A method for interpretable extraction of shock fault features based on algorithm-guided network

Abstract

The present invention discloses an interpretable extraction method for impact fault features based on an algorithm-guided network, comprising the following steps: constructing an impact fault simulation signal according to a mechanism signal model, truncating the signal into samples and dividing the data sets into training and test data sets; designing an impact fault precise reconstruction algorithm based on a wavelet transform algorithm framework to extract impact features submerged by strong noise; building an intrinsically interpretable convolutional sparse autoencoder and designing an interpretable channel attention module to screen qualified intrinsic modes; training the proposed network using gradient descent backpropagation and assigning different learning rates to it according to training parameters so that the network can adaptively identify intrinsic mode parameters of various orders in the signal; inputting test set samples into the proposed network to obtain recognition results of the impact fault features and training parameters, performing Hilbert envelope demodulation on the features to obtain an envelope spectrum, and further enhancing the credibility of the network output by analyzing and verifying the fault impact and its characteristic frequency.

Description

Technical Field

[0001] The present invention belongs to the field of mechanical intelligent fault diagnosis and signal processing, and particularly relates to a method for interpretable extraction of impact fault features based on an algorithm-guided network. Background Art

[0002] Rolling bearings are essential components in mechanical systems and are widely used in industries such as aerospace and energy. Rolling bearings often operate under harsh conditions, such as high speeds and heavy loads, making them prone to failure. Failure to accurately predict or diagnose these failures can severely impact the normal operation of industrial equipment and even lead to serious accidents, resulting in significant casualties and property damage.

[0003] With the rise of artificial intelligence (AI) technology, data-driven fault diagnosis methods, particularly those based on deep learning, have developed rapidly. By designing different learning methods and deep structures, neural networks can extract features while maintaining satisfactory fault classification accuracy. Convolutional autoencoders (CAEs) combine the architectures of autoencoders and convolutional neural networks, integrating the advantages of both in feature learning. Consequently, in recent years, a growing number of researchers have begun to study how to use CAEs to more effectively extract features from vibration signal inputs.

[0004] While these approaches have rapidly propelled deep learning to become a powerful fault diagnosis technique, they come at a significant cost: deep network structures lead to weaker interpretability. These models' decisions are difficult to understand through fault diagnosis before fully convincing users. However, the demands of industrial applications have prompted scholars to conduct interpretability research on basic deep learning models.

[0005] Post-hoc interpretability analysis aims to reveal and explain how a constructed network makes decisions, transforming hidden features into human-understandable objects. Related research has shown that this method effectively provides a basis for model output while maintaining performance. However, its effectiveness is limited to the input neighborhood, i.e., the boundaries of interpretability. This means that this method is sometimes unreliable and may even produce misleading outputs, highlighting the importance of making deep learning models interpretable in terms of both principle and structure.

[0006] Ex ante interpretability analysis involves designing a human-understandable network structure based on a priori assumptions. A leading approach is to integrate wavelet transforms into network structures, such as replacing the convolution kernels of the first convolutional layer in convolutional neural networks with Morlet and lifting wavelets. While features extracted from shallow layers in these models are understandable, the network's deeper structure and features remain opaque. Furthermore, numerous parameters and hyperparameters require training and tuning. A priori failure mechanisms for these networks are also unknown, making their structures and extracted features difficult to physically explain.

[0007] From a signal processing perspective, to optimize wavelet transform extraction, a wavelet basis with a waveform that most closely resembles the shock signature should be selected. From a fault mechanism perspective, the shock signature signal model of a rolling bearing is a superposition of several Laplace wavelets with specific scale parameters. Therefore, using Laplace wavelets for transformation and reconstruction theoretically allows for more accurate extraction of shock faults. However, in practice, this wavelet lacks properties such as orthogonality. Therefore, directly reconstructing the shock fault signature using a discrete Laplace wavelet transform will result in amplitude distortion, reducing the effectiveness of feature extraction. Furthermore, the number of Laplace wavelets and their parameters significantly influence the effectiveness of the shock signature, and their selection is a challenge that needs to be addressed.

[0008] A rolling bearing fault diagnosis method based on LMD decomposition and GWO-PNN (CN 2 02310394543.5) built a probabilistic neural network, which pre-processed each sample through LMD decomposition and KPCA dimensionality reduction, and then input the pre-extracted reconstructed feature vector into the probabilistic neural network to realize fault classification. However, in the above invention, the process and output of feature pre-extraction lack physical meaning, and the mechanism by which the network extracts its abstract features and uses them for classification cannot be explained by prior knowledge in the diagnosis field. Its classification results will lack basis and are unreliable. On the other hand, the present invention designs a neural network with a signal processing algorithm as the skeleton. The output of the network is the reconstructed impact feature. Its extraction process can be interpreted as the process of wavelet transform and wavelet reconstruction, and its learning process can be interpreted as the identification process of the inherent mode of the rolling bearing system, which has clear physical meaning. The interpretability of the proposed network structure and other aspects provides theoretical support for the quality of network performance, and the output of the network is credible and controllable. Summary of the Invention

[0009] To address the problems of the prior art, the present invention proposes a method for interpretable extraction of shock fault features based on an algorithm-guided network, using a Laplace wavelet kernel convolutional sparse auto-encoder (LW-CSAE). This method combines a shock fault mechanism signal model with wavelet transform and reconstruction techniques. First, a sparse Laplace wavelet reconstruction algorithm is derived and designed to accurately reconstruct shock features by addressing the problem of correcting amplitude distortion. Second, the proposed algorithm is used to guide the construction of a physically meaningful Laplace wavelet kernel convolutional sparse auto-encoder. Network training is then used to adaptively optimize the number and parameters of Laplace wavelets, ultimately enabling robust and reliable extraction of shock fault features from strong noisy signals.

[0010] The present invention is achieved through at least one of the following technical solutions.

[0011] The method for extracting interpretable shock fault features based on an algorithm-guided network includes the following steps:

[0012] Step 1. Construct a data set: Construct a simulation signal of the same-position impact fault based on the rolling bearing impact fault response signal mechanism model, add Gaussian white noise to simulate the interference component of the actual signal, and then cut the signal into multiple samples of the same length, and divide the samples into training data sets. and test dataset Where R and S are the number of samples in the training dataset and the test dataset respectively;

[0013] Step 2: Based on wavelet transform, a sparse Laplace wavelet reconstruction algorithm is derived and established to accurately reconstruct the impact fault characteristics. The algorithm includes two parts: wavelet transform and wavelet reconstruction. By designing the amplitude correction coefficient and the transition band correction coefficient, the transformation and reconstruction results are multiplied by the obtained coefficients.

[0014] Step 3: Using the sparse Laplace wavelet reconstruction algorithm as the kernel, construct a Laplace wavelet kernel convolution sparse autoencoder, including an encoder layer, an intermediate layer, and a decoder layer. Each layer has multiple channels corresponding to the excited modes of the identified impulse response. The encoder layer performs a Laplace wavelet transform on the input signal at a sparse scale and performs amplitude correction accordingly according to the sparse Laplace wavelet reconstruction algorithm. The intermediate layer corresponds to the wavelet coefficients of different modes. The decoder layer uses the Laplace wavelet, correction coefficient, and channel screening to output the impulse characteristics of the output of the intermediate layer.

[0015] Step 4: Input the training samples of the training data set into the Laplace wavelet kernel convolution sparse autoencoder, perform training based on the reconstruction loss of the shock feature, and use gradient descent backpropagation to update the Laplace wavelet parameters and channel screening weight parameters. This allows the model to learn the number of the sparsest wavelet bases and the parameters of the optimal wavelet base from the samples, thus achieving adaptive and robust extraction of similar shock faults.

[0016] Step 5: Input the test samples of the test data set into the trained network for testing to obtain the extracted impact fault features.

[0017] Furthermore, the simulation signal x(t) of the impact fault in step 1 is based on the rolling bearing impact fault response signal model x f (t) is constructed, taking into account the fact that the actual measured signal also has a frequency of the shaft rotation frequency f r and its harmonic components x rot (t) and background noise η(t), the input simulation signal is set to:

[0018] x(t)=x f (t)+x rot (t)+η(t) (1)

[0019] Where t is the time variable, and the shaft rotation component only takes the first-order frequency, that is, x rot (t)=sin(2πf r t), and at the same time, for the impact failure occurring in the inner ring of the rolling bearing, the impact response amplitude A i (t) will also be affected by f r The modulation, that is

[0020]

[0021] Where a i,j is the modulation amplitude of the j-th order frequency conversion component, and only the first-order frequency conversion modulation is considered.

[0022] Furthermore, in step 1, the sampling frequency f is set s The simulation signal is sampled to obtain a discrete signal x, which is truncated to obtain a sample with M sampling points in the R+S segment, and divided into training data sets according to the ratio and test dataset

[0023] Furthermore, in the sparse Laplace wavelet reconstruction algorithm of step 2, the Laplace wavelet is selected As a wavelet basis, it is the unit impulse response of the second-order underdamped linear time-invariant system, and its expression is:

[0024]

[0025] Where t is the time variable, and the modal parameters of the system include the natural frequency ω d and damping ratio ζ as the scale parameter of the wavelet, τ as the time shift parameter of the wavelet, and u(t) is the step function.

[0026] Furthermore, in step 2, the amplitude correction after the sparse Laplace wavelet transform includes: simulating that the Laplace wavelet kernel w(t) and the impulse fault characteristic signal f(t) both have the same natural frequency value ω d,0 and damping ratio ζ0, and set the impact time of signal f(t) τ0 = 0.2s, that is,

[0027]

[0028] and

[0029]

[0030] Where t is the time variable, u(t) is the step function, Take ω as the scale parameter d,0 and Laplace wavelet when ζ0, T is the support length of the wavelet; the signal f(t) is discretely Laplace transformed using w(t) to obtain the original wavelet coefficients, and the discrete value W[n] of the original wavelet coefficients corresponding to the nth sampling point is obtained, that is:

[0031]

[0032] Where f[n+i] is the discrete value of f(t) corresponding to the n+i-th sampling point, and w[i] is the discrete value of w(t) corresponding to the i-th sampling point. Multiply W[n] by the amplitude correction coefficient C0, which is calculated as follows:

[0033] C0=2 / N (7) Where N = T / f s is the sampling length of the discrete Laplace wavelet kernel, f s is the sampling frequency; at the same time, in order to compensate for the influence of the unilateral exponential window on the amplitude attenuation, the amplitude correction coefficient C1(ω d ,ζ), the expression of the coefficient is:

[0034]

[0035] C1(ω d ,ζ) is obtained by numerical integration, ω d is the natural frequency, and ζ is the damping ratio.

[0036] Furthermore, in step 2, the transition band correction before and after the sparse Laplace wavelet reconstruction is performed, which includes: in the process of performing the inner product of the shorter Laplace wavelet with non-zero value interval relative to the longer original signal at the time shift τ, the region where the amplitude of the inner product of the two is distorted due to the Laplace wavelet not completely moving into the non-zero region of the original signal is called the transition band; in the transition band (n0-1-N) / f s ≤τ<n0 / f s In the above, N is the sampling length of the discrete wavelet, n0 is the sampling time point corresponding to the impact time τ0 of the signal f(t), the original signal is 0, but after the discrete Laplace wavelet transform, it produces a non-zero value that does not actually exist. Therefore, the original wavelet coefficient discrete value W[n] is multiplied by the zero coefficient C2[n;n0] to perform transition band correction. The coefficient is expressed as:

[0037]

[0038] Corrected wavelet coefficient discrete value W C [n] is:

[0039] W C [n] = C0·C1(ω d ,ζ)·C2[n;n0]·W[n] (10)

[0040] To W C [n] combines w[n] and the following formula to reconstruct the original shock characteristics, and perform amplitude correction and transition band correction at the same time to obtain the reconstructed characteristic discrete value x r [n], that is:

[0041]

[0042] Where W C [i] is the discrete value of the corrected wavelet coefficient corresponding to the i-th sampling point, w[N-1-i] is the discrete value of the Laplace wavelet kernel corresponding to the N-1-i-th sampling point, and C3 is the amplitude and transition band correction coefficient, which is expressed as:

[0043] C3=2 / N′[n] (12)

[0044] Where N'[n] is x r [n] The number of sampling points of the discrete Laplace wavelet kernel that effectively participates in the reconstruction at the nth point, expressed as:

[0045]

[0046] For the original shock signal containing multiple intrinsic modal components, the same number of Laplace wavelets with the same intrinsic modal parameters are used to input the sparse Laplace wavelet reconstruction algorithm to reconstruct the corresponding shock components x r,i[n], and superimpose them to obtain the discrete value of the reconstructed feature, that is, the final reconstructed feature, that is:

[0047]

[0048] Furthermore, the encoder includes a convolutional layer and a singly connected layer. The convolutional layer uses Laplace wavelet as a convolution kernel to perform wavelet transform. The product of amplitude correction coefficients C0 and C1 is used as a weight coefficient in the singly connected layer. The bias vector is discarded. Each channel of the encoder outputs a set of amplitude-corrected wavelet coefficients.

[0049] The decoder includes a wavelet reconstruction layer and an interpretable channel attention module. The wavelet reconstruction layer contains a transposed convolution operation and transition band correction coefficients C2 and C3, which realizes the accurate reconstruction of the components contained in each channel of the impact feature. The interpretable channel attention module is a fully connected layer that removes the bias vector and shares an attention weight coefficient w in the same channel. After weighted summation and superposition, the reconstructed value of the impact feature is obtained as the output of the Laplace wavelet kernel convolution sparse autoencoder.

[0050] Furthermore, the only trainable parameters of the Laplace wavelet kernel convolutional sparse autoencoder are the natural frequency of each channel, the damping ratio, and the weight parameters in the interpretable channel attention module.

[0051] Furthermore, in order to enable the Laplace wavelet kernel convolution sparse autoencoder to adaptively search for the same number of natural modes as the impact fault input, the natural modes in the low-frequency region of a general rolling bearing are considered, and the number is set to Q. The number of channels of the convolution sparse autoencoder C>Q is set. Through training, the channels that can correctly identify a certain order of natural modes contained in the signal are adaptively selected to achieve sparse reconstruction. In the reconstruction experience loss L E Add sparse regularization term L on the basis R , using mean square error (MSE) loss and l1 norm as the metrics of the two respectively, the total loss function L of the Laplace wavelet kernel convolution sparse autoencoder is expressed as:

[0052]

[0053] Where ε is a hyperparameter, x f [n] is the impact characteristic simulation signal x corresponding to the nth sampling point f The discrete value of (t), w c is the attention weight of the cth channel, M is the number of samples, x r [n] is the final reconstructed feature.

[0054] Furthermore, in step 4, the weight w of L for the cth channel is calculated based on the chain rule cPartial derivative of Right now

[0055]

[0056] and the Laplace wavelet kernel ψ of the cth channel c The trainable parameters (·) in c The discrete value of the partial derivative Right now

[0057]

[0058] Where, (·) c Including the natural frequency ω d,c and damping ratio ζ c , ψ c Discrete values ​​of partial derivatives of both and Calculated by the following two formulas:

[0059]

[0060]

[0061] Where Δt is the time domain sampling interval, and the sampling frequency is Δt = 1 / f s Find, f s is the sampling frequency; different learning rates are used for different parameters, and the learning rate α of the damping ratio and natural frequency is ζ and The following constraints apply:

[0062]

[0063] Where, D(O(ω d )) indicates that the frequency is of the same order of magnitude as the natural frequency O(ω d ) constant; each parameter is updated during the network training process by calculating the partial derivative of each parameter and then back-propagating.

[0064] Furthermore, the output of the test set in step 5 is demodulated by Hilbert envelope to obtain an envelope spectrum, verifying that the reconstructed features contain prominent fault characteristic frequencies. At the same time, combined with the identification of network parameters, the reliability of the output results is confirmed so that they can be applied to the diagnosis of impact faults.

[0065] Compared with the prior art, the present invention has at least the following beneficial effects:

[0066] 1. The present invention combines the impact fault mechanism and the wavelet transform algorithm framework to derive and design a new method for high-precision sparse reconstruction of impact fault features using Laplace wavelet. This method can extract the submerged impact fault features from strong background noise.

[0067] 2. The present invention constructs an intrinsically interpretable neural network for the extraction of impact faults, called the Laplace wavelet kernel convolutional sparse autoencoder. The network is constructed under the guidance of the impact fault reconstruction algorithm. Its structure, characteristics, learning process and output are all interpretable. Its extraction process can be interpreted as the process of wavelet transform and wavelet reconstruction, and its learning process can be interpreted as the process of identifying the inherent modes of the rolling bearing system. The output of the network is the reconstructed impact fault characteristics, which provides theoretical support for the quality of network performance.

[0068] 3. The present invention designs an interpretable channel attention module, which configures trainable weights in each channel, so that the network can adaptively extract the number of inherent modes from various impact fault signals.

[0069] 4. This invention employs a training method that uses network parameters with clear physical meaning. This significantly reduces the number of trainable parameters in the designed neural network compared to traditional deep neural network models, and all parameters possess clear physical meaning. Learning rate constraints are then applied to the different training parameters, ensuring convergence in the model training process. Furthermore, by training the intrinsic modal parameters, the network can adaptively extract impact fault characteristics.

[0070] 5. The present invention provides a basis for model decision-making, combines the identification process and situation of training parameters, and provides a profound explanation of the performance of the neural network, further enhancing the reliability of the network output. It provides a credible attempt for the application of deep learning models in industrial scenarios and has certain engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 is an overall flow chart of the impact fault feature extraction according to an embodiment of the present invention;

[0072] Figure 2 1 is a flow chart of a sparse Laplace wavelet reconstruction algorithm according to an embodiment of the present invention;

[0073] Figure 3 is a structural diagram of a Laplace wavelet convolutional sparse autoencoder according to an embodiment of the present invention;

[0074] Figure 4 This is a comparison diagram of test loss curves of an embodiment of the present invention;

[0075] Figure 5 is a diagram of the identification process of training parameters according to an embodiment of the present invention;

[0076] Figure 6 3 is a comparison diagram of the effects of extracting impact features in a noisy situation according to an embodiment of the present invention. DETAILED DESCRIPTION

[0077] In order to make the technical solutions and purposes of the present invention more clearly understood, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific implementation steps described herein are only used to better illustrate the application of the present invention, but the technical features involved in the implementation methods of the present invention are not limited thereto.

[0078] See also Figure 1 The present invention provides an interpretable extraction method for impact fault characteristics based on an algorithm-guided network, comprising the steps of:

[0079] Step 1. Construct a data set: Construct a simulation signal of the same-position impact fault based on the rolling bearing impact fault response signal mechanism model, add Gaussian white noise to simulate the interference component of the actual signal, and then cut the signal into multiple samples of the same length, and divide the samples into training data sets. and test dataset Where R and S are the number of samples in the training dataset and the test dataset respectively;

[0080] In some embodiments of the present invention, the impact characteristic simulation signal x in step 1 f (t) is specifically constructed as follows:

[0081]

[0082] Where A i (t) is the impulse response amplitude of the i-th order natural mode at time t; ω d,i and ζ i are the i-th order natural frequency and damping ratio respectively; τ k is the random time shift at the kth actual impact occurrence moment, which is set to (0.1-0.2)T in this embodiment. n , where T n is the theoretical impact period, is the fault characteristic frequency f n The reciprocal of T n =1 / f n , so each impact moment τ 0k =τ k +kT f ; I and K represent the number of excited natural modes and impulse responses in the signal, respectively; u(t) is the step function.

[0083] In some embodiments of the present invention, it is considered that the actual measured signal also has a frequency of the shaft rotation frequency f r and its harmonic components x rot (t) and background noise η(t), so the input simulation signal is set to

[0084] x(t)=x f(t)+x rot (t)+η(t) (2) Where t is the time variable, and the rotation component of the shaft may be taken as the first-order frequency, that is, x rot (t)=sin(2πf r t). At the same time, for impact failures occurring on the inner ring of rolling bearings, the impact response amplitude will also be affected by f r The modulation, that is

[0085]

[0086] Where a i,j The modulation amplitude of the j-th order frequency conversion component is used. It is recommended to only consider the modulation of the first-order frequency conversion.

[0087] In some embodiments of the present invention, the sampling frequency f is set s The simulation signal is sampled to obtain a discrete signal x, which is truncated to obtain a sample with M sampling points in the R+S segment, and divided into training data sets according to the ratio and test dataset Where R and S are the number of samples contained in the two.

[0088] Step 2: Based on the wavelet transform, a sparse Laplace wavelet reconstruction algorithm is derived and designed to accurately reconstruct the impact fault signature. The algorithm framework consists of two parts: wavelet transform and wavelet reconstruction. By designing amplitude correction coefficients and transition band correction coefficients, and multiplying the transformed and reconstructed results by these coefficients, it can address amplitude distortion caused by signal truncation and discretization, as well as transition band distortion caused by discrete convolution, thereby accurately reconstructing the impact fault signature signal model.

[0089] In some embodiments of the present invention, the sparse Laplace wavelet reconstruction algorithm process and its examples designed in step 2 are shown in the attached Figure 2 The Laplace wavelet basis selected in the present invention is is the unit impulse response of the second-order underdamped linear time-invariant system, which is expressed as

[0090]

[0091] In the formula, the modal parameters of the system such as the natural frequency ω d The damping ratio ζ is used as the scale parameter of the wavelet, and τ is its time-shift parameter. It should be noted that the proposed reconstruction algorithm can achieve accurate restoration only when the parameters of the wavelet match the time-shift and modal parameters of the impact fault characteristics. Otherwise, the reconstructed amplitude will be greatly reduced, which reflects the algorithm's strong focus on impact characteristics.

[0092] In some embodiments of the present invention, the Laplace wavelet kernel w(t) and the impulse fault characteristic signal f(t) both have the same natural frequency value ω d,0 and damping ratio ζ0, and set the impact time of signal f(t) τ0 = 0.2s, that is,

[0093]

[0094] and

[0095]

[0096] Where, Take ω as the scale parameter d,0 and ζ0, T is the support length of the wavelet. The signal f(t) is Laplace transformed using w(t) to obtain the original wavelet coefficient W(τ), that is,

[0097]

[0098] In the formula, <·,·> is the inner product operator, which reflects the similarity between the two at the time shift τ. Discretize formula (7) to obtain the original wavelet coefficient discrete value W[n] corresponding to the nth sampling point, that is:

[0099]

[0100] Where f[i+n] is the discrete value of f(t) corresponding to the i+nth sampling point, and w[i] is the discrete value of w(t) corresponding to the i-th sampling point. The transformation can be regarded as applying a unilateral exponential window to the signal and performing Fourier transform. At the frequency ω d,0 Therefore, if the discrete form impulse signal f[n] is subjected to fast Fourier transform, W[n] needs to be multiplied by the amplitude correction coefficient C0

[0101] C0=2 / N (9) Where N = T / f s is the sampling length of the discrete Laplace wavelet kernel, f s is the sampling frequency. At the same time, in order to compensate for the influence of the unilateral exponential window on the amplitude attenuation, it is necessary to multiply the amplitude correction coefficient C1 (ω d ,ζ)

[0102]

[0103] C1(ω d ,ζ) is calculated by numerical integration.

[0104] On the other hand, in the process of performing inner product of a shorter Laplace wavelet with non-zero value interval with respect to a longer original signal at time shift τ, the region where the amplitude of the inner product of the two is distorted due to the Laplace wavelet not completely moving into the non-zero region of the original signal is called a transition band. In the transition band (n0-1-N) / f s ≤τ<n0 / f s In the above, N is the sampling length of the discrete wavelet, n0 is the sampling time point corresponding to the impact time τ0 of the signal f(t), the original signal is 0, but after the discrete Laplace wavelet transform of formula (8), a non-zero value that does not actually exist is generated. Therefore, W[n] is multiplied by the zero coefficient C2[n;n0] to perform transition band correction. The coefficient is expressed as:

[0105]

[0106] Different from the method of determining the moment of impact through correlation filtering in other patents, according to the physical meaning of the aforementioned wavelet coefficients, the moment when the peak value in the wavelet coefficients is located means that the original signal has an impact at this time. Therefore, the present invention can determine the moment of impact τ0 by searching for the peak value of the wavelet coefficients to determine the transition band correction coefficient C2.

[0107] Therefore, the corrected wavelet coefficient discrete value W C [n] is:

[0108] W C [n] = C0·C1(ω d ,ζ)·C2[n;n0]·W[n]. (12)

[0109] To W C [n] combines w[n] and the following formula to reconstruct the original shock characteristics, and at the same time corrects the amplitude and transition band to obtain the reconstructed characteristic discrete value x r [n], that is:

[0110]

[0111] Where W C [i] is the discrete value of the corrected wavelet coefficient corresponding to the i-th sampling point, w[N-1-i] is the discrete value of the Laplace wavelet kernel corresponding to the N-1-i-th sampling point, and C3 is the amplitude and transition band correction coefficient, which is expressed as:

[0112] C3=2 / N′[n] (14)

[0113] Where N'[n] is x r [n] The number of sampling points of the discrete Laplace wavelet kernel that effectively participates in the reconstruction at the nth point, expressed as:

[0114]

[0115] It should be noted that for the original shock signal containing multiple intrinsic modal components, it is necessary to use the same number of Laplace wavelets with the same intrinsic modal parameters to input the proposed algorithm to reconstruct the corresponding shock components x r,i [n], and superimpose them to obtain the final reconstruction feature, that is,

[0116]

[0117] Step 3: Using the designed sparse Laplace wavelet reconstruction algorithm as the kernel, a Laplace wavelet kernel convolutional sparse autoencoder is constructed, which includes an encoder layer, an intermediate layer, and a decoder layer. Each layer has multiple channels, corresponding to the excited modes of the identified impulse response. The encoder layer performs a Laplace wavelet transform on the input signal at a sparse scale and performs amplitude correction accordingly according to the sparse Laplace wavelet reconstruction algorithm. The intermediate layer corresponds to the wavelet coefficients of different modes. The decoder layer uses Laplace wavelet, correction coefficients, and channels to filter the output of the intermediate layer to obtain the impulse characteristics.

[0118] In some embodiments of the present invention, the structure of the Laplace wavelet kernel convolution sparse autoencoder in step 3 is shown in the attached Figure 2 . Unlike the classic convolutional autoencoder and other autoencoder variants in other patents, the encoder in the present invention includes a convolutional layer and a single connection layer. The convolutional layer uses Laplace wavelet as the convolution kernel for wavelet transform, and uses the product of amplitude correction coefficients C0 and C1 as the weight coefficient in the single connection layer. At the same time, the bias vector is discarded. Each channel of the encoder outputs a set of amplitude-corrected wavelet coefficients; the decoder includes a wavelet reconstruction layer and an interpretable channel attention module. The wavelet reconstruction layer includes a transposed convolution operation and transition band correction coefficients C2 and C3, so as to achieve accurate reconstruction of the components contained in the impact feature of each channel; the interpretable channel attention module is a fully connected layer that removes the bias vector, and the same channel shares an attention weight coefficient w, where w can be interpreted as the model's attention size to different channels, reflecting the model's judgment on the contribution of each channel to the final result. After weighting and superposition of each channel, the reconstruction value of the impact feature is obtained as the output of the Laplace wavelet kernel convolution sparse autoencoder.

[0119] In some embodiments of the present invention, unlike the large number of unexplainable trainable parameters and hyperparameters in deep models built by other patents, the trainable parameters of the autoencoder built by the present invention are only the natural frequency of each channel, the damping ratio and the weight parameters in the interpretable channel attention module, and they all have clear physical meanings and can provide a theoretical basis for the performance of the model. Each channel corresponds to an inherent mode that may exist in the input signal containing impact characteristics. In order to enable the model to adaptively search for the same number of inherent modes as the impact fault input, the present invention considers the inherent modes in the low-frequency region of general rolling bearings, and sets the number to Q. Let the number of channels of the convolutional sparse autoencoder C>Q, and adaptively screen out channels that can correctly identify a certain order of inherent modes contained in the signal through training to achieve sparse reconstruction. For this reason, in the reconstruction experience loss L E Add sparse regularization term L on the basis R , the present invention uses mean square error (MSE) loss and l1 norm as the metrics of the two respectively, then the total loss function L of the Laplace wavelet kernel convolution sparse autoencoder is expressed as

[0120]

[0121] Where ε is a hyperparameter, x f [n] is the impact characteristic simulation signal x corresponding to the nth sampling point f The discrete value of (t), w c is the attention weight of the c-th channel.

[0122] Step 4: Input the training samples of the training data set into the Laplace wavelet kernel convolution sparse autoencoder, perform training based on the reconstruction loss of the shock feature, and use gradient descent backpropagation to update the Laplace wavelet parameters and channel screening weight parameters. This allows the model to learn the number of the sparsest wavelet bases and the parameters of the optimal wavelet base from the samples, thus achieving adaptive and robust extraction of similar shock faults.

[0123] In some embodiments of the present invention, in step 4, the weight w of L for the cth channel is calculated based on the chain rule. c Partial derivative of Right now

[0124]

[0125] and the Laplace wavelet kernel ψ of the cth channel c The trainable parameters (·) in c The discrete value of the partial derivative Right now

[0126]

[0127] Where, (·) c Including the natural frequency ω d,c and damping ratio ζ c , ψ c Discrete values ​​of partial derivatives of both and Calculated by the following two formulas:

[0128]

[0129]

[0130] Where Δt is the time domain sampling interval, and the sampling frequency is Δt = 1 / f s It should be noted that the above gradient calculation formula shows that the gradients of different parameters have significant orders of magnitude differences. The present invention adopts different learning rates for different parameters, and the learning rate α of the damping ratio and natural frequency is ζ and The following constraints apply:

[0131]

[0132] Where, D(O(ω d )) represents a frequency with the same order of magnitude as the natural frequency O(ω d ) constant D. During the network training process, each parameter is updated by calculating the partial derivative of each parameter and then back-propagating.

[0133] Step 5: Input the test samples of the test data set into the trained network for testing to obtain the extracted impact fault features.

[0134] In some embodiments of the present invention, the output of the test set in step 5 is demodulated by performing Hilbert envelope demodulation on the output to obtain an envelope spectrum, and it is verified that the reconstructed features contain prominent fault characteristic frequencies. At the same time, combined with the identification of network parameters, the reliability of the output results is confirmed so that they can be applied to the diagnosis of impact faults.

[0135] The present invention is further described below with reference to the accompanying drawings and experimental cases.

[0136] According to equations (1) and (2), the impulse fault signal is constructed. The sampling time length of the simulation signal is 5s and the first two natural modes are considered, that is, I = 2. The frequency parameters such as rotation frequency and natural mode parameters are shown in Table 1. The impulse response amplitude corresponding to the first two natural modes is set to

[0137] A1(t)=5+4sin(2πf r t),A2(t)=3+1.6sin(2πf r t). (23) The simulation signal is truncated into multiple samples with a sampling length of M = 1024 points per segment, 80% of the samples are divided into a training set, and the rest are classified as a test set.

[0138] Table 1 Frequency and natural modal parameter settings

[0139]

[0140] The number of channels in the model is set according to the rule of intrinsic modal redundancy of the input impulse signal, and C is set to 8 here. The convolution kernel length N is set to 64, and the hyperparameter ε is set to 0.01. According to the physical meaning of each training parameter, the damping ratio, natural frequency, and channel attention weight are randomly initialized in the range of 0.001-0.1, (1000-5000) Hz, and 0-2, respectively. According to the order of magnitude difference of the gradient and the constraint formula (22), their learning rates are set to 10 -3 , 100 and 10 -2 . Set the model to perform a gradient update every 8 samples.

[0141] To demonstrate the superiority of the proposed method, two variants of autoencoders used in fault diagnosis were compared: a convolutional autoencoder and a denoising stacked autoencoder. The former's encoder and decoder each consist of three convolutional blocks, each containing a convolutional layer, a pooling layer, a batch normalization layer, and a Relu activation function. The convolutional blocks symmetrically positioned about the middle layer also utilize residual skip connections. The latter stacks three fully connected layers, and greedily trains the parameters of each layer.

[0142] All models were trained for 200 rounds and repeated 10 times. The average value of each result under each test set input was used as the object of analysis and comparison to avoid randomness of the results.

[0143] When the noise-free impact fault characteristic simulation input is used, the test loss curves of each model can be found in Figure 4 The initial loss of the proposed network is much smaller than that of the other networks, indicating that the features reconstructed by the developed algorithm can still roughly match the waveform of the input signal even when the network is untrained. In addition, the proposed network converges much faster than the other networks, which is due to the inner product nature of the proposed guidance algorithm and the similarity between the waveform of the Laplacian convolution kernel and the impulse feature.

[0144] In the noise-free training parameter identification results shown in Table 2, the proposed algorithm, using the same kernel as the input modal parameters, achieved an MSE loss of 0.0461, slightly larger than the MSE loss of the proposed network. This discrepancy is believed to be due to overfitting of the proposed network, which also causes a deviation between the trained modal parameters and the ideal modal parameters. For example, in the noise-free input case, the average natural frequency was 1694.70 Hz, with a relative error of 0.46%, a damping ratio of 0.0423, and an absolute error of 0.0076.

[0145] Table 2. Recognition results and errors of the proposed network for training parameters

[0146]

[0147]

[0148] The proposed network is also interpretable. Specifically, the credibility of the network output can be further confirmed by identifying the training parameters and their process. For the identification process, please refer to the attached Figure 5 As can be seen, in the first 170 rounds, the network continuously screens suitable channels (natural modes) and, after correctly identifying the second-order natural modes in the input, further optimizes the natural modes and damping ratio, ultimately achieving correct parameter identification. Given the nature of the proposed algorithm, which accurately reconstructs the impact signature only when the parameters match, it can be confirmed that the model's reconstruction of the impact signature is reliable.

[0149] Finally, the noise component intensity was set to 0dB, -5dB and -10dB and input into the training respectively. The parameter identification results are shown in Table 2. It can be seen that the model can accurately and stably identify the natural frequencies of each order, while the identification of the damping ratio has large fluctuations. This is because the damping ratio is related to the amplitude of the impact waveform. The random noise directly acts on the amplitude of the impact signal and also directly affects the model's identification of the damping ratio. Taking the case of -10dB noise input as an example, the outputs of the three methods and their Hilbert envelope demodulation spectra are listed as shown in the attached figure. Figure 6 As shown in the figure, it can be seen that the proposed model can better preserve the periodicity of the impulse characteristics than other methods in the time domain, and at the same time, it can also better preserve the fault characteristic frequency f in the envelope spectrum. t The recognition effect is similar to that of deep models such as convolutional autoencoders, which illustrates the noise robustness of the proposed model.

[0150] The present invention addresses the problems of the black box and reliability of existing deep learning models used in the field of fault diagnosis, and the problems of the fault feature extraction algorithm not having the ability to adaptively optimize feature parameters and having limited accuracy. Taking rolling bearings with impact-type faults as the research object, the algorithm for extracting fault features is designed based on the impact fault mechanism and wavelet transform priors, and guides the construction of an interpretable convolutional sparse autoencoder to achieve reliable, adaptive and accurate extraction of impact fault features and fault feature frequencies from strong noise impact fault signals, effectively improving the intelligent model's ability and reliability in extracting impact-type fault features of industrial equipment, and providing a decision-making basis and reliable input for further intelligent model fault diagnosis.

[0151] It should be noted that although the implementation of the present invention has been described in detail with reference to examples, it is easy for those skilled in the art to understand that any modifications, substitutions and improvements made without departing from the spirit and principles of the present invention as described in the appended claims should be included in the scope of protection of the present invention.

Claims

1. A method for interpretable extraction of impact fault features based on an algorithm-guided network, characterized in that: The following steps are involved: Step 1. Construct a data set: Construct a simulation signal of the same-position impact fault based on the rolling bearing impact fault response signal mechanism model, add Gaussian white noise to simulate the interference component of the actual signal, and then cut the signal into multiple samples of the same length, and divide the samples into training data sets. and test dataset Where R and S are the number of samples in the training dataset and the test dataset respectively; Step 2: Based on wavelet transform, a sparse Laplace wavelet reconstruction algorithm is derived and established to accurately reconstruct the impact fault characteristics. The algorithm includes two parts: wavelet transform and wavelet reconstruction. By designing the amplitude correction coefficient and the transition band correction coefficient, the transformation and reconstruction results are multiplied by the obtained coefficients. Step 3: Using the sparse Laplace wavelet reconstruction algorithm as the kernel, construct a Laplace wavelet kernel convolution sparse autoencoder, including an encoder layer, an intermediate layer, and a decoder layer. Each layer has multiple channels corresponding to the excited modes of the identified impulse response. The encoder layer performs a Laplace wavelet transform on the input signal at a sparse scale and performs amplitude correction accordingly according to the sparse Laplace wavelet reconstruction algorithm. The intermediate layer corresponds to the wavelet coefficients of different modes. The decoder layer uses the Laplace wavelet, correction coefficient, and channel screening to output the impulse characteristics of the output of the intermediate layer. The encoder includes a convolutional layer and a singly connected layer. The convolutional layer uses Laplace wavelet as the convolution kernel to perform wavelet transform. The product of amplitude correction coefficients C0 and C1 is used as the weight coefficient in the singly connected layer. The bias vector is discarded. Each channel of the encoder outputs a set of amplitude-corrected wavelet coefficients. The decoder includes a wavelet reconstruction layer and an interpretable channel attention module. The wavelet reconstruction layer includes a transposed convolution operation and transition band correction coefficients C2 and C3 to achieve accurate reconstruction of the components contained in the impact feature for each channel. The interpretable channel attention module is a fully connected layer that removes the bias vector and shares an attention weight coefficient w within the same channel. After weighted summation, the reconstructed value of the impact feature is obtained as the output of the Laplace wavelet kernel convolution sparse autoencoder. Step 4: Input the training samples of the training data set into the Laplace wavelet kernel convolution sparse autoencoder, perform training based on the reconstruction loss of the shock feature, and use gradient descent backpropagation to update the Laplace wavelet parameters and channel screening weight parameters. This allows the model to learn the number of the sparsest wavelet bases and the parameters of the optimal wavelet base from the samples, thus achieving adaptive and robust extraction of similar shock faults. Step 5: Input the test samples of the test data set into the trained network for testing to obtain the extracted impact fault features.

2. The method for extracting interpretable impact fault characteristics based on an algorithm-guided network according to claim 1, characterized in that: The simulation signal x(t) of the impact fault in step 1 is based on the rolling bearing impact fault response signal model x f (t) is constructed, taking into account the fact that the actual measured signal also has a frequency of the shaft rotation frequency f r and its harmonic components x rot (t) and background noise η(t), the input simulation signal is set to: x(t)=x f (t)+x rot (t)+η(t) (1) Where t is the time variable, and the shaft rotation component only takes the first-order frequency, that is, x rot (t)=sin(2πf r t), and at the same time, for the impact failure occurring in the inner ring of the rolling bearing, the impact response amplitude A i (t) will also be affected by f r The modulation, that is Where a i,j is the modulation amplitude of the j-th order frequency conversion component, and only the first-order frequency conversion modulation is considered.

3. The method for extracting interpretable impact fault characteristics based on an algorithm-guided network according to claim 1, characterized in that: In step 1, set the sampling frequency f s The simulation signal is sampled to obtain a discrete signal x, which is truncated to obtain a sample with M sampling points in the R+S segment, and divided into training data sets according to the ratio and test dataset 4. The method for extracting interpretable impact fault characteristics based on an algorithm-guided network according to claim 1, characterized in that: In the sparse Laplace wavelet reconstruction algorithm of step 2, select Laplace wavelet As a wavelet basis, it is the unit impulse response of the second-order underdamped linear time-invariant system, and its expression is: Where t is the time variable, and the modal parameters of the system include the natural frequency ω d and damping ratio ζ as the scale parameter of the wavelet, τ as the time shift parameter of the wavelet, and u(t) is the step function.

5. The method for extracting interpretable impact fault characteristics based on an algorithm-guided network according to claim 1, characterized in that: In step 2, the amplitude correction after sparse Laplace wavelet transform includes: simulating that the Laplace wavelet kernel w(t) and the impulse fault characteristic signal f(t) both have the same natural frequency value ω d,0 and damping ratio ζ0, and set the impact time of signal f(t) τ0 = 0.2s, that is, and Where t is the time variable, u(t) is the step function, Take ω as the scale parameter d,0 and Laplace wavelet when ζ0, T is the support length of the wavelet; the signal f(t) is discretely Laplace transformed using w(t) to obtain the original wavelet coefficients, and the discrete value W[n] of the original wavelet coefficients corresponding to the nth sampling point is obtained, that is: Where f[n+i] is the discrete value of f(t) corresponding to the n+i-th sampling point, and w[i] is the discrete value of w(t) corresponding to the i-th sampling point. Multiply W[n] by the amplitude correction coefficient C0, which is calculated as follows: C0=2 / N (7) Where N = T / f s is the sampling length of the discrete Laplace wavelet kernel, f s is the sampling frequency; at the same time, in order to compensate for the influence of the unilateral exponential window on the amplitude attenuation, the amplitude correction coefficient C1(ω d ,ζ), the expression of the coefficient is: C1(ω d ,ζ) is obtained by numerical integration, ω d is the natural frequency, and ζ is the damping ratio.

6. The method for extracting interpretable impact fault characteristics based on an algorithm-guided network according to claim 5, characterized in that: In step 2, the transition band correction before and after the sparse Laplace wavelet reconstruction is performed. The correction includes: when performing the inner product of the shorter Laplace wavelet with non-zero value interval relative to the longer original signal at the time shift τ, the region where the amplitude of the inner product of the two is distorted due to the Laplace wavelet not completely moving into the non-zero region of the original signal is called the transition band; in the transition band (n0-1-N) / f s ≤τ <n0 / f s In the above, N is the sampling length of the discrete wavelet, n0 is the sampling time point corresponding to the impact time τ0 of the signal f(t), the original signal is 0, but after the discrete Laplace wavelet transform, it produces a non-zero value that does not actually exist. Therefore, the original wavelet coefficient discrete value W[n] is multiplied by the zero coefficient C2[n;n0] to perform transition band correction. The coefficient is expressed as: Corrected wavelet coefficient discrete value W C [n] is: W C [n]=C0·C1(ω d ,ζ)·C2[n;n0]·W[n] (10) To W C [n] combines w[n] and the following formula to reconstruct the original shock characteristics, and perform amplitude correction and transition band correction at the same time to obtain the reconstructed characteristic discrete value x r [n], that is: Where W C [i] is the discrete value of the corrected wavelet coefficient corresponding to the i-th sampling point, w[N-1-i] is the discrete value of the Laplace wavelet kernel corresponding to the N-1-i-th sampling point, and C3 is the amplitude and transition band correction coefficient, which is expressed as: C3=2 / N′[n] (12) Where N'[n] is x r [n] The number of sampling points of the discrete Laplace wavelet kernel that effectively participates in the reconstruction at the nth point, expressed as: For the original shock signal containing multiple intrinsic modal components, the same number of Laplace wavelets with the same intrinsic modal parameters are used to input the sparse Laplace wavelet reconstruction algorithm to reconstruct the corresponding shock components x r,i [n], and superimpose them to obtain the discrete value of the reconstructed feature, that is, the final reconstructed feature, that is:

7. The method for extracting interpretable impact fault characteristics based on an algorithm-guided network according to claim 1, characterized in that: The only trainable parameters of the Laplace wavelet kernel convolutional sparse autoencoder are the natural frequency of each channel, the damping ratio, and the weight parameters in the interpretable channel attention module.

8. The method for extracting interpretable impact fault characteristics based on an algorithm-guided network according to claim 1, characterized in that: In order to enable the Laplace wavelet kernel convolution sparse autoencoder to adaptively search for the same number of natural modes as the impact fault input, the natural modes in the low-frequency region of a general rolling bearing are considered, and the number is set to Q. The number of channels of the convolution sparse autoencoder C>Q is set. Through training, the channels that can correctly identify a certain order of natural modes contained in the signal are adaptively selected to achieve sparse reconstruction. In the reconstruction experience loss L E Add sparse regularization term L on the basis R , using Mean Square Error (MSE) loss and l1 norm as the metrics of the two respectively, the total loss function L of the Laplace wavelet kernel convolution sparse autoencoder is expressed as: Where ε is a hyperparameter, x f [n] is the impact characteristic simulation signal x corresponding to the nth sampling point f The discrete value of (t), w c is the attention weight of the cth channel, M is the number of samples, x r [n] is the final reconstructed feature.

9. The method for extracting interpretable impact fault characteristics based on an algorithm-guided network according to claim 8, characterized in that: In step 4, the weight w of L for the cth channel is calculated based on the chain rule c Partial derivative of Right now and the Laplace wavelet kernel ψ of the cth channel c The trainable parameters (·) in c The discrete value of the partial derivative Right now Where, (·) c Including the natural frequency ω d,c and the damping ratio ζ c , ψ c Discrete values ​​of partial derivatives of both and Calculated by the following two formulas: Where Δt is the time domain sampling interval, and the sampling frequency is Δt = 1 / f s Find, f s is the sampling frequency; different learning rates are used for different parameters, and the learning rate α of the damping ratio and natural frequency is ζ and The following constraints apply: Where, D(O(ω d )) indicates that the frequency is of the same order of magnitude as the natural frequency O(ω d ) constant; each parameter is updated during the network training process by calculating the partial derivative of each parameter and then back-propagating.

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