Mechanical rotating component fault diagnosis method based on non-stationary nonlinear feature cancellation

Abstract

The application discloses a mechanical rotating component fault diagnosis method based on non-stationary nonlinear feature cancellation, and pre-acquires mechanical rotating component vibration signals under normal and fault states. i The original intrinsic mode component is obtained by using empirical mode decomposition to process the original signal, then a step parameter h is set, multi-step reconstruction is carried out, the reconstructed component is obtained, energy features are calculated, and a data set is established; an optimal kernel function is selected, a kernel matrix is constructed; the data is input into the kernel matrix, the kernel matrix is centralized, the characteristic value is calculated, the characteristic vector is sorted in size order, and the data set is reconstructed; the reconstructed data set is input into the SVM, the SVM classifier is trained by using the training set, the trained classifier is tested by using the test set, and precise fault classification is realized. The kernel principal component algorithm proposed in the application combines the empirical mode decomposition method, and can realize precise classification of mechanical rotating component faults for non-linear and non-stationary signals.

Description

Technical Field

[0001] This invention belongs to the field of intelligent fault diagnosis technology for vibration signals of mechanical rotating parts, and specifically relates to a fault diagnosis method for mechanical rotating parts based on the cancellation of non-stationary and nonlinear characteristics. Background Technology

[0002] With the development of social productivity, mechanical equipment is increasingly widely used in daily life and production. As a crucial component of mechanical equipment, rolling bearings often operate under harsh conditions such as high speed and high load, making them highly susceptible to damage and even failure, resulting in economic losses. Therefore, employing advanced technologies to process vibration signals and perform fault diagnosis is of great practical significance in reducing maintenance costs and preventing safety accidents.

[0003] Commonly used signal processing methods in fault diagnosis include short-time Fourier transform, wavelet transform, correlation analysis, Wigner-Ville distribution, blind source separation, and HHT transform. While these methods are effective for fault identification, rolling bearings exhibit nonlinear and non-stationary vibrations due to factors such as nonlinear contact between rolling elements and inner / outer rings, changes in contact stiffness under load, nonlinear load distribution, variations in the number of rollers in the load-bearing area, and defects generated during manufacturing and operation. Traditional signal processing methods, based on the assumption of stationary and linear signals, are prone to losing crucial information. Therefore, employing processing methods specifically designed for nonlinear and non-stationary signals is essential for improving the accuracy of fault diagnosis. Summary of the Invention

[0004] Purpose of the invention: This invention provides a fault diagnosis method for mechanical rotating parts based on the cancellation of non-stationary and nonlinear characteristics, which can accurately classify faults of mechanical rotating parts for nonlinear and non-stationary signals.

[0005] Technical Solution: This invention provides a fault diagnosis method for mechanical rotating components based on the cancellation of nonstationary and nonlinear characteristics, specifically including the following steps:

[0006] (1) Acquire vibration signals of mechanical rotating parts under normal and fault conditions in advance;

[0007] (2) The original signal is processed by empirical mode decomposition to obtain the original intrinsic mode components, and then the order parameter h is set. i Multi-order reconstruction is performed to obtain the reconstructed components, offsetting the influence of non-stationary characteristics, energy features are obtained, a dataset is established, and training and testing sets are divided.

[0008] (3) Select the optimal kernel function and construct the kernel matrix;

[0009] (4) After inputting the data into the kernel matrix, the kernel matrix is ​​centered, the eigenvalues ​​are calculated, and the eigenvectors are sorted in order of size to reconstruct the dataset;

[0010] (5) Input the reconstructed dataset into the SVM, train the SVM classifier using the training set, and test the trained classifier using the test set to achieve accurate fault classification.

[0011] Furthermore, the vibration signal of the mechanical rotating component under the fault state described in step (1) includes the vibration signals of the bearing inner ring, bearing rolling elements and bearing outer ring.

[0012] Furthermore, the implementation process of step (2) is as follows:

[0013] M data points are extracted from the raw signal acquired on the simulation test bench and subjected to EMD decomposition:

[0014]

[0015] In the formula, C i (t) represents the individual IMF components obtained from EMD decomposition; r n (t) represents the remainder after signal decomposition; i and n represent the number of decompositions, and N represents the total number of components;

[0016] Set the order parameter h i For the original component C respectively i Each component in (t) is decomposed twice according to the corresponding order parameter to obtain multi-order reconstructed components.

[0017] The formula for calculating the energy eigenvector and reconstructing the energy of the IMF components is as follows:

[0018]

[0019] After calculating the energy value of each IMF component, the total energy is calculated iteratively. Then, the percentage of each IMF component is calculated and stored to create a dataset, which is then divided into a training set and a test set.

[0020] Furthermore, the implementation process of step (3) is as follows:

[0021] The kernel matrix is ​​calculated based on the number of samples, and then centered; the radial basis function is chosen as the kernel function.

[0022]

[0023] Where x and y are the input sample features, and σ is the feature scaling scale.

[0024] Furthermore, the implementation process of step (4) is as follows:

[0025] The divided training and test sets are input into the KPCA model, and the samples are mapped to a high-dimensional feature space through nonlinear mapping to obtain the kernel matrix K, which is then centered.

[0026] Find the eigenvalues ​​λ1, λ2, ..., λ of the kernel matrix K. m The eigenvalues ​​are sorted in descending order, and the corresponding eigenvectors are selected as the kernel principal component eigenvectors.

[0027] The kernel principal component eigenvectors are used as the rolling bearing fault feature set to reconstruct the training and test sets.

[0028] Furthermore, the implementation process of step (5) is as follows:

[0029] Multi-class support vector machine is selected for network optimization to obtain the optimal penalty coefficient and SVM kernel parameters. The reconstructed training set and test set are then input into the SVM to achieve fault identification of rolling bearings.

[0030] Beneficial effects: Compared with the prior art, the beneficial effects of the present invention are as follows: The improved empirical mode decomposition, KPCA and SVM combined model is based on considerations of diagnostic difficulty, diagnostic process and the special characteristics of nonlinear and non-stationary signals. First, the energy features of the vibration signal are extracted by the improved empirical mode decomposition to construct samples. Then, the nonlinear features are extracted by KPCA and input into SVM for fault diagnosis. It combines the advantages of the three and can perform more accurate fault diagnosis for rolling bearing faults under nonlinear and non-stationary signals. Attached Figure Description

[0031] Figure 1 This is a flowchart of the present invention;

[0032] Figure 2 This is a schematic diagram of the multi-order component reconstruction principle of the present invention;

[0033] Figure 3 These are the IMF component diagrams of EMD decomposition, where (a) is the IMF component diagram of normal state; (b) is the IMF component diagram of inner ring failure; (c) is the IMF component diagram of rolling element failure; and (d) is the IMF component diagram of outer ring failure.

[0034] Figure 4 This is a training classification result diagram using the present invention;

[0035] Figure 5 This is a diagram showing the test classification results using the present invention. Detailed Implementation

[0036] The present invention will now be described in further detail with reference to the accompanying drawings.

[0037] This invention proposes a fault diagnosis method for mechanical rotating components based on the cancellation of nonstationary and nonlinear characteristics, such as... Figure 1 As shown, the specific steps include:

[0038] Step 1: Acquire vibration signals of mechanical rotating parts under normal and fault conditions in advance.

[0039] A mechanical vibration simulation test bench was constructed, and signal acquisition was performed using an LMS vibration and noise testing system. A contact-type triaxial accelerometer was installed at the faulty component to collect vibration signals, and a non-contact acoustic sensor was placed nearby to collect acoustic signals. The collected signals included four types of faults: normal operation, bearing inner ring faults, bearing rolling element faults, and bearing outer ring faults.

[0040] The non-stationary and nonlinear characteristics of mechanical vibration signals originate from two sources: firstly, the nonlinear contact and nonlinear load distribution between internal components such as shafts and gears; and secondly, the complex noise in the external working environment. Therefore, when constructing a mechanical vibration simulation test bench, to obtain the most realistic non-stationary and nonlinear signals, a gearbox containing shafts, gears, and bearings is installed on the test bench. In addition to using contact-type triaxial accelerometers 1A312E, 1A313E, and 356A15 for vibration signal acquisition, a non-contact acoustic sensor AWA14604 is also used to acquire ambient noise.

[0041] The sampling frequency was set to 25.6 kHz, the sampling time was 30 seconds, and a total of 768,000 data points were collected in one set. The data from the contact triaxial accelerometer was selected from the signal in the z-direction because vibrations in the z-direction are more pronounced than those in the other two directions.

[0042] Step 2: Process the original signal using empirical mode decomposition to obtain the original intrinsic mode components, and then set the order parameter h. i Multi-level reconstruction is carried out.

[0043] EMD cancellation of non-stationary characteristics: EMD preprocessing is performed before the vibration signal is input into the KPCA-SVM model to obtain 8 IMF components, and the order parameter h is set. i The components are reconstructed according to the corresponding order to obtain multi-order reconstructed components. The component energy value and total energy value are calculated, the proportion is obtained to obtain energy features, a preliminary dataset is established, and it is divided into training set and test set.

[0044] Common signal processing methods include Short-Time Fourier Transform (SFT), Wavelet Transform, Correlation Analysis, Wigner-Ville Distribution, Blind Source Separation, and HHT Transform. However, when dealing with nonlinear signals, these methods can easily lead to the loss of some information features. EMD (Extreme Mode Decomposition) decomposes signals based on their own time-scale characteristics without requiring any pre-defined basis functions, thus offering significant advantages in processing non-stationary and nonlinear signals. However, it also suffers from mode aliasing. Therefore, order parameters are added to improve it. Different order parameters are set for different components, and secondary decomposition is performed to ensure effective differentiation of frequency features. The principle is as follows: Figure 2 As shown.

[0045] First, 2400 data points were extracted from the raw signal collected on the simulation test bench and decomposed into 8 IMF components. The formula for EMD decomposition is as follows:

[0046]

[0047] In the formula, C i (t) represents the individual IMF components obtained from EMD decomposition; r n (t) represents the remainder after signal decomposition; i and n represent the number of decompositions, and N represents the total number of components.

[0048] The IMF component diagrams obtained from EMD decomposition under the four states are as follows: Figure 3 As shown, (a) is the IMF component diagram under normal conditions; (b) is the IMF component diagram for inner ring failure; (c) is the IMF component diagram for rolling element failure; and (d) is the IMF component diagram for outer ring failure. Then, the order parameter h is set. i For each component, a secondary decomposition and reconstruction is performed. When h = 1, it means that the component does not need to be decomposed. When h = n, it means that the component needs to be decomposed. The number of decomposition levels is n, and the value of n should be less than the number of initial decomposed components.

[0049] Calculate the energy eigenvector and the energy E of the IMF component. i :

[0050]

[0051] After calculating the capability value of each IMF component, the total energy is calculated iteratively. Then, the percentage of each IMF component is calculated and stored. A dataset is created and divided into training and test sets in a 4:1 ratio.

[0052] Step 3: Select the optimal kernel function to construct the kernel matrix.

[0053] The key to kernel principal component analysis lies in choosing an appropriate kernel function, because computations in the feature space cannot be completed using vectors of increased dimensionality; they can only be performed by the kernel function. We select a radial basis kernel function from the positive definite matrix to construct a high-dimensional mapping space.

[0054] In the KPCA method, the choice of kernel function is crucial because computations in the feature space cannot be performed using vectors with increased dimensionality; they can only be accomplished by the kernel function. According to functional theory, a kernel function satisfying the Mercer condition corresponds to an inner product in the feature space; therefore, the kernel function cannot be chosen arbitrarily. Currently, commonly used kernel functions mainly include polynomial kernels, sigmoid kernels, and radial basis kernels.

[0055] Among them, the polynomial kernel and the radial basis function kernel always satisfy Mercer's theorem, while the sigmoid kernel only satisfies Mercer's theorem when its parameters are selected for certain values. Under optimal parameter conditions, the polynomial kernel can only distinguish one state among multiple states, resulting in insufficient classification effectiveness. Therefore, the radial basis function kernel is chosen, and its expression is as follows:

[0056]

[0057] Where x and y are the input sample features, and σ is the feature scaling scale.

[0058] Kernel functions can be used to describe the mapping distribution of input data in the feature space using a low-dimensional KPCA subspace.

[0059] Step 4, Input data into KPCA and reconstruct samples: After inputting the data into the kernel matrix, the kernel matrix is ​​centered, the eigenvalues ​​are calculated, and the eigenvectors are sorted in order of size to reconstruct the dataset.

[0060] The predefined training and test sets are input into the KPCA model. The samples are mapped to a high-dimensional feature space through nonlinear mapping to obtain the kernel matrix K, which is then centered.

[0061] Then, the eigenvalues ​​λ1, λ2, ..., λ of the kernel matrix K are solved. m Then, the eigenvalues ​​are sorted in descending order, and the corresponding eigenvectors are selected as the kernel principal component eigenvectors.

[0062] Finally, the kernel principal component feature vectors are used as the rolling bearing fault feature set to reconstruct the training and test sets.

[0063] Step 5: Input the reconstructed dataset into the SVM, train the SVM classifier using the training set, and test the trained classifier using the test set to achieve accurate fault classification.

[0064] After reconstructing the KPCA feature set, a classifier is trained to classify faults. The SVM method is a supervised learning algorithm that can handle complex nonlinear problems using simple linear algorithms.

[0065] The input samples for the SVM are feature vectors extracted from rolling bearings set up on a test bench under normal conditions, inner ring failure, rolling element failure, and outer ring failure conditions. For each condition, 200 samples are selected, with 160 samples used as the training set and 40 samples as the test set. These feature vectors are labeled 1, 2, 3, and 4 respectively. Then, a 4-classifier is trained for fault classification.

[0066] Substitute the reconstructed training set into the training data, and the training results are as follows: Figure 4 As shown, the test results are as follows: Figure 5 As shown in the figure, the horizontal axis represents the sample number, and the vertical axis represents the sample category. The two figures demonstrate that the SVM classification accuracy on the training set reaches approximately 98.59%, and the SVM classification accuracy on the test set reaches 99.38%. Only a very small number of SVM output points are outside the expected region, indicating a very small error, thus proving the effectiveness of the proposed method. The multi-order reconstruction component improvement method proposed in this invention can significantly reduce the aliasing phenomenon of component features in empirical mode decomposition, effectively eliminate the influence of non-stationary signal characteristics, and, combined with the kernel principal component algorithm for nonlinear dimensionality reduction, can achieve accurate classification of mechanical rotating component faults for nonlinear and non-stationary signals.

Claims

1. A mechanical rotating component fault diagnosis method based on non-stationary nonlinear feature cancellation, characterized in that, It comprises the following steps: (1) pre-acquire normal state and fault state of mechanical rotating parts vibration signal; (2) The original signal is processed by using empirical mode decomposition to obtain an original intrinsic mode component, and then a order parameter h is set i , multi-order reconstruction is performed to obtain a reconstructed component, the influence of non-stationary characteristics is offset, an energy feature is calculated, a data set is established, and a training set and a test set are divided; (3) select the optimal kernel function, construct kernel matrix; (4) after inputting the data into the kernel matrix, the kernel matrix is centralized, the eigenvalue is calculated, and the eigenvector is sorted in size order, and the data set is reconstructed; (5) input the reconstructed data set into SVM, train SVM classifier using training set, test the trained classifier using test set, and realize accurate fault classification; The step (2) is implemented as follows: The original signal collected on the simulation test bench is intercepted M data points, and EMD decomposition is carried out: In the formula, C i (t) represents each IMF component obtained by EMD decomposition; r n (t) is the residual after signal decomposition; i and n are the decomposition times, and N is the total number of components; Setting the order parameter h i , respectively, each component in the original component C i (t) according to the corresponding order parameter to obtain multi-order reconstruction component Calculate the energy feature vector, and the formula for calculating the energy of the reconstructed IMF component is as follows: After calculating the energy value of each IMF component, the total energy is calculated, then the percentage of each IMF component is calculated and stored to establish the data set, and the training set and test set are divided; The step (3) is implemented as follows: According to the number of samples, the kernel matrix is calculated, and the kernel matrix is centralized; wherein the kernel function is selected as the radial basis kernel function: Wherein, x and y are input sample features, and sigma is the feature scaling scale; The step (4) is implemented as follows: The divided training set and test set are input into the KPCA model, the samples are mapped to a high-dimensional feature space through nonlinear mapping, the kernel matrix K is obtained, and then the center is centralized; Solving the eigenvalues λ1, λ2,..., λ m , and ordering the eigenvalues from large to small, selecting the corresponding eigenvectors as the kernel principal component features Take the kernel principal component eigenvector as the rolling bearing fault feature set, and reconstruct the training set and test set; The step (5) is implemented as follows: Select multi-class support vector machine for network optimization, obtain the optimal penalty coefficient and SVM kernel parameter, input the reconstructed training set and test set into SVM to realize fault identification of rolling bearing.

2. The non-stationary nonlinear feature cancellation based mechanical rotating component fault diagnosis method according to claim 1, characterized in that, The fault state of the mechanical rotating parts vibration signal in step (1) includes bearing inner ring, bearing rolling body and bearing outer ring vibration signal.

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