CN114964783B

CN114964783B - Gearbox fault detection model based on VMD-SSA-LSSVM

Info

Publication number: CN114964783B
Application number: CN202210884301.XA
Authority: CN
Inventors: 孟博; 余中舟; 郇战; 周静诺; 王佳晖
Original assignee: Jiangsu Lida Elevator Co ltd
Current assignee: Jiangsu Lida Elevator Co ltd
Priority date: 2022-07-26
Filing date: 2022-07-26
Publication date: 2022-11-15
Anticipated expiration: 2042-07-26
Also published as: CN114964783A

Abstract

The invention relates to a gearbox fault detection model based on a VMD-SSA-LSSVM, which comprises the following steps: combining VMD decomposition of the sampled data with wavelet packet threshold analysis to perform noise filtering and data reconstruction; extracting different characteristic features and characteristic combinations from the reconstructed data; training and testing the feature set, and measuring the recognition effect under different classifiers and the recognition effect under the VMD-SSA-LSSVM model after the sparrow algorithm optimizes the parameters of the gearbox data in the LSSVM training; and carrying out classified modeling on the vibration data of the gearbox under eight working conditions. Evaluation results show that the average recognition rate of the VMD-SSA-LSSVM model under ten continuous experimental tests is up to 99.5%, and the recognition effect is superior to that of the traditional fault recognition model and consumes less time; the process model provides a new direction for establishing a gearbox fault analysis model, and has important guiding significance for understanding of an optimization classifier model.

Description

Gearbox fault detection model based on VMD-SSA-LSSVM

Technical Field

The invention relates to the technical field of gearbox detection, in particular to a gearbox fault detection model based on a VMD-SSA-LSSVM (vector machine-based single phase support vector machine), and belongs to a mechanical rotator gearbox fault detection method.

Background

Gearboxes are of great interest in the modern industry for health monitoring and fault diagnosis of rotating machinery. Such as gearboxes, which play a crucial role in mechanical drive systems. Any failure of the gearbox can result in unnecessary downtime, expensive repairs, and even casualties. According to statistics, among various faults of the gear box, the gear fault accounts for 60%, and the rolling bearing fault only accounts for 19%. In recent years, for typical faults of gears, a large number of theoretical analysis works are carried out by domestic and foreign scholars, and through researching fault mechanisms of the key parts, the generation reasons of various typical faults and the corresponding relation between the faults and equipment state signals can be known, so that reliable priori knowledge and sufficient theoretical basis are provided for accurately identifying fault types and analyzing fault reasons.

The failure refers to the phenomenon that the mechanical equipment cannot normally operate due to structural change, mechanical property degradation and the like of parts of the mechanical equipment. When equipment has faults, at least one system characteristic or variable has an unallowable deviation, and the fault diagnosis technology identifies the operation state according to the operation information of the system, accurately judges whether the faults occur, further determines the fault position and the fault category and provides guidance for subsequent maintenance. Therefore, governments and related scientific research personnel in various countries pay great attention to the fault diagnosis technology of the mechanical equipment. The gear box contains many components, signals need to be transmitted among all components, mutual coupling and modulation occur, and the signals face various difficulties in the characteristic extraction process. A Support Vector Machine (SVM) is an intelligent fault diagnosis method based on a statistical learning theory. Most of the gearbox fault feature extraction methods use Empirical Mode Decomposition (EMD) or conventional normalization processing to filter noise in the data.

Disclosure of Invention

The invention provides a method for denoising based on the combination of Variational Modal Decomposition (VMD) and wavelet packet threshold analysis and parameter optimization of a least-squares support vector machine (LSSVM) by using a sparrow algorithm (SSA) to evaluate the quality of a model by using a classification recognition rate average value under multiple experiments, aiming at the problems of insufficient decomposition, modal aliasing and optimization of a classifier in a conventional Empirical Mode Decomposition (EMD) and EMD derivative method in the existing gearbox fault detection technology.

The invention is realized by the following technical scheme:

a gearbox fault detection model based on a VMD-SSA-LSSVM comprises the steps of data preprocessing and data reconstruction, feature extraction, establishment of an SSA-LSSVM model of the VMD and establishment of an evaluation strategy.

Data preprocessing and data reconstruction: and performing VMD decomposition and wavelet packet threshold analysis on the data to combine denoising, and reconstructing the data with the rest steady-state component data.

Further, the specific steps of data preprocessing and data reconstruction are as follows:

(1) The pretreatment process comprises the following steps: after data is imported, a signal decomposition layer number k is determined by using adaptive empirical mode decomposition, a k value is set as a decomposition layer number of variable mode decomposition to decompose the signal, and the content of noise in the signal is represented by comparing a decomposition component with a Pearson coefficient, a signal-to-noise ratio and a root-mean-square difference of an original signal, and then the signal is subjected to post-denoising processing.

a. Data acquisition: extracting data of a vibration sensor of the gearbox under different working conditions;

b. variational Modal Decomposition (VMD): the invention carries out the variable mode decomposition on the data of the vibration sensor, decomposes the complex signals into k amplitude modulation and frequency modulation signals at one time, and has the expression:

（1）

in the formula u _k (t) is the kth modal component, A _k (t) is u _k (t) instantaneous amplitude, [ phi ] _k (t) as the instantaneous phase.

In order to avoid the modal aliasing phenomenon, the method is realized by a method for controlling the bandwidth. The construction constraint variation problem is as follows:

（2）

in the formula u _k (t) is the k first modal component, δ (t) is the pulse function, ω _k Refers to the center frequency of each mode. Then, in order to convert the constraint variation problem into the unconstrained variation problem, a penalty factor alpha and a Lagrange operator lambda (t) are introduced, and an augmented Lagrange expression is constructed as follows:

（3）

wherein f (t) represents the original signal, u _k (t) represents a modal function, ω _k Refers to the center frequency of each mode;

solving the equation by a multiplicative operator alternation method to obtain an updating algorithm of the modal u (k) and the center frequency as follows:

（4）

（5）

ȗ (ω) is transformed from the frequency domain to the time domain by inverse FFT, and ȗ is obtained _k (ω). The decomposition component number k of the adaptive Empirical Mode Decomposition (EMD) is used in the VMD to realize the decomposition of the signal into k modal components. The method carries out denoising processing after the modal component of the signal decomposed by the VMD is selected by a threshold value.

(2) Denoising: and denoising the vibration signal component with high noise by using a wavelet packet threshold denoising method.

VMD-wavelet packet threshold joint denoising: because VMD decomposition can decompose the original signal into a plurality of modal components, the denoise result is not ideal because the denoise standard of the selected noise-containing signal is not standard. Through comparing the Pearson correlation coefficient of each modal component and the original signal, and screening by the correlation coefficient screening principle, the expression is as follows:

（6）

obtaining a threshold value rho of a signal needing denoising processing, and if the correlation coefficient is smaller than the parameter rho, denoising; if the correlation coefficient is greater than p, the modal component is considered to have good correlation with the original signal and is retained.

The sensors at two sides of the gear box collect high-frequency components of vibration signals, and a large amount of noise signals and gear box working characteristic information exist in the high-frequency components, so that the denoising part in the invention selects a wavelet packet threshold value superior to wavelet denoising for denoising. The method is to carry out threshold processing on wavelet coefficients obtained by decomposition through wavelet packet transformation. After wavelet packet decomposition, reconstructing a signal with a large wavelet coefficient to obtain a denoised modal quantity.

Define the following recursion relationship, let U _n (t) satisfies:

（7）

in the formula: h (k) and g (k) correspond to filter coefficients in multiresolution analysis, with g (k) = (-1) ^k h (k-1). The sequence constructed by the above formula is u ₀ = Φ (t), which is an orthogonal scale function, determines the wavelet packet.

Let g ⁿ _j ∈U ⁿ _j Then g is obtained ⁿ _j (t) can be expressed as:

（8）

the wavelet packet decomposition result can be obtained:

（9）

the wavelet packet reconstruction expression is:

（10）

in the wavelet packet thresholding, the 3-layer decomposition denoising is carried out on the noisy signal by using the hard thresholding of the heursure threshold and the wavelet basis function of sym 6. The sym6 wavelet basis function is an improvement on a db wavelet basis, has better symmetry and regularity, and effectively reduces the problem of phase distortion when decomposing and reconstructing signals.

(3) Signal reconstruction: adding residual errors to the denoised high-frequency signal component and the medium-low frequency component to reconstruct a pure reconstruction signal; feature extraction: different characteristic features and feature combinations are extracted for the reconstructed data.

And respectively extracting time domain characteristics, frequency domain characteristics and characteristics of time domain-frequency domain combination from the vibration reconstruction signals under the eight working conditions.

When the gear box breaks down, vibration energy can change greatly, and an impact vibration signal is generated generally. The time domain analysis can reflect the information of the characteristic quantity of the amplitude changing along with the time, and the characteristic quantity has the maximum value, the minimum value, the peak value, the mean value, the average amplitude, the square root amplitude, the variance, the standard deviation, the root mean square value, the kurtosis, the skewness, the wave form factor, the peak factor, the pulse factor, the margin factor, the clearance factor and the frequency domain characteristic, and has the center of gravity frequency, the mean square frequency, the frequency variance and the root mean square frequency. The total number of features is 21, 17 in the time domain and 4 in the frequency domain.

Establishing an SSA-LSSVM model of the VMD: and training and testing the feature set, and measuring the classification effect under different classifiers.

Further, the step of establishing the SSA-LSSVM optimization model by dividing the training set and the test set according to the feature group comprises the following steps:

(1) Comparison of different classifiers: and extracting the features with the same property from the reconstructed data of the gearbox under eight working conditions to form feature vectors, dividing a training test set for the feature vectors, putting the training set into five alternative classifiers, and evaluating the features and the traditional optimal classifier according to the classification result obtained by the classifier.

LSSVM employs an equality constraint instead of an inequality constraint of SVM, which uses a least squares linear system as a squared loss function, with the sum of the squared errors to select the hyperplane. Compared with the SVM, the method has the advantages of higher solving speed, higher convergence precision and lower calculation complexity. The objective function of the LSSVM optimization is:

（11）

wherein, ω is a weight coefficient vector; xi is an error; c is a punishment parameter, and controls punishment errors of the excess error samples; is a threshold value; the input of the original space is mapped to a function of the high-dimensional feature space under the nonlinear condition.

Introducing Lagrange multiplication operator a = [ a ] ₁ ，a ₂ ，…a _n The following results were obtained:

（12）

for parameters omega, b and xi in formula (12) _i 、a _i Partial derivatives are calculated and kernel functions k (x, x) are introduced _i ) The regression function that ultimately yields it is:

（13）

conventional kernel functions often include a linear kernel function k (x, x) _i ）=（x，x _i ): the method has few parameters and high speed, and is suitable for linear divisible conditions; polynomial kernel function (x, x) _i ）＝（x，x _i +1） ^r : the samples are easy to classify, but the parameters are many, the calculation complexity is high, and r is a dimension; radial Basis Function (RBF): the method has better classification effect on sample points close to each other and strong learning ability. In view of the strong processing capability of the RBF to the nonlinear relation, the invention adopts the RBF function as the kernel function of the LSSVM. The method comprises the following specific steps:

（14）

in the formula: γ = σ ² 。

Aiming at the problem of parameter selection of the LSSVM, two parameters C and sigma are closely related to the diagnosis precision and the model complexity thereof. The penalty parameter C controls the penalty error of the exceeding error sample, and the smaller the C is, the more inclusive the error is, and the lower the learning complexity is; and on the contrary, the inclusion is small, the selection of the kernel function parameter sigma is closely related to the space range of the sample, the under-fitting phenomenon is easy to generate when the sigma is too small, and on the contrary, the over-fitting is possible to reduce the algorithm performance.

(2) And optimizing regularization parameters and RBF kernel function parameters in a least square support vector machine by using a sparrow optimization algorithm (SSA algorithm), and evaluating to obtain an optimal classification model.

Currently, because no effective measures are available to find the optimal parameter value, the trial selection method is easy to consume a lot of time and cause errors. Therefore, a novel and advanced method should be adopted to optimize two parameters of the LSSVM, establish an LSSVM model and improve the diagnosis precision.

In the SSA algorithm, the sparrow group is divided into a finder and a follower according to the process of obtaining food. The discoverer is responsible for finding food for the whole sparrow population and providing foraging directions for followers, and has a wide foraging search range. Finder location update formula:

=

（15）

where t is the number of iterations, iter is the maximum number of iterations, X ^t _i,j The position of the ith sparrow in the jth dimension; a is [0,1]The random number of (2); r is ₂ And ST is an early warning value and a safety value, R ₂ ∈[0,1]，ST∈[0.5,1](ii) a Q is a random number which follows normal distribution; l is an identity matrix of 1*d.

The follower positions are changed by the finder position update, and as the iteration number is increased, the followers seizing more food can become discoverers, and the overall proportion of the followers to the population is kept unchanged. The location update formula of the follower is as follows:

（16）

wherein, X _p For the optimal position among the discoverers at present, X _worst Is the global worst position; a is a matrix of 1*d with each element being randomly 1 or-1,A ⁺ =A ^T （AA ^T ）-1，A ⁺ Moore-Penrose inverse of A.

When the danger is realized, the sparrow population can make anti-predation behaviors, 10% -20% of sparrows in total are randomly selected and are responsible for diffusing warning signals to the whole population, so that the population is close to the safe sparrow position, and the position updating formula of an early-warning person is as follows:

（17）

in the formula, X _best Is a global optimal position; beta is a step length control parameter, and obeys a normally distributed random number with the mean value of 0 and the variance of 1; k is a member of [ -1,1]Is called the step control parameter; f. of _i Is the fitness value of the ith current sparrow f _g And f _w And epsilon is a constant with infinitesimal size for the current globally optimal and worst sparrow individual fitness, and the fraction denominator is avoided to be 0.

The sparrow algorithm (SSA) specifically comprises the following steps:

step 1: initializing a sparrow population (the population scale is 100), wherein the proportion of discoverers is 20%, the proportion of early-warning users is 20%, the early-warning value is 0.6, the population scale is 100, and the iteration number is 50;

step 2: calculating the fitness value of the initial population;

step 3: and updating the position of the finder, the position of the follower and the position of the early-warning person according to the position formula, and calculating the fitness value at the moment. Repeatedly updating the formula until the minimum error is reached or the maximum iteration number is reached;

step 4: and outputting the optimal solution.

The best method for solving the local optimum is to increase the randomness of the algorithm, and the SSA algorithm well solves the defects that the traditional algorithm lacks randomness and is easy to fall into the local optimum. The randomness generation and the wide optimization of the discoverer, the follower and the early warning value in the SSA algorithm can ensure that the model is more stable and the situation of the local optimal solution is less likely to occur.

The method has the beneficial effects that:

in the rotator fault detection analysis, aiming at the problems of filtering and denoising processing, fault feature extraction, nonlinear and non-stationary characteristics of a gear box vibration signal and difficulty in effective extraction of fault features, the method combines Variation Modal Decomposition (VMD) and wavelet packet threshold processing to perform noise filtering processing and a sparrow algorithm optimized least square support vector machine (SSA-LSSVM) to perform classification and identification on faults. Experiments show that the model has better fault classification performance for the gear box, and the recognition rate is higher and stable.

Drawings

FIG. 1 is a flow chart of a VMD-SSA-LSSVM based gearbox fault detection model of the present invention;

FIG. 2 is a diagram of an inventive VMD-SSA-LSSVM based gearbox fault detection model preprocessing structure;

FIG. 3 is a graph of the visual comparison result after the model processes the vibration signal and the recognition rate line of the model of the invention detected many times;

FIG. 4 is a flow chart of the sparrow algorithm of the present invention;

FIG. 5 is a confusion matrix effect diagram of the optimal recognition result of the EMD-LSSVM;

FIG. 6 is a confusion matrix effect diagram of the optimal recognition result of the VMD-SSA-LSSVM;

fig. 7 is a graph of the recognition effect of vibration signals under different classification models.

Detailed Description

The following detailed description of specific embodiments of the invention is made with reference to the accompanying drawings in which: the present embodiment is implemented on the premise of the technical framework of the present invention, and a detailed implementation and operation process are given, but the scope of the present invention is not limited to the following embodiments.

As shown in FIGS. 1 and 2, the VMD-SSA-LSSVM-based gearbox fault detection model of the invention mainly comprises the following steps:

step one, preprocessing and data reconstruction are carried out on original data. VMD decomposition is carried out on the data of the vibration signal channel 2 acquired by the gearbox, and the sampling frequency is 66667Hz.

In the model optimization comparison, 2009 PHM challenge race gearbox data was selected. The gear box equipment mainly comprises a motor, a set of rotor bearing assembly, a two-stage fixed-shaft gear box and a magnetic powder brake. An acceleration sensor is respectively installed on the input side and the output side of the gear box, and the sensor parameters are as follows: sensitivity: 10mv/g, sampling rate 66.67KHz. The acquisition card is used for acquiring data of three channels, which are respectively as follows: channel 1: input side vibration sensor data; and (3) passage 2: outputting side vibration sensor data; and (3) passage: a rotational speed signal.

Data were collected at 30, 35, 40, 45 and 50HZ axial speeds, both at high and low load conditions.

TABLE 1 Pearson coefficients (imf for modal component signal, res for residual signal)

TABLE 2 SNR and RMS difference (cg is the reconstructed signal)

After the data preprocessing, the Pearson coefficient in Table 1 and the reconstructed signal in Table 2 are compared with the signal-to-noise ratio and the root-mean-square difference, and the wavelet packet threshold processing and the signal reconstruction are performed, 120 points are sampled to obtain a visual comparison result as shown in FIG. 3.

And step two, grouping data and selecting characteristics. And (3) carrying out data grouping on the reconstructed signal, wherein each fault type data acquisition lasts for 8 seconds under each working condition, so that each channel obtains 66.7KHz multiplied by 8 seconds =533307 data points in total for each fault type. And respectively sleeving the data of eight working conditions with labels of corresponding working conditions, wherein eight types of labels are provided. A total of 21 features were extracted per class. The data is then divided into 464 training sets and 200 test sets for test training.

And step three, establishing an SSA-LSSVM model of the VMD. According to the method, the parameters of the LSSVM are optimized through the sparrow algorithm, so that the situation that a local optimal solution is trapped in the optimizing process is reduced. And optimizing the regularization parameters and the radial basis function parameters in the LSSVM according to the step flow of optimizing the sparrow algorithm shown in FIG. 4 to find an optimal model. Then, the test set is carried out to test the identification rate.

The above analysis experiment results show that, as shown in fig. 5 and fig. 6, the results are confusion matrix results of EMD-LSSVM and VMD-SSA-LSSVM model classification. Through the confusion matrix, when the EMD-LSSVM model is used for classification, classification errors occur under a first working condition, a third working condition, a sixth working condition, a seventh working condition and an eighth working condition; the model classification effect of the VMD-SSA-LSSVM model is only two classification errors under the first working condition, the effect is superior to that of other models, in ten continuous experimental fault tests, the average recognition rate of the model is as high as 99.5%, and compared with other different classification models in the figure 7, the optimized model provided by the invention has better and more stable recognition effect.

Claims

1. A gearbox fault detection model based on a VMD-SSA-LSSVM is characterized by comprising the following steps:

s1, data preprocessing and data reconstruction: carrying out VMD decomposition and wavelet packet threshold analysis combined denoising on the data, and then reconstructing the data with the rest steady-state component data;

the specific steps of data preprocessing and data reconstruction are as follows:

(1) The pretreatment process comprises the following steps: after data are imported, determining a signal decomposition layer number k by using self-adaptive empirical mode decomposition, setting a k value as a decomposition layer number of variable mode decomposition to decompose the signal, and performing later-stage denoising processing on the content of the characteristic signal containing noise by comparing a decomposition component with a Pearson coefficient, a signal-to-noise ratio and a root-mean-square difference of an original signal;

(2) Denoising: denoising the vibration signal component with high noise by using a wavelet packet threshold denoising method;

(3) Signal reconstruction: adding residual errors to the denoised high-frequency signal component and the medium-low frequency component to reconstruct a pure reconstruction signal;

s2, feature extraction: extracting different characteristic features and feature combinations from the reconstruction data in the step S1;

s3, establishing an SSA-LSSVM model of the VMD: and (5) carrying out training test on the feature set in the step (S2) and measuring the classification effect under different classifiers.

2. The VMD-SSA-LSSVM based gearbox fault detection model of claim 1, wherein the step S2 of extracting the characteristics of different nature comprises the following steps:

and respectively extracting time domain characteristics, frequency domain characteristics and time domain-frequency domain combined characteristics from the vibration reconstruction signals under the eight working conditions.

3. The VMD-SSA-LSSVM based gearbox fault detection model of claim 2, wherein the specific steps of establishing the SSA-LSSVM model of the VMD in step S3 are as follows:

(1) Comparison of different classifiers: extracting features with the same property from reconstructed data of the gearbox under eight working conditions to form feature vectors, dividing a training test set for the feature vectors, putting the training set into five alternative classifiers, and evaluating the features and the traditional optimal classifier according to classification results obtained by the classifier;

(2) And optimizing regularization parameters and RBF kernel function parameters in a least square support vector machine by using a sparrow optimization algorithm, and evaluating to obtain an optimal classification model.

4. The VMD-SSA-LSSVM based gearbox fault detection model of claim 3, wherein the specific optimization steps of the sparrow optimization algorithm in step S3 are as follows:

a. initializing sparrow populations, and dividing the sparrow populations into discoverers and followers according to the process of obtaining food;

b. calculating the fitness value of the initial population;

c. updating the position of the finder, the position of the follower and the position of the early-warning person according to a position updating formula, calculating the fitness value at the moment, and repeating the position updating formula until the minimum error is reached or the maximum iteration times is reached;

d. and outputting the optimal solution.