data, reconstructing the visible layer data, adjusting and updating the parameters of the deep belief network model by utilizing a gradient descent method, wherein the updating difference values of the connection weight and the offset parameter are respectively as follows:
Δwij＝(<vihj>data-<vihj>recon)； (6)
Δai＝(<vi>data-<vi>recon)； (7)
Δbj＝(<hj>data-<hj>recon)； (8)
wherein, Δ wijVisible layer ith node v representing deep belief networkiWith the jth node h of the hidden layerjThe connection weight value w betweenijUpdate difference, Δ a, for performing an updateiAnd Δ bjRespectively represent ith nodes v of visible layeriBias parameter a ofiUpdating difference value and jth node h of hidden layer for updatingjBias parameter b ofjUpdating the updated difference value; in order to train the learning rate of the training,<·>datarepresenting a mathematical expectation over a distribution defined by the training data set,<·>reconrepresenting a mathematical expectation on the distribution of the reconstructed deep belief network model output;
training layer by layer until the output of the last hidden layer of the deep belief network model is obtained;
22) training a back propagation network for the output of the last hidden layer of the deep belief network model obtained in the step 21, propagating the classification error of the classification result output by training prediction and the actual classification result of the training sample backward layer by layer, and adjusting the connection weight of each layer of the deep belief network model; the method specifically comprises the following steps:
the training of the back propagation network is divided into a forward propagation process and a back propagation process; in the forward propagation process, the output of the last hidden layer of the deep belief network model obtained in the step 21 is propagated to an output layer by layer as input to obtain a predicted classification category, the actual classification result of the training sample is determined according to the working condition label of the training sample, then the predicted classification result is compared with the actual classification result of the training sample to obtain a classification error, and the classification error is transmitted back layer by layer, so that the parameters of the deep training network are adjusted; in the backward propagation process, the value of the sensitivity of each layer needs to be calculated, and the sensitivity is transmitted from top to bottom to correct the connection weight of the deep belief network model;
for the output layer, assume the actual output of the ith node is oiThe desired output is diThen, the calculation expression of the sensitivity of the ith node is:
i＝oi(1-oi)(di-oi)； (9)
for the mth hidden layer, the computational expression of the sensitivity of the ith node is:
wherein,indicating the sensitivity of the ith node of the mth hidden layer,indicating the sensitivity of the ith node of the (m + 1) th hidden layer,represents the output of the ith node of the mth hidden layer,representing the connection weight between the ith node of the mth hidden layer and the jth node of the (m + 1) th hidden layer;
after the sensitivity of each node in each hidden layer is obtained, the connection weight of the deep belief network model is updated and adjusted according to the following formula:
wherein,fine-tuningthe learning rate is shown to be adjusted and optimized,representing the bias parameter of the jth node of the mth hidden layer;
and finally determining the connection weight and the bias parameter of the whole depth belief network model after adjusting and optimizing the connection weight of each layer of the depth belief network model.
In the rolling bearing fault diagnosis method based on deep learning and support vector machine, as an optimal solution, the specific way of matching the test sample and the training sample in step 6) by using the support vector machine classification method is as follows:
61) in the training samples of four working conditions, aiming at the situation that the kth class training sample is regarded as a positive class, k belongs to {1,2,3,4}, other 3 classes of training samples are regarded as negative classes, and a classification decision function f of the kth class is obtained by a classification method of two classes of support vector machinesk(x)：
Wherein,classifying a decision function f for class kk(x) N-th training sample reconstructed signal xnA corresponding Lagrange coefficient; bkClassifying a decision function f for class kk(x) The optimal hyperplane position coefficient; y isnRepresenting the classification mark corresponding to the nth training sample, y when the nth training sample belongs to the positive classn1, y when the nth training sample belongs to the negative classn-1; n belongs to {1,2, …, N }, wherein N is the total number of training samples of four working conditions; k (x, x)n) Representing a classification decision function fk(x) Is compared with the n-th training sample to reconstruct the signal xnGaussian radial basis kernel function of (1);
thus obtaining a classification decision function corresponding to each working condition in the four working conditions;
62) and respectively taking the test sample reconstruction signals as input quantities of the classification decision functions corresponding to the four working conditions, calculating the four classification decision function values of the test sample reconstruction signals as the input quantities, and judging the working condition type corresponding to the largest classification decision function value as the working condition type of the test sample to obtain a fault diagnosis result of the rolling bearing to be tested.
Compared with the prior art, the invention has the following beneficial effects:
1. the rolling bearing fault diagnosis method based on deep learning and the support vector machine completes the feature extraction task required by fault diagnosis by utilizing a mature learning algorithm in a deep belief network theory, can automatically extract the essential features of input data from low level to high level without depending on manual selection from simple to complex, can save a large amount of manpower, can automatically dig out rich information hidden in known data, and is particularly suitable for noisy, uncertain and dynamic systems.
2. In the rolling bearing fault diagnosis method based on deep learning and the support vector machine, the support vector machine classification method is adopted to classify and identify the test samples, and the learning process in the support vector machine classification method can be regarded as a process for optimally searching an optimal solution, so that a previously designed effective method can be adopted to search and find a global minimum value of a target function, and the problem that a deep belief network possibly falls into a local optimal solution is solved.
3. Compared with the prior art, the rolling bearing fault diagnosis method can improve the accuracy and effectiveness of rolling bearing fault diagnosis, provides a new effective way for solving the problem of rolling bearing fault diagnosis, and can be widely applied to complex systems in the fields of chemical industry, metallurgy, electric power, aviation and the like.
Drawings
Fig. 1 is a flow chart of a rolling bearing fault diagnosis method based on deep learning and a support vector machine according to the invention.
Fig. 2 is an example graph of time domain distribution (time domain unit is ms) of an original vibration acceleration signal of a rolling bearing inner ring fault operation.
Fig. 3 is an example graph of the time domain distribution of the original vibration acceleration signal (time domain unit is ms) of the rolling element fault operation of the rolling bearing.
FIG. 4 is a model architecture diagram of the deep belief network model.
FIG. 5 is a schematic model diagram of a restricted Boltzmann machine.
FIG. 6 is a schematic diagram of the position relationship of the SVM normalized optimal classification hyperplane.
Detailed Description
In order to overcome the defects of the prior art, the rolling bearing fault diagnosis method based on deep learning and the support vector machine firstly adopts a deep belief network to learn the essential characteristics of training sample data, and then adopts the support vector machine classification method to classify and identify the test sample, so that the fault working condition category of the rolling bearing is determined, and the accuracy and the effectiveness of the fault diagnosis of the rolling bearing are improved.
The Deep Belief Network (DBN) has strong function expression capability and shows the excellent characteristic of learning essential characteristics of data from a few samples. Research shows that a deep network structure composed of multiple nonlinear mapping layers is more effective than a shallow structure, and has good effect and efficiency on complex function representation and complex classification. The deep belief network explains that the multi-hidden-layer neural network has excellent feature learning capability, and the learned features are more essential to data, so that the classification and visualization are facilitated.
The core idea of a Support Vector Machine (SVM) classifier is to map an input Vector to a high-dimensional feature space through some nonlinear mapping (kernel function) and construct an optimal classification hyperplane, thereby realizing classification and identification. The method has unique advantages in solving small sample, nonlinear and high-dimensional pattern recognition, can well limit over-learning, is particularly suitable for data processing of small sample sets, and can be applied to fault diagnosis and fault prediction.
Based on the above advantages of the deep belief network and the support vector machine, the rolling bearing fault diagnosis method of the invention integrates the above advantages of the deep belief network and the support vector machine, and utilizes the deep learning and the support vector machine to classify the fault conditions of the rolling bearing, so as to realize the identification and diagnosis of the rolling bearing fault, the specific operation flow is shown in fig. 1, and the method comprises the following steps:
1) when the rolling bearings under four different working conditions work in a rotating mode, vibration acceleration signals of the rolling bearings under each working condition working at different rotating speeds are collected through the acceleration sensors respectively, denoising pretreatment is carried out, working condition labels are added, and vibration acceleration signal data under various working conditions after pretreatment and working condition labels are added are used as training samples; the four working conditions are normal operation, bearing inner ring fault operation, bearing rolling element fault operation and bearing outer ring fault operation respectively.
For example, fig. 2 and fig. 3 respectively show time domain distribution diagrams (time domain unit is ms) of original vibration acceleration signals of the rolling bearing under the working conditions of inner ring fault operation and rolling body fault operation, and the signal difference is obvious. Therefore, the fault condition of the rolling bearing can be identified based on the vibration acceleration signal data of the rolling bearing under different working conditions.
2) Establishing a deep belief network model, training the deep belief network model by adopting a training sample, inputting the training sample into the deep belief network model, and performing layer-by-layer training and optimization by adopting an unsupervised greedy layer-by-layer training method to obtain a connection weight and an offset parameter of the deep belief network model.
A model architecture diagram of the deep belief network model is shown in fig. 4, and structurally, the deep belief network model is composed of a multilayer unsupervised Boltzmann machine (RBM) network and a layer of supervised back-propagation (BP) network.
The training of the deep training network model comprises 2 steps of "pre-training" and "tuning-tuning". The pre-training stage deep training network trains RBMs in each layer in a layer-by-layer (layerwise) training mode, and the hidden layer output of the RBMs in the lower layer is used as the visible layer input of the RBMs in the upper layer. And in the fine-tuning stage, the last layer of BP network is trained in a supervised learning mode, errors between actual output and expected output are propagated backwards layer by layer, and the weight of the whole deep training network is optimized. The training process of the RBM network can be actually regarded as the initialization of the weight of the deep BP network, so that the deep training network overcomes the defects of long training time and easy falling into a local optimal solution of the BP network due to the random initialization of the weight parameter.
A restricted boltzmann machine.
The constrained boltzmann machine is a typical energy-based model (EBM) which is composed of a visible layer (visible layer) and a hidden layer (hidden layer), and a schematic diagram of the model is shown in fig. 5. Wherein v and h respectively represent a visible layer and a hidden layer, and W represents a connection weight between the two layers. For the visible layer and the hidden layer, the connection relationship is that the neurons between the layers are fully connected, and no neuron in the layers is connected.
Assuming that the visible layer and the hidden layer are binary variables, the numbers of neurons in the visible layer and the hidden layer are I, J and v respectivelyiAnd hjRespectively representing the states of the ith visible layer neuron and the jth hidden layer neuron. For a particular set of (v, h), the joint distribution function of the deep belief network model is:
wherein θ ═ wij,ai,bj) For deep belief networksModel parameter, wijVisible layer ith node v representing deep belief networkiWith the jth node h of the hidden layerjThe connection weight value between aiAnd bjRespectively represent ith nodes v of visible layeriBias parameters and the jth node h of the hidden layerjThe bias parameter of (2);
and (3) obtaining the joint probability distribution of (v, h) by using the joint distribution function of the deep belief network model:
p(v,h|θ)＝e-E(v,h|θ)/Z(θ)； (2)
wherein,is a distribution function. In practical terms, we are most concerned with the distribution (likelihood function) defined by the RBM about the observed variable, i.e., p (v | θ), which is the edge distribution of the joint probability p (v, h | θ).
Due to the special structure of the RBM (no connection of neurons in the layers), the activation states of the various hidden layer nodes are independent of each other when given the state of a visible layer node. At this time, the jth node h of the hidden layerjThe activation probability of (c) is:
wherein σ (x) is 1/(1+ e)-x) Is sigmoid function. Similarly, given the state of the hidden layer node, the ith node v of the visible layeriThe activation probability of (c) is:
the RBM is trained in an iterative mode, and the training aims at learning a parameter theta (w)ij,ai,bj) To fit given training data. The parameter θ can be obtained by solving a maximum log likelihood function on a training sample set (assuming the total number of training samples as T), that is:
according to the activation probability, when a training sample is input to the visible layer node, after all nodes of the hidden layer are excited by adopting a joint distribution function of a deep belief network model, the next hidden layer node is excited, and thus the visible layer node is obtained again; and then, calculating the conditional distribution of the visible layer data by adopting a contrast divergence algorithm to obtain hidden layer data, calculating the visible layer data by using the conditional distribution of the hidden layer data obtained by calculation, reconstructing the visible layer data, and adjusting and updating the parameters of the deep belief network model by utilizing a gradient descent method. By using the Contrast Divergence (CD) algorithm proposed by Hinton, the updated difference values of the connection weight and the bias parameter can be obtained as follows:
Δwij＝(<vihj>data-<vihj>recon) (6)；
Δai＝(<vi>data-<vi>recon) (7)；
Δbj＝(<hj>data-<hj>recon) (8)；
wherein, Δ wijVisible layer ith node v representing deep belief networkiWith the jth node h of the hidden layerjThe connection weight value w betweenijPerforming an updated updateDifference, Δ aiAnd Δ bjRespectively represent ith nodes v of visible layeriBias parameter a ofiUpdating difference value and jth node h of hidden layer for updatingjBias parameter b ofjUpdating the updated difference value; in order to train the learning rate of the training,<·>datarepresenting a mathematical expectation over a distribution defined by the training data set,<·>reconrepresenting a mathematical expectation over the distribution of the reconstructed deep belief network model output.
And training layer by layer until the output of the last hidden layer of the deep belief network model is obtained.
Secondly, the output of the last hidden layer of the deep belief network model is subjected to the training of a back propagation network, the classification error of the classification result output by the training prediction and the actual classification result of the training sample is propagated backwards layer by layer, and the connection weight of each layer of the deep belief network model is optimized.
The back propagation network is a supervised classifier, classifies the feature vectors obtained by the RBM through pre-training, and plays a role in adjusting and optimizing parameters of the whole deep training network. The training of the back propagation network is divided into a forward propagation process and a back propagation process; in the forward propagation process, the output of the RBM is used as an input feature vector and is propagated to an output layer by layer to obtain a predicted classification category, the actual classification result of the training sample is determined according to the working condition label of the training sample, then the predicted classification result is compared with the actual classification result of the training sample to obtain a classification error, and the classification error is transmitted back layer by layer to adjust and optimize the parameters of the deep training network; in the backward propagation process, the value of the sensitivity of each layer needs to be calculated, and the sensitivity is transmitted from top to bottom to correct the connection weight of the deep belief network model.
For the output layer, assume the actual output of the ith node is oiThe desired output is diThen, the calculation expression of the sensitivity of the ith node is:
i＝oi(1-oi)(di-oi)； (9)
for the mth hidden layer, the computational expression of the sensitivity of the ith node is:
wherein,indicating the sensitivity of the ith node of the mth hidden layer,indicating the sensitivity of the ith node of the (m + 1) th hidden layer,represents the output of the ith node of the mth layer,representing the weight between the ith node of the mth layer and the jth node of the next layer;
after the sensitivity of each node in each hidden layer is obtained, the connection weight of the deep belief network model is updated and adjusted according to the following formula:
wherein,fine-tuningthe learning rate is shown to be adjusted and optimized,represents the jth node of the mth layerOf (1);
and finally determining the connection weight and the bias parameter of the whole depth belief network model after adjusting and optimizing the connection weight of each layer of the depth belief network model.
3) And respectively taking the training samples under various working conditions as the input of a deep belief network model for determining a connection weight and a bias parameter, carrying out deep learning on the training samples, and respectively reconstructing each training sample under each working condition by adopting the deep belief network model for determining the connection weight and the bias parameter to obtain a training sample reconstruction signal corresponding to each training sample under each working condition.
According to the characteristics of the deep belief network, the original data sample with lower error can be reconstructed by using the deep belief network model which is trained, adjusted and optimized and then determined to be connected with the weight and the offset parameter, so that the reconstructed signal of the data sample obtained by reconstruction can embody and depict the essential characteristics of the original data sample, and the essential characteristics can be used as the reference characteristics for classification and identification. Therefore, in the step, the deep belief network model for determining the connection weight and the offset parameter is used for reconstructing each training sample under each working condition, so that the training sample reconstruction signal corresponding to each training sample under each working condition is used as a matching reference for performing classification and identification on the test sample at a later stage.
4) And acquiring vibration acceleration signal data of the rolling bearing to be tested during rotation operation through the acceleration sensor, and performing denoising pretreatment to obtain a test sample.
5) And taking the test sample as the input of the depth belief network model for determining the connection weight and the offset parameter, carrying out depth learning on the test sample, and reconstructing the test sample by adopting the depth belief network model for determining the connection weight and the offset parameter to obtain a test sample reconstruction signal.
Similarly, the step reconstructs the test sample by using a depth belief network model for determining the connection weight and the offset parameter, and the obtained reconstructed signal of the test sample describes the essential characteristics contained in the vibration acceleration signal number of the rolling bearing to be tested, so that the intrinsic characteristics are matched with the essential characteristics embodied by the reconstructed signal of the training sample under various working conditions, and the identification of the fault working condition category of the rolling bearing to be tested is realized.
6) And taking the test sample reconstruction signal as the matching characteristic of the test sample, taking the training sample reconstruction signal corresponding to each training sample under each working condition as the matching reference, matching the test sample with the training sample by adopting a support vector machine classification method, and judging the working condition class to which the training sample most matched with the test sample belongs as the working condition class of the test sample, thereby obtaining the fault diagnosis result of the rolling bearing to be tested.
Support Vector Machines (SVMs) were proposed by Vapnik et al in AT & TBell laboratories in 1963, which are based on VC dimension theory and structure risk minimization principle in statistics, and seek an optimal compromise between model complexity (i.e., learning accuracy of a specific training sample) and learning ability (i.e., ability to correctly recognize an arbitrary sample) according to limited sample information to obtain the best popularization ability. The SVM maps the vectors into a higher-dimensional space, a maximum separation hyperplane is established in the high-dimensional space, two hyperplanes which are parallel to each other are established on two sides capable of separating the data hyperplanes, the separation hyperplane enables the distance between the two parallel hyperplanes to be maximized, and the larger the distance is, the smaller the error of the classification result is.
Fig. 6 is a schematic diagram of the position relationship of the normalized optimal hyperplane under two-dimensional two-class conditions, where H is a separating hyperplane H1, H2 are two mutually parallel hyperplanes, and H1, H2 are classification intervals d ═ 2/| | | w |. In order to ensure the linearization of the data, the data needs to be mapped to a kernel function space; meanwhile, in order to effectively separate the two classes, it should be ensured that the two classes are correctly separated to maximize the classification interval, i.e. the objective function is:
for the hyperplane H1, H2, there are:
equation (14) may be equivalent to:
wherein:denotes w andthe inner product of the two phases is,the table maps xi to kernel function space; b and C are constants;ithe variable > 0 is the relaxation variable,the error degree of the training sample is represented, and the larger the value of the error degree, the more the error sample is represented.
Applying Lagrange multiplier method to equations (13) and (15) yields:
wherein: alpha is alphai＞0,βiAnd the Lagrangian coefficient is more than 0, and the Lagrangian function is L (w, b, alpha).
The formula (16) is for w,iAnd the partial derivative of b is zero, yielding:
equation (17) is substituted for equation (16), and the solution of the optimal hyperplane is equivalent to the solution of the following dual problem.
Wherein:
using Lagrange multiplier method, the solution is obtained as:
the classification rule function for obtaining the optimal classification surface from equation (19) is:
the invention selects a Gaussian Radial Basis (RBF) kernel function:
wherein: σ is a parameter of the RBF kernel function.
The SVM algorithm seeks an optimal classification surface among data on the basis of statistics, and nonlinear data are mapped to a kernel function space to be linearized, so that the computational complexity is simplified, and a better classification effect is achieved.
In step 6), there are many specific classification methods that can be applied to the support vector machine classification method, such as one-to-one classification (OVO-SVM), one-to-many classification (also called one-to-many classification, OVR-SVM), directed acyclic graph classification (DAG-SVMs), decision tree classification, error correction output coding classification, and the like. However, considering that the method only relates to the fault working condition classification recognition of four working conditions, namely normal operation, bearing inner ring fault operation, bearing rolling element fault operation and bearing outer ring fault operation, the recognition categories are not many, and the factors of recognition efficiency and accuracy are comprehensively considered, the one-to-many SVM classification method is more suitable because the decision functions of the SVM classifiers needing to be established and subjected to recognition operation by the one-to-many classification method are only four (one for each fault working condition category), and after the vibration acceleration signal data of the rolling bearing under the four different working conditions is reconstructed by the deep belief network model, the difference of the essential characteristics is enough to be recognized, and the recognition accuracy can be better ensured.
In the method of the present invention, the step 6) preferably adopts a one-to-many support vector machine classification method to match the test sample with the training sample in the following specific way:
61) in the training samples of four working conditions, aiming at the situation that the kth class training sample is regarded as a positive class, k belongs to {1,2,3,4}, other 3 classes of training samples are regarded as negative classes, and a classification decision function f of the kth class is obtained by a classification method of two classes of support vector machinesk(x)：
Wherein,classifying a decision function f for class kk(x) N-th training sample reconstructed signal xnA corresponding Lagrange coefficient; bkClassifying a decision function f for class kk(x) The optimal hyperplane position coefficient; y isnRepresenting the classification mark corresponding to the nth training sample, y when the nth training sample belongs to the positive classn1, y when the nth training sample belongs to the negative classn-1; n belongs to {1,2, …, N }, wherein N is the total number of training samples of four working conditions; k (x, x)n) Representing a classification decision function fk(x) Is compared with the n-th training sample to reconstruct the signal xnGaussian radial basis kernel function of (1);
thus obtaining a classification decision function corresponding to each working condition in the four working conditions;
62) and respectively taking the test sample reconstruction signals as input quantities of the classification decision functions corresponding to the four working conditions, calculating the four classification decision function values of the test sample reconstruction signals as the input quantities, and judging the working condition type corresponding to the largest classification decision function value as the working condition type of the test sample to obtain a fault diagnosis result of the rolling bearing to be tested.
Through experimental data verification, the rolling bearing fault diagnosis method based on deep learning and the support vector machine carries out fault diagnosis according to the process, and under the condition of 600 training samples (150 training samples in each working condition), rolling bearing fault diagnosis and identification are carried out by random sampling for 800 times, the identification accuracy reaches 94.3 percent (the average fault identification accuracy in the industry is only about 83 percent), and the actual application requirements can be completely met.
In conclusion, the rolling bearing fault diagnosis method based on deep learning and the support vector machine of the invention utilizes the mature learning algorithm in the deep belief network theory to complete the feature extraction task required by fault diagnosis, can automatically extract the essential features of input data from simple to complex and from low level to high level without depending on manual selection, can save a large amount of manpower, can automatically dig out rich information hidden in known data, and is particularly suitable for noisy, uncertain and dynamic systems; in addition, because the support vector machine classification method is adopted to classify and identify the test samples, the learning process in the support vector machine classification method can be regarded as a process for optimally searching an optimal solution, so that a previously designed effective method can be adopted to search and find a global minimum value of a target function, and the problem that a deep belief network possibly falls into a local optimal solution is solved; compared with the prior art, the rolling bearing fault diagnosis method can improve the accuracy and effectiveness of rolling bearing fault diagnosis, provides a new effective way for solving the problem of rolling bearing fault diagnosis, and can be widely applied to complex systems in the fields of chemical industry, metallurgy, electric power, aviation and the like.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.
Claims (3)
1. The rolling bearing fault diagnosis method based on deep learning and a support vector machine is characterized by comprising the following steps:
1) when the rolling bearings under four different working conditions work in a rotating mode, vibration acceleration signals of the rolling bearings under each working condition working at different rotating speeds are collected through the acceleration sensors respectively, denoising pretreatment is carried out, working condition labels are added, and vibration acceleration signal data under various working conditions after pretreatment and working condition labels are added are used as training samples; the four working conditions are normal operation, bearing inner ring fault operation, bearing rolling element fault operation and bearing outer ring fault operation respectively;
2) establishing a deep belief network model, training the deep belief network model by adopting a training sample, inputting the training sample into the deep belief network model, and performing layer-by-layer training and optimization by adopting an unsupervised greedy layer-by-layer training method to obtain a connection weight and an offset parameter of the deep belief network model;
3) respectively taking training samples under various working conditions as input of a deep belief network model for determining a connection weight and a bias parameter, carrying out deep learning on the training samples, and respectively reconstructing each training sample under each working condition by adopting the deep belief network model for determining the connection weight and the bias parameter to obtain a training sample reconstruction signal corresponding to each training sample under each working condition;
4) acquiring vibration acceleration signal data of a rolling bearing to be tested during rotation work through an acceleration sensor, and performing denoising pretreatment to obtain a test sample;
5) taking the test sample as the input of a depth belief network model for determining a connection weight and a bias parameter, carrying out depth learning on the test sample, and reconstructing the test sample by adopting the depth belief network model for determining the connection weight and the bias parameter to obtain a test sample reconstruction signal;
6) and taking the test sample reconstruction signal as the matching characteristic of the test sample, taking the training sample reconstruction signal corresponding to each training sample under each working condition as the matching reference, matching the test sample with the training sample by adopting a support vector machine classification method, and judging the working condition class to which the training sample most matched with the test sample belongs as the working condition class of the test sample, thereby obtaining the fault diagnosis result of the rolling bearing to be tested.
2. The rolling bearing fault diagnosis method based on deep learning and support vector machine according to claim 1, wherein the joint distribution function of the deep belief network model established in the step 2) is:
wherein θ ═ wij,ai,bj) For deep belief network model parameters, wijVisible layer ith node v representing deep belief networkiWith the jth node h of the hidden layerjThe connection weight value between aiAnd bjRespectively represent ith nodes v of visible layeriBias parameters and the jth node h of the hidden layerjThe bias parameter of (2);
an unsupervised greedy layer-by-layer training method is adopted to carry out layer-by-layer training and optimization on the deep belief network model, and the specific mode is as follows:
21) training the limited Boltzmann machines in each layer of the deep belief network model in a layer-by-layer training mode, wherein the hidden layer output of the limited Boltzmann machine at the lower layer is used as the visible layer input of the limited Boltzmann machine at the upper layer until the output of the last hidden layer of the deep belief network model is obtained; the method specifically comprises the following steps:
the joint probability distribution probability p (v, h | θ) of the visible layer node and the hidden layer node is:
p(v,h|θ)＝e-E(v,h|θ)/Z(θ)；(2)
wherein, <math>
<mrow>
<mi>Z</mi>
<mrow>
<mo>(</mo>
<mi>θ</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munder>
<mi>Σ</mi>
<mi>v</mi>
</munder>
<munder>
<mi>Σ</mi>
<mi>h</mi>
</munder>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mi>E</mi>
<mrow>
<mo>(</mo>
<mi>v</mi>
<mo>,</mo>
<mi>h</mi>
<mo>|</mo>
<mi>θ</mi>
<mo>)</mo>
</mrow>
</mrow>
</msup>
</mrow>
</math> is a distribution function;
when the state of the visible layer node is given, the jth node h of the hidden layerjThe activation probability of (c) is:
given the state of the hidden layer node, the ith node v of the visible layeriThe activation probability of (c) is:
wherein σ (x) is 1/(1+ e)-x) Is sigmoid function;
according to the activation probability, when a given training sample is input to the visible layer node, after all nodes of the hidden layer are excited by adopting a joint distribution function of a deep belief network model, the nodes of the next hidden layer are excited, so that the visible layer node is obtained again; then, calculating the condition distribution of the visible layer data by adopting a contrast divergence algorithm to obtain hidden layer data, calculating the visible layer data by calculating the condition distribution of the hidden layer data, reconstructing the visible layer data, adjusting and updating the parameters of the deep belief network model by utilizing a gradient descent method, wherein the updating difference values of the connection weight and the offset parameter are respectively as follows:
Δwij＝(<vihj>data-<vihj>recon)；(6)
Δai＝(<vi>data-<vi>recon)；(7)
Δbj＝(<hj>data-<hj>recon)；(8)
wherein, Δ wijVisible layer ith node v representing deep belief networkiWith the jth node h of the hidden layerjThe connection weight value w betweenijUpdate difference, Δ a, for performing an updateiAnd Δ bjRespectively represent ith nodes v of visible layeriBias parameter a ofiUpdating difference value and jth node h of hidden layer for updatingjBias parameter b ofjUpdating the updated difference value; in order to train the learning rate of the training,<·>datarepresenting a mathematical expectation over a distribution defined by the training data set,<·>reconrepresenting a mathematical expectation on the distribution of the reconstructed deep belief network model output;
training layer by layer until the output of the last hidden layer of the deep belief network model is obtained;
22) training a back propagation network for the output of the last hidden layer of the deep belief network model obtained in the step 21, propagating the classification error of the classification result output by training prediction and the actual classification result of the training sample backward layer by layer, and adjusting the connection weight of each layer of the deep belief network model; the method specifically comprises the following steps:
the training of the back propagation network is divided into a forward propagation process and a back propagation process; in the forward propagation process, the output of the last hidden layer of the deep belief network model obtained in the step 21 is propagated to an output layer by layer as input to obtain a predicted classification category, the actual classification result of the training sample is determined according to the working condition label of the training sample, then the predicted classification result is compared with the actual classification result of the training sample to obtain a classification error, and the classification error is transmitted back layer by layer, so that the parameters of the deep training network are adjusted; in the backward propagation process, the value of the sensitivity of each layer needs to be calculated, and the sensitivity is transmitted from top to bottom to correct the connection weight of the deep belief network model;
for the output layer, assume the actual output of the ith node is oiThe desired output is diThen, the calculation expression of the sensitivity of the ith node is:
i＝oi(1-oi)(di-oi)；(9)
for the mth hidden layer, the computational expression of the sensitivity of the ith node is:
wherein,indicating the sensitivity of the ith node of the mth hidden layer,indicating the sensitivity of the ith node of the (m + 1) th hidden layer,represents the output of the ith node of the mth hidden layer,representing the connection weight between the ith node of the mth hidden layer and the jth node of the (m + 1) th hidden layer;
after the sensitivity of each node in each hidden layer is obtained, the connection weight of the deep belief network model is updated and adjusted according to the following formula:
wherein,fine-tuningthe learning rate is shown to be adjusted and optimized,representing the bias parameter of the jth node of the mth hidden layer;
and finally determining the connection weight and the bias parameter of the whole depth belief network model after adjusting and optimizing the connection weight of each layer of the depth belief network model.
3. The rolling bearing fault diagnosis method based on deep learning and support vector machine according to claim 1, wherein the specific way of matching the test sample and the training sample in step 6) by using the support vector machine classification method is as follows:
61) in the training samples of four working conditions, aiming at the situation that the kth class training sample is regarded as a positive class, k belongs to {1,2,3,4}, other 3 classes of training samples are regarded as negative classes, and a classification decision function f of the kth class is obtained by a classification method of two classes of support vector machinesk(x)：
Wherein,classifying a decision function f for class kk(x) N-th training sample reconstructed signal xnA corresponding Lagrange coefficient; bkClassifying a decision function f for class kk(x) The optimal hyperplane position coefficient; y isnRepresenting the classification mark corresponding to the nth training sample, y when the nth training sample belongs to the positive classn1, y when the nth training sample belongs to the negative classn-1; n belongs to {1,2, …, N }, wherein N is the total number of training samples of four working conditions; k (x, x)n) Representing a classification decision function fk(x) Is compared with the n-th training sample to reconstruct the signal xnGaussian radial basis kernel function of (1);
thus obtaining a classification decision function corresponding to each working condition in the four working conditions;
62) and respectively taking the test sample reconstruction signals as input quantities of the classification decision functions corresponding to the four working conditions, calculating the four classification decision function values of the test sample reconstruction signals as the input quantities, and judging the working condition type corresponding to the largest classification decision function value as the working condition type of the test sample to obtain a fault diagnosis result of the rolling bearing to be tested.
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