CN115290328A - Fault diagnosis and classification method and system based on rolling bearing sound vibration non-stationary signal - Google Patents

Abstract

The invention provides a fault diagnosis and classification method and system based on rolling bearing sound vibration non-stationary signals, wherein the method comprises the following steps: collecting a vibration signal of a fault in the bearing running process and taking the vibration signal as an original signal; performing local mean decomposition on an original signal to obtain a PF component of the original signal, reconstructing the original signal according to the PF component to obtain a reconstructed signal, and screening the PF component through mutual information; fusing the PF component obtained by screening with the time domain index of the vibration signal, and performing PCA (principal component analysis) dimensionality reduction processing on the fused feature to obtain a feature vector; and inputting the characteristic vectors into a fault diagnosis classification model to obtain the fault type of the bearing. The invention avoids the limitation that LMD decomposition selects PF component by means of experience judgment, selects proper PF component by using mutual information criterion, optimizes DBN network model by adopting PSO, selects optimal DBN network structure parameter, avoids the problem that DBN is easy to fall into local convergence, and improves the accuracy of fault diagnosis and classification.

Description

Fault diagnosis and classification method and system based on rolling bearing sound vibration non-stationary signals

Technical Field

The invention belongs to the field of fault diagnosis and identification of rolling bearings, and particularly relates to a fault diagnosis and classification method and system based on rolling bearing sound vibration non-stationary signals.

Background

The rolling bearing is an important component of rotary machinery and is widely applied to the industries of aerospace, metallurgy, transportation and the like. Due to uncertain factors such as severe working environment, load conversion and the like, the rolling bearing is one of the most prone to failure parts in equipment. Once a fault occurs, mechanical damage may occur, and even a serious safety accident may occur. Therefore, the monitoring of the working state of the rolling bearing has important engineering significance.

The fault vibration and the fault sound signal of the rolling bearing mostly present non-stationarity, and the periodic stationarity presented by the fault signal caused by the fluctuation of the rotating speed or load of the equipment and the periodic cycle working condition belongs to the non-stationarity signal. Therefore, the research of the non-stationary signal feature extraction method is one of the hot problems in the field of bearing fault diagnosis, the time-frequency domain analysis method is widely applied because the time-frequency domain analysis method can extract the vibration signal time-domain and frequency-domain feature information, and common time-frequency analysis methods include short-time fourier transform, hilbert yellow variation, winger distribution and the like, but the methods have some defects. For example, the time-frequency window size of the short-time fourier transform is fixed, the time-frequency resolution cannot be optimized, the hilbert-yellow transform takes too long time to process the assignment signal, cross terms are generated when the Winger distribution processes the multi-component signal, and the like.

Disclosure of Invention

In view of the defects of the prior art, the invention provides a fault diagnosis and classification method and a fault diagnosis and classification system based on a rolling bearing sound vibration non-stationary signal, so as to overcome the defects in the prior art.

In order to achieve the above objects and other related objects, the present invention provides a fault diagnosis and classification method based on rolling bearing acoustic vibration non-stationary signals, comprising:

s1, collecting vibration signals X of faults in the bearing running process ₁ (t) and using it as the original signal;

s2, performing local mean decomposition on the original signal to obtain a PF component of the original signal, and reconstructing the original signal according to the PF component to obtain a reconstructed signal X ₂ (t)；

S3, according to the reconstructed signal X ₂ (t) screening the PF components through mutual information;

s4, fusing the PF component obtained after screening with the time domain index of the vibration signal, and performing PCA (principal component analysis) dimension reduction processing on the fused feature to obtain a feature vector;

and S5, inputting the feature vectors into a fault diagnosis classification model to obtain the fault type of the bearing, wherein the fault diagnosis classification model adopts a depth confidence network model optimized by a particle swarm optimization.

In an embodiment of the present invention, the original signal is subjected to local mean decomposition to obtain a PF component thereof, and the original signal is reconstructed according to the PF component to obtain a reconstructed signal X ₂ The step of (t) comprises:

s21, carrying out local mean decomposition on the original signal to obtain a pure frequency modulation signal of the original signal, and obtaining an envelope spectrum estimation function obtained in the process of obtaining the pure frequency modulation signal;

s22, multiplying all envelope spectrum estimation functions obtained in the process of obtaining the pure frequency modulation signal to obtain an envelope signal, and multiplying the envelope signal by the pure frequency modulation signal to obtain a PF component;

s23, removing the PF component from the original signal to obtain a new first signal, taking the first signal as the original signal, skipping to the step S21, and repeating the process k ₁ Repeating until the first signal is a monotonic function, and obtaining k ₁ K in the course of a sub-iteration ₁ A PF component;

s24, mixing k ₁ The sum of a PF component and a monotonic function is constructed as the reconstructed signal X ₂ (t)。

In one embodiment of the invention, the reconstructed signal X is based on the reconstructed signal X ₂ (t) and screening the PF components by mutual information includes:

s31, mutual information values between each PF component and the vibration signals are calculated respectively;

s32, comparing the mutual information value with a threshold value to screen out PF components of which the mutual information values are larger than the threshold value, wherein the threshold value is determined according to the following formula:

wherein, I _max Represents the maximum of all mutual information values; i is _min Representing a minimum value of the mutual information values; eta is greater than 1And (4) the coefficient.

In one embodiment of the invention, the mutual information size is determined by the following formula:

wherein D is _PF Representing a set of PF components;

a set representing vibration signals; p (PF, X) ₁ (t)) represents the PF component and the vibration signal X ₁ (t) a joint probability distribution; p (PF) and p (X) ₁ (t)) respectively represent the PF component and the vibration signal X ₁ (t) the respective edge probabilities;

wherein if PF component and vibration signal X ₁ (t) are independent of each other, the mutual information value is zero; otherwise, if PF component and vibration signal X ₁ The stronger the correlation between (t), the larger its mutual information value.

In one embodiment of the invention, the time domain indicators include kurtosis indicators, skewness, absolute mean, and variance.

In an embodiment of the present invention, the step of fusing the filtered PF component with the time domain index of the vibration signal and performing PCA dimension reduction on the fused feature includes:

s41, forming a first matrix by the PF component obtained after screening and the time domain index of the vibration signal;

s42, carrying out zero averaging on each line of the first matrix, and solving a normalization matrix of the line;

s43, acquiring a covariance matrix of the image, and solving an eigenvalue of the covariance matrix and a corresponding eigenvector;

s44, arranging the eigenvectors into a second matrix from top to bottom according to the corresponding eigenvalue size, and taking the top k of the second matrix ₂ And forming a third matrix by taking the eigenvectors with the contribution rates larger than the preset variance contribution rate as principal components.

In one embodiment of the present invention, the step of optimizing the deep belief network model using a particle swarm optimization algorithm comprises:

s51, obtaining a plurality of particles according to the feature vectors by using an initial deep belief network structure to form a particle swarm, wherein each particle comprises the node number and the learning rate of the deep belief network structure;

s52, calculating the fitness value of each particle, and refreshing the particles corresponding to the global extreme value and the individual extreme value in the iteration history in the current round of particle swarm;

s53, updating the node number and the learning rate of all the particles;

s54, judging whether the iteration times are equal to the preset iteration times or not;

s55, if the iteration times are equal to the preset iteration times, completing the optimization of the deep confidence network model; otherwise, jumping to step S52 to iterate until the iteration number is equal to the preset iteration number; if the iteration times are equal to the preset iteration times, obtaining the optimal particles of the optimal particles, and constructing an optimal depth confidence network model according to the node number and the learning rate corresponding to the optimal particles.

In one embodiment of the invention, the position and velocity of all particles are updated by:

wherein, the first and the second end of the pipe are connected with each other,

denotes that the ith particle is at the kth ₃ The number of nodes in the secondary iteration;

indicates that the ith particle is at the kth ₃ A learning rate in the secondary iteration;

is shown at the k-th ₃ The optimal value of the node number in all the particles in the secondary iteration process is a global extreme value;

is represented at k ₃ The optimal value of the number of ith particle nodes in the secondary iteration process is an individual extreme value; e represents a weight; c. C ₁ And c ₂ Representing an acceleration parameter; r is ₁ And r ₂ Is represented by [0,1]A random value in between.

In one embodiment of the invention, the bearing failure includes one or more of a normal bearing, a rolling element single point failure, a rolling element multi point failure, an inner ring single point failure, an inner ring multi point failure, an outer ring single point failure, an outer ring multi point failure, an outer ring roller composite failure, and an inner ring roller composite failure.

The invention also provides a fault diagnosis and classification system based on the rolling bearing sound vibration non-stationary signal, which comprises the following steps:

the signal acquisition module is used for acquiring a vibration signal X of a fault in the running process of the bearing ₁ (t) and using it as the original signal;

a data preprocessing module, configured to perform local mean decomposition on the original signal to obtain a PF component thereof, and reconstruct the original signal according to the PF component to obtain a reconstructed signal X ₂ (t)；

The characteristic fusion module is used for screening the PF component according to the reconstruction signal and through mutual information; the system comprises a vibration signal acquisition unit, a parameter selection unit and a parameter selection unit, wherein the parameter selection unit is used for selecting a PF component obtained after screening and a time domain index of the vibration signal, and carrying out PCA (principal component analysis) dimension reduction processing on the feature after the screening to obtain a feature vector;

the model optimization module is used for optimizing the deep belief network model by utilizing a particle swarm algorithm;

and the fault diagnosis and classification module is used for inputting the feature vector as the input of the optimized deep confidence network model so as to diagnose and classify the bearing fault.

The invention provides a fault diagnosis and classification method and system based on rolling bearing sound vibration non-stationary signals, wherein a traditional local mean decomposition method (LMD) is combined with a depth confidence network (DBN), the limitation that the LMD decomposition selects PF components according to experience judgment is avoided, a proper PF component is selected by utilizing a mutual information criterion, the problem that the DBN is easy to fall into local convergence is avoided, and an optimal DBN network structure is constructed by utilizing a particle swarm optimization algorithm so as to improve the accuracy of fault diagnosis and classification.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.

Fig. 1 is a flowchart illustrating a fault diagnosis and classification method according to an embodiment of the invention.

FIG. 2 is an exploded view of an LMD of an outer ring fault bearing under a condition of 2KN-2000rpm according to an embodiment of the invention.

FIG. 3 is a diagram of a DBN network architecture including a 3-layer RBM.

FIG. 4 is a schematic representation of an RBM containing n visible neurons and m hidden neurons.

Fig. 5 is a flow chart illustrating a network structure of a PSO optimized DBN.

FIG. 6 is a block diagram of a fault diagnosis and classification system according to an embodiment of the invention.

Fig. 7 is a diagram of the original signals of the vibration signals of the rolling bearing under different working conditions.

FIG. 8 is a schematic diagram of a confusion matrix of diagnostic results.

Fig. 9 is a diagram illustrating the relationship between the evolution algebra of PSO and the fitness.

Detailed Description

The following embodiments of the present invention are provided by way of specific examples, and other advantages and effects of the present invention will be readily apparent to those skilled in the art from the disclosure herein. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention.

It should be noted that the drawings provided in the present embodiment are only for illustrating the basic idea of the present invention, and the components related to the present invention are only shown in the drawings rather than drawn according to the number, shape and size of the components in actual implementation, and the type, quantity and proportion of the components in actual implementation may be changed freely, and the layout of the components may be more complicated.

Referring to fig. 1, in the present embodiment, to solve the above technical problem, the present invention provides a fault diagnosis and classification method based on rolling bearing acoustic vibration non-stationary signals, which includes performing Local Mean Decomposition (LMD) on a source signal, determining a PF (Product function) Component according to mutual information, extracting features obtained by fusing the PF Component and time domain features by a Principal Component Analysis (PCA) method, using the extracted features as input vectors, inputting the input vectors into a PSO-DBN neural network model, and performing fault diagnosis and classification on a rolling bearing. It should be noted that the source signal may be an acoustic signal or a vibration signal, that is, the fault diagnosis and classification method based on rolling bearing acoustic vibration non-stationary signal is applicable to both a vibration signal and an acoustic signal, and the process of the fault diagnosis and classification method in which the source signal is an acoustic signal or a vibration signal is the same, in this embodiment, the vibration signal is taken as an example for description, and specifically, the fault diagnosis and classification method includes:

s1, collecting vibration signals X of different types of faults in the bearing running process ₁ (t) and using it as the original signal;

referring to fig. 1, in the present embodiment, an acceleration vibration sensor and a sound sensor are installed on a main shaft bearing testing machine to collect vibration signals X during the operation of a bearing ₁ (t), the spindle bearing tester is used for acquiring vibration signals once every 3min at the sampling frequency of 20480Hz with the experimental rotating speed of 2000rpm and the load of 25kN, and the sampling time is 1s. In the present embodiment, the bearing failure from the initial operation to the complete failure is collected by using an acceleration vibration sensor and a sound sensor provided on the spindle bearing testerLife cycle data.

S2, carrying out local mean decomposition on the original signal to obtain a PF component of the original signal so as to obtain a reconstructed signal X ₂ (t)；

Referring to fig. 1, in the present embodiment, the original signal is subjected to local mean decomposition to obtain a PF component thereof, so as to obtain a reconstructed signal X ₂ The step of (t) comprises:

s21, carrying out local mean decomposition on the original signal to obtain a pure frequency modulation signal of the original signal, and obtaining an envelope spectrum estimation function obtained in the process of obtaining the pure frequency modulation signal, wherein the method specifically comprises the following steps;

s211, determining all local extreme points of the original signal, and calculating the mean value of the continuous extreme values to obtain a local mean function m of the original signal _i (t)，m _i (t) represents the local mean function obtained during the ith iteration. Specifically, all two adjacent extreme points n are calculated _i And n _i+1 Then the average m of all two adjacent extreme points by moving average _i The connection line between the two is smoothed to obtain a local mean function m _i (t) of (d). In this embodiment, the first iteration is to determine the original vibration signal X ₁ (t) local mean function m ₁ (t)。

S212, combining the local mean value points to obtain the envelope estimation value between the adjacent extreme value points to obtain the envelope spectrum estimation function a thereof _i (t)，a _i And (t) represents an envelope spectrum estimation function obtained in the ith iteration process. Specifically, the envelope estimation value is calculated by formula

Calculated and then all adjacent envelope estimation values a are calculated by a moving average method _i The connecting line is smoothed to obtain an envelope spectrum estimation function a _i (t) of (d). In this embodiment, the first iteration is to determine the original vibration signal X ₁ (t) envelope spectrum estimation function a of its acquisition ₁ (t)。

S213, using the local mean function m _i (t) from theSeparating the original signal to obtain a signal h _i (t) and performs demodulation processing on it to obtain a demodulated signal S _i (t) if the demodulated signal S _i (t) the envelope spectrum estimation function satisfies

The demodulated signal S _i (t) is a pure frequency modulated signal; otherwise, the demodulation signal S is used _i (t) jumping to step S211 as the original signal, and repeating the process from step S211 to step S213 for n iterations until the demodulation result is the pure FM signal S _n (t) wherein h _i (t) indicates that a signal is obtained in the ith iteration, S _i (t) the demodulated signal obtained in the ith iteration process is represented, specifically, the method includes:

s2131, calculating the local mean function m _i (t) separating from said original signal to obtain a signal h _i (t) of (d). In this embodiment, the first iteration process is to use the original vibration signal X ₁ (t) local mean function m ₁ (t) from the original vibration signal X ₁ (t) separation to obtain a signal h ₁ (t), i.e. h ₁ (t)＝X ₁ (t)-m ₁ (t)；

S2132, using the signal h _i (t) division by an envelope spectrum estimation function a _i (t) to demodulate it to obtain a demodulated signal S _i (t) that is

In the present embodiment, the vibration signal X is converted into a vibration signal ₁ (t) as original signal in the first iteration process

It should be noted that, in the ideal case, if S _i (t) is a pure frequency modulated signal, then its envelope spectrum estimation function a _i+1 (t) will satisfy

If the condition is not satisfied, jumping to step S211 and mixing S _i (t) as the original signal and repeating the process of steps S211 to S213 n times until the demodulation result is a pure FM signal, i.e., -1 ≦ S _n (t) is less than or equal to 1, and the envelope spectrum estimation function a of the (t) is _n+1 (t) =1, the iterative process is as follows:

in the above formula:

it should be noted that, in order to obtain a pure frequency modulation signal with a relatively ideal value, the iteration termination condition is set as

If it is not satisfied

Then will S _n-1 (t) as the original signal, repeating the steps S211 to S213 until the demodulation result is the pure FM signal.

S22, multiplying all the envelope spectrum estimation functions obtained in the process of obtaining the pure frequency modulation signal to obtain an envelope signal a (t), namely

Multiplying the envelope signal a (t) by the pure FM signal S _n (t) to obtain a PF component, i.e., PF _j (t)＝a(t)S _n (t)，PF _j (t) Single component AM and FM signals, the instantaneous amplitude of which is the envelope signal a (t) and the instantaneous frequency of which can be determined from the pure FM signal, i.e.

S23, removing PF from the original signal _j (t) to obtain a new first signal u _j (t) converting the first signal u _j (t) jumping to step S21 as the original signal, and repeating the stepsProcess k of S21 to S23 ₁ Until the first signal

Stopping for a monotonic function, and obtaining k ₁ K in the course of a sub-iteration ₁ A PF component, wherein PF _j (t) represents a PF component obtained in a j-th iteration process; the iterative process is as follows:

s26, finally, k is added ₁ A PF component and a monotonic function

The sum is constructed as a reconstructed signal X ₂ (t) that is

S3, according to the reconstructed signal X ₂ (t) screening the PF components through mutual information, specifically, the method comprises the following steps:

s31, respectively calculating mutual information values between each PF component and the vibration signals;

wherein, the mutual information size is determined by the following formula:

wherein D is _PF Representing a set of PF components;

a set representing vibration signals; p (PF, X) ₁ (t)) represents the PF component and the vibration signal X ₁ (t) a joint probability distribution; p (PF) and p (X) ₁ (t)) respectively represent the PF component and the vibration signal X ₁ (t) edge probabilities of each.

Wherein if PF isMagnitude and vibration signal X ₁ (t) are independent of each other, the mutual information value is zero; otherwise, if PF component and vibration signal X ₁ The stronger the correlation between (t), the larger its mutual information value.

S32, comparing the mutual information value with a threshold value to screen out PF components of which the mutual information values are larger than the threshold value, wherein the threshold value is determined according to the following formula:

wherein, I _max Represents the maximum of all mutual information values; I.C. A _min Representing a minimum value among the mutual information values; η is a coefficient greater than 1.

In this embodiment, fig. 2 shows an LMD exploded view of a faulty outer ring bearing under a working condition of 2KN-2000rpm, a multi-component AM-FM (amplitude modulation-frequency modulation, frequency modulation-amplitude modulation) signal is decomposed into a single-component AM-FM signal, each decomposed component reflects different feature components contained in a source signal, and a PF component is obtained after mutual information screening, as shown in fig. 2, a PF is taken ₅ There is no information about the vibration signal, so that only the first four PF components are selected.

S4, fusing the PF component obtained after screening with a time domain index of the vibration signal, and performing PCA (principal component analysis) dimension reduction processing on the fused feature to obtain a feature vector, wherein the time domain index comprises a kurtosis index, a skewness, an absolute average value and a variance;

referring to fig. 1, in step S4, a time domain index of the vibration signal is extracted, where the time domain index includes a kurtosis index, a skewness, an absolute average value, and a variance, the time domain index is fused with the filtered PF component, and PCA dimension reduction is performed on the fused feature. It should be noted that PCA is an unsupervised learning method that can map n-dimensional features to k ₄ Dimension (k) ₄ <n) and making the data separable, the variance of the transformed data points being greatest along the new coordinate axis in the new spatial coordinate systemAnd (3) enlarging, meanwhile, the data points are not related in a line-row manner, the group of converted data is called principal components, the direction with the largest data variance is selected as a first principal component, a second principal component is selected according to the direction with the second largest variance, the direction is orthogonal to the first principal component, and the process is iterated until n principal components are found. The specific dimension reduction process is as follows:

s41, forming a first matrix Q with 8 rows and 8 columns by using the 4 PF components obtained after screening and time domain indexes of vibration signals, wherein Q = [ PF1, PF2, PF3, PF4, kurtosis index, skewness, absolute average value and variance ];

s42, carrying out zero equalization on each line of the first matrix Q, and obtaining a normalized matrix Z of the first matrix Q _ij Wherein zero-averaging each row of the first matrix Q is the mean value of subtracting the row

Wherein the mean and variance of the raw data matrix are given by the following formulas:

wherein j =1,2, \ 8230, n.

Wherein the normalization matrix is given by:

wherein, i =1,2, \8230m; j =1,2, \8230n.

S43, obtaining covariance matrix R _n×n And finding the covariance matrix R _n×n And a corresponding eigenvector λ, wherein the covariance matrix of the normalized matrix is given by:

wherein i, j =1,2, \8230n.

S44, in the embodiment, the eigenvectors lambda are arranged into a second matrix from top to bottom according to the corresponding eigenvalue size, and the top k of the second matrix is taken ₂ And forming a third matrix by taking the eigenvectors with the contribution rates larger than the preset variance contribution rate as principal components.

If it is

Just hold front k ₂ Specifically, the variance contribution ratio of the principal component is given by the following equation, the number of the principal components is set according to a judgment threshold of 85%, and the remaining principal components are ignored:

the first 3 rows are taken to form a third matrix P = [ PF1, PF2, PF3 ]]I.e. to reduce the fused matrix to 3 dimensions. In this embodiment, k in the above formula ₂ Equal to 3, n equal to 8.

In the present example, table 1 shows the ratio of 3 PF components having a contribution rate of 95%, and as can be seen from table 1, PF is expressed by ₁ The proportion of the component in the contribution is much higher than that of other main components, and the value is 92.31%, PF ₂ Component and PF ₃ The cumulative contribution rates of the components are 6.21% and 0.99%, so in this embodiment, only the first three PF components are taken, and after the PCA performs feature fusion and dimension reduction, the original 8-dimensional data is reduced to 3-dimensional data, and the feature dimension is reduced by 62.5%.

TABLE 1 ratio of 3 PF components with contribution up to 95%

And S5, inputting the feature vectors into a fault diagnosis classification model to obtain the fault type of the bearing, wherein the fault diagnosis classification model adopts a depth confidence network model optimized by a particle swarm optimization.

Referring to fig. 3 and 4, the deep belief network model is a feedforward neural network with many hidden layers, which is formed by stacking a plurality of Restricted Boltzmann Machine (RBM), the lower layers representing original data signals, and the upper layers representing attributes or characteristics of data. The DBN (Deep Belief Networks) structure model is shown in fig. 3 and 4, and the model is formed by stacking 3 RBMs, each RBM is formed by two layers of Networks, namely a visible layer v and a hidden layer h, the layers are connected by a weight, and neurons in the layers are not connected.

The visual layer V represents the input data, and the data is mapped to the hidden layer H ¹ ，V ¹ And H ¹ Form a first layer RBM (W) ¹ ). Input data H ¹ Mapping to hidden layer H via an activation function ¹ Then, H ¹ And as a second RBM (W) ² ) The visual layers of the layers, the data are sequentially transmitted layer by layer as such, so that a feature representation which is more abstract and has more representation capability is formed at a high layer than at a low layer, and the feature representation is the greedy learning strategy of the DBN layer by layer.

Let θ = { a, b, w } denote parameters in RBM, a and b denote bias vectors of a visible layer and a hidden layer, respectively, and w denotes a weight matrix connecting between the visible layer and the hidden layer, where a _n Indicates that n neurons are in a visible layer, and are respectively a ₁ ，a ₂ ，…，a _n Here a is _n Also represents the offset of each visible layer node; b is a mixture of _m Denotes m neurons in the hidden layer, each b ₁ ，b ₂ ，…，b _m Here b is _m Also represents the offset of each hidden layer node; w is a _nm Representing a weight matrix between the visible layer and the hidden layer. If n =3,m =4, then the weight matrix is w ₃₄ And 3 rows and 4 columns. All visible and hidden layer elements are binary variables, i.e. pairs

All have v _i ∈{0,1}，h _j E {0,1}. The RBM energy function is as follows:

when all parameters are determined, the energy function in the above equation can be represented by a joint probability distribution for each state { v, j } that occurs in the visible layer and the hidden layer, as shown in the following equation:

wherein Z (theta) = ∑ Σ _v.h E (v, h | θ) is a normalization factor, also called a partition function.

Since the neurons in each layer are not connected, the probability that the ith neuron in the visible layer is activated in the hidden layer state h is calculated according to the following formula:

according to the RBM symmetrical structure, the activation probability of the jth neuron of the hidden layer under the visible layer state v can be calculated, as shown in the following formula:

the Relu (x) function represents the activation function, and:

the DBN characteristic extraction process is a layer-by-layer learning process of stacking a plurality of RBMs, comprises forward learning and direction reconstruction, can map complex signals to output, and has good characteristic extraction capability.

RBM training can be summarized as follows: firstly, providing training data to neuron shift i in visual layer, then obtaining a certain unit h in hidden layer _i Probability of activation, repeating this process again to update neurons in the visual layer, and then neurons in the hidden layer willFurther "reconstruction" of v ⁱ And h ⁱ The state of (1). Weighting w between the visible layer and the hidden layer as the gradient of the joint likelihood function of the data changes _i The update rule of (1) is:

Δw _ij ＝L(<v _ij > _data -<v _ij > _recon )；

in the above formula:<v _ij > _data representing an expectation of training data;<v _ij > _recon representing the data expectation under the model distribution after reconstruction; l represents a learning rate, and L ∈ (0, 1).

In the DBN training classification process, main factors influencing the classification result are selection of the number of network layers, the number of hidden layers and setting of learning rate. At present, all the key parameters of the DBN are selected manually, so that the efficiency is low, and based on this, in this embodiment, a PSO (Particle Swarm Optimization) is adopted to optimize the key parameters in the DBN algorithm, and then the optimized key parameters are used to construct an optimal DBN network structure.

The DBN structure based on PSO algorithm optimization is mainly divided into two parts, namely 1) DBN structure initialization, and 2) PSO optimization DBN structure.

The process of the DBN network structure initialization is divided into two phases: the first stage is a forward stacking RBM learning process which is an unsupervised learning process and aims to provide prior knowledge of input data for a subsequent supervised learning process; the second stage is a backward fine tuning process of the DBN, and the model parameters of the lower layer are fine tuned by using the known label, so that in the DBN initialization process, the initialization of the theta parameters in each RBM is completed.

When a DBN network model is established, initial weights of a network structure of the DBN network model are generally randomly assigned, and during training, the initial weights are easily limited to local optimal solutions or convergence time extension. With the increase of the hidden layer, the classification error rate of the deep confidence network model is reduced, but when the number of the hidden layer is increased to four or more, the classification error rate of the model is increased, and the generalization capability is in a descending trend, so that in the embodiment, the number of the DBN network layers is selected to be 3. In PSO optimization, each optimization problem is searched for a solution in space, and all particles have a fitness value determined by an optimized function, and the fitness value determines the respective flight direction and distance through the speed. And optimizing the DBN network structure by using a PSO (particle swarm optimization) method, updating the initialized particles by tracking an individual extreme value (pbest) and a global extreme value (gbest) during each iteration, respectively searching an optimal value and a global optimal value of the initialized particles, and then constructing the optimal DBN network structure by using the optimal particles, namely the optimal hidden layer number, the node number and the learning rate.

For the DBN of FIG. 3 with three hidden layers, each layer is defined as m ₁ ,m ₂ ,m ₃ The number of neurons, the learning rate eta ∈ [0,1 ]. When encoding a particle swarm, each particle in the PSO is set as a four-dimensional vector H (m) ₁ ,m ₂ ,m ₃ Eta). The population number of the particle swarm is N, N is generally 10-20, N is selected to be 15, the number of PSO iterations is set to be 150.

Referring to fig. 5, the specific optimization process is as follows:

s51, obtaining a plurality of particles according to the feature vector by utilizing an initial deep belief network structure to form a particle swarm, wherein each particle comprises the node number and the learning rate of the deep belief network structure, and initializing the particle swarm to obtain an individual extreme value and a global extreme value corresponding to the initialized particle;

s52, calculating the fitness value of each particle, and refreshing the global extremum and the individual extremum in the iteration history in the current round of particle swarm, wherein if the fitness value of a certain particle is smaller than the fitness value of the particle corresponding to the individual extremum, the current particle replaces the previous particle to become a new individual extremum P _pbest Else, its individual extremum P _pbest The change is not changed; if the fitness value of a certain particle is smaller than that of the particle corresponding to the global extremum, the current particle is substituted for the former particle to become a new global extremum P _gbest Else its global extreme P _gbest And is not changed.

S53, updating the node number and the learning rate of all the particles, wherein the positions and the speeds of all the particles are updated through the following formula:

wherein the content of the first and second substances,

denotes that the ith particle is at the kth ₃ The number of nodes in the secondary iteration;

indicates that the ith particle is at the kth ₃ A learning rate in the secondary iteration;

is shown at the k ₃ The optimal value of the node number in all the particles in the secondary iteration process is a global extreme value;

is shown at k ₃ The optimal value of the number of ith particle nodes in the secondary iteration process is an individual extreme value; e represents a weight; c. C ₁ And c ₂ Representing an acceleration parameter; r is ₁ And r ₂ Is represented by [0,1]A random value in between.

S54, judging whether the iteration times are equal to a preset iteration time M;

s55, if the iteration times are equal to the preset iteration times M, completing the optimization of the deep confidence network model; otherwise, jumping to step S52, and repeating the iteration process until the iteration times are equal to the preset iteration times M; if the iteration times are equal to the preset iteration times M, obtaining the optimal particles of the iteration times, namely the particles corresponding to the optimal global extreme value, and constructing an optimal deep belief network model according to the node number and the learning rate corresponding to the optimal particles.

After the optimal depth confidence network model is constructed, the feature vectors obtained in the step S4 are input into a fault diagnosis classification model, and the fault types of the bearings are obtained and classified.

Referring to fig. 6, the invention further provides a fault diagnosis and classification system based on non-stationary signals of a rolling bearing, where the fault diagnosis and classification system 100 includes a signal acquisition module 10, a data preprocessing module 20, a feature fusion module 30, a model optimization module 40, and a fault diagnosis and classification module 50, the signal acquisition module 10 is configured to acquire vibration signals of different types of faults during a bearing operation process, the data preprocessing module 20 is configured to perform local mean decomposition on the vibration signals to acquire reconstructed signals, and the feature fusion module 30 is configured to filter PF components according to the reconstructed signals and through mutual information; the feature fusion module 30 is further configured to fuse the PF component obtained after the screening with a time domain indicator of the vibration signal, and perform PCA dimension reduction on the fused feature to obtain a feature vector, where the time domain indicator includes a kurtosis indicator, a skewness, an absolute average value, and a variance, the model optimization module 40 is configured to optimize a depth confidence network model by using a particle swarm optimization algorithm, and the fault diagnosis classification module 50 is configured to use the feature vector as an input of the optimized depth confidence network model to diagnose and classify the bearing fault.

In a specific embodiment, vibration signals are collected for bearings of the type NU1010EM and N1010EM single-row cylindrical roller bearings, and bearing parameters are shown in Table 2.

TABLE 2 Experimental bearing parameters

In order to obtain bearings with different faults, the faults of the inner ring of the bearing are obtained by laser processing, and the faults of the outer ring and the roller are obtained by linear cutting. According to different damage positions and damage degrees of the rolling bearings, the experimental bearings are divided into 9 fault types, labels are defined for the different fault types, and detailed description of the fault types is shown in table 3.

TABLE 3 Rolling bearing failure types

Bearing model	Failure mode	Size and number of damage points
			NU1010EM	Normal bearing	0
N1010EM	Single point of failure of rolling body	9X 0.2mm-1
			N1010EM	Multi-point fault of rolling body	9X 0.2mm-3
NU1010EM	Inner ring single point failure	9X 0.2mm-1
			NU1010EM	Inner ring multi-point failure	9X 0.2mm-3
N1010EM	Single point failure of outer ring	9X 0.2mm-1
			N1010EM	Outer ring multi-point fault	9X 0.2mm-3
N1010EM	Composite fault of outer ring roller	9X 0.2mm-2
			NU1010EM	Composite failure of inner ring roller	9X 0.2mm-2

The working conditions of the test bearing are shown in table 4, eight working conditions are provided, wherein 2K represents that the radial load is 2000N, and the rest is analogized.

TABLE 4 bearing Condition parameters

Referring to fig. 7, fig. 7 shows an original signal diagram of rolling bearing vibration signals of different working conditions used for verification in this embodiment, LMD decomposition is performed on data collected in fig. 7, PF components are determined through mutual information, the PF components are determined to be the first 4 PF components, the decomposed first four PF components are fused with the screened time domain index, and the fused data is subjected to dimensionality reduction through PCA and then input into the DBN network structure optimized through PSO. The DBN network parameters after PSO optimization are shown in table 5.

TABLE 5 DBN network parameters after PSO optimization

Parameter name	Parameter value
		Number of iterations	150
Batch size	70
		Number of neurons in first hidden layer m1	917
Number of neurons in first hidden layer m2	785
		Number of neurons in first hidden layer m3	863
Learning rate	0.3058
		Number of RBM layers	3
PSO acceleration factor	c1＝c2＝1.5
		PSO training iteration number M	150
PSO inertial weight e	0.6
		Number of PSO particle groups N	15

In the embodiment, 60% of the collected data is randomly selected as a training set of the PSO-DBN, and the rest data is used as a testing set, and then the fault diagnosis work is performed. Fig. 8 is a confusion matrix of the diagnosis results, and it can be seen from fig. 8 that the diagnosis accuracy of the PSO-DBN diagnosis result at the roller 3K-2R, i.e. the working condition 6, is 92% respectively, because the working conditions selected in this embodiment are very similar, the diagnosis difficulty is high, and the phenomenon of misclassification is inevitable under the condition of feature classification. Besides, when the normal 2K-2R, the normal 2K-3R, the outer ring fault 2K-2R, the outer ring fault 2K-3R, the roller fault 3K-3R and the inner ring fault 4K-2R are identified, the accuracy of the inner ring fault 4K-3R is 100%, and the average diagnosis and classification accuracy of the LMD-based PSO-DBN rolling bearing fault diagnosis system reaches 99%.

Fig. 9 shows a relationship between the evolution generations of the PSO and the fitness, and it can be seen from an analysis of fig. 9 that the fitness is stabilized at 99% in the first 2 generations of the PSO algorithm evolution, and the fitness is maintained at 99.5% in the PSO optimization algorithm after the PSO algorithm evolves to 2 generations and then to 8 generations, which indicates that the PSO algorithm has a fast optimization speed for the DBN neural network structure and a good fitness, and can achieve 99% fitness only in 8 generations.

In order to verify the advantages of the method provided by the invention, the method is respectively compared with DBN (Back Propagation) neural network and BP (Back Propagation neural network) neural network and SVM (support vector machines) diagnosis methods which are not optimized, namely the same reconstructed feature vector data are respectively input into each fault diagnosis neural network structure for testing, and the comparison result of each algorithm is shown in Table 6.

TABLE 6 comparison of the algorithms

Algorithm	Rate of accuracy/%)	Calculating time/s
			DBN	88.75	234.6
BP	92.36	197.4
			SVM	95064	156.4
PSO-DBN	99	287.3

From table 6, the diagnosis accuracy of the non-optimized DBN neural network structure is only 88.75%, the calculation time reaches 234.6 seconds, the accuracy of the BP neural network structure is 92.36%, the calculation time is 197.4s, the classification accuracy of the support vector machine is 95.64%, the calculation time is 156.4 seconds, while the accuracy of the PSO-DBN neural network model herein reaches 99%, and the calculation time is 287.3 seconds. Experiments show that the DBN network result optimized through PSO has higher recognition rate in fault diagnosis and classification of the rolling bearing.

In conclusion, the method provided by the invention is combined with a PSO-DBN neural network on the basis of LMD decomposition and is used for fault diagnosis and classification of the rolling bearing. After the LMD decomposes the source signal, the first 4 PF components with the highest correlation with the source signal are screened out by adopting mutual information, the separated PF components are fused with the selected time domain index, and the PF components are input into the DBN network structure optimized by the PSO after the PCA dimensionality reduction to obtain a recognition diagnosis model, and the result shows that the PSO-DBN rolling bearing fault diagnosis classification method based on the LMD decomposition can effectively recognize the working state and the fault type of the rolling bearing, and the accuracy is superior to that of a BP, an SVM and the DBN neural network structure which is not optimized; the PSO method is adopted to optimize the structural parameters of the DBN network, the optimal hidden layer number, the optimal node number and the optimal learning rate are obtained, the optimal DBN network is constructed by the parameters, and the method has important significance for improving the fault identification and diagnosis rate of the rolling bearing in the operation process.

The invention provides a fault diagnosis and classification method and system based on rolling bearing sound vibration non-stationary signals, wherein a traditional local mean decomposition method (LMD) is combined with a depth confidence network (DBN), the limitation that the LMD decomposition selects PF components according to experience judgment is avoided, a proper PF component is selected by utilizing a mutual information criterion, the problem that the DBN is easy to fall into local convergence is avoided, and an optimal DBN network structure is constructed by utilizing a particle swarm optimization algorithm so as to improve the accuracy of fault diagnosis and classification.

The above description is only a preferred embodiment of the present application and an explanation of the technical principle applied, and it should be understood by those skilled in the art that the scope of the present application is not limited to the technical solution of the specific combination of the above technical features, and also covers other technical solutions formed by any combination of the above technical features or their equivalent features, for example, the technical solutions formed by mutually replacing the above technical features (but not limited to) having similar functions disclosed in the present application, without departing from the inventive concept.

Other technical features than those described in the specification are known to those skilled in the art, and are not described herein in detail in order to highlight the innovative features of the present invention.

Claims (10)

1. A fault diagnosis and classification method based on rolling bearing sound vibration non-stationary signals is characterized by comprising the following steps:

s1, collecting a fault vibration signal X in the bearing running process ₁ (t) and using it as the original signal;

s2, performing local mean decomposition on the original signal to obtain a PF component of the original signal, and reconstructing the original signal according to the PF component to obtain a reconstructed signal X ₂ (t)；

S3, according to theReconstruction of a signal X ₂ (t) screening the PF components through mutual information;

s4, fusing the PF component obtained after screening with the time domain index of the vibration signal, and performing PCA (principal component analysis) dimension reduction processing on the fused feature to obtain a feature vector;

and S5, inputting the characteristic vectors into a fault diagnosis classification model to obtain the fault type of the bearing, wherein the fault diagnosis classification model adopts a depth confidence network model optimized by a particle swarm optimization.

2. The method for diagnosing and classifying faults based on rolling bearing sound-vibration non-stationary signals according to claim 1, characterized in that the original signals are subjected to local mean decomposition to obtain PF components thereof, and the original signals are reconstructed according to the PF components to obtain reconstructed signals X ₂ The step of (t) includes:

s21, carrying out local mean decomposition on the original signal to obtain a pure frequency modulation signal of the original signal, and obtaining an envelope spectrum estimation function obtained in the process of obtaining the pure frequency modulation signal;

s22, multiplying all envelope spectrum estimation functions obtained in the process of obtaining the pure frequency modulation signal to obtain an envelope signal, and multiplying the envelope signal by the pure frequency modulation signal to obtain a PF component;

s23, removing the PF component from the original signal to obtain a new first signal, taking the first signal as the original signal, skipping to the step S21, and repeating the process k ₁ Repeating until the first signal is a monotonic function, and obtaining k in the k1 iterations ₁ A PF component;

s24, adding k ₁ The sum of a PF component and a monotonic function is constructed as the reconstructed signal X ₂ (t)。

3. The method for fault diagnosis and classification based on rolling bearing vibro-acoustic non-stationary signals according to claim 1, characterized in that according to said reconstructed signal X ₂ (t) and screening the PF components by mutual information includes:

s31, respectively calculating mutual information values between each PF component and the vibration signals;

s32, comparing the mutual information value with a threshold value to screen out PF components of which the mutual information values are larger than the threshold value, wherein the threshold value is determined according to the following formula:

wherein, I _max Represents the maximum value of all mutual information values; i is _min Representing a minimum value among the mutual information values; η is a coefficient greater than 1.

4. The fault diagnosis and classification method based on rolling bearing sound vibration non-stationary signals according to claim 3, characterized in that the mutual information size is determined by the following formula:

wherein D is _PF Representing a set of PF components;

a set representing vibration signals; p (PF, X) ₁ (t)) represents the PF component and the vibration signal X ₁ (t) a joint probability distribution; p (PF) and p (X) ₁ (t)) respectively represent the PF component and the vibration signal X ₁ (t) respective edge probabilities;

wherein if PF component and vibration signal X ₁ (t) are independent of each other, the mutual information value is zero; otherwise, if PF component and vibration signal X ₁ The stronger the correlation between (t), the larger its mutual information value.

5. The fault diagnosis classification method based on rolling bearing sound vibration non-stationary signals according to claim 1, characterized in that the time domain indicators include kurtosis indicator, skewness, absolute mean and variance.

6. The fault diagnosis and classification method based on the rolling bearing sound vibration non-stationary signal according to claim 1, characterized in that the step of fusing the PF component obtained after screening with the time domain index of the vibration signal and performing PCA (principal component analysis) dimension reduction on the fused feature comprises:

s41, forming a first matrix by the PF components obtained after screening and time domain indexes of the vibration signals;

s42, carrying out zero averaging on each line of the first matrix, and solving a normalization matrix of the line;

s43, acquiring a covariance matrix of the image, and solving an eigenvalue of the covariance matrix and a corresponding eigenvector;

s44, arranging the eigenvectors into a second matrix from top to bottom according to the corresponding eigenvalue size, and taking the top k of the second matrix ₂ And forming a third matrix by taking the eigenvectors with the contribution rates larger than the preset variance contribution rate as principal components.

7. The fault diagnosis and classification method based on rolling bearing sound vibration non-stationary signals according to claim 1, characterized in that the step of optimizing the deep confidence network model by using a particle swarm optimization algorithm comprises:

s51, obtaining a plurality of particles according to the feature vectors by utilizing an initial deep belief network structure to form a particle swarm, wherein each particle comprises the node number and the learning rate of the deep belief network structure;

s52, calculating the fitness value of each particle, and refreshing the particles corresponding to the global extreme value and the individual extreme value in the iteration history in the current round of particle swarm;

s53, updating the node number and the learning rate of all the particles;

s54, judging whether the iteration times are equal to the preset iteration times or not;

s55, if the iteration times are equal to the preset iteration times, completing the optimization of the deep belief network model; otherwise, jumping to step S52 to iterate until the iteration number is equal to the preset iteration number; if the iteration times are equal to the preset iteration times, the optimal particles are obtained, and an optimal deep belief network model is constructed according to the node number and the learning rate corresponding to the optimal particles.

8. The fault diagnosis classification method based on rolling bearing vibro-acoustic non-stationary signals according to claim 1, characterized in that the position and the speed of all the particles are updated by:

wherein the content of the first and second substances,

denotes that the ith particle is at the kth ₃ The number of nodes in the secondary iteration;

denotes that the ith particle is at the kth ₃ A learning rate in the secondary iteration;

is shown at the k ₃ The optimal value of the node number in all the particles in the secondary iteration process is a global extreme value;

is shown at k ₃ The optimal value of the number of ith particle nodes in the secondary iteration process is an individual extreme value; e represents a weight; c. C ₁ And c ₂ Representing an acceleration parameter; r is ₁ And r ₂ Is represented by [0,1]A random value in between.

9. The fault diagnosis and classification method based on the rolling bearing sound vibration non-stationary signal according to claim 1, wherein the bearing fault includes one or more of a normal bearing, a rolling element single point fault, a rolling element multipoint fault, an inner ring single point fault, an inner ring multipoint fault, an outer ring single point fault, an outer ring multipoint fault, an outer ring roller composite fault and an inner ring roller composite fault.

10. A fault diagnosis classification system based on rolling bearing sound vibration non-stationary signals is characterized by comprising:

the signal acquisition module is used for acquiring a vibration signal X of a fault in the running process of the bearing ₁ (t) and using it as the original signal;

a data preprocessing module for performing local mean decomposition on the original signal to obtain a PF component thereof, and reconstructing the original signal according to the PF component to obtain a reconstructed signal X ₂ (t)；

The characteristic fusion module is used for screening the PF components according to the reconstruction signals and through mutual information; the system is used for fusing the PF component obtained after screening with the time domain index of the vibration signal and performing PCA (principal component analysis) dimensionality reduction processing on the fused feature to obtain a feature vector;

the model optimization module is used for optimizing the deep confidence network model by utilizing a particle swarm algorithm;

and the fault diagnosis and classification module is used for inputting the feature vector as the input of the optimized deep confidence network model so as to diagnose and classify the bearing fault.

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