Gabor wavelet neural network-based gearbox fault identification method

Abstract

The invention discloses a gearbox fault identification method based on a Gabor wavelet neural network, and the method comprises the steps: inputting a gearbox vibration signal into a wavelet neural network, generating a Gabor wavelet, and converting the Gabor wavelet into a wavelet kernel; synchronously extracting a real component and an imaginary component of a wavelet kernel by adopting a dual-channel complex filtering mechanism, and performing normalization operation on the wavelet kernel by combining an energy normalization strategy; in each layer of the wavelet neural network, carrying out time-frequency feature extraction through forward propagation, carrying out iterative optimization on a wavelet kernel through back propagation, and outputting a complex feature map extracted from the time-frequency features of each layer; and inputting the plurality of feature maps into a convolutional neural network for advanced abstract feature extraction to obtain a fault diagnosis result of the gearbox. According to the method, wavelet transform is embedded into the deep network end to end, adaptive modeling of time-frequency characteristics of input signals is realized, various fault characteristics of the gearbox can be adaptively and accurately matched, and the resolution and accuracy of time-frequency analysis are remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of gearbox fault analysis, and particularly relates to a gearbox fault identification method based on Gabor wavelet neural network. Background Technique

[0002] As a mature signal processing tool, wavelet transform exhibits significant advantages in the analysis of non-stationary signals by virtue of its superior time-frequency localization ability and multi-scale analysis characteristics. Compared with the Fourier transform, wavelet transform can simultaneously localize the time and frequency information of a signal, making it suitable for complex signals with rich time-frequency characteristics. Its basis functions achieve multi-scale modeling through dilation and translation operations, enabling the adaptive analysis of different frequency components. It can capture both the low-frequency structural changes and the high-frequency transient impact characteristics. In addition, wavelet transform has good mathematical properties such as orthogonality, compact support, and reversibility, ensuring information fidelity and reversible reconstruction during the transformation process. At the same time, its coefficients are sparse, which helps to improve the efficiency of feature extraction and reduce the computational complexity, making it more suitable for processing non-stationary signals.

[0003] In recent years, researchers have proposed a new research idea, which is to combine wavelet transform with deep learning to more effectively process and analyze signals. This method fully exploits the advantages of wavelet transform in time-frequency feature extraction, while leveraging the powerful feature representation and classification capabilities of deep learning to achieve accurate modeling and fault identification of complex non-stationary signals. Tang et al. proposed a convolutional neural network (NCNN) framework based on batch normalization, combined with synchronous compressed wavelet transform technology to process signal data. Dong et al. proposed a rolling bearing fault classification method based on empirical wavelet transform (EWT) and one-dimensional improved self-attention enhanced convolutional neural network (1D-ISACNN). Liang et al. proposed a fault diagnosis method based on wavelet transform and improved residual network (WT-IResNet), which adaptively extracts features through a new pooling layer for dimensionality reduction and global singular value decomposition (SVD), and introduces a new loss function with adjustable parameters to improve the fault identification performance under label noise conditions. These existing methods of combining wavelet with deep learning usually only use wavelet transform as a preprocessing step for feature extraction, failing to deeply integrate with the deep learning framework, and the pre-defined wavelet basis functions lack adaptability to specific fault patterns, restricting the model's feature extraction ability and thus affecting the identification of different fault types. Summary of the Invention

[0004] Aiming at the above deficiencies in the prior art, the gearbox fault identification method based on Gabor wavelet neural network provided by the present invention solves the problem of low diagnostic accuracy caused by the insufficient frequency domain modeling of traditional deep learning for time-varying signals.

[0005] To achieve the above-mentioned invention objective, the technical solution adopted by the present invention is: a gearbox fault identification method based on a Gabor wavelet neural network, comprising the following steps:

[0006] S1. Input the vibration signal of the gearbox into the wavelet neural network to generate Gabor wavelets, and transform the Gabor wavelets into wavelet kernels controlled by the center frequency, bandwidth, phase, and time displacement;

[0007] S2. Adopt a dual-channel complex filtering mechanism to synchronously extract the real and imaginary components of the wavelet kernel, and perform a normalization operation on the wavelet kernel in combination with the energy normalization strategy to obtain the normalized wavelet kernel;

[0008] S3. In each layer of the wavelet neural network, perform time-frequency feature extraction according to the input wavelet kernel and the vibration signal of the gearbox through forward propagation, and perform iterative optimization on the wavelet kernel through backward propagation, and output the complex feature maps of time-frequency feature extraction for each layer;

[0009] S4. Input the complex feature map into a convolutional neural network for high-level abstract feature extraction to obtain the fault diagnosis result of the gearbox.

[0010] Furthermore: In S1, the expression of the Gabor wavelet is specifically:

[0011]

[0012] where t is the time variable, is the time displacement, is the bandwidth, used to control the time domain width, is the center frequency, which determines the main oscillation frequency of the wavelet, is the phase, and j represents the imaginary part.

[0013] Furthermore: In S2, the method for performing the normalization operation on the wavelet kernel is specifically:

[0014] S21. Perform a discretization operation on the wavelet kernel, and expand it according to the real and imaginary parts to obtain the real and imaginary components of the wavelet kernel;

[0015] S22. Calculate the total energy of the real and imaginary components of the wavelet kernel at all discrete time points, and then calculate the normalization factor, and calculate the normalized wavelet kernel according to the normalization factor.

[0016] Furthermore: In S21, the real component and the imaginary component of the wavelet kernel are specifically expressed as:

[0017]

[0018]

[0019] In the formula, is a discrete time point, and its expression is specifically:

[0020]

[0021] In the formula, is the time interval, n is the number of discrete time points, is the wavelet kernel length, and L is the length of a single sample;

[0022]

[0023] .

[0024] Furthermore: In S22, the expression for calculating the total energy E of the real and imaginary components of the wavelet kernel at all discrete time points is specifically:

[0025]

[0026] The expression for calculating the normalization factor is specifically:

[0027]

[0028] In the formula, is a preset constant to prevent division by zero;

[0029] Calculate the real component of the normalized wavelet kernel and the imaginary component The expressions are specifically:

[0030]

[0031] .

[0032] Furthermore: In S3, during the forward propagation process, the output complex feature map of the (l + 1)-th layer of the wavelet neural network has the following expression:

[0033]

[0034] In the formula, is the real part of the output complex feature map of the (l + 1)-th layer, is the imaginary part of the output complex feature map of the (l + 1)-th layer;

[0035]

[0036]

[0037] In the formula, It is the feature of the vibration signal of the gearbox for the b-th sample and the c-th channel of the l-th layer input. K is the size of the convolution kernel. It is the floor function. It is the real part of the optimized wavelet kernel. It is the imaginary part of the optimized wavelet kernel.

[0038] Furthermore, in S3, the method for iteratively optimizing the wavelet kernel is specifically as follows:

[0039] Calculate the backpropagation gradient of the key parameters of the wavelet kernel according to the loss function, and iteratively update the key parameters of the wavelet kernel. Among them, calculating the backpropagation gradient of the key parameters of the wavelet kernel The specific expression is:

[0040]

[0041] In the formula, It is the loss function. It is the key parameter of the wavelet kernel. .

[0042] Furthermore, in S3, the specific expression for iteratively updating the center frequency is:

[0043]

[0044] In the formula, It is the learning rate. It is the center frequency of the m-th iterative update. It is the center frequency of the (m + 1)-th iterative update. It is the backpropagation gradient of the center frequency;

[0045]

[0046] In the formula, A1 is the intermediate term formula. , represents , which is the cosine term of the phase rotation caused by the center frequency and the time displacement , represents , which is the sine term of the same phase rotation;

[0047] The specific expression for iteratively updating the time displacement is:

[0048]

[0049] In the formula, It is the time displacement of the m-th iterative update. It is the time displacement of the (m + 1)-th iterative update. The backpropagation gradient for time displacement;

[0050]

[0051] The expression for iteratively updating the bandwidth is specifically:

[0052]

[0053] In the formula, is the bandwidth for the m-th iterative update, is the bandwidth for the (m + 1)-th iterative update, is the backpropagation gradient of the bandwidth;

[0054]

[0055] The expression for iteratively updating the phase is specifically:

[0056]

[0057] In the formula, is the phase for the m-th iterative update, is the phase for the (m + 1)-th iterative update, is the backpropagation gradient of the phase;

[0058] .

[0059] The beneficial effects of the present invention are:

[0060] (1) The present invention provides a gearbox fault identification method based on a Gabor wavelet neural network, which controls the wavelet function using four learnable wavelet kernel parameters, namely the center frequency, bandwidth, phase, and time displacement, and embeds the wavelet transform end-to-end into a deep network to realize the adaptive modeling of the time-frequency characteristics of the input signal. By automatically optimizing these parameters during the training process, the wavelet neural network can adaptively and accurately match various fault characteristics of the gearbox, significantly improving the resolution and accuracy of time-frequency analysis.

[0061] (2) The present invention realizes a dual-channel complex filtering mechanism, retains the complete phase information (real part + imaginary part) for complex-domain signal processing, and improves the sensitivity to early weak faults and transient impact characteristics in industrial fault diagnosis. This mechanism combines energy normalization processing to ensure the balanced contribution of high and low frequency components in the gearbox vibration signal during feature extraction, enhancing the model's ability to distinguish various gearbox fault modes.

[0062] (3) Experimental results show that in the experimental verification of the four datasets of BJTU-Dataset, HUST-Dataset, XJTU-Dataset, and THU-Dataset, the method of the present invention achieves a high accuracy rate of 96-99% on all datasets. The verification loss remains at a low level, demonstrating excellent generalization ability. Compared with other complex models, the method proposed by the present invention has a simple structure and still has a high accuracy rate. Especially in complex working conditions and different datasets, it has strong adaptability, and this method can still maintain a stable diagnostic accuracy rate, verifying its excellent performance.

[0063] (4) The method of the present invention demonstrates good generalization ability and robustness on different gearbox vibration datasets and fully utilizes the advantages of wavelet transform in non-stationary signal analysis, adaptively adjusting the time-frequency analysis parameters, overcoming the problems of insufficient frequency-domain modeling and loss of phase information of traditional CNN in time-varying signals such as vibration and acoustics, providing new ideas for industrial intelligent diagnosis. Description of the Drawings

[0064] Figure 1 It is a flow chart of a gearbox fault identification method based on a Gabor wavelet neural network. Specific Embodiments

[0065] The following describes the specific embodiments of the present invention to facilitate those skilled in the art of the present technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions created using the concept of the present invention are within the scope of protection.

[0066] As Figure 1 shown, in an embodiment of the present invention, a gearbox fault identification method based on a Gabor wavelet neural network includes the following steps:

[0067] S1. Input the gearbox vibration signal into the wavelet neural network to generate a Gabor wavelet, and transform the Gabor wavelet into a wavelet kernel controlled by the center frequency, bandwidth, phase, and time displacement.

[0068] S2. Adopt a dual-channel complex filtering mechanism to synchronously extract the real component and the imaginary component of the wavelet kernel, and perform a normalization operation on the wavelet kernel in combination with an energy normalization strategy to obtain a normalized wavelet kernel.

[0069] S3. In each layer of the wavelet neural network, perform time-frequency feature extraction through forward propagation according to the input wavelet kernel and the gearbox vibration signal, and perform iterative optimization on the wavelet kernel through backward propagation to output the complex feature maps of time-frequency feature extraction for each layer.

[0070] S4. Input the complex feature maps into a convolutional neural network for high-level abstract feature extraction to obtain the fault diagnosis result of the gearbox.

[0071] In S1, the expression of the Gabor wavelet is specifically:

[0072]

[0073] where t is the time variable, is the time shift, is the bandwidth, which is used to control the time-domain width, is the central frequency, which determines the main oscillation frequency of the wavelet, is the phase, and j represents the imaginary part.

[0074] In this embodiment, the Gabor wavelet is a complex-valued function. By decomposing it into the real part and the imaginary part, it can capture the in-phase (real part) and quadrature-phase (imaginary part) components of the signal respectively. This complex representation form makes the wavelet sensitive to phase information. For non-linear signal analysis, such as the vibration signal of a gearbox, because such fault features often manifest as phase modulation or phase jump.

[0075] In S2, the method for normalizing the wavelet kernel is specifically:

[0076] S21. Perform a discretization operation on the wavelet kernel, and expand it according to the real part and the imaginary part to obtain the real part component and the imaginary part component of the wavelet kernel;

[0077] S22. Calculate the total energy of the real part component and the imaginary part component of the wavelet kernel at all discrete time points, and then calculate the normalization factor. Calculate the normalized wavelet kernel according to the normalization factor.

[0078] In S21, the real part component and the imaginary part component of the wavelet kernel have the following specific expressions:

[0079]

[0080]

[0081] where is the discrete time point. In this embodiment, based on the above continuous Gabor wavelet function, the wavelet kernel is discretized into the same number of equally spaced points as the convolution kernel length. The expression of the discrete time point is specifically:

[0082]

[0083] where is the time interval, n is the number of discrete time points, is the wavelet kernel length, L is the length of a single sample;

[0084]

[0085] .

[0086] Among them, set L = kernel_size / 2, so as to ensure the discrete time point Symmetrically distributed in the interval In the above, no matter the wavelet kernel size is odd or even, center alignment is satisfied.

[0087] In S22, the expression for calculating the total energy E of the real and imaginary components of the wavelet kernel at all discrete time points is specifically:

[0088]

[0089] The expression for calculating the normalization factor is as follows:

[0090]

[0091] In the formula, is a preset constant to prevent division by zero;

[0092] Calculate the real part of the normalized wavelet kernel and the imaginary component The specific expression is:

[0093]

[0094] .

[0095] In this embodiment, the normalized wavelet kernel satisfies In wavelet neural networks, normalization can prevent the signal amplitude from being deviated due to the difference in wavelet kernel energy. and the imaginary component Normalization calculations can balance gradients, avoid parameter update oscillations, and resist input amplitude changes and numerical calculation problems.

[0096] In S3, wavelet neural networks are crucial in effectively capturing features of different frequencies and time scales in time series signal processing. Wavelet neural networks provide a unique method that combines wavelet analysis in traditional signal processing with deep learning, accurately extracts signal features through the time-frequency localization characteristics of Gabor wavelets, and automatically optimizes wavelet kernel parameters with the help of the end-to-end back-propagation mechanism of deep neural networks, achieving global feature adaptive learning from raw input to final output.

[0097] During the forward propagation process, for the input tensor of the wavelet neural network , where B is the batch size, C is the number of channels, and T is the time length, the output complex feature map of the (l + 1)-th layer of the wavelet neural network has the following specific expression:

[0098]

[0099] In the formula, is the real part of the output complex feature map of the (l + 1)-th layer, is the imaginary part of the output complex feature map of the (l + 1)-th layer;

[0100]

[0101]

[0102] In the formula, is the feature of the gearbox vibration signal of the b-th sample in the batch and the c-th channel of the input of the l-th layer, K is the convolution kernel size, ensures central alignment, is the floor function, is the real part of the optimized wavelet kernel, is the imaginary part of the optimized wavelet kernel, where the subscript r represents the real part and the subscript i represents the imaginary part.

[0103] In this embodiment, is the optimized wavelet kernel, .

[0104] In S3, the method for iteratively optimizing the wavelet kernel is specifically as follows:

[0105] Calculate the backpropagation gradient of the key parameters of the wavelet kernel according to the loss function, and iteratively update the key parameters of the wavelet kernel;

[0106] Among them, according to the chain rule, the expression for calculating the backpropagation gradient of the key parameters of the wavelet kernel is specifically as follows:

[0107]

[0108] In the formula, is the loss function, is the key parameter of the wavelet kernel, , and are the backpropagation gradients of the loss function for the real and imaginary components of the next layer of the normalized wavelet kernel, and They respectively refer to the gradient of the real part of the wavelet kernel with respect to the parameter and the gradient of the imaginary part of the wavelet kernel with respect to the parameter. According to the expression of the normalized wavelet kernel, the partial derivatives of the real part and the imaginary part of the wavelet kernel with respect to the parameter are specifically as follows:

[0109]

[0110]

[0111] Combined with the normalization factor, The expression of is shown as follows:

[0112]

[0113] According to the above results, the gradient of the key parameters of the wavelet kernel is calculated. The derivation steps of the gradient of each key parameter are specifically as follows:

[0114] The expression for iteratively updating the center frequency is specifically:

[0115]

[0116] In the formula, is the learning rate, is the center frequency of the m-th iterative update, is the center frequency of the (m + 1)-th iterative update, is the backpropagation gradient of the center frequency; the derivation steps of the backpropagation gradient of the center frequency are:

[0117] The partial derivative formula of the loss function with respect to is as follows:

[0118]

[0119] Among them, the real part kernel and the imaginary part kernel The partial derivative formula with respect to is shown as follows:

[0120]

[0121]

[0122] and are the unnormalized real and imaginary part kernels respectively, and their solution processes are as follows:

[0123]

[0124]

[0125] Since the gradient magnitude and the time displacement is proportional. For the gradient formula of the unnormalized factor, the corresponding linear weight needs to be introduced. Then, the gradient of the normalized factor with respect to frequency is:

[0126]

[0127] Substitute , and into the real part kernel and the imaginary part kernel in the partial derivative formula with respect to to obtain the backpropagation gradient of the center frequency ;

[0128]

[0129] In the formula, A1 is the intermediate term formula, , represents , which is the cosine term of the phase rotation caused by the center frequency and the time shift ; represents , which is the sine term of the same phase rotation;

[0130] The specific expression for the iterative update of the time shift is:

[0131]

[0132] In the formula, is the time shift of the m-th iterative update, is the time shift of the (m + 1)-th iterative update, is the backpropagation gradient of the time shift; The derivation steps of the backpropagation gradient of the time shift are:

[0133] The time shift determines the position of the wavelet on the time axis. The gradient reflects the signal alignment error, and the process of its gradient derivation is:

[0134]

[0135] Among them, the real part kernel and the imaginary part kernel The partial derivative process with respect to is as follows:

[0136]

[0137]

[0138] and They are the unnormalized real and imaginary parts of the kernel, and the solution process is shown in the formula:

[0139]

[0140]

[0141] The partial derivative of the normalization factor N with respect to the parameter is shown in the formula:

[0142]

[0143] Substitute the formulas of formula , and into formula to get:

[0144]

[0145] The expression for iteratively updating the bandwidth is specifically:

[0146]

[0147] In the formula, is the bandwidth of the m-th iterative update, is the bandwidth of the (m + 1)-th iterative update, is the backpropagation gradient of the bandwidth; the derivation steps of the backpropagation gradient of the bandwidth are:

[0148] When directly optimizing the bandwidth , it is necessary to ensure that σ > 0 (because the bandwidth must be a positive number). At the same time, when converting the gradient from space to space, a scaling factor needs to be multiplied. This is because 's change has a multiplicative relationship (rather than an additive relationship) with . When is very small , will be shrunk to avoid too large an optimization step; when is relatively large, the gradient is amplified accordingly to accelerate convergence. Then is parameterized as:

[0149] The process of its gradient derivation is shown in the formula:

[0150]

[0151] Among them, the real part of the kernel and the imaginary part of the kernel The partial derivative with respect to is shown in the formula:

[0152]

[0153]

[0154] and are the unnormalized real and imaginary parts of the kernel, respectively. The solution process is shown in the formula:

[0155] The partial derivative of the normalization factor N with respect to the parameter is shown in the formula:

[0156]

[0157] Similarly, substituting the above into the formula, we get:

[0158]

[0159] The specific expression for iteratively updating the phase is:

[0160]

[0161] In the formula, is the phase of the m-th iterative update, is the phase of the (m + 1)-th iterative update, is the backpropagation gradient of the phase; the derivation steps of the backpropagation gradient of the phase are:

[0162] This part associates the local changes in the time-frequency characteristics of the signal (through ) with the global loss function (through ) to ensure that the physical meanings of the normalization constraint and bandwidth adjustment are taken into account simultaneously when updating the parameters.

[0163] When analyzing the phase parameter of the wavelet transform, the calculation of its gradient needs to consider the sensitivity of the orthogonal components of the complex signal to the phase change simultaneously. The phase gradient reflects the influence of the small phase shift of the signal in the time-frequency domain on the overall waveform and is one of the key parameters for optimizing the time-frequency analysis model. The calculation process is shown in the formula:

[0164]

[0165] Among them, the partial derivatives of the real part kernel and the imaginary part kernel with respect to are shown in the formula:

[0166]

[0167]

[0168] and are the unnormalized real and imaginary parts of the kernel, respectively. The solution process is shown in the formula:

[0169]

[0170]

[0171] The partial derivative of the normalization factor N with respect to is shown in the formula:

[0172]

[0173] When optimizing the phase the total gradient is obtained by aggregating the responses of the real and imaginary components of the signal at all time points to the phase change. This gradient directly reflects the overall impact of the phase shift on the loss function. Similarly, substituting the above formula into formula, we get:

[0174]

[0175] In this embodiment, the gradient calculation of the four key parameters forms a complete optimization framework. The gradient of each parameter is decomposed into the product of the sensitivity of the loss function to the real and imaginary parts of the signal and the response of the signal component to the parameter change through the chain rule, and finally the global gradient aggregation is realized through the summation in the time dimension. This process not only unifies the mathematical representation of time-frequency domain features, but also precisely captures the complex dependence of the signal energy distribution and waveform morphology on parameter adjustment through the coupled calculation of the normalization factor, phase rotation term and Gaussian window function, laying a theoretical foundation for the end-to-end optimization of the model.

[0176] To verify the effectiveness of the gearbox fault identification method (AGWCN) based on Gabor wavelet neural network proposed in the present invention, this embodiment also provides data description, ablation experiments, and comparative experiments. To comprehensively evaluate the model performance, the present invention uses five evaluation metrics for quantitative analysis: ACC = (TP + TN) / (TP + TN + FP + FN) is used to measure the overall classification accuracy of the model; PRE = TP / (TP + FP) evaluates the accuracy of predicting positive class samples; Recall = TP / (TP + FN) reflects the integrity of the model in identifying positive class samples; F1-score = 2×(PRE × Recall) / (PRE + Recall) is used as the harmonic mean of precision and recall to balance the weights of the two; MAP = (1 / N)×Σ(APi) evaluates the multi-classification performance by calculating the mean of the average precisions of each class. These metrics evaluate the classification performance of the model from different perspectives and provide an objective evaluation criterion for the optimization of the algorithm.

[0177] (1) Data description:

[0178] As a key component in the mechanical transmission system, the health status monitoring of the gearbox is crucial for ensuring the safe operation of the equipment. To verify the effectiveness of the method proposed in the present invention for gearbox faults, the present invention conducts experiments on four public gearbox fault diagnosis datasets: The THU-Dataset dataset contains multi-mode fault data under time-varying rotational speed and time-varying load conditions; The HUST-Dataset dataset collects vibration signals of three health states (normal, tooth breakage, and tooth defect) under four different rotational speed conditions; The BJTU-Dataset dataset contains fault data of a wind turbine planetary gearbox under various working conditions; The XJTU-Dataset dataset provides various fault type data of planetary gearboxes and ordinary gearboxes.

[0179] The characteristics of these datasets are as follows: (1) They cover common gearbox fault types, including gear surface wear, tooth defect, root crack, and tooth breakage, etc.; (2) They contain multi-modal signals under constant working conditions and continuously varying working conditions, which are closer to industrial application scenarios; (3) Multiple datasets provide signal acquisition from multiple sensors and multiple directions, facilitating signal fusion research; (4) Some datasets also contain compound fault situations, such as bearing-gear simultaneous faults. The detailed introduction of the datasets is shown in Table 1.

[0180] Table 1 Detailed introduction of the datasets

[0181]

[0182] (2) Ablation experiments:

[0183] To verify the effectiveness of wavelet kernels of different sizes and the impact of the number of wavelet layers on the performance of the proposed network, this experiment was tested on four public datasets, and the results are shown in Tables 2 and 3.

[0184] Table 2 Evaluation of various indicators at different resolutions

[0185]

[0186] Experimental data shows that in the tests of the HUST-Dataset, BJTU-Dataset, XJTU-Dataset, and THU-Dataset datasets, using multi-size wavelet kernels (K = 64 & 16) and a single kernel size setting brought significant improvements. Compared with K = 16, the multi-scale wavelet kernel increased the accuracy of HUST-Dataset by about 24%; the accuracy of BJTU-Dataset by about 3.5%; the accuracy of XJTU-Dataset by about 1.6%; the accuracy of THU-Dataset by about 17%, and the MAP increased by about 6%. Compared with K = 64, the hybrid configuration also had obvious improvements, with an increase in accuracy of about 1.9% in the HUST-Dataset, about 7.2% in the BJTU-Dataset, about 4.8% in the XJTU-Dataset, and about 12.2% in the THU-Dataset. These results indicate that the hybrid kernel size can capture features of different scales simultaneously, combining the advantages of K = 16 in fine-grained feature extraction and K = 64 in global feature extraction, effectively improving the model performance.

[0187] Table 3 Influence of wavelet neural network layers on performance

[0188]

[0189] It can be seen from the data in Table 3 that using a two-layer wavelet convolution structure has achieved better classification performance on most datasets. For example, on the THU-Dataset, the ACC increased from 85.92% in one layer to 96.42% in two layers, with an increase of 12.23%; on the HUST-Dataset, it increased from 95.44% to 97.22%, an increase of 1.87%; on the XJTU-Dataset, it increased from 97.13% to 98.73%, an increase of 1.65%. The performance gain in this stage is obvious, indicating that the multi-scale feature extraction ability of wavelet convolution has been well reflected in the two-layer structure.

[0190] However, when the structure is expanded from two layers to three and four layers, although the network complexity (such as the number of parameters and the amount of computation) increases exponentially - taking the superposition of the number of convolutional kernels and the dimension of feature maps per layer as an example, the structural complexity of the three-layer is approximately 1.5 - 2 times higher than that of the two-layer, and the four-layer is 3 - 4 times higher - the performance improvement is relatively limited. For example, on the HUST-Dataset, the ACC of the three-layer and four-layer only increases from 97.22% to 97.33% and 98.89% respectively, with improvements of 0.11% and 1.67%; on the BJTU-Dataset, the ACC only increases by 0.87% between the two-layer and four-layer, almost reaching performance saturation; on the THU-Dataset, the gap between the three-layer, four-layer and two-layer is no more than 0.33%.

[0191] In summary, the two-layer wavelet convolution achieves a better balance between performance and complexity, avoiding unnecessary model bloat while obtaining significant performance improvements. The benefits brought by further increasing the number of layers are far less than the computational overhead and overfitting risks they bring, and the cost performance drops significantly. Therefore, from the perspective of deep learning model design, adopting a two-layer wavelet convolution structure is more practical and valuable for engineering promotion.

[0192] (3) Comparative experiments:

[0193] To verify the effectiveness of the proposed method, this paper selects four current mainstream fault diagnosis methods for comparison. Yan et al. proposed a coarse-to-fine dual-scale time-frequency attention fusion network, and the key innovation is the introduction of a signal-to-image coding unit containing an improved constant-Q non-stationary Gabor transform, which effectively extracts the time-frequency features of vibration and acoustic multi-modal signals. Zhang et al. proposed a feature fusion Transformer based on time segments (FFTR), which effectively integrates multi-modal sensor information through segmented feature extraction and time-aligned fusion strategies, and uses Transformer to achieve global feature modeling and high-precision fault classification, improving the comprehensiveness and accuracy of mechanical fault diagnosis. Zhang et al. proposed a multi-modal data cross-domain fusion network (MCAN-T) that fuses vibration signals and thermal images, which effectively improves the fault diagnosis robustness and generalization ability of gearboxes under different working conditions through one-dimensional and two-dimensional convolutional feature extraction, maximum mean discrepancy alignment, and cross-modal consistency learning. Hua et al. proposed a multi-sensor residual convolution fusion network (MRCFN), which realizes multi-source feature extraction by coupling convolutional pooling modules and double-loop residual modules, and introduces a spatial channel reconstruction and global interactive fusion mechanism, which has a good effect on multi-channel data classification. The test results of the above four methods and the method proposed in this invention on four datasets are shown in Table 4.

[0194] Table 4 Results of comparing different methods

[0195]

[0196] Experimental results show that AGWCN demonstrates significant performance advantages on all four datasets, especially on the BJTU-Dataset and XJTU-Dataset with extremely different data complexities. In the BJTU-Dataset, AGWCN achieves an accuracy of 99.60%, which is 2.07% higher than that of MCAN-T. While on the most challenging XJTU-Dataset, AGWCN maintains a high accuracy of 98.73%, far exceeding 40.13% of MRCFN. This stable high performance across datasets is attributed to the unique feature extraction mechanism and stronger model generalization ability of AGWCN, enabling it to effectively process data with different distribution characteristics and still maintain robust classification accuracy when facing complex data with non-linear relationships, which is of great significance for processing multi-source heterogeneous data in practical application scenarios.

[0197] In summary, the present invention provides a gearbox fault identification method based on the Gabor wavelet neural network, which deeply integrates wavelet transform with a deep neural network, enhancing the ability to model key features such as frequency and phase in non-stationary fault signals while maintaining the end-to-end training ability. By designing parametric Gabor wavelets, the convolutional kernel is transformed into a learning wavelet function controlled by center frequency, bandwidth, phase, and displacement parameters, realizing the adaptive optimization of the wavelet kernel. At the same time, the implemented dual-channel complex filtering mechanism retains the complete phase information and improves the sensitivity to weak fault and transient impact features. In the experimental verification on the BJTU-Dataset, HUST-Dataset, XJTU-Dataset, and THU-Dataset, the AGWCN model achieves high accuracies of 96 - 99% on all datasets, and the validation loss continuously remains at a low level, showing superior generalization ability. Compared with other complex models, the structure proposed in the present invention is simple and still has a relatively high accuracy. Especially in complex working conditions and different datasets, it has strong adaptability, and this method can still maintain a stable diagnostic accuracy, verifying its superior performance. Experimental results show that such a network architecture based on signal processing theory presents significant performance advantages in mechanical fault diagnosis tasks compared to the traditional CNN that simply migrates image processing methods to the signal field, providing a more professional and effective methodological basis for the application of deep learning in the field of signal processing.

[0198] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by terms such as "center", "thickness", "upper", "lower", "horizontal", "top", "bottom", "inner", "outer", "radial", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus cannot be understood as a limitation to the present invention. In addition, the terms "first", "second", and "third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the number of technical features. Therefore, the features defined by "first", "second", and "third" may explicitly or implicitly include one or more of such features.

Claims

1. A gearbox fault identification method based on a Gabor wavelet neural network, characterized in that, It includes the following steps: S1. Input the vibration signal of the gearbox into the wavelet neural network to generate Gabor wavelets, and transform the Gabor wavelets into wavelet kernels controlled by the center frequency, bandwidth, phase, and time shift; S2. Adopt a two-channel complex filtering mechanism to synchronously extract the real component and the imaginary component of the wavelet kernel, and perform a normalization operation on the wavelet kernel in combination with the energy normalization strategy to obtain the normalized wavelet kernel; S3. In each layer of the wavelet neural network, perform time-frequency feature extraction according to the input wavelet kernel and the gearbox vibration signal through forward propagation, and perform iterative optimization on the wavelet kernel through backpropagation, and output the complex feature maps of time-frequency feature extraction for each layer; S4. Input the complex feature map into a convolutional neural network for high-level abstract feature extraction to obtain the fault diagnosis result of the gearbox.

2. The gearbox fault identification method based on Gabor wavelet neural network according to claim 1, wherein In S1, the expression of the Gabor wavelet is specifically: where t is the time variable, is the time displacement, is the bandwidth, which is used to control the time domain width, is the center frequency, which determines the main oscillation frequency of the wavelet, is the phase, and j represents the imaginary part.

3. The gearbox fault identification method based on the Gabor wavelet neural network according to claim 2, wherein In S2, the method for performing the normalization operation on the wavelet kernel is specifically: S21. Perform a discretization operation on the wavelet kernel, and expand it according to the real and imaginary parts to obtain the real component and the imaginary component of the wavelet kernel; S22. Calculate the total energy of the real component and the imaginary component of the wavelet kernel at all discrete time points, and then calculate the normalization factor, and calculate the normalized wavelet kernel according to the normalization factor.

4. The gearbox fault identification method based on the Gabor wavelet neural network according to claim 3, characterized in that, In S21, the real part component of the wavelet kernel and the imaginary part component are specifically expressed as follows: wherein, is a discrete time point, and its expression is specifically: wherein, is the time interval, n is the number of discrete time points, is the wavelet kernel length, and L is the length of a single sample; 。 5. The gearbox fault identification method based on the Gabor wavelet neural network according to claim 4, characterized in that, In S22, the expression for calculating the total energy E of the real component and the imaginary component of the wavelet kernel at all discrete time points is specifically: The expression for calculating the normalization factor is specifically: In the formula, is a preset constant to prevent division by zero; Calculate the real part component of the normalized wavelet kernel and the imaginary part component The specific expressions are as follows: 。 6. The gearbox fault identification method based on the Gabor wavelet neural network according to claim 5, characterized in that, In S3, during the forward propagation process, the output of the (l + 1)-th layer of the wavelet neural network is a complex feature map and its specific expression is as follows: wherein, is the real part of the complex feature map output by the (l + 1)-th layer, is the imaginary part of the complex feature map output by the (l + 1)-th layer; wherein, is the feature of the gearbox vibration signal of the b-th sample and the c-th channel input in the l-th layer, K is the convolution kernel size, is the floor function, is the real part of the optimized wavelet kernel, is the imaginary part of the optimized wavelet kernel.

7. The gearbox fault identification method based on the Gabor wavelet neural network according to claim 6, characterized in that, In S3, the method for performing iterative optimization on the wavelet kernel is specifically: Calculate the backpropagation gradient of the key parameters of the wavelet kernel according to the loss function, and iteratively update the key parameters of the wavelet kernel. Among them, calculating the backpropagation gradient of the key parameters of the wavelet kernel The specific expression is: In the formula, is the loss function, is the key parameter of the wavelet kernel, .

8. The gearbox fault identification method based on the Gabor wavelet neural network according to claim 7, characterized in that, In S3, the expression for iteratively updating the center frequency is: In the formula, is the learning rate, is the center frequency updated at the m-th iteration, is the center frequency updated at the (m + 1)-th iteration, is the backpropagation gradient of the center frequency; where, A1 is the intermediate term formula, , represents , which is the cosine term of the phase rotation caused by the center frequency and time displacement , and represents , which is the sine term of the same phase rotation; The expression for iteratively updating the time shift is: wherein, is the time displacement updated at the m-th iteration, is the time displacement updated at the (m + 1)-th iteration, is the backpropagation gradient of the time displacement; The expression for iteratively updating the bandwidth is: In the formula, is the bandwidth updated at the m-th iteration, is the bandwidth updated at the (m + 1)-th iteration, is the backpropagation gradient of the bandwidth; The expression for iteratively updating the phase is: wherein, is the phase updated at the m-th iteration, is the phase updated at the (m + 1)-th iteration, is the backpropagation gradient of the phase; 。

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