Full-ceramic ball bearing crack tracing method based on fusion of vibration signals and machine learning

Abstract

The invention discloses a full-ceramic ball bearing crack tracing method based on fusion of vibration signals and machine learning. The method comprises the following steps: collecting the vibration signals and preprocessing the vibration signals into a standardized sequence; performing multi-resolution complex wavelet packet transformation and time window normalization to generate a frequency adaptive feature tensor; inputting an improved echo state network to generate a frequency band state matrix through recursion; after splicing, inputting into a cross-frequency aggregation reserve pool to execute feedback coupling, and generating an aggregation state vector; reconstructing the topological state tensor of the bearing according to the structure sequence; constructing an energy-kurtosis gating factor updating tensor, outputting a gating state sequence, obtaining a crack result through position classification and severity regression, and performing iterative correction; and outputting a crack result and writing into a maintenance archive. According to the method, multi-structure crack accurate tracing is realized, and the diagnosis precision and the recognition stability can be improved.

Description

Technical Field

[0001] This invention relates to the field of intelligent crack tracing technology, and in particular to a crack tracing method for all-ceramic ball bearings based on the fusion of vibration signals and machine learning. Background Technology

[0002] In high-precision, high-reliability mechanical systems, all-ceramic ball bearings have been widely used in key equipment such as aerospace and precision instruments due to their excellent corrosion resistance, high temperature resistance, and high speed performance. However, all-ceramic materials are brittle and cracks are difficult to heal themselves. Once a crack occurs, it will rapidly expand and lead to bearing failure, which in turn will cause major equipment failure. Therefore, accurate tracking and intelligent identification of crack status in all-ceramic ball bearings has become a key research direction.

[0003] Existing bearing fault diagnosis methods mainly rely on vibration signal analysis and traditional machine learning algorithms. They often use frequency domain index extraction and models such as support vector machines and random forests for classification and identification. Some studies have introduced convolutional neural networks or long short-term memory networks to improve time series modeling capabilities. However, they still face problems such as insufficient modeling capabilities for high-frequency complex non-stationary signals, weak cross-frequency information correlation, and inaccurate crack location and severity assessment. Moreover, there are defects such as imbalance of response amplitude in different frequency bands and lack of modeling of time delay characteristics in the process of multi-frequency band feature fusion, making it difficult to achieve full-process, structured, and traceable tracking of crack states.

[0004] Existing methods generally lack detailed modeling of the structure within the vibration signal frequency band, neglecting the coupling relationship between various structural components and the frequency band response. This makes it difficult to accurately infer the crack location and quantitatively assess its severity, thus limiting their usability and interpretability in practical engineering. Therefore, there is an urgent need to develop an intelligent crack tracing method with cross-frequency fusion, temporal memory, and structural region analysis capabilities to improve the accuracy and robustness of fault identification in all-ceramic ball bearings. Summary of the Invention

[0005] One objective of this invention is to propose a crack tracing method for all-ceramic ball bearings based on the fusion of vibration signals and machine learning. This invention uses an improved echo state network to recursively model and map the multi-frequency vibration characteristics, and describes in detail the processing of crack location identification and severity scoring. It has the advantages of high identification accuracy, strong tracing capability and clear structural differentiation.

[0006] The crack tracing method for all-ceramic ball bearings based on the fusion of vibration signals and machine learning according to embodiments of the present invention includes the following steps: Step 1: Collect bearing vibration signals and preprocess them to obtain a standardized vibration sequence; Step 2: Perform multi-resolution complex wavelet packet transform and time window normalization on the vibration sequence to extract low-frequency, mid-frequency, and high-frequency feature tensors and concatenate them to generate frequency-adaptive feature tensors; Step 3: Inject the frequency adaptive feature tensor into the improved echo state network composed of low-frequency, mid-frequency and high-frequency reservoirs respectively, and recursively calculate the internal weight matrix according to the instantaneous kurtosis factor of each reservoir to output the frequency band reservoir state matrix. Step 4: Input the state matrix of the reservoir into the cross-frequency aggregated reservoir after time delay splicing, and perform adjustable feedback coupling according to the delay coefficient to generate the state vector of the aggregated reservoir. Step 5: Divide and combine the state vectors of the aggregated reservoir according to the order of outer ring, inner ring, rolling element, and cage to form the bearing topology state tensor; Step 6: Calculate the frequency band energy and kurtosis value of the bearing topology state tensor, construct the energy-kurtosis gating factor, update the bearing topology state tensor and output the gated state sequence, input the gated state sequence into the location classification head and severity regression head to obtain the probability of crack location and crack severity score. If the confidence is lower than the threshold, use the readout layer error signal to iteratively correct the cross-frequency aggregation reservoir coupling weight until the termination condition is met, and output the final crack tracing result. Step 7: Write the final crack tracing results to the maintenance archive to generate crack tracing records.

[0007] Optionally, the bearing vibration signal acquired in step one is the original time-domain acceleration signal acquired by a triaxial accelerometer under different load and speed combinations. The preprocessing includes performing bandpass filtering, symmetric wavelet thresholding denoising, Hilbert transform to extract the envelope, angular domain resampling, and amplitude normalization on the original time-domain acceleration signal in sequence to generate a standardized vibration sequence with a consistent time scale and a unified energy distribution standard.

[0008] Optionally, step two specifically includes: A complex wavelet packet transform is performed on the standardized vibration sequence, and a full-band multi-scale decomposition is performed using a complex symmetric wavelet basis function of a set order to obtain a multi-resolution wavelet packet coefficient set containing low-frequency coefficient matrix, mid-frequency coefficient matrix and high-frequency coefficient matrix. Phase correction and modulus normalization are performed on each coefficient matrix in the multi-resolution wavelet packet coefficient set to generate low-frequency feature tensors, mid-frequency feature tensors and high-frequency feature tensors respectively. Mean normalization and resampling operations are performed on the low-frequency, mid-frequency, and high-frequency feature tensors respectively within a sliding time window of a set length, maintaining consistency on the time scale to form a time-window normalized feature tensor sequence. The time-window normalized feature tensor sequence is then concatenated along the frequency band dimension to generate a frequency-adaptive feature tensor.

[0009] Optionally, step three specifically includes: The frequency-adaptive feature tensor is divided into low-frequency, mid-frequency and high-frequency channels, and then input into the corresponding low-frequency, mid-frequency and high-frequency reservoirs respectively. A sliding time window is set in each frequency band reserve pool, and the kurtosis value is calculated for the current channel characteristics within the window; Construct an instantaneous kurtosis factor based on the kurtosis value, scale the original internal connectivity matrix of the corresponding reservoir proportionally, and generate a dynamic internal connectivity matrix. Under the influence of the dynamic internal connection matrix, the current channel characteristics are combined with the previous state of the reserve pool to perform state recursion, update the current state vector of the reserve pool, and output the frequency band reserve pool state matrix.

[0010] Optionally, step four specifically includes: The frequency band reserve pool state matrix is ​​spliced ​​into a unified time-delay state sequence in chronological order; The unified time-delay state sequence is input into the constructed cross-frequency aggregation reserve pool; The set of preset delay coefficients for the cross-frequency aggregation reserve pool is indexed and activated. Based on the delay coefficient selected at the current time step, the corresponding historical state vector is extracted and superimposed with the current state input vector to form a delay input vector. Based on the magnitude difference between the delayed input vector and the aggregated reservoir state vector of the previous time step in each channel dimension, a feedback adjustment factor is constructed, and the delayed input vector is weighted at the channel level using the feedback adjustment factor as the weight. The weighted delayed input vector is superimposed element by element with the aggregated reserve state vector of the previous time step to form the aggregated state update term of the current time step, which replaces the original state vector and is written into the aggregated reserve. The aggregated state update items at all time steps are arranged into a sequence in chronological order, which is used as the state vector sequence of the aggregated reserve pool.

[0011] Optionally, the process of updating the bearing topology state tensor and outputting the gated state sequence in step five includes: Calculate the channel amplitude energy of each structural region in the bearing topology state tensor in the low-frequency, mid-frequency and high-frequency dimensions to obtain the structure-frequency band two-dimensional energy matrix. Calculate the kurtosis value of each structural region in the bearing topology state tensor in the corresponding frequency band dimension to obtain the structure-frequency band two-dimensional kurtosis matrix; The structure-frequency band two-dimensional energy matrix and the structure-frequency band two-dimensional kurtosis matrix are normalized according to the channel dimension and fused according to the preset weight coefficients to form an energy-kurtosis gating factor matrix; The energy-kurtosis gated factor matrix is ​​used to perform a channel-by-channel weighted modulation operation on the bearing topology state tensor, and the state amplitude of each structural region in the tensor is adjusted to generate an updated bearing topology state tensor. The updated bearing topology state tensor is expanded along the time dimension and spliced ​​in the order of structural regions to generate a gated state sequence.

[0012] Optionally, the output process of the final crack tracing result specifically includes: The gating state sequence input position classification readout head is used to perform multi-structure region crack location probability calculation and output the probability distribution of crack locations in the outer ring, inner ring, rolling elements and cage. The gating state sequence is synchronously input into the severity regression readout head, multi-channel regression operation is performed, and the crack severity score vector of the corresponding structural region is output. The maximum probability value of the probability distribution of the crack location and the mean severity score are used to form the identification confidence index. When the index is lower than the preset threshold, the output error signal of the classification and regression readout head is recorded. The error signal is back-mapped to the gating state sequence generation source and further projected to the cross-frequency aggregation reserve pool. Based on the frequency band and structural region distribution of the error, the corresponding coupling weight is fine-tuned and updated. Under the updated coupling weights, the state propagation, tensor construction, and gating modulation operations are re-executed to obtain a new gating state sequence. This process is repeated until the confidence index reaches a preset threshold or the maximum number of iterations is reached. After the termination condition is met, the outputs of the current classification head and regression head are used as the final crack tracing result, which includes the structural part classification label and the corresponding crack severity score.

[0013] Optionally, the final crack tracing result includes the bearing structure area label corresponding to the crack, the frequency band label where the crack is located, the crack severity score, and the confidence index.

[0014] The beneficial effects of this invention are: (1) Improve the accuracy of crack location identification. This invention constructs an improved echo state network structure composed of low-frequency, mid-frequency, and high-frequency segmented reservoirs and cross-frequency aggregated reservoirs. Combined with a kurtosis-driven dynamic weight adjustment mechanism, it achieves high-fidelity modeling and state expression of vibration characteristics in different frequency bands, thereby improving the accuracy of crack location identification in all-ceramic ball bearings. It also has excellent performance in the early stage of weak faults.

[0015] (2) Enhance the ability to classify crack severity. By introducing an energy-kurtosis gating mechanism to perform multi-channel weighted modulation of the bearing topology state tensor, and combining the location classification head and the severity regression head to output the crack spatial distribution probability and crack development degree score respectively, the crack identification result not only has spatial positioning capability, but also has continuous quantitative damage assessment capability, supporting accurate maintenance decision-making.

[0016] (3) Achieve high confidence crack tracing output: In the model readout stage, the present invention introduces an error signal feedback iteration mechanism. When the confidence of identification is insufficient, the feedback coupling weight of the cross-frequency aggregation reserve pool is automatically corrected to achieve adaptive optimization and update of the output results, ensuring that the final crack tracing results have higher stability and credibility, and meeting the requirements of high reliability fault tracing in industrial scenarios. Attached Figure Description

[0017] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 This is an overall flowchart of the crack tracing method for all-ceramic ball bearings based on the fusion of vibration signals and machine learning proposed in this invention; Figure 2 This is a diagram of the improved echo state network structure of the all-ceramic ball bearing crack tracing method based on the fusion of vibration signal and machine learning proposed in this invention. Figure 3 This diagram illustrates the crack tracing readout and feedback optimization mechanism of the all-ceramic ball bearing crack tracing method based on the fusion of vibration signals and machine learning proposed in this invention. Detailed Implementation

[0018] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0019] refer to Figure 1-3 A crack tracing method for all-ceramic ball bearings based on the fusion of vibration signals and machine learning includes the following steps: Step 1: Collect bearing vibration signals and preprocess them to obtain a standardized vibration sequence; Step 2: Perform multi-resolution complex wavelet packet transform and time window normalization on the vibration sequence to extract low-frequency, mid-frequency, and high-frequency feature tensors and concatenate them to generate frequency-adaptive feature tensors; Step 3: Inject the frequency adaptive feature tensor into the improved echo state network composed of low-frequency, mid-frequency and high-frequency reservoirs respectively, and recursively calculate the internal weight matrix according to the instantaneous kurtosis factor of each reservoir to output the frequency band reservoir state matrix. Step 4: Input the state matrix of the reservoir into the cross-frequency aggregated reservoir after time delay splicing, and perform adjustable feedback coupling according to the delay coefficient to generate the state vector of the aggregated reservoir. Step 5: Divide and combine the state vectors of the aggregated reservoir according to the order of outer ring, inner ring, rolling element, and cage to form the bearing topology state tensor; In this embodiment, after the aggregation reservoir state vector sequence is generated, in order to construct a bearing topology state tensor with structural partitioning features, the present invention divides the aggregation reservoir state vector according to the channel dimension of the structural regions of the outer ring, inner ring, rolling element and cage, based on the typical structural composition order of the all-ceramic ball bearing. Specifically, the aggregation reservoir state vector is divided into four sub-vectors according to the predefined channel index interval, corresponding to the outer ring feature vector, inner ring feature vector, rolling element feature vector and cage feature vector respectively. The four sub-vectors are spliced ​​according to the structural order to form a bearing structural partitioning feature vector group with a four-partition structure. In order to enhance the semantic distinguishability between regional features, the present invention reconstructs the feature vector group composed of the four sub-vectors into a four-dimensional tensor structure along the newly set structural channel dimension, which sequentially represents the time step, channel dimension, structural region and embedding dimension, and finally forms the bearing topology state tensor. Step Six: Calculate the frequency band energy and kurtosis value of the bearing topology state tensor, construct the energy-kurtosis gating factor, update the bearing topology state tensor and output the gated state sequence. Input the gated state sequence into the location classification head and severity regression head to obtain the crack location probability and crack severity score. If the confidence level is lower than the threshold, iteratively correct the cross-frequency aggregation reservoir coupling weights using the readout layer error signal until the termination condition is met, and output the final crack tracing result. The location classification head and severity regression head serve as back-end functional extension modules of the improved echo state network in this invention, used to process the aggregated gated state sequence. The system performs structural location and quantitative assessment tasks, working in conjunction with the main network to complete the entire crack tracing process. The location classification head performs feature mapping and classification projection on the input gated state sequence, outputting the probability distribution corresponding to the four types of crack locations: outer ring, inner ring, rolling element, and cage. The severity regression head constructs a residual mapping relationship based on this sequence, outputting a crack severity score associated with the degree of structural damage. The two task heads can share some of the previous layer mapping parameters and are trained collaboratively through a joint optimization mechanism, enabling the main network to simultaneously possess the ability of spatial location and damage quantification, thus forming a complete crack tracing and discrimination system for all-ceramic ball bearings.

[0020] Step 7: Write the final crack tracing results to the maintenance archive to generate crack tracing records.

[0021] In this embodiment, the bearing vibration signal acquired in step one is the original time-domain acceleration signal acquired by a triaxial accelerometer under different load and speed combinations. The preprocessing includes performing bandpass filtering, symmetric wavelet threshold denoising, Hilbert transform to extract the envelope, angular domain resampling, and amplitude normalization on the original time-domain acceleration signal in sequence to generate a standardized vibration sequence with a consistent time scale and a unified energy distribution standard.

[0022] In this embodiment, symmetric wavelet thresholding denoising involves selecting complex symmetric wavelet basis functions with symmetry and tight support, such as Symlet wavelet basis functions and Coiflet wavelet basis functions, during the wavelet decomposition and reconstruction process. After multi-scale decomposition of the vibration signal, soft or hard threshold functions are applied to the wavelet coefficients at each level to suppress high-frequency noise components. By symmetrically reconstructing the coefficients after thresholding, a smooth denoised signal that retains key features is restored.

[0023] In this embodiment, step two specifically includes: A complex wavelet packet transform is performed on the standardized vibration sequence, and a full-band multi-scale decomposition is performed using a complex symmetric wavelet basis function of a set order to obtain a multi-resolution wavelet packet coefficient set containing low-frequency coefficient matrix, mid-frequency coefficient matrix and high-frequency coefficient matrix. In this embodiment, a complex wavelet packet transform is performed on the standardized vibration sequence, and a multi-scale decomposition across the entire frequency band is performed using complex symmetric wavelet basis functions of a set order. This aims to improve the accuracy and resolution of frequency domain information extraction from the vibration signal. Traditional real-valued wavelets suffer from phase distortion and bandwidth leakage when processing mechanical vibration signals with strong non-stationarity and phase information characteristics. Therefore, this invention selects the complex wavelet packet transform as the decomposition tool and introduces complex symmetric wavelet basis functions, such as Symlet and Coiflet. These wavelet basis functions possess good symmetry, analytical properties, and phase fidelity.

[0024] Specifically, the decomposition order N is preset, and the standardized vibration sequence is then processed. The recursive division of sub-bands multiplies the bandwidth resolution of each layer, thereby covering the entire signal spectrum and enabling fine-grained analysis across the entire frequency band. In each sub-band, complex symmetric wavelet basis functions are applied to perform filtering and reconstruction operations, extracting low-frequency, mid-frequency, and high-frequency coefficient matrices to form a multi-resolution wavelet packet coefficient set.

[0025] Phase correction and modulus normalization are performed on each coefficient matrix in the multi-resolution wavelet packet coefficient set to generate low-frequency feature tensors, mid-frequency feature tensors and high-frequency feature tensors respectively. Mean normalization and resampling operations are performed on the low-frequency, mid-frequency, and high-frequency feature tensors respectively within a sliding time window of a set length, maintaining consistency on the time scale to form a time-window normalized feature tensor sequence. The time-window normalized feature tensor sequence is then concatenated along the frequency band dimension to generate a frequency-adaptive feature tensor.

[0026] In this embodiment, step three specifically includes: The frequency-adaptive feature tensor is divided into low-frequency, mid-frequency and high-frequency channels, and then input into the corresponding low-frequency, mid-frequency and high-frequency reservoirs respectively. In this embodiment, the frequency-adaptive feature tensor is a three-dimensional tensor obtained by multi-resolution complex wavelet packet decomposition and feature concatenation operations. It represents the energy changes and morphological characteristics of the bearing vibration signal at different frequency bands and time windows. To divide the feature tensor into low-frequency, mid-frequency, and high-frequency channels, an energy concentration partitioning strategy based on frequency bandwidth is adopted. Specifically, the frequency domain is divided according to the full-band decomposition tree corresponding to the selected wavelet packet decomposition order N. For each frequency band, the energy density is calculated. Based on the energy density distribution pattern, the set of frequency bands whose cumulative energy accounts for the top 30% of the total energy is defined as the low-frequency channel, the set of frequency bands whose cumulative energy accounts for 30% to 70% is defined as the mid-frequency channel, and the set of frequency bands whose cumulative energy accounts for more than 70% is defined as the high-frequency channel. Each channel contains several frequency bands. The frequency bands within a channel are spliced ​​together in the original order to form independent sub-tensors, which ultimately constitute the low-frequency channel feature tensor, the mid-frequency channel feature tensor, and the high-frequency channel feature tensor.

[0027] A sliding time window is set in each frequency band reserve pool, and the kurtosis value of the current channel characteristics is calculated within the window; Based on the kurtosis values, an instantaneous kurtosis factor is constructed, and the original internal connectivity matrix of the corresponding reservoir is scaled proportionally to generate a dynamic internal connectivity matrix; the specific steps are as follows: In each frequency band reserve pool, a sliding time window of length T is set, and the kurtosis value is calculated for the input vibration feature sequence within the window. The kurtosis value is calculated from the sample mean, standard deviation and fourth central moment within the window, which reflects the peak degree of the current signal. A linear normalization function is used to map the kurtosis value to a preset weight scaling interval [a,b], generating an instantaneous kurtosis factor λ∈[a,b], where a and b represent the boundary values ​​of weight suppression and amplification, respectively. The instantaneous kurtosis factor λ is applied to the internal circular connection matrix of the corresponding reservoir, and the connection strength is dynamically adjusted in an element-level scaling manner to complete the state propagation structure modulation operation at the current moment.

[0028] This construction and modulation process is executed independently at each time step, giving the network dynamic nonlinear adjustment capabilities and enhancing its sensitivity and ability to distinguish peak-type vibration characteristics.

[0029] Under the influence of the dynamic internal connection matrix, the current channel characteristics are combined with the previous state of the reserve pool to perform state recursion, update the current state vector of the reserve pool, and output the frequency band reserve pool state matrix.

[0030] In this embodiment, to achieve the dynamic response of the improved echo state network to the characteristics of vibration signals in different frequency bands, a state recursion operation based on a dynamic internal connection matrix needs to be performed in each frequency band reserve pool. The operation is periodic at each time step and specifically includes: Receive the vibration feature vector under the sliding window in the current frequency band channel, retrieve the state vector of the corresponding reservoir at the previous time step as the starting point for recursion, and the dynamic internal connection matrix of the current time step has been obtained by scaling the original internal connection matrix of the previous time step with the instantaneous kurtosis factor to reflect the transient change characteristics of the current input signal. The state vector of the reservoir at the previous time step is input into the dynamic internal connection matrix of the current time step to obtain the state propagation term, which represents the evolution trend of the internal structure of the reservoir under the current topology. At the same time, the current input vibration feature vector is mapped through the input connection weights corresponding to the frequency band and used as the external driving term of the current time step. It is introduced into the system to jointly regulate the activation of the current neurons with the state propagation term. The state propagation term and the external driving term are weighted and fused, and transformed through a nonlinear activation mechanism to output the reservoir state vector at the current time step. The reservoir state vector records the instantaneous response of the current frequency band input and the modulation result of the dynamic connection structure, which has a composite effect of frequency band characteristic adaptation and transient feature enhancement. The state vector of the reservoir output at the current time step is written into the state matrix of the current frequency band and used as the state recursion input for the next time step. After the state updates of all time steps are completed in sequence, the complete frequency band reservoir state matrix is ​​output, including the low-frequency reservoir state matrix, the mid-frequency reservoir state matrix, and the high-frequency reservoir state matrix.

[0031] In this embodiment, step four specifically includes: The frequency band reserve pool state matrix is ​​spliced ​​into a unified time-delay state sequence in chronological order; The unified time-delay state sequence is input into the constructed cross-frequency aggregation reserve pool; In this embodiment, in order to achieve unified expression and fusion of low-frequency, mid-frequency and high-frequency characteristic channels, the present invention constructs a cross-frequency aggregation reservoir structure with a dynamic feedback modulation mechanism. The structure is composed of three main parts: frequency band splicing input interface, adjustable delay feedback coupling module and state update unit.

[0032] The splicing input interface is used to receive state matrices output from the frequency band reserve pools. After the state matrices are aligned according to a uniform time step length, they are spliced ​​in the channel dimension to generate a uniform time-delay state sequence, ensuring the synchronization of information in different frequency bands in the time dimension and the decomposability in the channel dimension. The adjustable delay feedback coupling module is a key component in this invention for achieving deep coupling of cross-frequency information. The module has multiple preset delay paths, each corresponding to a set of adjustable delay coefficients, which are used to dynamically select state information at different historical time steps and fuse it with the current input state. The coupling strength weight in the feedback path can be iteratively adjusted during training to enhance the robustness and responsiveness of the cross-frequency signal under specific frequency disturbances or instantaneous impacts. Through this structure, the reservoir can capture the instantaneous features of the current input and integrate historical cross-frequency responses to form a dynamic state representation with a memory mechanism. At each time step, the state update unit is driven by the current concatenated input and the feedback delay input to perform nonlinear mapping and state transition, generating the aggregated state output at the current time step. The state vector has multiple structural characteristics such as cross-frequency information fusion, adaptive memory and delay feedback adjustment.

[0033] The set of preset delay coefficients for the cross-frequency aggregation reserve pool is indexed and activated. Based on the delay coefficient selected at the current time step, the corresponding historical state vector is extracted and superimposed with the current state input vector to form a delay input vector. In this embodiment, in order to achieve the synergistic effect of historical state information and current state input in the cross-frequency aggregation reserve pool, the aggregation reserve pool state vector corresponding to the time step is first extracted from the historical state sequence formed by splicing the frequency band reserve pool state matrix according to the delay coefficient activated at the current time step, and used as the historical state input; the state vector generated by the splicing input at the current time step is obtained simultaneously, and the historical state vector and the current state input vector are weighted and superimposed element by element in each channel dimension according to the set fusion ratio to form the fused delay input vector.

[0034] Based on the magnitude difference between the delayed input vector and the aggregated reservoir state vector of the previous time step in each channel dimension, a feedback adjustment factor is constructed, and the delayed input vector is weighted at the channel level using the feedback adjustment factor as the weight. In this embodiment, the process of constructing feedback adjustment factors based on amplitude differences includes: calculating the amplitude difference between the current delayed input vector and the state vector at the previous moment for each channel dimension; performing normalization processing on the amplitude difference to limit the range to the [0,1] interval; performing nonlinear mapping on the normalization result through a set exponential compression function to improve the response sensitivity to key changing dimensions and generate a channel-level feedback adjustment factor vector. The weighted delayed input vector is superimposed element by element with the aggregated reserve state vector of the previous time step to form the aggregated state update term of the current time step, which replaces the original state vector and is written into the aggregated reserve. The aggregated state update items at all time steps are arranged into a sequence in chronological order, which is used as the state vector sequence of the aggregated reserve pool.

[0035] In this embodiment, the process of updating the bearing topology state tensor and outputting the gated state sequence in step five includes: Calculate the channel amplitude energy of each structural region in the bearing topology state tensor in the low-frequency, mid-frequency and high-frequency dimensions to obtain the structure-frequency band two-dimensional energy matrix. Calculate the kurtosis value of each structural region in the bearing topology state tensor in the corresponding frequency band dimension to obtain the structure-frequency band two-dimensional kurtosis matrix; The structure-frequency band two-dimensional energy matrix and the structure-frequency band two-dimensional kurtosis matrix are normalized according to the channel dimension and fused according to the preset weight coefficients to form an energy-kurtosis gating factor matrix; The energy-kurtosis gated factor matrix is ​​used to perform a channel-by-channel weighted modulation operation on the bearing topology state tensor, and the state amplitude of each structural region in the tensor is adjusted to generate an updated bearing topology state tensor. In this embodiment, during the energy-kurtosis gating modulation process, the bearing topology state tensor is decomposed at the channel level according to the three channels of low frequency, medium frequency and high frequency to obtain the original state amplitude vector of each structural region (outer ring, inner ring, rolling element and cage) under each frequency band channel. The energy-kurtosis gating factor matrix calculated in the previous stage is multiplied element by element with the original state amplitude vector. That is, the gating factor value at the corresponding position of structure-frequency band is used as the modulation weight to scale the original state amplitude vector proportionally.

[0036] The purpose of channel-wise weighted modulation is to dynamically adjust the state amplitude of each structural region according to the energy release characteristics and impact significance of each region in different frequency bands, enhance the state response of crack-sensitive regions, and suppress the amplitude fluctuations in background noise-dominated regions. The modulated state vectors of each frequency band are recombined in the structural region dimension to form the updated bearing topology state tensor.

[0037] The updated bearing topology state tensor is expanded along the time dimension and spliced ​​in the order of structural regions to generate a gated state sequence.

[0038] In this embodiment, the output process of the final crack tracing result specifically includes: The gating state sequence input position classification readout head is used to perform multi-structure region crack location probability calculation and output the probability distribution of crack locations in the outer ring, inner ring, rolling elements and cage. Specifically, the updated gated state sequence is divided into four structural regions along the structural channel dimension: outer ring, inner ring, rolling element, and cage. Temporal feature aggregation is performed on each structural region state subsequence to generate a structural region embedding representation vector. The embedding representation vector is input into a structural region classification network consisting of a set of fully connected layers, and nonlinear transformation and normalization are performed. The crack occurrence probability corresponding to each structural region is output through the softmax function to form a structural region crack location probability vector. The gating state sequence is synchronously input into the severity regression readout head, multi-channel regression operation is performed, and the crack severity score vector of the corresponding structural region is output. Specifically, in the multi-channel regression operation, state subsequences corresponding to the low-frequency, mid-frequency, and high-frequency channels are extracted for the updated gated state sequence. For each frequency band state subsequence, time window division is performed to divide the entire sequence into several overlapping time segments. Statistical feature parameters, including root mean square value, peak factor, kurtosis factor, and waveform factor, are calculated for each time segment to form a statistical feature vector describing the concentration of vibration energy and non-Gaussian characteristics. The statistical feature vector is input into a fully connected regression network, which consists of two linear mapping layers and one ReLU activation layer, and outputs the crack severity score for this frequency band channel. The score is a continuous real number in the interval [0,1], representing the severity of the crack signal in the frequency band.

[0039] The maximum probability value of the probability distribution of the crack location and the mean severity score are used to form the identification confidence index. When the index is lower than the preset threshold, the output error signal of the classification and regression readout head is recorded. Specifically, the method includes: in the location classification head, performing probability prediction of crack locations in multi-structure regions based on the gated state sequence, obtaining the crack probability distribution vectors of the corresponding outer ring, inner ring, rolling element, and cage, and extracting the maximum probability value as the maximum confidence value for crack location determination; in the severity regression head, performing multi-channel regression operations for the low-frequency, mid-frequency, and high-frequency channels respectively, outputting the crack severity score value for each channel, and performing arithmetic averaging to obtain the mean crack severity score; this invention uses the maximum confidence value of the crack location and the mean crack severity score to constitute the identification confidence index of the current crack tracing result, which is used to determine whether the error feedback correction mechanism of the cross-frequency aggregation reserve pool coupling weight is triggered.

[0040] The error signal is back-mapped to the gating state sequence generation source and further projected to the cross-frequency aggregation reserve pool. Based on the frequency band and structural region distribution of the error, the corresponding coupling weight is fine-tuned and updated. Specifically, this involves mapping the error signal generated by the readout layer back to the gating state sequence generation path, further tracing it to the internal structure of the cross-frequency aggregation reservoir, analyzing the corresponding frequency band source (low frequency, medium frequency, or high frequency) and bearing structure area label (outer ring, inner ring, rolling element, or cage) for each error signal component, establishing an error location index between the frequency band and the structure area, and performing fine-tuning operations on the feedback coupling channels in the aggregation reservoir corresponding to the frequency band and the structure area based on the error location index. Specifically, this involves adjusting the current coupling weight value based on the amplitude and direction of the error signal, iteratively updating the direction to reduce the error, thereby achieving a refined and regionally controllable coupling weight correction process.

[0041] Under the updated coupling weights, the state propagation, tensor construction, and gating modulation operations are re-executed to obtain a new gating state sequence. This process is repeated until the confidence index reaches a preset threshold or the maximum number of iterations is reached. After the termination condition is met, the outputs of the current classification head and regression head are used as the final crack tracing result, which includes the structural part classification label and the corresponding crack severity score.

[0042] In this embodiment, the final crack tracing result includes the bearing structure area label corresponding to the crack, the frequency band label where the crack is located, the crack severity score, and the confidence index.

[0043] Example 1

[0044] To verify the feasibility of this invention in practice, it was applied to a scenario of tracing the crack evolution of ceramic ball bearings in a typical precision operating equipment. This type of equipment requires extremely high operational stability. Due to factors such as high speed, high load, and micro-dust particles in its operating environment, traditional metal bearings often experience failure phenomena such as fatigue pitting, spalling, or even breakage. In order to improve durability, all-ceramic ball bearings have been gradually adopted. However, in the early stage of crack occurrence, it is often difficult to accurately identify the location and severity of cracks using conventional vibration threshold or frequency domain methods.

[0045] In the experiment, structurally intact all-ceramic ball bearing samples were selected as initial control samples. Artificial crack induction was achieved in different structural regions (e.g., outer ring, inner ring, rolling elements, cage) using a controlled impact loading device, constructing a bearing sample library containing multiple structural regions and different crack grades. Vibration signals were collected from all samples under set rotational speeds (e.g., 1800 rpm, 2500 rpm, 3200 rpm) and loading conditions (e.g., 50 N, 100 N) using a high-sensitivity triaxial accelerometer. The raw signals were preprocessed using symmetrical wavelet threshold denoising and Z-score normalization to generate standardized vibration sequences.

[0046] In the processing stage, the standardized sequence is subjected to multi-resolution complex wavelet packet transform and three-band segmentation to form a frequency adaptive tensor, which is then injected into the low-frequency, mid-frequency, and high-frequency reservoirs respectively. The weights inside the reservoirs are dynamically adjusted using an instantaneous kurtosis factor, and the frequency band state matrix is ​​obtained by performing state recursion. The matrix is ​​then entered into the cross-frequency aggregation reservoir through delayed splicing. Temporal information is fused under an adjustable feedback coupling mechanism to output a set of structural feature vectors, which are further reconstructed into a bearing topology state tensor. The frequency band energy and kurtosis are calculated for the bearing topology state tensor to construct a gating factor, which is then gated and modulated and input into the position classification head and severity regression head respectively to obtain the final crack identification result.

[0047] The comparative results show that the proposed solution improves the accuracy of identifying cracks in different locations compared to traditional methods based on spectral analysis or convolutional neural networks. Through a confidence-gated feedback mechanism, the system automatically performs error-driven coupling weight correction when the confidence level falls below a threshold, reducing early misjudgments and false alarms. The following is a comparison table of crack tracing performance: Table 1: Comparison of Crack Tracing Performance Data Sample number Crack area Crack grade The accuracy of this invention in tracing Severity error of this invention Traditional CNN accuracy Traditional CNN error Accuracy based on spectrum analysis Based on spectral analysis error S01 Outer ring moderate 96.2% 0.074 89.1% 0.132 81.4% 0.187 S02 Inner circle Mild 94.5% 0.059 88.7% 0.098 76.9% 0.146 S03 Rolling body serious 95.1% 0.083 87.6% 0.124 79.5% 0.193 S04 cage moderate 92.8% 0.067 74.2% 0.136 69.8% 0.202 S05 cage Mild 90.7% 0.048 72.1% 0.101 66.3% 0.157 S06 Inner circle serious 97.4% 0.089 90.2% 0.133 84.7% 0.197 In the task of tracing cracks in the outer ring, the method of this invention demonstrates excellent localization and scoring capabilities, with a tracing accuracy of 96.2% and a severity scoring error controlled at 0.074. This is far superior to the 89.1% accuracy and 0.132 scoring error of the traditional CNN model, and also superior to the 81.4% and 0.187 of the spectrum analysis-based model. This indicates that the improved echo state network has higher expressive power in the feature extraction and recognition of the outer ring structure.

[0048] For inner-circle crack samples, especially mild crack scenarios, this invention still maintains high-precision recognition performance with an accuracy of 94.5% and a severity scoring error of only 0.059. This is superior to the 88.7% accuracy and 0.098 error of traditional CNNs. Even when the crack severity increases, the method of this invention can still maintain a high accuracy of 97.4% and good scoring control capabilities, highlighting the robustness of this invention in feature dynamic modeling and feedback correction.

[0049] In rolling element crack identification tasks, traditional methods generally achieve an accuracy of around 80%, while the accuracy of this invention is improved to 95.1%, with a severity error of 0.083. Considering the significant vibration interference and signal overlap present in rolling elements, this invention effectively separates the feature contribution channels, enhancing the traceability resolution.

[0050] For the most challenging cage crack identification task, the model of this invention achieved an accuracy of 90.7% (mild) and 92.8% (moderate), both higher than the 72.1% and 74.2% of traditional CNNs and the 66.3% and 69.8% of spectral analysis methods, with errors controlled at the levels of 0.048 and 0.067.

[0051] In summary, the data in the table fully demonstrates the wide adaptability and high identification accuracy of the present invention in various structural parts and different crack levels. It is particularly outstanding in the early diagnosis of minor cracks and the tracing of difficult-to-locate areas, verifying the practical application value of the present invention in the fault diagnosis and visualized crack tracing of all-ceramic ball bearings.

[0052] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for tracing cracks in all-ceramic ball bearings based on the fusion of vibration signals and machine learning, characterized in that, Includes the following steps: Step 1: Collect bearing vibration signals and preprocess them to obtain a standardized vibration sequence; Step 2: Perform multi-resolution complex wavelet packet transform and time window normalization on the vibration sequence to extract low-frequency, mid-frequency, and high-frequency feature tensors and concatenate them to generate frequency-adaptive feature tensors; Step 3: Inject the frequency adaptive feature tensor into the improved echo state network composed of low-frequency, mid-frequency and high-frequency reservoirs respectively, and recursively calculate the internal weight matrix according to the instantaneous kurtosis factor of each reservoir to output the frequency band reservoir state matrix. Step 4: Input the state matrix of the reservoir into the cross-frequency aggregated reservoir after time delay splicing, and perform adjustable feedback coupling according to the delay coefficient to generate the state vector of the aggregated reservoir. Step 5: Divide and combine the state vectors of the aggregated reservoir according to the order of outer ring, inner ring, rolling element, and cage to form the bearing topology state tensor; Step 6: Calculate the frequency band energy and kurtosis value of the bearing topology state tensor, construct the energy-kurtosis gating factor, update the bearing topology state tensor and output the gated state sequence, input the gated state sequence into the location classification head and severity regression head to obtain the probability of crack location and crack severity score. If the confidence is lower than the threshold, use the readout layer error signal to iteratively correct the cross-frequency aggregation reservoir coupling weight until the termination condition is met, and output the final crack tracing result. Step 7: Write the final crack tracing results to the maintenance archive to generate crack tracing records.

2. The method for tracing cracks in all-ceramic ball bearings based on the fusion of vibration signals and machine learning as described in claim 1, characterized in that, The bearing vibration signal acquired in step one is the raw time-domain acceleration signal acquired by a triaxial accelerometer under different load and speed combinations. The preprocessing includes performing bandpass filtering, symmetric wavelet threshold denoising, Hilbert transform to extract the envelope, angular domain resampling, and amplitude normalization on the raw time-domain acceleration signal in sequence to generate a standardized vibration sequence with a consistent time scale and a unified energy distribution standard.

3. The method for tracing cracks in all-ceramic ball bearings based on the fusion of vibration signals and machine learning as described in claim 2, characterized in that, Step two specifically includes: A complex wavelet packet transform is performed on the standardized vibration sequence, and a full-band multi-scale decomposition is performed using a complex symmetric wavelet basis function of a set order to obtain a multi-resolution wavelet packet coefficient set containing low-frequency coefficient matrix, mid-frequency coefficient matrix and high-frequency coefficient matrix. Phase correction and modulus normalization are performed on each coefficient matrix in the multi-resolution wavelet packet coefficient set to generate low-frequency feature tensors, mid-frequency feature tensors and high-frequency feature tensors respectively. Mean normalization and resampling operations are performed on the low-frequency, mid-frequency, and high-frequency feature tensors respectively within a sliding time window of a set length, maintaining consistency on the time scale to form a time-window normalized feature tensor sequence. The time-window normalized feature tensor sequence is then concatenated along the frequency band dimension to generate a frequency-adaptive feature tensor.

4. The method for tracing cracks in all-ceramic ball bearings based on the fusion of vibration signals and machine learning as described in claim 3, characterized in that, Step three specifically includes: The frequency-adaptive feature tensor is divided into low-frequency, mid-frequency and high-frequency channels, and then input into the corresponding low-frequency, mid-frequency and high-frequency reservoirs respectively. A sliding time window is set in each frequency band reserve pool, and the kurtosis value is calculated for the current channel characteristics within the window; Construct an instantaneous kurtosis factor based on the kurtosis value, scale the original internal connectivity matrix of the corresponding reservoir proportionally, and generate a dynamic internal connectivity matrix. Under the influence of the dynamic internal connection matrix, the current channel characteristics are combined with the previous state of the reserve pool to perform state recursion, update the current state vector of the reserve pool, and output the frequency band reserve pool state matrix.

5. The method for tracing cracks in all-ceramic ball bearings based on the fusion of vibration signals and machine learning as described in claim 4, characterized in that, Step four specifically includes: The frequency band reserve pool state matrix is ​​spliced ​​into a unified time-delay state sequence in chronological order; The unified time-delay state sequence is input into the constructed cross-frequency aggregation reserve pool; The set of preset delay coefficients for the cross-frequency aggregation reserve pool is indexed and activated. Based on the delay coefficient selected at the current time step, the corresponding historical state vector is extracted and superimposed with the current state input vector to form a delay input vector. Based on the magnitude difference between the delayed input vector and the aggregated reservoir state vector of the previous time step in each channel dimension, a feedback adjustment factor is constructed, and the delayed input vector is weighted at the channel level using the feedback adjustment factor as the weight. The weighted delayed input vector is superimposed element by element with the aggregated reserve state vector of the previous time step to form the aggregated state update term of the current time step, which replaces the original state vector and is written into the aggregated reserve. The aggregated state update items at all time steps are arranged into a sequence in chronological order, which is used as the state vector sequence of the aggregated reserve pool.

6. The method for tracing cracks in all-ceramic ball bearings based on the fusion of vibration signals and machine learning as described in claim 5, characterized in that, The process of updating the bearing topology state tensor and outputting the gated state sequence in step five includes: Calculate the channel amplitude energy of each structural region in the bearing topology state tensor in the low-frequency, mid-frequency and high-frequency dimensions to obtain the structure-frequency band two-dimensional energy matrix. Calculate the kurtosis value of each structural region in the bearing topology state tensor in the corresponding frequency band dimension to obtain the structure-frequency band two-dimensional kurtosis matrix; The structure-frequency band two-dimensional energy matrix and the structure-frequency band two-dimensional kurtosis matrix are normalized according to the channel dimension and fused according to the preset weight coefficients to form an energy-kurtosis gating factor matrix; The energy-kurtosis gated factor matrix is ​​used to perform a channel-by-channel weighted modulation operation on the bearing topology state tensor, and the state amplitude of each structural region in the tensor is adjusted to generate an updated bearing topology state tensor. The updated bearing topology state tensor is expanded along the time dimension and spliced ​​in the order of structural regions to generate a gated state sequence.

7. The method for tracing cracks in all-ceramic ball bearings based on the fusion of vibration signals and machine learning as described in claim 6, characterized in that, The output process of the final crack tracing result in step six specifically includes: The gating state sequence input position classification readout head is used to perform multi-structure region crack location probability calculation and output the probability distribution of crack locations in the outer ring, inner ring, rolling elements and cage. The gating state sequence is synchronously input into the severity regression readout head, multi-channel regression operation is performed, and the crack severity score vector of the corresponding structural region is output. The maximum probability value of the probability distribution of the crack location and the mean severity score are used to form the identification confidence index. When the identification confidence index is lower than the preset threshold, the output error signal of the classification and regression readout head is recorded. The error signal is back-mapped to the gating state sequence generation source and further projected to the cross-frequency aggregation reserve pool. Based on the frequency band and structural region distribution of the error, the corresponding coupling weight is fine-tuned and updated. Under the updated coupling weights, the state propagation, tensor construction, and gating modulation operations are re-executed to obtain a new gating state sequence. This process is repeated until the confidence index reaches a preset threshold or the maximum number of iterations is reached. After the termination condition is met, the outputs of the current classification head and regression head are used as the final crack tracing result, which includes the structural part classification label and the corresponding crack severity score.

8. The method for tracing cracks in all-ceramic ball bearings based on the fusion of vibration signals and machine learning as described in claim 7, characterized in that, The final crack tracing results include the bearing structure area label corresponding to the crack, the frequency band label where the crack is located, the crack severity score, and the confidence index.

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