A small sample bearing compound fault decoupling method and system based on frequency-aware continuous latent dynamics

Abstract

The application discloses a kind of frequency-aware continuous potential dynamics small sample bearing compound fault decoupling method and system, belong to mechanical condition monitoring technical field.Aiming at the problem that discrete network mapping under the constraint of strong noise and small sample is easy to cause feature entanglement, its steps are:1.acquisition bearing operation vibration signal constructs small sample data set;2.use phase-preserving frequency attention encoder to process vibration signal, extract initial state feature after noise reduction;3.feature decoupling is set as continuous initial value problem controlled by neural differential equation, replace discrete layer structure by dynamic integral evolution of continuous potential dynamics, and use solver to solve decoupled features along disjoint trajectories;4.according to decoupled feature output bearing compound fault diagnosis result.The application is mainly used for rotating machinery diagnosis under harsh conditions, realize feature topology decoupling and state evaluation under low signal-to-noise ratio and sparse label conditions.

Description

Technical Field

[0001] This invention relates to the field of intelligent condition monitoring and deep learning, specifically to a method and system for decoupling small-sample bearing composite faults with frequency-aware continuous potential dynamics, and particularly to a continuous-time dynamic evolution scheme that can overcome feature entanglement caused by discrete space mapping and achieve highly robust fault decoupling under strong noise. Background Technology

[0002] The reliability of rotating machinery largely depends on the structural integrity of rolling bearings. In practical industrial applications, mechanical degradation typically occurs as complex faults rather than isolated defects. Constrained by severe noise and sparse tagging data, diagnosing concurrent complex mechanical faults has become a persistent core bottleneck in condition monitoring. This is because the dominant vibrational energy of severe defects can mask the weak high-frequency pulses of earlier secondary faults, and strong non-stationary background noise can disrupt signal phase, leading to highly coupled fault characteristics.

[0003] Existing technical solutions for decoupling and diagnosing complex faults can be mainly divided into three categories, all of which have significant technical shortcomings in practical applications: The first category consists of traditional advanced signal processing methods, such as Variational Mode Decomposition (VMD). These methods perform well in stable environments, but struggle to effectively separate overlapping cross-modulation signals when faced with strong non-stationary background noise and a lack of concurrent multi-component fault lifecycle data. The second category comprises traditional deep learning frameworks based on discrete spatial transformations (such as CNN, ResNet, and Transformer). These methods process vibration signals through discrete, layer-by-layer spatial transformations. Under constraints of strong noise (e.g., -4dB) and small sample sizes (e.g., 10-shot), these coarse jumps between hidden states can trigger sudden topological distortions. The network often fails to establish smooth boundaries between intertwined features, leading to hyperplane collapse and severe feature entanglement, resulting in a loss of decoupling reliability. The third category includes Generative Adversarial Enhancement (GANs) and Zero-Shot Learning (ZSL) methods to address data scarcity. Although such methods can synthesize training distributions, their large number of parameters increases the risk of overfitting, and deploying large generation pipelines under industrial noise introduces huge computational overhead, making them difficult to deploy practically on resource-constrained edge devices.

[0004] Furthermore, existing diagnostic models typically treat fault classification as a single-label problem or use standard multi-label evaluation metrics (such as Macro-F1) that assign partial scores to incomplete predictions, failing to rigorously verify whether overlapping physical features are truly decoupled. There is an urgent need for a closed-loop diagnostic technology solution that is lightweight in architecture, parameter-efficient, and conforms to physical laws. Summary of the Invention

[0005] To address the technical problems of existing deep learning diagnostic frameworks relying on discrete space mapping under strong noise and small sample conditions, leading to decision boundary collapse, feature entanglement, and excessive computational overhead, this invention proposes a small-sample bearing composite fault decoupling method and system based on frequency-aware continuous latent dynamics. This method, by constructing a frequency-aware continuous dynamics (FA-NODE) ​​framework, for the first time sets fault feature decoupling as a continuous initial value problem (IVP) controlled by neural ordinary differential equations (ODEs). The system integrates a phase-preserving frequency attention denoising encoder (FADE) to provide a noise-filtered initial state, enabling the ODE solver to guide overlapping and entangled features to smoothly decouple along disjoint continuous trajectories according to the Picard-Lindelöf theorem. This invention achieves a paradigm shift from discrete space mapping to continuous-time dynamic evolution, effectively improving the model's noise robustness and decoupling accuracy with extremely low parameter counts. The technical solution adopted in this invention includes the following steps:

[0006] Step 1: Construct a data acquisition and preprocessing module to obtain the original mixed vibration signal of the rotating machinery and perform noise addition and preprocessing operations;

[0007] Step 2: Construct a phase-preserving frequency attention denoising encoder (FADE). During training, the amplitude and phase spectra of the input signal are decoupled. While adaptively reconstructing the amplitude mask, the physical phase geometric features are strictly preserved. The output denoised signal is used as the initial state for subsequent continuous evolution.

[0008] 2.1 Processing one-dimensional raw input signals using a dual-path encoder By combining wide receptive field convolution to extract low-frequency structural contours and using micro residual bypass to extract high-frequency components, a deep latent intermediate representation is obtained. The calculation formula is:

[0009]

[0010] in, The original input vibration signal is N, where N is the number of sampling points per sample. This represents compound operations (including batch normalization and non-linear activation functions). For wide receptive field convolution kernels, This is a Qualcomm bypass convolution kernel; For the fused deep potential intermediate representation, C=32 is the number of output channels.

[0011] 2.2 Apply Real-DFT to each channel sequence The amplitude spectrum of the decoupled signal Phase spectrum ;

[0012] 2.3 Apply adaptive amplitude modulation and utilize the learned frequency attention mask Recalibrate the amplitude spectrum to obtain the enhanced amplitude. At the same time, strictly maintain the phase spectrum Unchanged, to preserve the original geometric and temporal form of the mechanical impact;

[0013] 2.4 Features are reconstructed using Inverse Real Discrete Fourier Transform (IFFT), and a hybrid fusion strategy is employed to prevent excessive smoothing of minute fault pulses. The calculation formula is as follows:

[0014]

[0015] in, An empirical coefficient for controlling the proportion of the original high-frequency random components retained.

[0016] Step 3: Construct a continuous neural dynamics evolution module, project the denoised mixed signal as the initial state onto the continuous phase space, and use the neural constant differential equation engine to drive the dynamic evolution of features.

[0017] 3.1 Project the denoised hybrid signal x_hybrid output by the FADE module onto the latent space to define the initial state vector for the continuous initial value problem. Where D=64 is the number of encoder output channels.

[0018] 3.2 Through shared neural network weights Parameterized autonomous velocity field Control the hidden state During continuous integration time The evolution within is calculated using the following formula:

[0019]

[0020] 3.3 The continuous neurodynamics evolution module uses a fourth-order Runge-Kutta RK4 numerical solver to integrate the velocity field to obtain the terminal decoupled state. Feature topological entanglement is prevented by integrating non-crossing trajectories;

[0021] The continuous neurodynamic evolution module is performed using the accompaniment sensitivity method. Backward gradient optimization for memory efficiency, defining the adjoint state as The gradient of the parameters is calculated by inverse time integration, and the formula is as follows:

[0022]

[0023] in, This represents the transpose of the adjoint vector.

[0024] 3.4 A global residual connection is introduced to form the final decoupled representation, and the calculation formula is as follows: Pool(·) is a global adaptive average pooling operation that calculates the average value of each channel along the time dimension, compresses the sequence into a single scalar, and outputs a fixed size of 1.

[0025] Step 4: Construct a label-related multi-label diagnosis and joint optimization mechanism, identify concurrent states through the correlation matrix, and perform end-to-end joint training;

[0026] 4.1 Extracted continuous features Projection is based on logic values And through a learnable label correlation matrix Calculate cross-tag interactions and derive relevant logical outputs. ;

[0027] 4.2 Construct a multi-task joint optimization objective and integrate a multi-label focus loss function. Reconstruction loss function with mean square error Total loss The calculation formula is:

[0028]

[0029] Step 5: Encapsulate the trained optimized model into a target task inference system, and output composite fault diagnosis results based on a rigorous 3-bit exact match metric (Comp_Acc). Furthermore, the method uses a continuous differential topology as a physical inductive bias to maintain consistent parameter configuration across different datasets and mixed noise settings. Moreover, a strict exact match composite accuracy (Comp_Acc) metric is employed to reject local score biases, ensuring industrial-grade reliability.

[0030] A frequency-aware, continuous latent dynamics-based small-sample bearing composite fault decoupling system includes:

[0031] The data acquisition and configuration module is used to acquire one-dimensional vibration signals of mechanical rotating bodies under strong background noise and sparse sample constraints.

[0032] The phase-preserving frequency attention denoising coding (FADE) module has a built-in wide receptive field and micro residual dual-path structure to decouple the amplitude and phase spectrum of the input signal. It reconstructs the amplitude mask under the premise of absolutely locking the physical phase geometric features and outputs denoising features to alleviate the numerical rigidity of the subsequent continuous solver.

[0033] The continuous phase space projection and neural dynamics solution module has a built-in neural ordinary differential equation (ODE) solver, which is used to set the denoised features as initial vectors and perform continuous integral calculations based on the autonomous velocity field that satisfies the Lipschitz continuity condition, mapping the original overlapping features to independent decision manifolds.

[0034] The multi-label classification and high memory efficiency optimization module is used to perform strict multi-label concurrent judgment based on the label association matrix of dynamic learning, and to perform high parameter efficiency optimization by using the adjoint integral in the backpropagation.

[0035] The lightweight model inference application module is used to encapsulate diagnostic models with extremely low parameter counts, and to perform real-time, highly robust, and accurate matching diagnostic outputs in the presence of strong noise.

[0036] Compared with the prior art, the beneficial effects of the present invention are:

[0037] (1) Filling architectural gaps and realizing paradigm innovation. This invention is the first to transform the decoupling of complex faults into the initial value problem of continuous ordinary differential equations. By replacing discrete spatial transformation with continuous dynamic evolution of neurons, it fundamentally prevents the hyperplane collapse and feature entanglement phenomena that are common in traditional deep learning models under strong noise and small sample conditions.

[0038] (2) Precise denoising and preservation of physical features. The designed FADE module can suppress -4dB high-intensity mixed noise while strictly locking the phase geometry features of mechanical impact, avoiding the problem of excessive smoothing of small fault pulses caused by traditional convolution denoising, providing an extremely stable initial state for the continuous solver and avoiding numerical rigid divergence.

[0039] (3) High robustness and accurate diagnosis under extreme constraints. Under extreme constraints of only 10 training samples and a severe signal-to-noise ratio of -4dB, this method can still maintain highly reliable accurate matching and decoupling performance, avoiding the missed detection or misjudgment of concurrent faults by traditional models. Its generalization ability and robustness are significantly better than existing parallel capsule networks (PCN) and Transformer architectures.

[0040] (4) Extremely low computational overhead, easy to deploy at the edge. Thanks to the accompanying sensitivity optimization method and continuous mapping mechanism, the model of this invention only requires about 19.8K parameters. Its computational memory usage is much lower than that of traditional network structures. It does not require the huge data synthesis overhead of generative adversarial networks (GANs), making it extremely suitable for deployment on resource-constrained industrial edge devices. Attached Figure Description

[0041] Figure 1 The overall architecture and workflow diagram of the FA-NODE framework of this invention;

[0042] Figure 2 Detailed architecture diagram of the FADE module of this invention;

[0043] Figure 3 The present invention presents a comparison of three-dimensional spectrum visualizations before and after applying the FADE module on different datasets.

[0044] Figure 4 A 2D visualization comparison of feature extraction trajectories from continuous potential dynamic evolution and traditional discrete spatial mapping in this invention;

[0045] Figure 5 A schematic diagram comparing the multi-label concurrent prediction output mechanism of this invention with that of a traditional classifier;

[0046] Figure 6 The waveform comparison of signal degradation with noise on the real dataset (HUST) and the synthetic dataset (Custom-Lab) is shown in the present invention.

[0047] Figure 7 Radial histogram comparing the Comp_Acc performance of this invention under different signal-to-noise ratio constraints;

[0048] Figure 8 A comparison of the deep latent features t-SNE visualization distribution of this invention and the baseline model. Detailed Implementation

[0049] According to an embodiment of the present invention, a method for decoupling small-sample bearing composite faults based on frequency-aware continuous potential dynamics is provided. The specific implementation method is described in detail below.

[0050] The frequency-aware continuous latent dynamics-based small-sample bearing composite fault decoupling method provided in this embodiment is implemented based on the PyTorch deep learning framework. It has been validated on the HUST public benchmark dataset and a custom-lab dataset for concurrent mechanical fault diagnosis tasks. The specific implementation steps are as follows:

[0051] 1. System overall architecture and workflow. Figure 1 The overall architecture and workflow of the FA-NODE closed-loop decoupling system of this invention are presented. The system consists of four stages: First, data is collected through a test bench and mixed noise is injected, including 80% Gaussian interference and 20% high-energy random pulses to simulate a real industrial degradation environment; then, the damaged signal is input into the FADE module, decoupled, and the key phase structure is retained for filtering; next, the filtered features are projected onto a continuous phase space, and the neural ODE engine performs continuous-time extrapolation to demodulate the cross-modulation; finally, the concurrent state is identified through correlation-aware multi-label head and the accurate matching result is output.

[0052] 2. FADE module construction and initialization phase, Figure 2 This is the detailed architecture of the FADE module. The module employs a dual-path encoder: the upper path is a wide receptive field convolution with a kernel size of 31, used to extract the low-frequency structural contours such as the fundamental frequency and harmonics of the bearing rotation; the lower path is a point-by-point convolution bypass with a kernel size of 1, used to preserve the high-frequency transient edges of the fault impact pulse. The two outputs are batch normalized and activated by GELU before being added and fused into a deep latent space. Subsequently, a real-valued discrete Fourier transform is performed on each channel to decouple the signal into amplitude and phase spectra. Here, only the amplitude portion is calibrated and amplified using a learnable frequency attention mask, while the phase spectrum remains strictly unchanged, thus filtering out background noise without destroying the temporal location information of the mechanical impact event. After inverse FFT reconstruction, a hybrid fusion strategy is used to output a denoised signal: α is an empirical coefficient, which defaults to 0.2 and is used to control the proportion of high-frequency random components in the original signal to be retained, preventing weak early fault pulses from being over-smoothed. Figure 3 By comparing the three-dimensional spectra before and after FADE processing under different noise levels, it can be seen that the peak position and peak shape of the spectrum after FADE noise reduction are basically consistent with those of the clean target spectrum. It can still effectively recover the characteristic frequency under -4dB strong noise, while the fault frequency peak in the unprocessed -4dB signal is completely submerged in the noise substrate.

[0053] 3. Continuous latent dynamics solution and optimization stage. During training, the mixed signal output by FADE is encoded, subjected to two layers of one-dimensional convolution with a stride of 2, increasing the number of channels from 1 to 32 to 64. The final layer of adaptive average pooling compresses the time dimension to 16 and projects it onto the continuous phase space to obtain the initial state vector. The evolution of the state over abstract time t∈[0,1] is controlled by an autonomous velocity field parameterized by a small convolutional network: The forward solution employs the fourth-order Runge-Kutta (RK4) method for numerical integration to obtain the terminal state z(1), which is then processed by global residual concatenation and global average pooling to form the final decoupled feature: . Figure 4 The continuous dynamic evolution is compared with the traditional layer-by-layer discrete mapping. The discrete mapping trajectory on the left jumps drastically, with different types of paths intersecting; the continuous evolution trajectory on the right is a smooth flow described by Bézier curves, with the four types of faults converging to their respective decision regions along non-intersecting paths. This property is guaranteed by the Picard-Lindelöf theorem—the velocity field satisfying the Lipschitz continuity condition has a unique solution given an initial value; therefore, integral trajectories with different initial values ​​cannot intersect, mathematically preventing feature entanglement. In backpropagation, if all intermediate integral states are stored using conventional methods, the memory overhead is proportional to the number of integration steps. This embodiment uses the adjoint sensitivity method: defining adjoint states... By inverse time integration To propagate gradients, memory usage is kept at the O(1) level and does not increase with the number of integration steps.

[0054] 4. Multi-label joint optimization and deployment verification. Instead of using Softmax mutual exclusion classification at the network end, a 3-bit multi-label prediction head is deployed to encode normal / abnormal, inner circle fault, and outer circle fault as independent binary classification tasks. Figure 5 Two output mechanisms were compared: the traditional Softmax treats the four states as mutually exclusive options, failing to represent concurrent failures where both the inner and outer rings fail simultaneously; the 3-bit scheme allows bit 1 and bit 2 to be activated simultaneously, naturally supporting the combined representation of complex failures. Furthermore, a learnable label correlation matrix is ​​introduced. This is used to capture the statistical co-occurrence relationships of concurrent failures of physical components, making the diagnostic results more consistent with the degradation patterns of mechanical systems. The training loss function consists of a weighted combination of two parts: multi-label focus loss. Used to address the inherent imbalance of composite fault samples, mean square error loss for signal reconstruction. The physical structure used to constrain the noise-reduced output from deviating from the original signal. The total loss is... ,in .

[0055] 5. Model performance testing and verification. Figure 6 The waveform degradation process of the signal under the superposition of different noise components is shown: from the original clean signal (column I), to the blurred pulse edges after the superposition of Gaussian noise (column II), to the sharp pseudo-impact after the injection of high-energy random pulses (column III), to the final mixed noise signal where weak fault features are almost completely submerged (column IV). Figure 7 A radial comparison of the Comp_Acc index for each model under different signal-to-noise ratios is presented. Within the range of 4dB to -4dB, the method of this invention maintains the highest exact matching accuracy at all signal-to-noise ratios; under the extreme conditions of -4dB and 10-shot, the Comp_Acc of traditional discrete models drops significantly due to feature entanglement, while the method of this invention still maintains stable performance. Figure 8 The t-SNE 2D projection of the deep features of each model reveals significant overlap in the category clusters of the traditional discrete model, especially the blurred boundaries between the composite fault class and other classes. In contrast, the four clusters of this method are clustered together with uniform spacing, and the composite fault cluster is located between IF and OF but with clear boundaries. The overall model has approximately 19.8K parameters and can be directly deployed on edge devices without additional data synthesis or model compression.

Claims

1. A method for decoupling composite bearing faults with frequency-aware continuous latent dynamics, characterized in that, Includes the following steps: Step 1: Construct a data acquisition and processing module to obtain the raw vibration signals of rotating machinery and perform noise addition and preprocessing operations; Step 2: Construct a phase-preserving frequency attention noise reduction encoder (FADE) to map the original signal to a multi-channel latent space. While preserving the kinematic impact time structure, it adaptively reconstructs the spectral amplitude to suppress mixed background noise and outputs a filtered mixed signal. Step 3: Construct a continuous neural dynamics evolution module, project the denoised mixed signal as the initial state vector onto the continuous phase space, and use the neural ordinary differential equation ODE engine to drive the dynamic evolution of features in continuous time, guiding the overlapping and entangled fault features to separate along non-intersecting trajectories. Step 4: Construct a label-related multi-label diagnosis and joint optimization mechanism, identify concurrent physical fault states through the correlation matrix, and complete end-to-end training of the model through a multi-task objective function of joint reconstruction and classification. Step 5: Package and deploy the trained diagnostic model with extremely low parameter count as the target task inference system, receive test data and output accurately matched composite fault diagnosis results.

2. The method according to claim 1, characterized in that, Step 2 specifically includes: Step 2.1: Process the input one-dimensional raw vibration signal sequence using a dual-path structure encoder, extract the low-frequency structural contour using wide receptive field convolution, and extract the high-frequency components using micro-residual bypass. The resulting fusion yields a deep latent intermediate representation, calculated using the following formula: in, The original input signal, This represents a composite operation involving batch normalization and a non-linear activation function. and These are the learnable weight matrices for the corresponding paths; Step 2.2: Apply Real-DFT to each channel sequence to decouple the signal amplitude spectrum. Phase spectrum ; Step 2.3: Apply adaptive amplitude modulation and utilize the learned frequency attention mask. The amplitude spectrum is recalibrated while the phase spectrum remains unchanged, preserving the original geometry of the mechanical impact. Step 2.4: Reconstruct features using inverse real discrete Fourier transform, and employ a hybrid fusion strategy to prevent excessive smoothing of minute fault pulses, outputting the features. The calculation formula is: in, An empirical coefficient for controlling the proportion of the original high-frequency random components retained. This is the denoised signal output by the frequency attention denoising encoder.

3. The method according to claim 1, characterized in that, Step 3 specifically includes: Step 3.1: Convert the noise-reduced mixed signal output by the FADE module Projected onto the latent space, the initial state vector of the continuous initial value problem IVP of the God ordinary differential equations is defined. ; Step 3.2: Through shared neural network weights Parameterized autonomous velocity field Control the hidden state During continuous integration time The dynamic evolution within the region is calculated using the following formula: Step 3.3: The continuous neurodynamics evolution module uses a fourth-order Runge-Kutta RK4 numerical solver to integrate the velocity field to obtain the terminal decoupled state. Feature topological entanglement is prevented by integrating non-crossing trajectories; Step 3.4: Introduce global residual connections to form the final decoupling feature. The calculation formula is as follows: in This represents the global average pooling operation.

4. The method according to claim 3, characterized in that, In step 3.3, the continuous neurodynamic evolution module performs [the process] using the accompaniment sensitivity method. Backward gradient optimization for memory efficiency, defining the adjoint state as The gradient of the parameters is calculated by inverse time integration, and the formula is as follows: in, This represents the transpose of the adjoint vector.

5. The method according to claim 1, characterized in that, Step 4 specifically includes: Step 4.1: Extract the continuous decoupling features Based on linear layer projection as the fundamental logic value ; Step 4.2: To capture the co-occurrence relationship of concurrent failures of physical components under multi-tag configuration, a learnable tag correlation matrix is ​​introduced. Perform cross-tag interactive calculations to obtain relevant logical outputs. The calculation formula is: Step 4.3: Construct a multi-task joint optimization objective and integrate the multi-label focus loss function to handle imbalanced composite labels. Mean squared error reconstruction loss function used to ensure robustness of feature extraction under low signal-to-noise ratio Total loss The calculation formula is: in, These are scalar weighting coefficients.

6. A small-sample bearing composite fault decoupling system with frequency-aware continuous latent dynamics, used to implement the method described in any one of claims 1-5, characterized in that, include: The data acquisition and configuration module is used to acquire one-dimensional vibration signals of mechanical rotating bodies under strong background noise and sparse sample constraints. The phase-preserving frequency attention denoising coding (FADE) module has a built-in wide receptive field and micro residual dual-path structure to decouple the amplitude and phase spectrum of the input signal and reconstruct the amplitude mask under the premise of absolutely locking the physical phase geometric features, and output denoising features to alleviate the numerical rigidity of the subsequent solver. The continuous phase space projection and neural dynamics solution module has a built-in neural ordinary differential equation ODE solver, which is used to set the denoised features as initial vectors and perform continuous integral calculations based on the autonomous velocity field that satisfies the Lipschitz continuity condition, mapping the original overlapping physical features to independent decision manifolds along parallel non-intersecting paths. The multi-label classification and high memory efficiency optimization module is used to perform strict three-bit multi-label concurrent judgment based on the label association matrix of dynamic learning, and to perform high parameter efficiency optimization by using the adjoint integral in the backpropagation. The lightweight model inference application module is used to encapsulate diagnostic models with extremely low parameter counts, and to perform real-time, highly robust, and accurate matching diagnostic outputs in the presence of strong noise.

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