Method for sparse time-frequency representation of gear local fault signals based on matching pursuit network

Abstract

This invention discloses a sparse time-frequency representation method for gear local fault signals based on a matching pursuit network. The method includes: acquiring noiseless and noisy simulated signals of gear impact fault responses; preprocessing the signals and using noiseless signal samples as training labels and noisy signal samples as a time-spectrum training set; constructing a matching pursuit network model; using the simulated training samples and labels to train the matching pursuit network to obtain optimal network state parameters; inputting test samples into the trained matching pursuit network model for feature extraction to obtain a sparse time-frequency representation of the gear local fault signal samples; and using the sparse time-frequency representation of the gear local fault signal for fault diagnosis. The signal time-frequency representation obtained by this invention combines time-frequency sparsity with ridge continuity, which is beneficial for achieving high-precision fault diagnosis of rotating machinery.

Description

Technical Field

[0001] This invention belongs to the field of rotating machinery fault diagnosis and relates to a sparse time-frequency representation method for gear local fault signals based on a matching pursuit network. Background Technology

[0002] Rotating machinery plays a vital role in the machinery industry. Gears and bearings, as indispensable components of rotating machinery such as automotive transmissions and wind turbines, are of great significance for fault diagnosis in rotating machinery. In fault diagnosis of rotating machinery, the normal operation of the equipment can be determined by processing and analyzing the vibration signals collected on the equipment. When a fault occurs, the collected vibration signals usually contain corresponding fault characteristic frequencies. Based on these fault characteristic frequencies, fault diagnosis can be performed. However, according to the uncertainty principle, common time-frequency representation methods have problems such as difficulty in obtaining satisfactory time-frequency energy concentration and large deviations in the fault time-frequency characteristic lines extracted against a strong noise background, which cannot meet the requirements of fault diagnosis.

[0003] The ideal time-frequency representation of local fault signals in rotating machinery is inherently sparse. Sparse representation methods can improve the sparsity of fault signals in the time-frequency domain. Researchers have attempted to combine sparse representation and time-frequency representation methods to obtain better sparse time-frequency representations. For example, Yang et al. applied a sparse time-frequency representation method based on Wigner-Ville Distribution (WVD) to fault diagnosis of wind turbine gearboxes (Yang B., Liu R., Chen X. Sparse time-frequency representation for incipient fault diagnosis of wind turbine drive train[J]. IEEE Transactions on Instrumentation and Measurement, 2018, 67(11):2616-2627.). Hou et al. applied a sparse time-frequency representation method based on Short-Time Fourier Transform (STFT) to fault diagnosis of rolling bearings (Hou F., Selesnick I., Chen J., et al. Fault diagnosis for rolling bearings under unknown time-varying speed conditions with sparse Representation[J]. Journal of Sound and Vibration, 2021, 494: 115854.). These studies show that sparse time-frequency representation can effectively improve the problem of time-frequency energy concentration in the time-frequency representation of rotating machinery vibration signals.

[0004] However, these application methods still have their limitations when faced with increasingly complex rotating machinery vibration signals. For example, the sparse time-frequency representation method involves solving sparse time-frequency coefficients, which requires a large number of algorithm iterations, resulting in high computational complexity. Under strong noise backgrounds, both the time-frequency redistribution method and the sparse time-frequency representation method cannot simultaneously combine the time-frequency sparsity characteristics and ridge continuity characteristics of the vibration signal, which is not conducive to achieving high-precision rotating machinery fault diagnosis under non-stationary conditions.

[0005] Therefore, the existing technology cannot meet the needs of actual industrial applications and needs to be improved and enhanced. Developing an intelligent diagnostic algorithm that combines the time-frequency sparsity characteristics of the Gu Zhen motion signal with the ridge line continuity characteristics has become an urgent need. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a sparse time-frequency representation method for local fault signals in gears based on a matching pursuit network. First, this invention utilizes a fault signal response model to construct simulated signals as the training set and labels for the model's time-frequency spectrum, avoiding the difficulty in obtaining measured signal training sets and labels for network training in practical engineering. Then, a matching pursuit network model is built and trained using simulated signals to obtain the optimal network state parameters. Finally, the trained model is used to extract sparse features from the actual collected gear vibration experimental vibration signal data. The resulting time-frequency representation of the signal balances time-frequency sparsity and ridge continuity, which is beneficial for achieving high-precision fault diagnosis of rotating machinery.

[0007] This invention is achieved using the following technical solution:

[0008] A sparse time-frequency representation method for gear local fault signals based on a matching pursuit network includes the following steps:

[0009] The simulation signals of gear impact fault response with and without noise were obtained. The signals were preprocessed and the samples with and without noise were used as training labels. The samples with and without noise were used as the training set of time-spectrum graphs.

[0010] A matching pursuit network model is constructed, which includes a preprocessing part, a matching pursuit part, and a tail processing part. The preprocessing part is used to preprocess the input. The matching pursuit part includes multiple MP units, which are used to extract ridge features from the time spectrum of the input and expand the receptive field of the convolutional kernel. The tail processing part is used to obtain the estimation of the potential noiseless signal from the integrated signal.

[0011] Simulated training samples and labels are used to train the matching tracking network to obtain the optimal network state parameters;

[0012] The test samples are input into the trained matching and tracking network model for feature extraction, resulting in a sparse time-frequency representation of the gear local fault signal samples. The sparse time-frequency representation of the gear local fault signal is then used for fault diagnosis.

[0013] Furthermore, the step of acquiring noiseless and noisy gear impact fault response simulation signals, preprocessing the signals and using noiseless signal samples as training labels, and using noisy signal samples as the time-spectrum training set, includes:

[0014] (1) Based on the gear vibration signal model, the simulation signal of the noiseless gear impact fault response is obtained. The expression of the simulation signal s(t) is shown in the following formula:

[0015]

[0016] In the formula, s1(t) is the harmonic component, s2(t) is the impulse component, h(t) is the unit impulse response function, and the harmonic frequency f is... j Including rotational frequency and meshing frequency, τ is the initial moment of impact, T is the impact failure period, and A j and A k Indicates the amplitude.

[0017] (2) Add Gaussian white noise to the noiseless simulation signal to obtain a noisy simulation signal;

[0018] (3) Preprocess the noiseless simulation signal and the noisy simulation signal respectively. Use the time spectrum obtained by preprocessing the noiseless simulation signal as the training label and the time spectrum obtained by preprocessing the noisy simulation signal as the training sample. Construct the required training sample pair to obtain the required time spectrum training set.

[0019] Furthermore, the sample dataset was set with a sampling frequency of 10kHz and a sampling duration of 4000s. The signal was divided into segments of 8s each, resulting in a total of 500 samples.

[0020] Furthermore, the preprocessing of the simulation signal includes: segmenting the time-series vibration signal, then performing Hilbert demodulation on the signal segment and extracting its envelope spectrum, and then using STFT transformation to extract the analysis spectrum matrix according to the frequency band of interest.

[0021] Furthermore, the main frequency components in the envelope spectrum obtained by Hilbert demodulation will be the rotational frequency of the shaft where the faulty gear is located and its higher-order harmonics.

[0022] Furthermore, the preprocessing part of the matching pursuit network model includes a batch normalization function, which makes the processing of sample feature data more convenient and faster, and facilitates comparison. The matching pursuit part includes multiple MP units, each of which includes three layers of square dilated convolutional functions. The three layers of square dilated convolutional functions are concatenated to extract ridge features from the input time spectrum and significantly expand the receptive field of the convolutional kernel. The tail processing part includes a batch normalization function and an activation function concatenated to perform detailed processing on the integrated signal to obtain an estimate of the potential noise-free signal.

[0023] Furthermore, the specific steps of feature extraction in the matching tracking network model can be represented as follows:

[0024] (1) Input noisy signal x=y+n o Where y is the noiseless signal (or feature signal) that the matching pursuit network expects to extract, and n o Let x be the corresponding noise component. Suppose the input signal x undergoes batch normalization operation B. p The signal obtained after (·) is the initial residual signal R1, then the following equation holds:

[0025] R1 = B p (x)

[0026] (2) Effective component x extracted after the first MP unit e1 As shown in the following formula:

[0027] x e1 =θ1(R1)

[0028] In the formula, θ i (·) is the characteristic function of the i-th MP unit, and the remaining residual signal R2 can be expressed as follows:

[0029] R2 = R1 - x e1 =R1-θ1(R1)

[0030] (3) The matching pursuit network model inputs the residual signal obtained from the previous MP unit decomposition into the next MP unit to continue extracting effective components. After n MP units, a total of n effective components x can be obtained. en =θ n (R n ), its remaining residual signal R n+1 satisfy:

[0031] R n+1 =R n -x en =R n -θ n (R n )

[0032] Finally, the feature signal extracted by the matching pursuit network is a linear superposition of the weighted effective component signals, as shown in the following equation:

[0033]

[0034] In the formula, a i To measure the contribution of each MP unit's extracted effective component to the potential noiseless signal, the weight gain is used. Since each effective component inevitably contains noise, the effective components with more noise are given smaller weights, and the effective components with less noise are given larger weights to enhance the signal representation.

[0035] (4) Through tail processing operation T p (·) Perform detailed processing to obtain an estimate of the noiseless signal y. As shown in the following formula:

[0036]

[0037] Furthermore, the noiseless signal label y and the estimated signal When the negative structural similarity loss function converges, it can be considered that sparse feature extraction of the input signal has been successfully performed. The negative structural similarity loss function can be expressed as:

[0038]

[0039] y i This represents the label of the i-th noiseless signal. This represents the corresponding i-th estimated signal; the noisy input signal x and the corresponding noiseless signal label y constitute a training sample pair. N represents the number of training sample pairs; and They represent The mean and variance, and They represent y respectively i The mean and variance, express and y i The covariance, c1 and c2 are two constants used to maintain the stability of the loss.

[0040] Furthermore, the dilation rate used in the dilated convolution operation of each layer in step two satisfies the following formula:

[0041] max{r i+1 -2r i ,2r i -r i+1 ,r i}≤K i

[0042] Where r i K represents the dilation rate of the dilated convolution layer i. i This represents the kernel width of the i-th dilated convolution layer.

[0043] Furthermore, the vibration signal data of the gear vibration experiment was collected through an experimental platform consisting of a drive motor, a five-speed gearbox, and other transmission components. The speed range of the collected signal segments was higher than the training operating condition speed range, within the training operating condition speed range, and lower than the training operating condition speed range, respectively, to verify the generalization performance of the matching pursuit network model for gear local fault diagnosis.

[0044] Furthermore, the acquired signal segments are preprocessed using the same method as the training labels and training dataset. Unlike the preprocessing of simulation data, gears in actual engineering often have slight eccentricity and misalignment during machining or assembly, which will cause smooth modulation and interfere with fault diagnosis of the gears after Hilbert demodulation. Therefore, after obtaining the experimental signal segments, the signal segments should be high-pass filtered first, then Hilbert demodulated, and then the test signal should be converted from the time domain to the time-frequency domain using STFT and the time-frequency matrix should be extracted for analysis.

[0045] Furthermore, the performance of sparse time-frequency representation on the actual experimental signal is analyzed, including:

[0046] (1) Further extract time-frequency ridges from the time-frequency representation diagrams obtained from various time-frequency representation methods;

[0047] (2) Calculate the curve rate of each complete time-frequency ridge extracted from the sample to determine the accuracy of the extracted ridge. Calculate the curve rate of the theoretical fault characteristics collected. Further compare the relative differences between the extracted time-frequency ridge and the ideal time-frequency ridge curve rate based on the relative error. The formula for calculating the relative error is as follows:

[0048]

[0049] In the formula, g m The curvature of the extracted m-th ridge line satisfies the following formula:

[0050]

[0051] N c τ represents the total number of sequence points for each curve. i f is the time corresponding to point i. m (τ i ) represents the m-th ridge line at τ i The ridge frequency corresponding to time f b (τ i ) is τ i The fundamental frequency of the gear fault characteristic frequency corresponding to the time; if the relative error of the curve rate is within the tolerance error range, the accuracy of extracting the fault feature ridge is high, and the fault location can be further determined and directly used for fault diagnosis.

[0052] Compared with the prior art, the beneficial effects of the present invention are:

[0053] 1. This invention can use the noiseless and noisy simulation signals derived from the gear vibration signal model as training labels and training datasets to train the network model, thus avoiding the problem of difficulty in collecting signal labels and datasets from actual engineering vibration experiments.

[0054] 2. This invention exhibits excellent noise resistance. Compared with traditional methods, the time-frequency spectrum obtained by feature extraction of rotating machinery signals has almost no noise interference and is highly sparse overall. The fault feature ridges are continuous, and the relative error between the obtained time-frequency ridges and the ideal fault feature time-frequency ridges is smaller, resulting in higher accuracy. Therefore, the extracted fault feature ridges can be directly used in fault diagnosis while taking into account both time-frequency sparsity and ridge continuity. For example, compared with the Fourier synchronous compressed transform method, the proposed method has better time-frequency energy concentration; compared with the sparse short-time Fourier transform method, the fault feature time-frequency ridges extracted by the proposed method are continuous and highly sparse.

[0055] 3. This invention proposes a matching pursuit network architecture with strong interpretability. The matching pursuit network model built based on this architecture can be used for time-spectral inputs of different sizes and resolutions.

[0056] 4. When the rotational speed change rate of the sample signal in the constructed gear dataset covers the rotational speed change rate of the actual working condition signal, the matching pursuit network model has a good generalization ability for the measured gear vibration signal. After training, it can perform sparse time-frequency representation and fault diagnosis of the fault signal of rotating machinery. Attached Figure Description

[0057] Figure 1 This is a flowchart of the algorithm for implementing the sparse time-frequency representation method of gear local fault signals based on matching pursuit network;

[0058] Figure 2 This is a schematic diagram of the matching pursuit network structure in this invention;

[0059] Figure 3 This is a schematic diagram of the training label and dataset signal preprocessing process in this invention;

[0060] Figure 4 This is a schematic diagram of the inference output of the matching pursuit network on non-stationary working condition verification samples after training. (a), (b), and (c) are schematic diagrams of the input time-frequency plot, the label time-frequency plot, and the output time-frequency plot, respectively.

[0061] Figure 5 This is a schematic diagram of the working conditions and speed range of the experimental platform input shaft speed setting when acquiring signal samples in an embodiment of the present invention. (a) is a schematic diagram of deceleration, and (b) is a schematic diagram of speed increase.

[0062] Figure 6 This is a schematic diagram comparing the time-frequency diagrams obtained by the STFT time-frequency representation method of the six signal samples ((a) to (f)) in the embodiment of the present invention with the time-frequency diagrams obtained by the method of the present invention;

[0063] Figure 7This is a schematic diagram comparing the time-frequency representation methods of a sample obtained by STFT (Figure (a)), FSST (Figure (b)), STFR-STFT (Figure (c)) and the time-frequency representation method of Matching Pursuit Network (Figure (d)). Detailed Implementation

[0064] The present invention will now be described in detail with reference to the accompanying drawings and specific implementation steps, but the embodiments of the present invention are not limited thereto.

[0065] like Figure 1 As shown, the present invention provides a sparse time-frequency representation method for gear local fault signals based on a matched pursuit network. This method, through a matched pursuit network, can provide a sparse time-frequency representation of rotating machinery fault signals and exhibits good noise resistance. The extracted time-frequency spectrum has better time-frequency energy concentration compared to traditional methods, and it can balance time-frequency sparsity and ridge continuity. The method includes the following steps:

[0066] Step 1: Based on the gear vibration signal model, obtain the noiseless and noisy gear impact fault response simulation signals, preprocess the signals and use the noiseless signal samples as training labels, and use the noisy signal samples as the time spectrum training set.

[0067] The specific contents of step one are as follows:

[0068] (1) Based on the gear vibration signal model, the simulation signal of the noiseless gear impact fault response is obtained. The expression of the simulation signal s(t) is shown in the following formula:

[0069]

[0070] In the formula, s1(t) is the harmonic component, s2(t) is the impulse component, and h(t) is the unit impulse response function, satisfying the following equation:

[0071]

[0072] In the formula, the harmonic frequency f j It includes rotational frequency and meshing frequency, t represents time, τ is the initial moment of impact, T is the impact failure period, and f dl Let ξ be the l-th natural frequency. l For the damping ratio corresponding to the natural frequency, A j and A k Let j and k represent the amplitude, and j and k represent the different orders of the formulas accumulated in the harmonic and impulse component functions, respectively.

[0073] (2) Add noise to the noiseless simulation signal to obtain a noisy simulation signal;

[0074] In some embodiments of the present invention, Gaussian white noise with an intensity of -10dB is added.

[0075] (3) Preprocess the noiseless simulation signal and the noisy simulation signal respectively. Use the time spectrum obtained by preprocessing the noiseless simulation signal as the training label and the time spectrum obtained by preprocessing the noisy simulation signal as the training sample. Construct the required training sample pair to obtain the required time spectrum training set.

[0076] In some embodiments of the present invention, the sample dataset in step one is set with a sampling frequency of 10kHz and a sampling duration of 4000s. The signal is divided into segments of 8s each, and a total of 500 samples can be obtained.

[0077] In some embodiments of the present invention, when preprocessing the simulation signal in step one, the time-series vibration signal is first segmented, then the signal segment is demodulated by Hilbert and its envelope spectrum is obtained, and then the analysis spectrum matrix is ​​extracted according to the specific frequency band of interest through STFT transformation.

[0078] Step 2: Build a matching pursuit network model based on the matching pursuit algorithm idea, where the number of MP units is determined according to the complexity of the features to be extracted.

[0079] In step two, the matching pursuit network model is based on a convolutional neural network with n neural units. Its specific architecture mainly includes a preprocessing part, a matching pursuit part, and a tail processing part. The preprocessing part includes a batch normalization function, which makes the processing of sample feature data more convenient and faster, facilitating comparison. The matching pursuit part includes multiple MP units, each of which learns and outputs the residual signal from the previous layer. The more layers of dilated convolutional functions in the MP unit, the larger the receptive field of the convolution. In some embodiments of this invention, each MP unit includes three cascaded square dilated convolutional functions, used to extract ridge features from the input time-frequency spectrum and significantly expand the receptive field of the convolutional kernel. The tail processing part includes a batch normalization function and an activation function, which are cascaded together to perform detailed processing on the integrated signal to obtain an estimate of the potential noise-free signal. A schematic diagram of the matching pursuit network structure is shown below. Figure 2 As shown.

[0080] In step two, the dilation rate used in the dilated convolution operation of each layer satisfies the following formula:

[0081] max{r i+1 -2r i ,2r i -r i+1 ,r i}≤K i

[0082] Where r i K represents the dilation rate of the dilated convolution layer i. i This represents the kernel width of the i-th dilated convolution layer.

[0083] In step two, when building the matching tracking network, in some embodiments of the present invention, three MP units are selected to extract local fault features of the gear.

[0084] In step two, the principle of network feature extraction is as follows: Let the input noisy signal be x = y + n. o y is the expected noiseless signal, n o That is the corresponding noise component. Let B be... p (·) is the batch normalization operation function. After the input signal undergoes the batch normalization operation, the initial residual signal R1 is obtained, i.e., R1 = B. p (x).

[0085] The effective components extracted after passing through the first MP unit are shown in the following formula:

[0086] x e1 =θ1(R1)

[0087] In the formula, x e1 θ represents the effective component extracted by the first MP unit. n (·) represents the characteristic function of the nth MP unit, and then the remaining residual signal for the next step is obtained, as shown in the following formula:

[0088] R2 = R1 - x e1 =R1-θ1(R1)

[0089] The residual signal obtained from each MP unit is input into the next MP unit. The decomposition and extraction process in each MP unit can be represented by the following formula:

[0090] x en =θ n (R n )

[0091] In the formula, x en To match the effective components extracted by the tracking network model after the nth MP unit, R n It is the residual signal from the (n-1)th iteration; after extraction by n MP units, the feature signal extracted by the matching pursuit network model. The weighted linear superposition of the various effective component signals satisfies the following equation:

[0092]

[0093] In the formula, a iThe contribution of the effective components extracted by each MP unit to the potential noiseless signal was measured and obtained through network learning.

[0094] Finally, through tail processing operations Finally, the estimated signal is obtained. This is the final output of the matching pursuit network model. Specifically, when the extracted estimated signal... If the negative structural similarity loss with the expected noiseless signal label converges, the matching pursuit network model is considered to have successfully extracted sparse features from the input signal.

[0095] Among them, R n+1 The remaining residual signal of the nth iteration satisfies the following equation:

[0096] R n+1 =R n -x en =R n -θ n (R n )

[0097] The essence of the residual decomposition calculation in step two of the matching pursuit network lies in selecting the dictionary atoms most relevant to the signal to continuously decompose the energy of the residual signal until the condition is met.

[0098] When the input signals are the same, the characteristic function of the nth MP unit can be considered as θ. n (·)=F n (·); After n iterations The sum of the effective components extracted each time satisfies the following formula:

[0099]

[0100] In the formula, <·> represents the inner product calculation. <R n ,d n >d n d represents the effective signal component obtained in the nth iteration. n Represents the relationship with residual R n The most relevant unitized dictionary atom, F n (x) is the feature function of the match tracking network, which can be expressed as follows:

[0101] F n (x)=d n (d n T d n ) -1 d n T x

[0102] In the formula, dn T Represents dictionary atom d n The remaining residual signal R is obtained after n iterations from the transpose of the given signal. n+1 Satisfy the following formula:

[0103] R n+1 =R n - <R n ,d n >d n

[0104] That is, the final input signal x can be expressed as follows:

[0105]

[0106] Step 3: Use the simulation training samples and labels to train the matching tracking network, obtain the optimal network state parameters, and verify the model performance using simulation signals under different operating conditions.

[0107] In some embodiments of the present invention, the batch size for training the matching tracking network model is set to 40, the number of iterations is 50, the Adam optimization algorithm is used, the ratio of training set to validation set is set to 4:1, the initial learning rate is set to 0.01, and the adaptive update rule of the learning rate is: when the average loss of the validation set samples does not decrease for 4 consecutive times, the learning rate is reduced by 0.4 times.

[0108] In some embodiments of the present invention, the ability of the matching pursuit network model to extract signals under steady-state operating conditions is verified by constructing a constant-speed gear impact-type fault simulation signal with a signal-to-noise ratio of -7dB and containing two natural frequencies. The rotational shaft speed is set to 3000 r / min, i.e., the rotational frequency f. r =50Hz, the signal sampling frequency is 8000Hz, the first natural frequency and damping ratio are 1500Hz and 0.05 respectively, the second natural frequency and damping ratio are 2500Hz and 0.06 respectively, the rotational shaft frequency is 50Hz, the impact amplitude is randomly selected between 0.5m / s² and 1m / s², and the sampling time is 4s. To make this signal closer to the experimental signal, two harmonic signals with rotational frequencies of 0.2m / s² and 0.15m / s² are added to the signal, and the resulting signal is denoted as x. s The signal is input into the trained matching pursuit network model, and the output time spectrum is almost completely free of noise interference, approximating the label time spectrum.

[0109] In some embodiments of the present invention, to further verify the generalization ability of the matching pursuit network model and its generalization capability under non-stationary conditions, a simulation signal of a variable-speed gear impact fault with a signal-to-noise ratio of -8dB and containing two natural frequencies is constructed. The rotational speed n of the rotating shaft is set as...r The law governing the change of (t) satisfies the following formula:

[0110]

[0111] The signal sampling frequency is 12000Hz, with a first-order natural frequency and damping ratio of 2000Hz and 0.06, respectively, and a second-order natural frequency and damping ratio of 3600Hz and 0.08, respectively. The rotational shaft frequency is 50Hz, and the impact amplitude is randomly selected between 0.5m / s² and 1m / s². The sampling duration is 12s. To make the signal closer to the experimental signal, two harmonic signals with a rotational frequency and an amplitude of 0.1m / s² are added to the signal. The resulting signal is denoted as x. ns The output result is as follows Figure 4 As shown, the input time-frequency spectrum contains significant noise interference, making it difficult to extract fault feature ridges. However, the output result almost completely removes all noise from the input time-frequency graph, approximating the labeled time-frequency spectrum. Compared to the labeled spectrum, the output has very little amplitude loss and exhibits higher sparsity, indicating that the trained matching pursuit network possesses excellent feature extraction capabilities.

[0112] Step 4: Collect vibration signal data from the gear vibration experiment, and preprocess the vibration signal data to obtain test samples.

[0113] In some embodiments of the present invention, vibration signal data of gear vibration experiment is collected through an experimental platform consisting of a drive motor, a five-speed gearbox and other transmission components. An acceleration sensor is placed on the five-speed gearbox, and non-stationary vibration signals obtained by the position sensor at the measuring point in the positive Z-axis direction are used to construct test samples.

[0114] Furthermore, the sampling frequency of the experimental signal was set to 12kHz, and signal segments from three different speed ranges were collected under each of the two operating conditions, with each signal segment lasting 12 seconds. For example... Figure 5 As shown, the collected speed ranges are [1412,1383] r / min, [1077,926] r / min, [764,627] r / min and [637,795] r / min, [983,1105] r / min, [1245,1367] r / min. The speeds of the signal segments are higher than the training operating condition speed range, the speed ranges of two signal segments are within the training operating condition speed range, and the speeds of the other two signal segments are lower than the training operating condition speed range, in order to verify the generalization performance of the proposed matching pursuit network model for gear local fault diagnosis.

[0115] The acquired signal segments were preprocessed using the same method as the training labels and training dataset. In actual engineering, gears often have slight eccentricity and misalignment during machining or assembly, which will cause smooth modulation and interfere with the fault diagnosis of the gears after Hilbert demodulation. Therefore, after obtaining the experimental signal segments, the signal segments were first subjected to high-pass filtering, then Hilbert demodulation, and then the test signal was converted from the time domain to the time-frequency domain and the time-frequency matrix was extracted and analyzed using STFT with the same time-frequency resolution as the training samples.

[0116] The time resolution of the time spectrum is set to 0.1s, the frequency resolution to 1Hz, and the fault analysis frequency to 120Hz. To eliminate the DC effect, the final analysis frequency band is set to [3,122]Hz. The size of the time spectrum is (120,120).

[0117] Step 5: Input the test samples into the trained matching pursuit network model for feature extraction to obtain the sparse time-frequency representation of the gear local fault signal samples. Analyze its time-frequency representation performance against the actual experimental signals and use the sparse time-frequency representation results of the gear local fault signals for fault diagnosis.

[0118] Furthermore, the preprocessed measured gear vibration signal from step four is input into the trained matching tracking network, such as... Figure 6 As shown, although the rotational frequency of the shaft where the faulty gear is located and its higher-order harmonics are present in the STFT time spectrum of the above 6 test signals, they also contain a large number of noise components. After feature extraction by the matching pursuit network model of this application, the obtained time spectrum is almost free of noise interference, and the overall performance is highly sparse, and the fault feature ridge is continuous.

[0119] The time-frequency ridges are further extracted from the time-frequency spectra obtained by various time-frequency representation methods, and the relative error of the curve rate between the actual ridge frequency and the theoretical fault characteristic frequency is calculated, as shown in the following formula:

[0120]

[0121] In the formula, g m N represents the curve rate of the extracted m-th ridge. c τ represents the total number of sequence points for each curve. i f is the time corresponding to point i. m (τ i ) represents the m-th ridge line at τ i The ridge frequency corresponding to time f b (τ i ) is τ i The fundamental frequency of the gear fault characteristic frequency corresponding to the given moment.

[0122] In the six experimental signals, the relative error of the curvature of all ridges was less than 2%, as shown in Table 1. All were below the upper limit of error tolerance (5%). Therefore, the fault feature ridges extracted by the method of this invention have high accuracy and can be directly used for fault diagnosis.

[0123] Table 1 shows the relative error (%) of the time-frequency ridge curve obtained by the proposed method.

[0124]

[0125] like Figure 7 The figure shows a comparison of the time-frequency representation methods obtained by STFT, FSST, STFR-STFT, and the matched pursuit network time-frequency representation method for a sample. As can be seen from the figure, while the FSST method effectively sharpens the time-frequency representation compared to STFT, it cannot improve the discontinuity of the time-frequency ridges. Although the time-frequency spectrum obtained by the STFR-STFT method has better sparsity than STFT and FSST, it exacerbates the discontinuity of the time-frequency ridges. Obviously, this discontinuity of the time-frequency ridges can easily lead to misdiagnosis when the rotational speed changes at a large rate. In contrast, the matched pursuit network provided by this invention can effectively compensate for these shortcomings. The time-frequency ridges of the extracted fault features are continuous and highly sparse, while also possessing excellent visual representation capabilities.

[0126] Furthermore, the energy concentration of the time-frequency representation obtained by the method of this invention is evaluated using Rényi entropy. The Rényi entropy decreases as the time-frequency energy concentration increases. For the evaluated time-frequency spectrum, the time-frequency energy density function is denoted as M[p,q], and the β-order Rényi entropy value... Defined as:

[0127]

[0128] M[p,q] represents the signal strength at time p and frequency q; in some embodiments of the present invention, the Rényi entropy at β=3 can well measure the time-frequency energy concentration of most signals and has good stability.

[0129] Choosing β=3, Table 2 lists the Rényi entropy values ​​of the time-frequency representations of STFT, FSST, STFR-STFT, and matched pursuit network. It can be seen that the Rényi entropy values ​​of all samples obtained by the method of the present invention are smaller than those of STFT, and except for samples (b) and (e) whose Rényi entropy values ​​are slightly larger than those of the STFR-STFT method, the Rényi entropy values ​​of the other samples are lower than those of the comparison method, indicating that the time-frequency representation obtained by the method of the present invention has better time-frequency energy concentration.

[0130] Table 2 Rényi entropy values ​​at different time frequencies

[0131]

[0132] In summary, compared with the traditional STFT, FSST and STFR-STFT methods, the proposed method has a superior time-frequency characterization capability for gear local fault signals.

[0133] The aforementioned embodiment provides a method that utilizes a matching pursuit network that employs convolutional neural network units to replace dictionary atoms to extract feature information layer by layer from the time-frequency spectrum of the residual signal. This effectively removes noise from fault signals in complex and noisy backgrounds, ensuring that the extracted time-frequency spectrum balances time-frequency sparsity with continuous ridge characteristics. Simultaneously, during training, noiseless and noisy simulation signals derived from the gear vibration signal model are used as training labels and datasets to train the matching pursuit network model. This avoids the difficulty of collecting actual engineering vibration experiment signal labels and datasets, making it easier to train and improve the network model. The time-frequency spectrum obtained by feature extraction from the actually collected gear vibration signal using the trained matching pursuit network model is almost free of noise interference and exhibits better time-frequency energy concentration compared to traditional methods. The extracted fault feature time-frequency ridges are continuous and highly sparse. By further extracting high-precision fault signal time-frequency ridges, it can be directly used for fault diagnosis of rotating machinery.

[0134] Finally, it should be noted that the above embodiments are merely descriptions of a preferred embodiment of the present invention and are not intended to limit the scope of protection of the present invention. Any equivalent changes, modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should be included within the scope of the patent application of the present invention.

Claims

1. A sparse time-frequency representation method for gear local fault signals based on a matching pursuit network, characterized in that, Including the following steps: The simulation signals of gear impact fault response with and without noise were obtained. The signals were preprocessed and the samples with and without noise were used as training labels. The samples with and without noise were used as the training set of time-spectrum graphs. A matching pursuit network model is constructed, which includes a preprocessing part, a matching pursuit part, and a tail processing part. The preprocessing part is used to preprocess the input. The matching pursuit part includes multiple MP units, which are used to extract ridge features from the time spectrum of the input and expand the receptive field of the convolutional kernel. The tail processing part is used to obtain the estimation of the potential noiseless signal from the integrated signal. Simulated training samples and labels are used to train the matching tracking network to obtain the optimal network state parameters; The test samples are input into the trained matching and tracking network model for feature extraction, resulting in a sparse time-frequency representation of the gear local fault signal samples. In the matching pursuit network model, each MP unit learns and outputs the residual signal from the previous layer. Each MP unit includes multiple cascaded square dilated convolution functions, and the dilation rate used in each dilated convolution operation satisfies the following formula: in Indicates the first The expansion rate of layer void convolution, Indicates the first The kernel width of the layered dilated convolution; In the matching pursuit network model, the essence of residual decomposition lies in selecting the dictionary atoms most relevant to the signal to continuously decompose the energy of the residual signal until a condition is met. The input signal of the matching pursuit network model... It can be expressed as the following formula: In the formula, The sum of the effective components extracted each time satisfies the following formula: In the formula, Represents inner product calculation, Representing the n The effective signal components obtained in the next iteration Represents the residual The most relevant unitized dictionary atoms, To match the feature functions of the tracking network model; Representative process n The residual signal obtained after the next iteration; The residual signal obtained from each MP unit is input into the next MP unit. The decomposition and extraction process in each MP unit can be represented by the following formula: In the formula, To match the tracking network model after the first... n Effective components extracted from MP units It is the first The remaining residual signal after the next iteration; n After extracting MP units, the feature signals extracted by the matching pursuit network model The characteristic signal is a linear superposition of the weighted effective component signals. Satisfy the following formula: In the formula, The contribution of the effective components extracted by each MP unit to the potential noiseless signal was measured. Extracted from the network n There are 1 effective component, satisfying the following formula: In the formula, For the first n Characteristic functions of MP units; For the first n The remaining residual signal of the next iteration.

2. The sparse time-frequency representation method for gear local fault signals based on matching pursuit networks according to claim 1, characterized in that, The process of acquiring noiseless and noisy gear impact fault response simulation signals, preprocessing the signals and using noiseless signal samples as training labels, and using noisy signal samples as the time-spectrum training set includes: Based on the gear vibration signal model, the noiseless gear impact fault response simulation signal is obtained. The expression is shown in the following formula: In the formula, Harmonic components, As an impact component, It is a unit impulse response function. t Indicates time, To impact the initial moment, To impact the fault cycle, and Indicates amplitude. Harmonic frequencies; Add noise to a noiseless simulation signal to obtain a noisy simulation signal; The noiseless simulation signal and the noisy simulation signal are preprocessed separately. The time spectrum of the noiseless simulation signal is obtained as the training label, and the time spectrum of the noisy simulation signal is obtained as the training sample. The required training sample pairs are constructed to obtain the required time spectrum training set.

3. The sparse time-frequency representation method for gear local fault signals based on matching pursuit networks according to claim 2, characterized in that, The simulation signal is preprocessed, including: segmenting the time-series vibration signal, demodulating the signal segment and extracting its envelope spectrum, and then extracting the analysis spectrum matrix.

4. The sparse time-frequency representation method for gear local fault signals based on matching pursuit networks according to any one of claims 1-3, characterized in that, Before inputting the test samples into the trained matching and tracking network model for feature extraction, the following steps are also included: collecting vibration signal data from the gear vibration experiment and preprocessing the experimental vibration signal data to obtain the test samples.

5. The sparse time-frequency representation method for gear local fault signals based on matching pursuit networks according to claim 4, characterized in that, The experimental vibration signal data was preprocessed by first segmenting the time-series vibration signal, then demodulating the signal segment with Hilbert and taking its envelope spectrum, then performing high-pass filtering on the obtained signal segment to eliminate stationary modulation, and finally performing STFT transformation and extracting the analysis spectrum matrix.

6. A sparse time-frequency representation device for gear local fault signals based on a matching pursuit network, characterized in that, For implementing the method of any one of claims 1-5, the apparatus comprises the following modules: The signal acquisition module is used to acquire noiseless and noisy gear impact fault response simulation signals, preprocess the signals and use noiseless signal samples as training labels, and noisy signal samples as time spectrum training set. The model building module is used to build a matching pursuit network model. The matching pursuit network model includes a preprocessing part, a matching pursuit part, and a tail processing part. The preprocessing part is used to preprocess the input. The matching pursuit part includes multiple MP units, which are used to extract ridge features from the time spectrum of the input and expand the receptive field of the convolutional kernel. The tail processing part is used to obtain the estimate of the potential noiseless signal from the integrated signal. The model training module is used to train the matching tracking network using simulated training samples and labels to obtain the optimal network state parameters; The sparse time-frequency representation module is used to input test samples into a trained matching tracking network model for feature extraction, thereby obtaining a sparse time-frequency representation of the gear local fault signal samples.

7. An electronic device, characterized in that, The device includes a processor and a memory, the memory for storing instructions or computer programs, and the processor for executing the instructions or computer programs in the memory to cause the electronic device to perform claim 1.

5. The method described in any one of the above.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores instructions that, when executed, cause the device containing the instructions to perform claim 1.

5. The method described in any one of the above.

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