A bearing vibration signal enhancement method based on VMD-TEO multi-channel fusion

Abstract

The present application relates to mechanical fault diagnosis and signal processing, and discloses a bearing vibration signal enhancement method based on VMD-TEO multi-channel fusion, comprising the following processes: first, the original signal is obtained, a constraint variation optimization model is constructed through the VMD method, and a plurality of IMF components are adaptively decomposed; then, TEO transient energy operation is carried out on each IMF component point by point, the timing information is completely retained, and the frequency-domain fault shock feature enhancement is realized; finally, the multi-path enhanced components are spliced and standardized along the channel dimension, and a three-dimensional feature tensor with regular dimension is constructed. The present application avoids the defects of modal aliasing and noise amplification of the traditional method, effectively highlights the weak fault features and improves the signal-to-noise ratio through the two-stage collaborative mechanism of frequency domain decoupling and time domain enhancement, can provide high-differentiation and high-robustness standardized input features for the bearing intelligent fault diagnosis model, and is suitable for the complex low-speed heavy-load working conditions of the port.

Description

Technical Field

[0001] This invention relates to mechanical fault diagnosis and signal processing, specifically to a bearing vibration signal enhancement method based on VMD-TEO multi-channel fusion. Background Technology

[0002] Rolling bearings are core support components of large rotating machinery in ports, and their operating status directly affects the efficiency and safety of the port logistics system. Port machinery rolling bearings often operate under low-speed, high-load conditions (below 100 rpm). Under these conditions, the transient impact energy caused by a fault is positively correlated with the square of the rotational speed, leading to a significant attenuation of the fault signal energy. Simultaneously, the fault characteristic frequency falls into the low-frequency range as the rotational speed decreases, easily aliasing with low-frequency vibrations and gravity components of the mechanical structure, causing weak fault features to be submerged by strong background noise. Existing conventional signal processing methods struggle to extract weak fault pulses from the mixed noise. When directly analyzing faults based on the original signal, the amplitude of the periodic impact features corresponding to the fault is weak, and the spectral peaks are covered by the noise floor, resulting in extremely low fault identification. Therefore, it is urgent to use targeted feature enhancement algorithms to amplify transient impact energy and filter out redundant background interference, transforming the hidden fault features submerged in noise into explicit features with prominent amplitudes and clear patterns, providing a reliable data foundation for accurate subsequent rolling bearing fault identification.

[0003] Existing signal processing and feature enhancement techniques have significant shortcomings when dealing with the above scenarios: ① Traditional methods such as spectrum analysis and short-time Fourier transform are limited by the Heisenberg uncertainty principle, with fixed time and frequency resolution, making it difficult to take into account both transient impacts and steady-state characteristics. They also cannot effectively separate fault characteristics from noise at low signal-to-noise ratios. ②Although variational mode decomposition can achieve adaptive frequency domain decoupling, its time-domain impulse characteristics are not prominent when used alone, and the parameter selection depends on experience, making it difficult to accurately extract weak fault information. ③The Teager energy operator has good instantaneous energy capture capability, but when directly applied to noisy raw signals, it will simultaneously amplify the noise components, resulting in limited enhancement effect; ④ Existing studies typically use the above methods individually or in simple series, failing to fully leverage the complementary advantages of frequency domain decoupling and time domain enhancement. When dealing with the high-intensity, wide-band noise interference unique to ports, there is still room for improvement in the robustness and efficiency of feature enhancement.

[0004] Therefore, there is an urgent need to develop a robust feature enhancement method that can deeply coordinate frequency domain decoupling and time domain energy enhancement to solve the technical problem of difficulty in extracting weak fault features of low-speed rolling bearings under high noise background. Summary of the Invention

[0005] This invention aims to overcome existing defects and provide a bearing vibration signal enhancement method based on VMD-TEO multi-channel fusion. Through the synergistic mechanism of frequency domain adaptive decomposition, full component time domain energy enhancement and multi-channel feature fusion, it effectively suppresses high noise background, significantly enhances the weak fault impact characteristics of low-speed rolling bearings, and improves the accuracy and robustness of subsequent fault diagnosis.

[0006] This invention provides the following technical solution: a bearing vibration signal enhancement method based on VMD-TEO multi-channel fusion, comprising the following steps: Step 1: Obtain the raw signal of the rolling bearing ; Step 2: Construct a constrained variational optimization model based on the variational mode decomposition method. By introducing a quadratic penalty factor and Lagrange multipliers, the constrained variational optimization model is transformed into an unconstrained variational optimization model. The original signal is input into the unconstrained variational optimization model to obtain preliminary modal function components. The alternating direction multiplier method is used to iteratively update the modal function components, center frequency, and Lagrange multipliers. Convergence is determined based on the iterative relative rate of change, and the modal function components are obtained. Step 3: Using the modal function components as input, the Hilbert energy operator is used to perform instantaneous energy calculations component by component to obtain the enhanced modal function components after TEO. Step 4: The enhanced modal function components are spliced ​​along the channel dimension to construct a multi-channel feature tensor, which is then standardized to obtain a three-dimensional feature tensor.

[0007] Furthermore, the specific process of obtaining the modal function components in step 2 is as follows: Step 2.1 Construct a variational optimization model with constraints, as shown in the following expression:

[0008]

[0009] In the formula, This represents the time partial derivative, i.e., the gradient operator. For the Dirac function, For the Hilbert transform kernel function, For convolution operations, For frequency shifting operators, It is the L2 norm. for Group of preliminary modal function components; Through secondary penalty factors With Lagrange multipliers The constrained variational optimization model is transformed into an unconstrained variational optimization model, as shown in the following expression:

[0010] In the formula, As a secondary penalty factor, For Lagrange multipliers, Indicates inner product operation; For an unconstrained Lagrangian function, The center frequency; The original signal is transformed using a variational optimization model with constraints. The optimization process involves minimizing the L2 norm sum after sequential Hilbert transform, frequency shift, and time-domain differentiation. Simultaneously, an equality constraint is added stating that "the sum of all modal function components equals the original signal," resulting in a modal-containing signal. and center frequency A constrained variational optimization model is derived; a quadratic penalty factor is introduced. With Lagrange multipliers The transformation from a constrained variational optimization model to an unconstrained variational optimization model is completed, and preliminary modal function components are obtained. Step 2.2 Based on the unconstrained variational optimization model, iterative updates are performed using the alternating direction multiplier method, including updating the initial modal component frequency domain, updating the center frequency, updating the Lagrange multipliers, and determining convergence, as detailed below: (1) Update the frequency domain of the initial modal components: First update the frequency domain of the initial modal function components. After Fourier transforming to the frequency domain, the frequency domain representation of the corresponding mode function components is obtained. Next, the residuals between the original signal and the initial modal function components are calculated. Then, using a weight term constructed from the center frequency and penalty factor, the frequency domain components near the center frequency in the residuals are extracted, and the updated first-order component is output. Frequency domain representation of each modal function component Its expression is:

[0011] In the formula, Indicates Fourier transform, The Fourier transform of the original signal This represents the frequency domain representation of the modal function components. For the frequency domain representation of Lagrange multipliers, For the first In the nth iteration The center frequency of each modal function component; (2) Update the center frequency: based on the updated number of... Frequency domain representation of each modal function component As input, the power spectrum centroid calculation formula is used to... The power spectrum is obtained by performing modulo-square operation, and then multiplied by the center frequency. Integrate to obtain the numerator integral; integrate the power spectrum over the same interval to obtain the denominator integral; divide the numerator and denominator integrals to obtain the updated center frequency. Its expression is:

[0012] In the formula, Power spectrum, To perform integration on the power spectrum along the frequency axis; (3) Update the Lagrange multipliers: Correct the Lagrange multipliers by updating the step size of the multipliers. Summation operation, Subtracting the sum yields the residual data; multiplying the residual data by the multiplier update step size, and then adding it to the frequency domain representation of the Lagrange multipliers, we obtain the updated frequency domain representation of the Lagrange multipliers. Its expression is:

[0013] In the formula, For the first Frequency domain representation of Lagrange multipliers in the next iteration To update the step size for the multiplier, This is the sum of the frequency domain representations of all modal function components after the update; (4) Convergence criterion: Calculate the relative rate of change of the modal function components. If the relative rate of change is less than the preset tolerance, If the iteration converges, the iteration stops and the optimal value is output. One modal function component; otherwise, repeat the above steps until the preset accuracy is reached, iterating until the convergence condition is met. The expression for the convergence condition is:

[0014] In the formula, For the first In the nth iteration Time-domain representation of each modal function component For the first In the nth iteration Time-domain representation of each modal function component This is the preset tolerance.

[0015] Furthermore, the specific process of obtaining the TEO-enhanced modal function components in step 3 is as follows: Constructing the Hilbert Energy Operator (TEO) for continuous-time signals The instantaneous energy value is calculated by combining its amplitude with its first and second derivatives. The operational expression for its TEO is as follows:

[0016] In the formula, for The first time derivative, for The second time derivative, For TEO operators; Based on the Hilbert energy operator TEO, the modal function components are used as inputs, i.e., discrete-time signals. By approximating the derivative with a difference, a TEO calculation formula adapted to discrete sequences is constructed, and sampling points are extracted. Modal function components at the location Perform squaring operations to generate square terms. Then extract adjacent sampling points. , Corresponding modal function components , The product term of adjacent points is obtained through multiplication; the instantaneous energy data is obtained by subtracting the product term from the squared term and performing TEO nonlinear operations. The sequence is padded with adjacent values ​​at the beginning and end of the sampling points to unify the sequence length, and the energy-enhanced modal components are output, with the following expression:

[0017] In the formula, The first discrete-time input signal One sampling point, The modal function components of the previous sampling point. For the modal function components of the next sampling point, The sampling point number; Finally, the instantaneous energy of TEO at any time is calculated using multiple sampling points, without requiring the entire signal segment to participate in the calculation.

[0018] Furthermore, the specific process of obtaining the three-dimensional feature tensor is as follows: Using the modal function components enhanced by TEO as input, multi-channel feature fusion, temporal alignment, numerical standardization and dimensional regularization are completed, and a suitable three-dimensional feature tensor is output. First, TEO enhanced mode components with different frequency bands and different fault characteristics are spliced ​​and fused along the channel dimension to construct multi-channel features; each channel feature has a clear physical semantics: channel 1 (IMF1) carries the low-frequency trend and basic energy distribution characteristics of the signal, channels 2-3 (IMF2, IMF3) mainly carry the core fault characteristics of the bearing fault resonance frequency band, and channel 4 (IMF4) retains the high-frequency weak impact and detailed fault characteristics. Multi-channel splicing achieves complete coverage of fault characteristics across the entire frequency band; Secondly, the timing of all channels is strictly aligned throughout the process, and the sampling points of all modal function components correspond one-to-one with the timing of the original signal. Finally, the concatenated multi-channel features are numerically standardized, and multiple sets of samples are stacked along the batch dimension to construct a normalized three-dimensional feature tensor. The output tensor has a dimension of [missing value]. ,in 4 represents the batch size, 4 represents the number of feature channels, and 1024 represents the time-series sampling length of a single sample.

[0019] Compared with existing technologies, this invention provides a bearing vibration signal enhancement method based on VMD-TEO multi-channel fusion, which has the following beneficial effects: (1) Achieving time-frequency domain collaborative feature enhancement effectively avoids the defects of traditional algorithms. Existing traditional methods such as EMD and single TEO enhancement generally suffer from problems such as modal aliasing, endpoint effects, noise amplification, and inaccurate feature extraction, making it difficult to adapt to the non-stationary and low signal-to-noise ratio vibration signals of low-speed bearings. This invention adopts a collaborative mechanism of first VMD frequency division and then TEO enhancement. Through VMD, the original mixed signal is adaptively decomposed into frequency-domain independent and physically semantically clear modal components, completing the frequency band separation of fault features and background noise in advance, thus avoiding secondary amplification of noise from the root. Then, by utilizing the high sensitivity of the TEO operator to the instantaneous energy changes of each modal component, the weak periodic impact features caused by bearing faults are accurately captured, realizing the bidirectional collaboration of frequency domain noise reduction and time domain feature enhancement, and significantly improving the identifiability of weak fault features.

[0020] (2) Significantly optimizes the time-frequency representation of the signal, accurately highlighting the fault characteristic frequencies. After processing by this method, the vibration signal, which was originally hidden in strong noise in the time domain, becomes clear and regular, with obvious periodic characteristics; in the frequency domain envelope spectrum, the fault characteristic frequencies and harmonic peaks corresponding to the inner and outer rings of the bearing are more sharp and prominent, greatly improving the feature identification, while the broad-spectrum background noise is effectively suppressed. Compared with the original signal and single processing methods, this invention can accurately distinguish the fault characteristics of different types of bearings, taking into account both the common laws and individual differences of fault characteristics, and adapting to the bearing fault extraction needs of multiple scenarios.

[0021] (3) Outstanding quantization performance and excellent signal enhancement and noise reduction capabilities. Through multi-dimensional quantitative index ablation experiments and comparative verification, the VMD-TEO strategy of full-component multi-channel fusion of this invention is significantly superior to single VMD, single TEO and processing methods that directly input the original signal in terms of core fault characteristic indicators such as kurtosis, peak factor and envelope spectrum peak significance. At the same time, this method can achieve an average signal-to-noise ratio gain of about 8.5dB, effectively solving the core problem of difficulty in extracting weak fault characteristics under heavy load and strong interference conditions of low-speed bearings in ports, and greatly improving the stability and reliability of signal preprocessing.

[0022] (4) Adaptable to intelligent diagnostic models, with strong engineering practicality. The final output of this invention is a three-dimensional multi-channel feature tensor with unified dimensions, complete temporal sequence, and clear physical meaning. It eliminates the model training imbalance problem caused by the difference in modal energy levels and can directly adapt to the batch operation requirements of various deep learning diagnostic models. It provides high-quality and robust input features for intelligent diagnosis of early weak faults in low-speed bearings and has good engineering implementation and promotion application value. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the overall process of the present invention; Figure 2 This is a flowchart of the VMD algorithm of the present invention; Figure 3 This is the flowchart of the VMD-TEO fault feature enhancement method of the present invention; Figure 4 This is a diagram of the PU experimental platform of the present invention; Figure 5 This is a comparison diagram of the original signal and the time-domain enhanced signal of this invention_KA05 outer ring fault diagram; Figure 6 This is a comparison diagram of the original signal and the time-domain enhanced signal of this invention_KA06 outer ring fault diagram; Figure 7 This is a comparison diagram of the original signal and the time-domain enhanced signal of this invention_KI05 inner circle fault diagram; Figure 8 This is a comparison diagram of the original signal and the time-domain enhanced signal of the present invention_KI07 inner circle fault diagram; Figure 9 This is a comparison diagram of the envelope spectrum of the original signal and the frequency domain enhanced signal of the present invention_KA05 outer ring fault diagram; Figure 10 This is a comparison diagram of the envelope spectrum of the original signal and the frequency domain enhanced signal of the present invention_KA06 outer ring fault diagram; Figure 11 This is a comparison diagram of the envelope spectra of the original signal and the frequency domain enhanced signal of the present invention_KI05 inner circle fault diagram; Figure 12 This is a comparison diagram of the envelope spectrum of the original signal and the frequency domain enhanced signal of the present invention_KI07 inner circle fault diagram. Detailed Implementation

[0024] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments and accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] To make the inventive objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be further described in detail below with reference to the accompanying drawings: In order to better understand the above-mentioned objectives, features, and advantages of this invention, the advantages of this invention will be further illustrated below by comparing the embodiments with the accompanying drawings and specific implementation methods.

[0026] This invention proposes a bearing vibration signal enhancement method based on VMD-TEO multi-channel fusion, such as... Figure 1 The process of this method is described in detail below: Step 1: Obtain the raw signal of the low-speed rolling bearing The original signal comes from the publicly available bearing dataset from Paderborn University (PU) in Germany. This dataset is a standard benchmark dataset in the field of mechanical fault diagnosis. It is collected based on a dedicated motor-bearing test platform and covers states such as health, inner ring fault, and outer ring fault. It includes vibration data under low speed conditions of 900 rpm and a sampling frequency of 64 kHz, which can effectively simulate the actual operating conditions of port machinery with low speed and strong noise. Step 2: Construct a constrained variational optimization model based on the variational mode decomposition method. By introducing a quadratic penalty factor and Lagrange multipliers, the constrained variational optimization model is transformed into an unconstrained variational optimization model. The original signal is input into the unconstrained variational optimization model to obtain preliminary modal function components. The alternating direction multiplier method is used to iteratively update the modal function components, center frequency, and Lagrange multipliers. Convergence is determined based on the iterative relative rate of change, and the modal function components are obtained. Step 3: Using the modal function components as input, the Hilbert energy operator is used to perform instantaneous energy calculations component by component to obtain the enhanced modal function components with unified dimensions and complete temporal sequence after TEO. Step 4: The enhanced modal function components are spliced ​​along the channel dimension to construct a multi-channel feature tensor, which is then standardized to obtain a three-dimensional feature tensor. This process fully preserves multi-band fault information, constructs a unified feature scale, stabilizes model training, improves fault discrimination accuracy, and provides a unified, standardized, and directly deployable feature input interface for engineering real-time diagnosis.

[0027] Specifically, the process of obtaining the modal function components in step 2 is as follows: Step 2.1 Variational Mode Decomposition (VMD) is an adaptive, fully non-recursive signal decomposition method that can adaptively decompose each component in the signal frequency domain. It overcomes the endpoint effects and mode function component aliasing problems of the EMD method, effectively reducing the non-stationarity of complex and highly nonlinear time series. A constrained variational optimization model is constructed using the variational mode decomposition method, which is then converted into an unconstrained model. The mode function components are then iteratively solved using the Alternating Direction Multiplier Method (ADMM). The flowchart of the VMD algorithm is shown below. Figure 2 As shown; specifically as follows: Construct a variational optimization model with constraints, expressed as follows:

[0028] In the formula, This represents the time partial derivative, also known as the gradient operator, used to calculate the rate of change of a signal in the time domain. The Dirac function, when convolved with the signal, preserves the signal itself. The Hilbert transform kernel function, when convolved with the signal, can construct an analytic signal. For convolution operations, For frequency shifting operators, with the center frequency Based on this, it was moved to zero frequency (baseband). It is the L2 norm, used to quantize signal energy; Based on the constrained variational optimization model, through a quadratic penalty factor With Lagrange multipliers This model is then converted into an unconstrained model, an unconstrained Lagrangian function is constructed, and the constraints are removed, providing a calculable mathematical model for subsequent iterative solutions using the alternating direction multiplier method. Among them, the secondary penalty factor Used to control the bandwidth compactness of each modal component; the larger the penalty factor value, the stronger the constraint on the modal spectrum bandwidth, the stronger the modal frequency domain compactness, and the stronger the noise interference resistance; Lagrange multipliers The equality constraint relationship used to dynamically enhance the superposition of the original signal and modal components minimizes signal reconstruction deviation and ensures decomposition accuracy; the expression for the unconstrained Lagrangian function is:

[0029] In the formula, It is a quadratic penalty factor that controls the compactness of the modal bandwidth. The larger the value, the stronger the constraint on the modal bandwidth. These are Lagrange multipliers used to enforce equality constraints; Indicates inner product operation; It is an unconstrained Lagrangian function; The original signal is transformed using a variational optimization model with constraints. The optimization process involves minimizing the L2 norm sum after sequential Hilbert transform, frequency shift, and time-domain differentiation. Simultaneously, an equality constraint is added stating that "the sum of all modal function components equals the original signal," resulting in a modal-containing signal. and center frequency A constrained variational optimization model is derived; a quadratic penalty factor is introduced. With Lagrange multipliers The transformation from a constrained variational optimization model to an unconstrained variational optimization model is completed, yielding preliminary modal function components (IMF components). Each IMF component has a finite bandwidth and is concentrated at its corresponding center frequency. nearby; Step 2.2 Based on the unconstrained variational optimization model, iterative updates are performed using the Alternating Direction Multiplier Method (ADMM) algorithm, including updating the initial modal component frequency domain, updating the center frequency, updating the Lagrange multipliers, and determining convergence, as detailed below: (1) Update the frequency domain of the initial modal components: First update the frequency domain of the initial modal function components. After Fourier transforming to the frequency domain, the frequency domain representation of the corresponding mode function components is obtained. Next, the residuals between the original signal and the initial modal function components are calculated. Then, using a weight term constructed from the center frequency and penalty factor, the frequency domain components near the center frequency in the residuals are extracted, and the updated first-order component is output. Frequency domain representation of each modal function component Its expression is:

[0030] In the formula, Indicates Fourier transform, The Fourier transform of the original signal This represents the frequency domain representation of the modal function components. For the frequency domain representation of Lagrange multipliers, For the first In the nth iteration The center frequency of each modal function component; (2) Update the center frequency: based on the updated number of... Frequency domain representation of each modal function component As input, the power spectrum centroid calculation formula is used to... The power spectrum is obtained by performing modulo-square operation, and then multiplied by the center frequency. Integrate to obtain the numerator integral; integrate the power spectrum over the same interval to obtain the denominator integral; divide the numerator and denominator integrals to obtain the updated center frequency. Its expression is:

[0031] In the formula, Power spectrum, To perform integration on the power spectrum along the frequency axis; (3) Update the Lagrange multipliers: Correct the Lagrange multipliers by updating the step size of the multipliers. Summation operation, Subtracting the sum yields the residual data; multiplying the residual data by the multiplier update step size, and then adding it to the frequency domain representation of the Lagrange multipliers, we obtain the updated frequency domain representation of the Lagrange multipliers. Strengthening equality constraints and reducing reconstruction bias, its expression is:

[0032] In the formula, For the first Frequency domain representation of Lagrange multipliers in the next iteration To update the step size for the multiplier, This is the sum of the frequency domain representations of all modal function components after the update; (4) Convergence judgment: After each round of parameter update, calculate the relative rate of change of the modal function components. If the relative rate of change is less than the preset tolerance, the convergence judgment is made. If the iteration converges, the iteration stops and the optimal value is output. One modal function component; otherwise, repeat the above steps until the preset accuracy is reached, iterating until the convergence condition is met. The expression for the convergence condition is:

[0033] In the formula, For the first In the nth iteration Time-domain representation of each modal function component For the first In the nth iteration Time-domain representation of each modal function component Preset tolerance; Specifically, the process of obtaining the TEO-enhanced modal function components in step 3 is as follows: To extract and enhance the transient energy features corresponding to fault impacts from modal function components, the Hilbert Energy Operator (TEO) is used for processing to achieve time-domain enhancement of the transient impact features of bearing faults. The TEO is a nonlinear operator capable of extracting instantaneous energy information from signals. It can directly extract instantaneous energy information from time-domain signals and has extremely high sensitivity to amplitude and frequency abrupt changes in signals, accurately capturing the transient impact features caused by faults. The Hilbert Energy Operator TEO is constructed for continuous-time signals... By combining its amplitude with its first and second derivatives, the instantaneous energy value is calculated. It is highly sensitive to sudden changes in signal amplitude and frequency, and can accurately capture the transient impact characteristics caused by faults. The TEO calculation expression is as follows:

[0034] In the formula, for The first time derivative of represents its rate of change. for The second time derivative of represents the rate of change of its rate of change. This is the TEO operator, used to calculate the instantaneous energy value of a signal; The calculation based on the Hilbert energy operator TEO actually takes the modal function components as input, i.e., discrete-time signals. By approximating the derivative with a difference, a TEO calculation formula adapted to discrete sequences is constructed, and sampling points are extracted. Modal function components at the location Perform squaring operations to generate square terms. Then extract adjacent sampling points. , Corresponding modal function components , The product term of adjacent points is obtained through multiplication; the instantaneous energy data is obtained by subtracting the product term from the squared term and performing TEO nonlinear operations. The sequence is padded with adjacent values ​​at the beginning and end of the sampling points to unify the sequence length, and the energy-enhanced modal components are output, with the following expression:

[0035] In the formula, The first discrete-time input signal One sampling point, The modal function components of the previous sampling point. For the modal function components of the next sampling point, The sampling point number; Finally, the instantaneous energy of TEO at any time is calculated using three sampling points, without requiring the entire signal to participate in the calculation.

[0036] Specifically, the process of obtaining the three-dimensional feature tensor is as follows: Using the modal function components enhanced by TEO as input, multi-channel feature fusion, temporal alignment, numerical standardization and dimensional regularization are completed, and a suitable three-dimensional feature tensor is output to achieve deep fusion of frequency domain physical features and time domain energy features. First, TEO enhanced mode components with different frequency bands and different fault characteristics are spliced ​​and fused along the channel dimension to construct multi-channel features; each channel feature has a clear physical semantics: channel 1 (IMF1) carries the low-frequency trend and basic energy distribution characteristics of the signal, channels 2-3 (IMF2, IMF3) mainly carry the core fault characteristics of the bearing fault resonance frequency band, and channel 4 (IMF4) retains the high-frequency weak impact and detailed fault characteristics. Multi-channel splicing achieves complete coverage of fault characteristics across the entire frequency band; Secondly, the timing of all channels is strictly aligned throughout the process, and the sampling points of all modal function components correspond one-to-one with the timing of the original signal, fully preserving the timing correlation of the original signal and realizing cross-domain correlation and fusion of frequency band partitioning characteristics and time-domain transient energy characteristics. Finally, the concatenated multi-channel features are numerically standardized to eliminate the model training imbalance caused by differences in energy levels among different modal components. Simultaneously, multiple sets of samples are stacked along the batch dimension to construct a normalized three-dimensional feature tensor, with the output tensor having a dimension of [missing information]. ,in 4 represents the batch size, 4 represents the number of feature channels, and 1024 represents the time-series sampling length of a single sample. After this step, a standardized three-dimensional feature tensor with unified dimensions, complete temporal sequence, high feature recognition, and clear physical meaning is finally obtained. It can be directly used as high-quality input data for subsequent intelligent bearing fault diagnosis models, effectively solving the technical problem of difficulty in identifying strong noise and weak fault features of low-speed bearings in ports.

[0037] Example 1: Example of a method to enhance vibration signals during bearing faults This embodiment is based on the aforementioned bearing vibration signal enhancement method based on VMD-TEO multi-channel fusion, which is constructed as a three-stage collaborative architecture of frequency division, enhancement, and fusion. Frequency domain decomposition and time domain enhancement are organically combined to form a complete fault feature enhancement process, such as... Figure 3As shown, the specific steps are as follows, executed in sequence: Step 1: Obtain the raw signal of the low-speed rolling bearing ; Step 2: Addressing the non-stationary characteristics and high noise background of low-speed bearing vibration signals in ports, this module, based on the aforementioned VMD theory and employing a parameterized optimization strategy, achieves efficient and robust frequency domain feature separation. In the overall method, the VMD decomposition module performs the function of frequency domain preprocessing; its core task is to decompose the original one-dimensional vibration signal into... These components are approximately orthogonal IMF components (modal function components); oscillation modes in different center frequency ranges are captured by these components, and a high-quality input basis is thus provided to the subsequent TEO time-domain enhancement stage; Based on the variational optimization framework, this module uses the ADMM algorithm to iteratively solve the IMF components in the frequency domain. The parameter configuration is set according to the empirical analysis results of the spectral characteristics of the vibration signal of the low-speed bearing in the port, aiming to balance decomposition accuracy, computational efficiency, and robustness to noise. Its implementation process includes the following: (1) Original signal It performs data format reconstruction processing, converting one-dimensional time series data into a standard single-channel time series tensor format. It also supports automatic batch stacking and parallel computing of large batch sample data, and supports GPU parallel computing. (2) Four initial center frequencies are evenly set to cover the area. Frequency domain range; through spectrum analysis, it was verified that the main energy of the port bearing signal is concentrated in four significant frequency bands, corresponding to the low-frequency trend, fault resonance frequency band, and high-frequency noise; the number of modes was set. It can cover the physical scale of fault characteristics, avoiding mode mixing caused by under-decomposition or spurious components introduced by over-decomposition; when At this time, multi-band decoupling cannot be achieved, and the fault resonance characteristic components will severely overlap with low-frequency trends and high-frequency noise components, resulting in mode aliasing and making it impossible to separate effective fault features; when At this time, a large number of redundant decomposition components are generated, introducing spurious modes without physical meaning, which greatly increases the computational load of algorithm iteration, causing a doubling of computational cost and a reduction in operational efficiency. At the same time, it is easy to dilute the real fault characteristics. It can be seen that the frequency domain representation of the four modal function components is obtained, and its expression is:

[0038] This operation essentially constitutes an adaptive bandpass filtering process, in which a penalty factor is set. Punishment factor Its function is to control the frequency domain bandwidth compactness of each IMF modal component. This value is determined through grid search optimization. As its value increases, the bandwidth of each IMF narrows accordingly, and the frequency domain compactness is enhanced, thereby improving the noise suppression effect. Given that the background noise spectrum is relatively wide under port operation conditions, reasonable selection can keep the center frequency interval of each IMF component clear and effectively reduce energy leakage between modes. In addition, this parameter is compatible with the signal sampling frequency of 12kHz to prevent the loss of impact characteristics due to excessive smoothing. The centroids of the power spectra of each IMF are calculated as follows:

[0039] To enable the center frequency to adaptively track the energy concentration band, a convergence tolerance is set. After each iteration, the relative error is checked to ensure that the condition is met. The algorithm terminates prematurely if the convergence condition is too strict; strict convergence conditions are required to ensure decomposition stability; excessively loose tolerance can lead to premature termination of iterations, insufficient modal decomposition, incomplete frequency band decoupling, and residual mode aliasing; conversely, excessively tight tolerance settings can significantly increase the number of invalid iterations, increasing computation time without improving decomposition accuracy; experiments show that... It converges in an average of 15 iterations, balancing efficiency and accuracy. (3) Finally, four IMF components were obtained. Each component exhibits compact support characteristics in the frequency domain; the initial center frequency is uniformly distributed, effectively avoiding convergence fluctuations caused by random initialization; each component contains no DC component because the bearing signal has undergone pre-descaling processing; the Lagrange multiplier update step size. The default gradient update strategy is used to ensure the overall decomposition quality.

[0040] Therefore, the key to the VMD algorithm lies in accurately determining the optimal... and To achieve the best noise reduction effect, this parameter optimization process is crucial to ensuring the effectiveness and reliability of VMD in signal processing.

[0041] Step 3: Apply TEO operations to each IMF component after VMD decomposition, instead of directly processing the original signal, to avoid amplifying noise components and achieve the synergistic advantages of frequency division enhancement. The implementation steps are as follows: (1) Input preprocessing: Receive the four IMF components generated by VMD decomposition. Each component has a length of 1024 points; (2) Point-by-point TEO calculation: TEO calculation is performed independently on the internal data points of each IMF component, excluding the first and last points. The expression is as follows:

[0042] In the formula, For the first After the IMF component is processed by TEO, the first... The instantaneous energy value of each sampling point. For the first The first IMF component One original sampling point, For the first The first IMF component One sampling point, For the first The first IMF component One sampling point; (3) Boundary processing: The neighbor point copying strategy is adopted for the first and last points of the sequence to ensure the integrity of the sequence; specifically: the first point copies the TEO operation result of the second point, and the last point copies the TEO operation result of the 1023rd point, so that the length of the enhanced IMF component is still 1024 points, maintaining the temporal continuity, without data loss, and avoiding feature breaks caused by the first and last points not participating in the operation. (4) Output reconstruction: Generate 4 enhanced IMF components They are pieced together along the channel dimension to form a shape. The three-dimensional feature tensor provides input for subsequent diagnostic models; This mechanism, together with the VMD decomposition module, forms a two-stage collaboration in the frequency and time domains. VMD adaptively decomposes the signal into IMF components with clear physical meaning, initially separating fault features from noise. Based on the principle of TEO, the TEO operator is sensitive to sudden changes in signal frequency or amplitude, and can observe obvious abrupt changes at the moment of change. This makes the TEO operator very suitable for analyzing transient signals. The design of this mechanism ensures that the weak fault features of low-speed bearings can be effectively extracted and enhanced under the strong noise conditions of the port, providing high-quality and highly discriminative input features for subsequent diagnostic models.

[0043] Step 4: Using the modal function components enhanced by TEO as input, complete multi-channel feature fusion, temporal alignment, numerical standardization and dimensional regularization, and output a suitable three-dimensional feature tensor; First, TEO enhanced mode components with different frequency bands and different fault characteristics are spliced ​​and fused along the channel dimension to construct multi-channel features; each channel feature has a clear physical semantics: channel 1 (IMF1) carries the low-frequency trend and basic energy distribution characteristics of the signal, channels 2-3 (IMF2, IMF3) mainly carry the core fault characteristics of the bearing fault resonance frequency band, and channel 4 (IMF4) retains the high-frequency weak impact and detailed fault characteristics. Multi-channel splicing achieves complete coverage of fault characteristics across the entire frequency band; At the same time, the timing of all channels is strictly aligned throughout the process, and the sampling points of all modal function components correspond one-to-one with the timing of the original signal. Finally, the concatenated multi-channel features are numerically standardized, and multiple sets of samples are stacked along the batch dimension to construct a normalized three-dimensional feature tensor. The output tensor has a dimension of [missing value]. ,in 4 represents the batch size, 4 represents the number of feature channels, and 1024 represents the time-series sampling length of a single sample.

[0044] Example 2: Simulation Verification of the Example To verify the effectiveness of the VMD-TEO collaborative fault feature enhancement method, this embodiment uses the publicly available rolling bearing dataset from the University of Paderborn (PU) for experimental verification. It should be noted that low-speed conditions are explicitly defined as speeds below 100 rpm. Among widely used public datasets, the 900 rpm condition in the PU dataset represents the lowest achievable speed. This section uses this dataset for experiments to preliminarily verify and analyze the feature enhancement effect of the proposed method at relatively low speeds. The PU experimental platform consists of five parts: a drive motor, a torque measurement shaft, a rolling bearing test module, a flywheel (balancing load), and a load motor. An accelerometer is installed on the outer ring of the bearing housing to collect bearing vibration signals at a sampling frequency of 64 kHz. Figure 4 As shown, the technical effects of the present invention are verified by simulation. The specific implementation process is as follows: The sensor data acquisition object was the bearing vibration signal collected under the conditions of a drive motor speed of 900 rpm, a load of 0.7 Nm, and a radial force of 1000 N. The bearing model was a deep groove ball bearing SKF6203, which included one normal state and four fault states. Faults were artificially added to the rolling bearing using an electric engraving machine, including two types of faults: inner ring faults and outer ring faults. Each fault severity level had two levels. The detailed experimental data are shown in Table 1.

[0045] Table 1 PU Dataset

[0046] The original signal has 256,000 data points. To accommodate the input requirements of the subsequent ResNet1D model, a fixed-length sliding window is used to segment the signal. The sliding window length is set to 1024 points, with an overlap rate of 50%, resulting in a sliding step size of 512. For a length of... The number of samples obtainable from the original signal by sliding window segmentation The calculation formula is:

[0047] Each complete signal yields 499 samples. The experiment used data from 5 different bearing conditions: 1 normal condition and 4 fault conditions; therefore, the total number of samples is [number missing]. Each sample is a 1024-dimensional one-dimensional vibration sequence.

[0048] To further improve data consistency, each individual sample is normalized and scaled to adjust its numerical range to [value range missing]. Interval. Normalization calculation is as follows:

[0049] In the formula: The original amplitude sequence of the sample; This is the minimum value of the signal sequence; This is the maximum value of the signal sequence, designed to eliminate differences in signal amplitude dimensions and accelerate model training convergence.

[0050] During the dataset partitioning process, the order of all samples was shuffled to ensure the uniformity of data distribution across categories. Samples were allocated to the training, validation, and test sets in a 7:2:1 ratio. The training set contained 1746 samples, the validation set contained 499, and the test set contained 250, totaling 2495 samples, all collected under the same operating conditions—900 rpm, 0.7 Nm of load torque, and 1000 N of radial force. This partitioning strategy effectively maintained data randomness, providing sufficient and independent data support for model training, parameter tuning, and performance evaluation.

[0051] To examine the feature enhancement capabilities of the VMD-TEO method in bearing fault diagnosis, this study constructed a complete time-frequency domain comparison experimental framework. The experiments were conducted using the PU public dataset, covering four typical fault scenarios: KA05 outer ring fault, KA06 outer ring fault, KI05 inner ring fault, and KI07 inner ring fault. All samples were truncated using the sliding window method and uniformly normalized to the [0,1] interval to eliminate the influence of dimensional differences. The experiment consisted of two parts: time-domain enhancement analysis and frequency-domain enhancement analysis, with the specific configuration as follows: Time-domain analysis aims to visually demonstrate the effectiveness of VMD-TEO in extracting transient impact components and suppressing noise in the original vibration signal. The experiment selects the first sample from the training set for each type of fault, with a sampling frequency set to... The corresponding time length is 102.4 ms. VMD mode count Punishment factor After decomposition, four intrinsic mode functions (IMFs) are obtained. The Teager energy operator is applied to each IMF for nonlinear energy tracking. The four IMF components after TEO processing are added point by point to reconstruct a one-dimensional enhanced signal sequence, which is used to compare the time-domain waveform with the original signal.

[0052] Frequency domain analysis focuses on the prominence of fault characteristic frequencies and background noise suppression capabilities within the envelope spectrum. Using the same four experimental samples, Hilbert envelope spectra were calculated for both the original signals and the VMD-TEO enhanced signals. A Hilbert transform was performed to obtain the analytic signal; the modulus was taken to obtain the instantaneous envelope; the envelope mean was removed; a Fast Fourier Transform was performed, and the first half of the spectrum was extracted; the spectral amplitude was normalized to obtain the normalized envelope amplitude. The frequency range was limited to 0-300Hz, covering the bearing fault characteristic frequencies and their main harmonic components.

[0053] Figures 5 to 8 These are comparison charts of the original vibration signals and time-domain enhanced signals for KA05 outer ring fault Level 1, KA06 outer ring fault Level 2, KI05 inner ring fault Level 1, and KI07 inner ring fault Level 2.

[0054] The original vibration signal exhibits significant non-stationarity and complexity, a result of the combined effects of background noise and transmission path modulation. In the Level 1 state of minor damage, the periodic transient impacts, masked by strong background noise, are excited by local defects in the bearing, making their fault characteristics difficult to identify visually. In the Level 2 state of severe damage, although the impact amplitude increases, dense oscillations and waveform distortion still make it difficult to extract the individual impact components. Even with increased impact intensity, waveform interference is not significantly reduced. Experimental figures show that effective separation of fault information is constrained by both noise masking and signal distortion.

[0055] exist Figure 7 and Figure 8 The method effectively reconstructs characteristic waveforms. Under condition KI05, the originally chaotic time-domain waveform is transformed into a sparsely distributed pulse sequence, clearly revealing the periodic fault characteristics. Under condition KI07, the main energy concentration areas at 35ms, 65ms, and 90ms are effectively reproduced, and the amplitudes of each peak highly correspond to the violently oscillating parts in the original signal. After VMD processing, the bearing signal exhibits reduced noise components, becoming more periodic and regular. Simultaneously, it reduces the impact of noise on the similarity of similar samples, making waveforms more similar between data of the same type and different between data of different types.

[0056] Figures 9 to 12Comparison of the envelope spectra of the original signals and the frequency-domain enhanced signals of KA05, KA06, KI05, and KI07.

[0057] Experiments reveal that the envelope spectrum of the original signal, while exhibiting several high-amplitude peaks in the low-frequency band, displays significant spikes overall, with a high and chaotic background noise floor. This complex spectral structure often results in the true fault characteristic frequencies being submerged in a large number of interference components, making accurate frequency identification and demodulation analysis difficult. The enhanced envelope spectrum processed by VMD-TEO effectively filters out high-frequency random noise and non-fault-related modulation sidebands, resulting in a smoother spectral baseline and significantly improved signal-to-noise ratio. Furthermore, the VMD-TEO method concentrates the dispersed energy at the fault characteristic frequencies and their harmonics.

[0058] exist Figure 9 and Figure 10 In the enhanced spectrum, multiple false peaks mixed in the original spectrum are effectively suppressed, and the energy is mainly concentrated in the fundamental frequency and its harmonics in the low frequency band, clearly reflecting the periodic impact characteristics of the outer ring fault.

[0059] exist Figure 11 and Figure 12 In the original spectrum, the inner ring fault is usually accompanied by complex modulation effects, making it appear particularly chaotic. However, the enhanced spectrum not only retains the main fault characteristic frequency components but also clearly presents the sideband structure with frequency shift intervals. This indicates that VMD-TEO removes noise and preserves the key modulation information in the inner ring fault vibration signal quite well.

[0060] The combined analysis results in the time and frequency domains show that after processing by the VMD-TEO method, the periodic impulse components of signals with different fault types and damage levels are highlighted in the time domain, and they also exhibit purer and more concentrated characteristic frequencies and modulation sidebands in the frequency domain, which is beneficial for subsequent fault feature extraction and diagnosis.

[0061] To verify the enhancement effect of the proposed full-component VMD-TEO synergistic enhancement mechanism on fault characteristics at the signal level, this study empirically demonstrates the necessity and advantages of the synergistic operation of VMD decomposition and TEO energy operator from multiple dimensions, including impulse characteristics, signal-to-noise ratio, and frequency domain concentration, through direct comparison with baseline methods.

[0062] This study employed four comparative methods: using the original signal as a baseline without any processing; performing only VMD decomposition and taking the IMF component with the highest energy as representative; directly performing TEO transformation on the original signal; and using a full-component collaborative enhancement strategy. Kujicin, peak factor, signal-to-noise ratio, and envelope spectrum peak significance were used for evaluation. The key performance indicators of the different methods are compared in Table 2.

[0063] Table 2 Comparison of Key Indicators for Different Methods

[0064] In summary, through comparative experiments, the VMD-TEO fault feature enhancement method demonstrates significant effectiveness, achieving the highest values ​​in both kurtosis and peak factor. This is because processing low-frequency signals results in longer fault periods, leading to an overly large scale of the structural element chosen based on the selection principle in the verification method. This causes the filtering process to completely cover the fault features, failing to effectively extract them. This indicates that besides the optimal IMF carrying the main fault information, other IMF components also contain valuable impact margins related to the fault. Superimposing their TEO energy can significantly enhance the fault impact features. The trend of this strategy is consistent with the impact index, and it achieves the highest signal-to-noise ratio, improving it by approximately 8.5 dB compared to the original signal, indicating that it has the best noise suppression effect when enhancing fault features. The peak significance of the envelope spectrum is a key indicator, and this strategy improves it to 12.5, proving that the peak values ​​of the fault feature frequencies in the envelope spectrum of the processed signal are extremely prominent and clear relative to the background noise.

[0065] The relevant modules involved in this system are all hardware system modules or functional modules that combine computer software programs or protocols with hardware in the prior art. The computer software programs or protocols involved in these functional modules are technologies known to those skilled in the art and are not improvements to this system. The improvement of this system lies in the interaction or connection between the modules, that is, in improving the overall structure of the system to solve the corresponding technical problems that this system aims to address.

[0066] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for enhancing bearing vibration signals based on VMD-TEO multi-channel fusion, characterized in that, The specific process is as follows: Step 1: Obtain the raw signal of the rolling bearing ; Step 2: Construct a constrained variational optimization model based on the variational mode decomposition method. By introducing a quadratic penalty factor and Lagrange multipliers, the constrained variational optimization model is transformed into an unconstrained variational optimization model. The original signal is input into the unconstrained variational optimization model to obtain preliminary modal function components. The alternating direction multiplier method is used to iteratively update the modal function components, center frequency, and Lagrange multipliers. Convergence is determined based on the iterative relative rate of change, and the modal function components are obtained. The specific process for obtaining the modal function components in step 2 is as follows: Step 2.1 Construct a variational optimization model with constraints, as shown in the following expression: ， , In the formula, This represents the time partial derivative, i.e., the gradient operator. For the Dirac function, For the Hilbert transform kernel function, For convolution operations, For frequency shifting operators, It is the L2 norm. for Group of preliminary modal function components; Through secondary penalty factors With Lagrange multipliers The constrained variational optimization model is transformed into an unconstrained variational optimization model, as shown in the following expression: ， In the formula, As a secondary penalty factor, For Lagrange multipliers, Indicates inner product operation; For an unconstrained Lagrangian function, The center frequency; The original signal is transformed using a variational optimization model with constraints. The optimization process involves minimizing the L2 norm sum after sequential Hilbert transform, frequency shift, and time-domain differentiation. Simultaneously, an equality constraint is added stating that "the sum of all modal function components equals the original signal," resulting in a modal-containing signal. and center frequency A constrained variational optimization model is derived; a quadratic penalty factor is introduced. With Lagrange multipliers The transformation from a constrained variational optimization model to an unconstrained variational optimization model is completed, and preliminary modal function components are obtained. Step 2.2 Based on the unconstrained variational optimization model, iterative updates are performed using the alternating direction multiplier method, including updating the initial modal component frequency domain, updating the center frequency, updating the Lagrange multipliers, and determining convergence, as detailed below: (1) Update the frequency domain of the initial modal components: First update the frequency domain of the initial modal function components. After Fourier transforming to the frequency domain, the frequency domain representation of the corresponding mode function components is obtained. Next, the residuals between the original signal and the initial modal function components are calculated. Then, using a weight term constructed from the center frequency and penalty factor, the frequency domain components near the center frequency in the residuals are extracted, and the updated first-order component is output. Frequency domain representation of each modal function component ; Its expression is: ， In the formula, Indicates Fourier transform, The Fourier transform of the original signal This represents the frequency domain representation of the modal function components. For the frequency domain representation of Lagrange multipliers, For the first In the nth iteration The center frequency of each modal function component; (2) Update the center frequency: based on the updated number of... Frequency domain representation of each modal function component As input, the power spectrum centroid calculation formula is used to... The power spectrum is obtained by performing modulo-square operation, and then multiplied by the center frequency. Integrate to obtain the numerator integral; integrate the power spectrum over the same interval to obtain the denominator integral; divide the numerator and denominator integrals to obtain the updated center frequency. Its expression is: , In the formula, Power spectrum, To perform integration on the power spectrum along the frequency axis; (3) Update the Lagrange multipliers: Correct the Lagrange multipliers by updating the step size of the multipliers. Summation operation, Subtracting the sum yields the residual data; multiplying the residual data by the multiplier update step size, and then adding it to the frequency domain representation of the Lagrange multipliers, we obtain the updated frequency domain representation of the Lagrange multipliers. Its expression is: , In the formula, For the first Frequency domain representation of Lagrange multipliers in the next iteration To update the step size for the multiplier, This is the sum of the frequency domain representations of all modal function components after the update; (4) Convergence criterion: Calculate the relative rate of change of the modal function components. If the relative rate of change is less than the preset tolerance, If the iteration converges, the iteration stops and the optimal value is output. One modal function component; otherwise, repeat the above steps until the preset accuracy is reached, iterating until the convergence condition is met. The expression for the convergence condition is: , In the formula, For the first In the nth iteration Time-domain representation of each modal function component For the first In the nth iteration Time-domain representation of each modal function component Preset tolerance; Step 3: Using the modal function components as input, the Hilbert energy operator is used to perform instantaneous energy calculations component by component to obtain the enhanced modal function components after TEO. The specific process for obtaining the TEO-enhanced modal function components in step 3 is as follows: Constructing the Hilbert Energy Operator (TEO) for continuous-time signals The instantaneous energy value is calculated by combining its amplitude with its first and second derivatives. The operational expression for its TEO is as follows: , In the formula, for The first time derivative, for The second time derivative, For TEO operators; Based on the Hilbert energy operator TEO, the modal function components are used as inputs, i.e., discrete-time signals. By approximating the derivative with a difference, a TEO calculation formula adapted to discrete sequences is constructed, and sampling points are extracted. Modal function components at the location Perform squaring operations to generate square terms. ; Then extract adjacent sampling points , Corresponding modal function components , The product term of adjacent points is obtained through multiplication; the product term is subtracted from the squared term, and the instantaneous energy data is obtained through TEO nonlinear operation. The sequence's first and last boundary sampling points are padded with adjacent values ​​to unify the sequence length. The energy-enhanced modal components are then output, with the following expression: ， In the formula, The first discrete-time input signal One sampling point, The modal function components of the previous sampling point. For the modal function components of the next sampling point, The sampling point number; Finally, the instantaneous energy of TEO at any time is calculated using multiple sampling points without the need for the entire signal to participate in the calculation; Step 4: The enhanced modal function components are spliced ​​along the channel dimension to construct a multi-channel feature tensor, which is then standardized to obtain a three-dimensional feature tensor.

2. The low-power passive underwater wake-up receiving system based on acoustic black holes according to claim 1, characterized in that, The specific process for obtaining the three-dimensional feature tensor is as follows: Using the modal function components enhanced by TEO as input, multi-channel feature fusion, temporal alignment, numerical standardization and dimensional regularization are completed, and a suitable three-dimensional feature tensor is output. First, First, TEO-enhanced modal components with different frequency bands and fault characteristics are spliced ​​and fused along the channel dimension to construct multi-channel features. Second, strict timing alignment of all channels is ensured throughout the process, with each sampling point of the modal function component corresponding one-to-one with the timing of the original signal. Finally, the spliced ​​multi-channel features are numerically standardized, and multiple sets of samples are stacked along the batch dimension to construct a normalized three-dimensional feature tensor. The output tensor has a dimension of [missing information]. .

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