Bearing fault diagnosis method based on virtual acoustic modal priori and physical constraint state space
By using a virtual acoustic modal generator and a physically constrained state-space encoder, multimodal information expansion and time-frequency domain calibration are achieved in bearing fault diagnosis. Combined with a sliding mode robust classifier, the problems of limited sensor configuration and weak noise robustness are solved, thereby improving the accuracy and reliability of bearing fault diagnosis.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ANHUI UNIV OF SCI & TECH
- Filing Date
- 2026-04-28
- Publication Date
- 2026-07-21
AI Technical Summary
Existing deep learning-based bearing fault diagnosis methods suffer from problems such as limited sensor configuration leading to single feature representation, lack of physical mechanism constraints, weak noise robustness of traditional classifiers, and inability to reject unknown faults.
A virtual acoustic modal generator is constructed to map single-channel vibration acceleration signals into virtual sound pressure sequences. A physical constraint state-space encoder is designed to inject acoustic-vibration coupling physical priors. A spectrum-time dynamic recalibration module is used for time-frequency domain calibration. A sliding mode robust classifier based on the Lyapunov stability criterion is designed to enhance the robustness of classification decisions and the rejection capability.
Multimodal information extension is achieved without adding sensors, which improves the accuracy and robustness of bearing fault diagnosis. It can effectively identify known faults and reject unknown faults, and improves diagnostic performance in noisy environments.
Smart Images
Figure CN122432775A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a bearing fault diagnosis method based on virtual acoustic modal priors and physical constraint state space, which belongs to the fields of pattern recognition, signal processing and intelligent mechanical fault diagnosis. Background Technology
[0002] Rolling bearings are core operating components in industrial equipment such as machinery, automobiles, and wind turbines, and their operating status directly affects the safety and reliability of the entire equipment system. Timely and accurate fault diagnosis of rolling bearings can effectively prevent equipment downtime and production interruptions caused by bearing failure, thereby improving production efficiency and extending equipment lifespan. In recent years, deep learning technology has made significant progress in the field of rolling bearing fault diagnosis. Models such as convolutional neural networks, long short-term memory networks, and Transformers have been widely applied to feature extraction and fault identification of vibration signals, achieving high diagnostic accuracy. However, existing deep learning-based bearing fault diagnosis methods still face the following key technical challenges: First, sensor configuration in industrial settings is constrained by cost and space, typically deploying only single-channel vibration acceleration sensors, resulting in a single input feature representation that is difficult to fully capture the multi-physics information caused by the fault; Second, most deep learning models lack physical constraints that match the actual fault mechanism of bearings; Third, traditional softmax classifiers use an exponential normalization mechanism to make the classification boundary exhibit smooth transition characteristics, which can easily lead to high-confidence misjudgments under the noise disturbances and feature drift conditions commonly present in industrial settings, and cannot effectively reject unknown fault types not seen during the training phase, posing a safety hazard. To this end, based on the theory of deep learning and physical information fusion, this invention constructs a virtual acoustic mode generator based on the acoustic-vibration coupling mechanism, mapping single-channel vibration acceleration signals into virtual sound pressure sequences with clear physical meaning, thus achieving multimodal information expansion without adding sensors. Building upon this, a physically constrained state-space encoder is designed to inject acoustic-vibration coupling physical priors during discrete state updates. Furthermore, a spectrum-time dynamic recalibration module is proposed, using virtual acoustic modes as prior information to perform controllable weighted calibration in the time-frequency domain. Finally, a sliding mode robust classifier based on the Lyapunov stability criterion is designed to enhance the robustness of classification decisions to noise disturbances and support the rejection detection of unknown faults. Through these innovations, a complete processing chain is formed, from physical prior injection, temporal dynamic modeling, time-frequency joint optimization to robust classification decisions, effectively improving the accuracy and robustness of bearing fault diagnosis. Summary of the Invention
[0003] To address the problems of limited sensor configuration in industrial settings leading to simplistic feature representations, insufficient interpretability of deep learning models due to a lack of physical constraints, and the weak noise robustness and inability of traditional classifiers to identify unknown faults, this invention constructs a bearing fault diagnosis model based on virtual acoustic modal priors and a physically constrained state space. Through the collaborative work of four core components—physical prior generation, temporal state modeling, time-frequency dynamic calibration, and robust classification decision-making—efficient and reliable bearing fault diagnosis is achieved. The specific implementation steps of this invention are as follows: 1. Acquire single-channel vibration acceleration signals of rolling bearings to obtain a set of vibration data samples. ,in Indicates the first A one-dimensional vibration acceleration sequence of samples, each sample consisting of... The data consists of several consecutive sampling points, and is divided into training and test sets proportionally.
[0004] 2. A virtual acoustic mode generator is constructed based on the physical mechanism of acoustic-vibration coupling to map single-channel vibration acceleration signals into virtual sound pressure sequences.
[0005] The specific construction steps of the virtual acoustic modality generator are as follows: (2a) Based on fundamental acoustic principles, structural vibrations caused by local bearing faults constitute the direct excitation source of near-field sound radiation. The spatiotemporal evolution of the sound pressure field is described by a non-homogeneous wave equation:
[0006] in is the Laplace operator, representing the second-order differential of a physical quantity in space; Indicates the speed of sound in the medium; The static density of the medium; Let be the acceleration vector of the vibration source surface; Let represent the sound pressure at the current moment. The sound source term on the right-hand side of the equation clearly characterizes the physical coupling relationship between the sound pressure field and the vibration acceleration divergence; the greater the spatial rate of change of acceleration, the stronger the sound radiation.
[0007] (2b) The continuous partial differential equations are simplified and discretized in one dimension. Considering that the bearing fault vibration signal mainly manifests as a one-dimensional time series along the sensor measurement direction, the spatial propagation term is ignored, and the first-order time derivative of the acceleration is approximated using the finite difference method. The first time derivative is defined as follows: Virtual acoustic modal signals at each sampling point as follows:
[0008] in, For the first Vibration acceleration values at each sampling point; The sampling time interval, The sampling frequency; The finite difference approximation of the first-order time derivative of acceleration characterizes the sensitivity of acoustic radiation to the rate of change of vibration and shock. The physical coupling coefficient controls the relative weight of the derivative term in the virtual acoustic mode; The superimposed micro-Gaussian white noise is used to simulate the unavoidable environmental thermal noise in acoustic measurements, and its standard deviation is... The standard deviation of the original vibration signal is set to 1% to enhance the generalization robustness of the model without changing the main characteristics of the signal.
[0009] 3. Design a physical constraint state-space encoder to inject acoustic-vibration coupled physical priors into the discrete state update process, thereby enhancing the temporal modeling capability and physical consistency.
[0010] The specific construction steps of the physical constraint state-space encoder are as follows: (3a) Based on the state-space model, its continuous-time linear state-space equations are in general form as follows:
[0011] in It is in a hidden state. As input features, These are the state transition matrix, input projection matrix, and coefficient matrix, respectively.
[0012] Then, the continuous system is dynamically scaled in discrete time according to the input dependence. Discretization, the discretized form is expressed as:
[0013] in , . Indicates the first Discrete state vector of each sampling point; Input features; An adaptive time scale factor controls the effective receptive field of Mamba under different input states.
[0014] (3b) Construct physical context features based on virtual acoustic modes. Extract high-frequency impact structures by performing one-dimensional convolution stacking on the virtual acoustic mode signals:
[0015] in These are virtual acoustic modes generated by a virtual acoustic mode generator. This represents a one-dimensional convolution stack, used to extract high-frequency impact structures contained in virtual acoustic signals; That is, in an acoustic sense, it emphasizes the contextual enhancement features of the impact structure.
[0016] Next, the physical context of the actual vibration mode and the acoustic mode is concatenated to construct a physically guided context fusion vector:
[0017] in Indicates feature splicing, It includes the overall capability changes of real vibration and high-frequency impact information extracted from virtual acoustics; secondly, the real vibration signal and the virtual acoustic signal are complementary, which can simultaneously provide steady-state characteristics and transient impact information, making the generated... It can include physical a priori properties.
[0018] (3c) Design an adaptive time scale for generating positive values using a learnable mapping. The specific calculation formula is as follows:
[0019] in For linear mapping, ensure ; Through the physical context vector of virtual acoustic modes control This enables the physically constrained state-space encoder to adaptively reduce the step length and improve the time resolution when a fault impulse occurs. Secondly, The generation is driven by the display of physical information, rather than by pure data statistics.
[0020] Then, the vibration channel is physically modulated to amplify the corresponding pulse response when a fault impact occurs:
[0021] in For learnable gating coefficients, For the Sigmoid function, The input is the actual vibration after being modulated by physical constraints.
[0022] (3d) The state space update of the physical constraint state space encoder is driven by the input modulated with physical information:
[0023] Two Mamba channels independently update the real and virtual acoustic modes, followed by residual normalization.
[0024] 4. Design a spectrum-time dynamic recalibration module, which uses virtual acoustic modes as prior information to learn a spectrum mask in the time-frequency domain, performs controllable weighted calibration on the vibration complex spectrum and inversely transforms and fuses it into the time domain.
[0025] The specific construction steps of the spectrum-time dynamic recalibration module are as follows: (4a) Let and They represent the first The sequence of real vibrations and virtual acoustic latent states at each time step. First, STFT is performed on each channel and each sample to map the time-domain sequence to a time-frequency representation:
[0026] in For window functions, The length of the Fourier transform point. For time resolution, For frequency index, For time indexing, The representation is transformed Sequence. The main reason for using STFT is that bearing faults involve both short-term impacts and periodic harmonics. STFT can simultaneously reveal the time-frequency distribution of both, which facilitates spectrum-based localization and filtering.
[0027] Furthermore, the STFT calculates the complex-valued spectral tensor for each channel separately. Then, the amplitude spectrum of the virtual acoustic signal channel is taken to obtain physical information:
[0028] in The amplitude spectrum of the virtual acoustic channel. Indicates the length of the composite mold.
[0029] (4b) Rearrange the amplitude spectrum in terms of dimensions and input it into a two-dimensional convolutional network to generate a spectral mask:
[0030] in The sigmoid function constrains the network output to... between, This is a two-dimensional convolution transformation. This is the physical spectrum mask.
[0031] (4c) Design learnable fusion coefficients Construct a weighted calibration mask and apply the weighted mask to the true complex spectrum to obtain the calibrated complex spectrum representation:
[0032] Where the constant This means that the identity-preserving channel does not change the spectrum, thus achieving a smooth rollback of the mask; These are learnable fusion coefficients that control the strength of the physical mask's influence on the true spectrum.
[0033] Next, the calibrated complex spectrum was analyzed. Perform inverse short-time Fourier transform (iSTFT) to return to the time domain representation:
[0034] The reconstruction length of the inverse short-time Fourier transform is related to the length of the original time-domain sequence. Alignment; The time-domain enhancement representation obtained from the inverse transform of the calibration spectrum.
[0035] Finally, to preserve the original time-domain information and incorporate the enhancement effect of frequency-domain calibration, residual connections and normalization are used to fuse the calibration results with the original hidden states to obtain the final output:
[0036] in For temporal implicit representation; Representation layer normalization ensures scale stability.
[0037] 5. Design a sliding mode robust classifier based on the Lyapunov stability criterion to enhance the robustness of classification decisions to noise disturbances and support the detection of unknown faults.
[0038] The specific steps for constructing a sliding mode robust classifier are as follows: (5a) Inspired by the variable structure switching concept in sliding mode control theory, a learnable sliding mode classification surface is constructed for each fault category k:
[0039] in This is the fused feature vector output by the time-spectrum dynamic recalibration module. and For the first Learnable parameters of sliding surfaces Total number of fault categories. Sliding surface. Indicates the current sample up to the th The absolute value of the coincidence distance of the decision hyperplane. The smaller the value, the closer the sample is to the decision boundary of that category.
[0040] Nonlinear mapping of the sliding surface output using a saturation function:
[0041] in This is the boundary layer width parameter. This design allows the classifier to operate at the boundary layer... The system maintains a linear response to ensure classification sensitivity, while outside the boundary layer, the output saturates to resist the impact of noise disturbances on decision-making, thus achieving an effective balance between sensitivity and robustness.
[0042] (5b) Based on the Lyapunov stability analysis method, a hybrid loss function integrating cross-entropy and sliding mode constraints is constructed. Lyapunov terms are designed to drive the sliding surface value of the correct class to approach zero:
[0043] in represents the true class label of the sample. Minimizing this term is equivalent to driving the sample to infinitely approach the sliding surface of its class, thus achieving stable classification.
[0044] The design interval constraint term will expel error categories outside the boundary layer:
[0045] This constraint applies to all error categories. Greater than the boundary layer width This creates a structure that separates classes, effectively preventing cross-class misjudgments caused by feature perturbations.
[0046] Construct a hybrid loss function by combining cross-entropy loss:
[0047] in For the cross-entropy loss based on the sliding surface distance, and These are the sliding mode loss weight and the interval term weight, respectively.
[0048] (5c) During the inference phase, the classification decision criterion is to select the category with the smallest absolute value of the sliding surface as the prediction result. Furthermore, a rejection criterion is defined: if all categories... If so, the current sample is determined to be an unknown fault, where This is the rejection threshold. When a sample is far from the sliding surface of all known classes, the classifier refuses to make a decision and outputs a warning signal.
[0049] The method of the present invention has the following advantages: (1) This invention constructs a virtual acoustic modal generator, proposes a sound-vibration coupling physical mechanism and starts from the first principle of physics, deterministically maps the single-channel vibration acceleration signal into a virtual sound pressure sequence with clear physical meaning, realizes multimodal information expansion without increasing sensor hardware, and explicitly amplifies the high-frequency radiation characteristics of fault impact through the high-pass filtering characteristics of first-order difference, providing a more discriminative physical feature view for subsequent encoders; (2) The present invention designs a physical constraint state space encoder, injects acoustic-vibration coupling physical priors into the continuous-discrete framework of the Mamba state space model, and adaptively modulates the time scale and vibration state evolution through virtual acoustic modes, so that the model can adaptively improve the time resolution and amplify the impulse response when the impact event occurs, thereby enhancing the ability to represent the time sequence of repeated impact cycles and local acceleration changes, and solving the problem that the traditional Mamba is difficult to accurately capture transient impacts in strong noise and weak fault scenarios. (3) The present invention proposes a spectrum-time dynamic recalibration module, which uses the virtual acoustic amplitude spectrum as a priori learning time-frequency importance mask, performs gated calibration on the real vibration complex spectrum and then inverse transforms and fuses it into the time domain, effectively bridging the difference between frequency domain spectral information and time domain transient characterization, and improving the ability to detect early weak faults and noise masking features. (4) The present invention designs a sliding mode robust classifier based on the Lyapunov stability criterion. By constructing a learnable sliding mode classification surface with a boundary layer structure for each fault category, the sample is driven to converge toward the correct category decision boundary and move away from the wrong category, thereby enhancing the robustness of the classification decision to noise disturbance and supporting the rejection detection of unknown fault types. This significantly improves the reliability and safety of the fault diagnosis system in an open industrial environment. Attached Figure Description
[0050] The present invention will be further described below with reference to the accompanying drawings and examples.
[0051] Figure 1 This is a flowchart of the overall network architecture of the present invention. Figure 2 The confusion matrix of the comparative experiments of various methods on the AUST dataset. Figure 3 The graph shows the feature dimensionality reduction and classification results of various methods on the CWRU dataset. Detailed Implementation
[0052] The specific implementation steps of this invention are as follows: 1. Acquire single-channel vibration acceleration signals of rolling bearings. The Anhui University of Science and Technology Self-Acquired Bearing Dataset (AUST) and the Case Western Reserve University Bearing Dataset (CWRU) were selected for validation. The CWRU dataset uses vibration acceleration signals acquired from the drive end. The experimental conditions were set as follows: motor speed 1797 r / min, load 0 hp, and sampling frequency 12 kHz. The dataset includes 10 states: healthy state, three sizes of inner ring faults, three sizes of outer ring faults, and three sizes of rolling element faults. The AUST dataset was acquired using an experimental platform consisting of a servo motor, servo driver, deep groove ball bearing test module, and manual hydraulic loading device. The sampling frequency was 12 kHz, and it includes four fault states: inner ring fault, rolling element fault, combined fault, and healthy state. Each sample consists of 1024 continuous sampling points, and each category is divided into training and test sets in a 7:3 ratio.
[0053] 2. Based on the vibration data collected in step 1 above, each vibration acceleration sample is mapped to a virtual acoustic modal signal using a virtual acoustic modal generator. Specifically, according to the formula... For each sampling point, the physical coupling coefficient is calculated. The noise standard deviation was set based on the characteristics of the experimental dataset. Set to 1% of the standard deviation of the original vibration signal. The generated virtual acoustic modes and the original vibration signal together constitute a dual-channel input.
[0054] 3. The dual-channel input is fed into the physical constraint state-space encoder. The physical constraint state-space encoder first extracts physical context features by performing one-dimensional convolutional stacking on the virtual acoustic signal, and then concatenates these features with the real vibration features to form a fusion vector. Based on the fusion vector, an adaptive time scale factor is generated through a learnable mapping to modulate the discretization step size of the state-space model. Simultaneously, a gating mechanism is used to physically modulate the vibration channel. Two Mamba channels independently update the states of the real vibration and virtual acoustic modes, respectively, and then fuse them through residual normalization to output dual-channel temporal hidden states.
[0055] 4. The dual-channel temporal hidden states output by the physical constraint state-space encoder are fed into the spectrum-time dynamic recalibration module. The spectrum-time dynamic recalibration module performs a short-time Fourier transform on the dual-channel hidden states to obtain complex spectra, extracts the amplitude spectrum of the virtual acoustic channel as a physical prior, learns a time-frequency importance mask through a two-dimensional convolutional network, constructs a weighted mask through learnable fusion coefficients to perform gated calibration on the complex spectrum of the real vibration channel, and then performs an inverse short-time Fourier transform back to the time domain, integrates it into the original time domain representation in a residual normalization manner, and outputs the enhanced fusion features.
[0056] 5. The fused features output from the spectral-temporal dynamic recalibration module are fed into a sliding mode robust classifier based on the Lyapunov stability criterion. The sliding mode robust classifier constructs a learnable sliding mode classification surface for each fault category, achieving a balance between sensitivity and robustness through a boundary layer saturation function. A hybrid loss function is used during the training phase. End-to-end optimization is performed. During the inference phase, the category with the smallest absolute value of the sliding surface is selected as the prediction result, while also supporting the detection of unknown faults.
[0057] The effectiveness of this invention was further verified through the following experiments: On the AUST dataset, the method of this invention achieved an average accuracy of 100.00% in 5 independent experiments, with precision, recall, and F1 score all reaching 100.00%, achieving perfect classification. On the CWRU dataset, the method of this invention achieved an average accuracy of 99.84%, demonstrating excellent classification performance in 10 fault identification tasks. Compared with other methods such as 1D-CNN (88.88% / 93.72%), CNN-LSTM (88.31% / 97.06%), CNN-BiGRU (93.03% / 97.31%), WDCNN (94.75% / 95.87%), Transformer (92.71% / 97.85%), LSNet (99.13% / 99.25%), ResNet18 (97.97% / 99.38%), and FasterNet (95.00% / 99.53%), this invention achieves the best performance on both datasets.
[0058] Ablation experiments show that with the gradual introduction of the virtual acoustic modality generator, the physical constraint state space encoder, the spectral-temporal dynamic recalibration module, and the sliding mode robust classifier, the model diagnostic performance exhibits a monotonically increasing trend, verifying the effectiveness and complementarity of the four core modules.
[0059] Noise robustness experiments show that the method of this invention maintains optimal performance as the signal-to-noise ratio decreases from 10 dB to -10 dB. Even under the most stringent SNR condition of -10 dB, it maintains a diagnostic accuracy of 96.44%, significantly outperforming all comparative methods, thus verifying the synergistic noise suppression capability of physical prior constraints and the sliding mode robust classifier.
[0060] Cross-dataset unknown fault rejection experiments show that the sliding mode robust classifier of the present invention achieves the best rejection performance in both cross-dataset rejection scenarios, with rejection rates of 89.38% and 92.58%, respectively, and false rejection rates of only 2.34% and 1.09%, respectively. The AUROC values are 0.9459 and 0.9971, respectively, which verifies the robustness of the sliding surface distance criterion to distribution shift.
Claims
1. A bearing fault diagnosis method based on virtual acoustic modal priors and physical constraint state space, characterized in that, The method includes the following steps: (1) A virtual acoustic mode generator is constructed based on the physical mechanism of acoustic-vibration coupling to map the single-channel vibration acceleration signal into a virtual sound pressure sequence; (2) Design a physical constraint state space encoder to inject acoustic-vibration coupling physical priors into the discrete state update process to enhance the temporal modeling capability and physical consistency; (3) Design a spectrum-time dynamic recalibration module, which uses virtual acoustic modes as prior information to learn the spectrum mask in the time-frequency domain, performs controllable weighted calibration on the vibration complex spectrum and inversely transforms and fuses it to the time domain; (4) Design a sliding mode robust classifier based on the Lyapunov stability criterion to enhance the robustness of classification decisions to noise disturbances and support the rejection detection of unknown faults.
2. The bearing fault diagnosis method based on virtual acoustic modal prior and physical constraint state space according to claim 1, characterized in that... (1) The virtual acoustic mode generator based on the acoustic-vibration coupling physical mechanism is constructed to map the single-channel vibration acceleration signal into a virtual sound pressure sequence. The steps are as follows: (2a) Based on the fundamental principles of acoustics, the structural vibration caused by a local fault in the bearing constitutes the direct excitation source of near-field sound radiation; the spatiotemporal evolution of the sound pressure field is described by a non-homogeneous wave equation: in is the Laplace operator, representing the second-order differential of a physical quantity in space; Indicates the speed of sound in the medium; The static density of the medium; Let be the acceleration vector of the vibration source surface; Let be the sound pressure at the current moment; the sound source term on the right-hand side of the equation clearly characterizes the physical coupling relationship between the sound pressure field and the vibration acceleration divergence. The greater the spatial rate of change of acceleration, the stronger the sound radiation; (2b) The continuous partial differential equation is simplified and discretized in one dimension. Considering that the bearing fault vibration signal is mainly manifested as a one-dimensional time series along the sensor measurement direction, after ignoring the spatial propagation term, the finite difference method is used to approximate the first-order time derivative of the acceleration, and the first time derivative is defined as . Virtual acoustic modal signals at each sampling point as follows: in, For the first Vibration acceleration values at each sampling point; The sampling time interval, The sampling frequency; The finite difference approximation of the first-order time derivative of acceleration characterizes the sensitivity of acoustic radiation to the rate of change of vibration and shock. The physical coupling coefficient controls the relative weight of the derivative term in the virtual acoustic mode; The superimposed micro-Gaussian white noise is used to simulate the unavoidable environmental thermal noise in acoustic measurements, and its standard deviation is... The standard deviation of the original vibration signal is set to 1% to enhance the generalization robustness of the model without changing the main characteristics of the signal.
3. The bearing fault diagnosis method based on virtual acoustic modal priors and physical constraint state space according to claim 1, characterized in that... (2) The design of the physical constraint state-space encoder, which injects acoustic-vibration coupling physical priors into the discrete state update process to enhance the temporal modeling capability and physical consistency, is carried out as follows: (3a) Based on the state-space model, its continuous-time linear state-space equation is in general form as follows: in It is in a hidden state. As input features, These are the state transition matrix, input projection matrix, and coefficient matrix, respectively; then, the continuous system is dynamically scaled in discrete time according to the input-dependent step size. Discretization, the discretized form is expressed as: in , ; Indicates the first Discrete state vector of each sampling point; Input features; An adaptive time scale factor controls the effective receptive field of Mamba under different input states; (3b) Construct physical context features based on virtual acoustic modes, and extract high-frequency impact structures by one-dimensional convolution stacking of virtual acoustic mode signals: in These are virtual acoustic modes generated by a virtual acoustic mode generator. This represents a one-dimensional convolution stack, used to extract high-frequency impact structures contained in virtual acoustic signals; That is, emphasizing the context-enhanced features of the impact structure in an acoustic sense; then concatenating the physical context of the actual vibration modes with that of the acoustic modes to construct a physically guided context fusion vector: in Indicates feature splicing, It includes the overall capability changes of real vibration and high-frequency impact information extracted from virtual acoustics; secondly, the real vibration signal and the virtual acoustic signal are complementary, which can simultaneously provide steady-state characteristics and transient impact information, making the generated... It can include physical priors; (3c) Design an adaptive time scale that can generate positive values from learnable mappings, the specific calculation formula is as follows: in For linear mapping, ensure ; Through the physical context vector of virtual acoustic modes control This enables PI-Mamba to adaptively reduce the step size and improve temporal resolution when fault impacts occur; secondly, The generation is driven by physical information display, rather than pure data statistics; then the vibration channel is physically modulated to amplify the corresponding pulse response when a fault impact occurs: in For learnable gating coefficients, For the Sigmoid function, The input is the actual vibration after physical constraint modulation; the state space update of (3d) PI-Mamba is driven by the input modulated by physical information. Two Mamba channels independently update the real and virtual acoustic modes, followed by residual normalization.
4. The bearing fault diagnosis method based on virtual acoustic modal prior and physical constraint state space according to claim 1, characterized in that... The design spectrum-time dynamic recalibration module described in step (3) uses virtual acoustic modes as prior information to learn a spectrum mask in the time-frequency domain, performs controllable weighted calibration on the vibration complex spectrum and inversely transforms and fuses it to the time domain. The steps are as follows: (4a) Let and They represent the first The sequence of real vibrations and virtual acoustic latent states at each time step; first, STFT is performed on each channel and each sample to map the time-domain sequence to a time-frequency representation: in For window functions, The length of the Fourier transform point. For time resolution, For frequency index, For time indexing, The representation is transformed The sequence; the main reason for using STFT is that bearing faults involve both short-term impacts and periodic harmonics, and STFT can simultaneously reveal the time-frequency distribution of both, facilitating spectrum-based localization and filtering; furthermore, STFT calculates the complex-valued spectral tensor for each channel separately. Then, the amplitude spectrum of the virtual acoustic signal channel is taken to obtain physical information. in The amplitude spectrum of the virtual acoustic channel. (4b) Represent the complex modulus length; rearrange the dimensions of the amplitude spectrum and input it into a two-dimensional convolutional network to generate a spectral mask: in The sigmoid function constrains the network output to... between, This is a two-dimensional convolution transformation. (4c) Design learnable fusion coefficients for the physical spectrum mask. Construct a weighted calibration mask and apply the weighted mask to the true complex spectrum to obtain the calibrated complex spectrum representation: Where the constant This means that the identity-preserving channel does not change the spectrum, thus achieving a smooth rollback of the mask; The learnable fusion coefficients control the intensity of the physical mask's influence on the true spectrum; then the calibrated complex spectrum is... Perform an inverse short-time Fourier transform (iSTFT) to return to the time domain representation: The reconstruction length of the iSTFT is related to the length of the original time-domain sequence. Alignment; The time-domain enhanced representation is obtained from the inverse transform of the calibration spectrum. Finally, to preserve the original time-domain information and introduce the enhancement effect of frequency-domain calibration, the calibration result and the original hidden state are fused using residual connection and normalization to obtain the final output. in For temporal implicit representation; Representation layer normalization ensures scale stability.
5. The bearing fault diagnosis method based on virtual acoustic modal prior and physical constraint state space according to claim 1, characterized in that... Step (3) describes the design of a sliding mode robust classifier based on the Lyapunov stability criterion, which enhances the robustness of classification decisions to noise disturbances and supports the rejection detection of unknown faults. The steps are as follows: (5a) Inspired by the variable structure switching concept in sliding mode control theory, a learnable sliding mode classification surface is constructed for each fault category k: in This is the fused feature vector output by the time-spectrum dynamic recalibration module. and For the first Learnable parameters of sliding surfaces The total number of fault categories, slip surface Indicates the current sample up to the th The absolute value of the coincidence distance of the decision hyperplane. The smaller the value, the closer the sample is to the decision boundary of that category; Nonlinear mapping of the sliding surface output using a saturation function: in This is the boundary layer width parameter; this design allows the classifier to operate at the boundary layer. The system maintains a linear response to ensure classification sensitivity, while outside the boundary layer, the output saturates to resist the impact of noise perturbations on decision-making, thus achieving an effective balance between sensitivity and robustness. (5b) Based on the Lyapunov stability analysis method, a hybrid loss function integrating cross-entropy and sliding mode constraints is constructed; a Lyapunov term is designed to drive the sliding surface value of the correct class to approach zero: in The true class label of the sample is used. Minimizing this term is equivalent to driving the sample to infinitely approach the sliding surface of its class, thus achieving stable classification. The margin constraint term is designed to expel misclassified classes from the boundary layer. This constraint applies to all error categories. Greater than the boundary layer width This creates a structure that separates classes, effectively preventing cross-class misclassification caused by feature perturbations; a hybrid loss function is constructed by combining cross-entropy loss: in For the cross-entropy loss based on the sliding surface distance, and These are the sliding mode loss weights and the interval term weights, respectively. (5c) During the inference phase, the classification decision criterion is to select the category with the smallest absolute value of the sliding surface as the prediction result; in addition, the rejection criterion is defined as follows: if all categories If so, the current sample is determined to be an unknown fault, where The rejection threshold is set when a sample is far from the sliding surface of all known classes. The classifier refuses to make a decision and outputs a warning signal.