Bearing fault diagnosis method based on symmetry point distribution image construction

Abstract

The application discloses a bearing fault diagnosis method based on a symmetry point distribution (SDP) image, and belongs to the field of mechanical equipment state monitoring. The method collects vibration acceleration signals of a driving end bearing, performs segmentation and normalization processing, maps one-dimensional vibration signals into two-dimensional images through SDP transformation, and constructs a fault image dataset. On this basis, a polar coordinate attention mechanism is introduced into a deep residual network, the characteristics are adaptively weighted in the radial and angular directions, a polar coordinate attention residual fault diagnosis model is established, and feature extraction and classification of bearing faults are realized. The application improves the feature expression capability and diagnosis accuracy, and is suitable for state recognition of rolling bearings under complex working conditions.

Description

Technical Field

[0001] This invention relates to a bearing fault diagnosis method, and more specifically to a bearing fault diagnosis method based on a symmetrical point distribution image. Background Technology

[0002] In the field of rolling bearing fault diagnosis, vibration signal analysis is one of the most important condition monitoring methods because vibration response can reflect the impact and modulation characteristics generated by internal bearing defects. A large body of literature has systematically reviewed the application and development of traditional vibration signal processing methods, including time-domain analysis, frequency-domain analysis, and time-frequency-domain analysis. Time-domain analysis assesses vibration changes caused by faults by statistically analyzing parameters such as amplitude, mean, and variance of the signal; frequency-domain analysis uses Fourier transform to extract frequency component changes to find typical fault frequencies; time-frequency-domain analysis, such as wavelet transform, further reveals the local dynamic characteristics of the signal in the joint time and frequency domains, aiming to overcome the limitations of simple time-domain or frequency-domain analysis in representing non-stationary signals. Although these methods are widely used in academia and engineering, the inherent nonlinearity and non-stationarity of vibration signals, coupled with the influence of transmission paths, mechanical coupling, and environmental noise during the acquisition process, make it difficult for these traditional methods to extract fault features under complex working conditions and low signal-to-noise ratio conditions, thus hindering high robustness and high recognition accuracy. ([Chongqing University of Science and Technology][1])

[0003] For example, an existing bearing fault diagnosis technology based on domain adaptation extracts traditional features from labeled historical vibration data and target vibration data, and constructs a manifold projection by selecting sensitive feature sets using distance indices and principal component analysis to achieve data adaptation and state identification between different operating conditions. Although this technology has been partially optimized for changes in operating conditions, it relies on traditional feature extraction and shallow feature statistics, and its ability to capture the deep structure and nonlinear relationships of complex dynamic vibration modes is insufficient. Its diagnostic performance remains significantly limited when facing high-noise and complex alternating load conditions. ([Google Patent][2])

[0004] Furthermore, although recent studies have converted one-dimensional vibration signals into two-dimensional feature images and combined them with convolutional neural networks for fault identification, these methods still largely rely on predefined transformations such as spectrograms or short-time Fourier transforms and other traditional spectral forms. Moreover, the generated image features often fail to fully preserve the dynamic structure of nonlinear and non-stationary characteristics in the original signal at different scales, thus limiting the generalization performance of deep learning models in real-world complex working conditions.

[0005] In summary, existing vibration analysis techniques suffer from the following major technical problems that urgently need to be addressed: First, traditional time-domain and frequency-domain features are limited, making it difficult to comprehensively characterize the complex dynamic features of nonlinear and non-stationary signals; second, existing time-frequency domain methods lack robustness to noise and have limited adaptability to dynamic operating conditions; third, existing image-based methods struggle to construct a comprehensive representation of vibration signals in polar coordinate structure, symmetry, and temporal correspondence, resulting in insufficient feature extraction efficiency and robustness of deep learning models under complex conditions. These core problems are precisely the engineering pain points that the novel image construction mechanism and polar coordinate attention network collaborative mechanism proposed in this invention aim to directly solve. Summary of the Invention

[0006] In view of the shortcomings of the existing technology, the purpose of this invention is to provide a bearing fault diagnosis method based on symmetrical point distribution images.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for fault diagnosis of deep groove ball bearings that integrates frequency domain features and an improved residual network, characterized by comprising the following steps:

[0008] Step 1: Collect vibration signals from a vibration acceleration sensor installed at the drive end bearing, construct a raw dataset of bearing faults based on the collected vibration signals, and preprocess the vibration signals; the preprocessing includes at least signal segmentation and normalization to obtain standardized vibration signal data for subsequent image transformation.

[0009] The signal segmentation process involves dividing the acquired vibration signal into segments according to a preset data length, treating each segment as an independent sample. The normalization process employs a maximum-minimum normalization method to linearly map the segmented vibration signal, ensuring that the vibration signal amplitude falls within a preset numerical range.

[0010] Step 2: Perform Symmetric Point Distribution (SDP) image transformation processing on the standardized vibration signal data obtained in Step 1 to map the one-dimensional vibration signal into a two-dimensional symmetric point distribution image, generate the corresponding bearing fault SDP image dataset, and store the SDP image dataset in the fault server as input data for the bearing fault diagnosis model.

[0011] The SDP image transformation maps the standardized vibration signal to polar coordinate space and generates multiple sets of mirror-symmetric points. The mapping relationship satisfies the following formula:

[0012]

[0013]

[0014]

[0015] Where: i represents the sampling point number; This represents the vibration amplitude at the i-th sampling point; and These represent the minimum and maximum values ​​of the vibration signal, respectively. Represents the polar radius in polar coordinates; and These represent the clockwise and counterclockwise polar angles, respectively. Indicates the number of planes of symmetry; The time interval parameter represents the generation of mirror-symmetric points; This represents the angular magnification factor, used to control the angular distribution range of symmetrical points in polar coordinate space.

[0016] Step 3: Introduce the polar coordinate attention mechanism into the deep residual neural network to construct a polar coordinate attention residual network fault diagnosis model.

[0017] The polar coordinate attention mechanism constructs radial and angular feature sequences to characterize the feature distribution in different radial and angular regions by grouping and statistically analyzing the input features along both radial and angular indices. The statistical method for the radial feature sequences satisfies the following:

[0018]

[0019] in, Indicates the first The first channel in the Statistical characteristics on radial indices; This indicates the spatial location of the input feature map in channel c. eigenvalues ​​at that location and These represent the width and height of the input feature map, respectively. Indicates the total number of radial indices.

[0020] The radial index judgment function Defined as

[0021]

[0022] in, Indicates spatial location The corresponding radial index.

[0023] Similarly, by grouping and statistically analyzing the input features based on the angular index, an angular feature sequence is constructed, and the statistical method satisfies:

[0024]

[0025] in, Indicates the angular index number, This indicates the total number of angular indices.

[0026] Angular index determination function Defined as

[0027]

[0028] in, Indicates spatial location The corresponding angular index.

[0029] Based on this, the radial feature sequences are respectively... and angular feature sequences Feature mapping is performed to generate radial and angular weight sequences, whose generation relationship satisfies:

[0030]

[0031]

[0032] in, and These represent the radial weight sequence and the angular weight sequence, respectively. and The transformation function represents the mapping of sequence features and can be implemented by one-dimensional convolution, fully connected layers, or linear transformations. This represents a non-linear activation function used to limit the weights within a preset range.

[0033] A polar coordinate attention mechanism is introduced into a deep residual neural network to construct a fault diagnosis model for a polar coordinate attention residual network.

[0034] Specifically, based on the representation of the symmetrical point distribution image in polar coordinate space, the corresponding radial and angular indices are determined for each pixel position in the input features, and the correspondence between the input features and the polar coordinate indices is established. On this basis, the input features are grouped and statistically analyzed on the radial and angular indices respectively to generate radial feature sequences and angular feature sequences for characterizing the feature distribution of different radial and angular regions. Furthermore, the corresponding radial weight sequences and angular weight sequences are obtained through feature mapping.

[0035] Subsequently, based on the radial index and angular index, the input features are subjected to polar coordinate attention modulation using the radial weight sequence and angular weight sequence, and the modulation relationship satisfies:

[0036]

[0037] in This represents element-wise multiplication. This represents the features before modulation by the polar coordinate attention mechanism. This represents the features modulated by the polar coordinate attention mechanism;

[0038] The features modulated by polar coordinate attention are embedded into the residual structure, and feature fusion and updating are completed through residual connections. The residual update relationship satisfies:

[0039]

[0040] in This represents the output characteristics of the residual main branch. This represents an identity mapping or a linear mapping. This represents the output characteristics of the residual block.

[0041] The residual structure is used to form the feature extraction layer of a deep residual neural network, thereby completing the construction of a polar coordinate attention residual network fault diagnosis model.

[0042] Step 4: Using the polar coordinate attention residual network fault diagnosis model constructed in Step 3 as the bearing fault diagnosis model, perform feature extraction and fault classification processing on the bearing fault SDP image obtained in Step 2, and output the corresponding rolling bearing fault diagnosis results.

[0043] Compared with the prior art, the present invention has at least the following beneficial effects:

[0044] Compared with existing technologies, this invention does not rely on a single technical means to improve bearing fault diagnosis performance. Instead, it fundamentally improves the problem of unstable extraction of rolling bearing fault features under complex working conditions by synergistically designing vibration signal characterization methods, feature attention mechanisms, and deep feature learning structures. It has at least the following beneficial effects.

[0045] First, this invention transforms the rolling bearing vibration signal into a symmetrical point distribution image, mapping the originally non-stationary, nonlinear one-dimensional time series signal into a two-dimensional image representation with symmetrical structural features. This allows the temporal variation and amplitude distribution characteristics of the vibration signal to be uniformly expressed in the spatial structure. This image-based approach weakens the influence of local noise disturbances on the amplitude at a single moment, transforming the periodic impacts and modulation characteristics caused by the fault into a stable geometric distribution pattern, thereby improving the identifiability of fault features under complex transmission paths and noise interference conditions.

[0046] Secondly, based on the representational characteristics of symmetrical point distribution images in polar coordinate space, this invention introduces an attention mechanism for joint radial and angular modeling. By statistically analyzing and weighting the feature distributions of different radial and angular regions, the model can distinguish the intensity of fault information carried in different spatial directions at the structural level. This mechanism does not simply enhance local features, but rather establishes a correspondence between features and vibration evolution laws through polar coordinate indexing, thereby highlighting key areas highly correlated with bearing damage mechanisms, while suppressing redundant and random interference information, thus improving the stability and robustness of fault identification.

[0047] Furthermore, this invention embeds the aforementioned polar coordinate attention mechanism into a deep residual neural network. Through the residual structure, features are transferred and fused layer by layer, avoiding the degradation problem of deep network training while enhancing the modeling ability for complex nonlinear fault modes. The resulting diagnostic model maintains high recognition accuracy and generalization ability under complex operating conditions, variable loads, and low signal-to-noise ratios, demonstrating significant technological advancements compared to traditional signal processing methods and conventional deep learning models, and possessing excellent engineering application value. Attached Figure Description

[0048] Figure 1 A schematic diagram of the overall process of a bearing fault diagnosis method based on symmetrical point distribution images provided by the present invention;

[0049] Figure 2 This is a schematic diagram illustrating the generation of a symmetrical point distribution image from a vibration signal through a symmetrical point distribution transformation in an embodiment of the present invention;

[0050] Figure 3 This is a schematic diagram of the polar coordinate attention module in an embodiment of the present invention;

[0051] Figure 4 This is a schematic diagram of the residual structure in an embodiment of the present invention. Figure 5 This is a schematic diagram of the classification confusion matrix of the industrial bearing multi-fault state diagnosis model in an embodiment of the present invention; Figure 6 This is a t-SNE dimensionality reduction visualization diagram of the multi-fault state characteristics of industrial bearings in an embodiment of the present invention. Detailed Implementation

[0052] The technical solution of the present invention will now be clearly and completely described through specific embodiments. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0053] This embodiment will be described in detail with reference to the accompanying drawings:

[0054] like Figure 1 As shown, a bearing fault diagnosis method based on a symmetrical point distribution image is provided, including the following steps:

[0055] Step 1: Collect vibration signals from a vibration acceleration sensor installed at the drive end bearing, construct a raw dataset of bearing faults based on the collected vibration signals, and preprocess the vibration signals; the preprocessing includes at least signal segmentation and normalization to obtain standardized vibration signal data for subsequent image transformation.

[0056] The signal segmentation process involves dividing the acquired vibration signal into segments according to a preset data length, treating each segment as an independent sample. The normalization process employs a maximum-minimum normalization method to linearly map the segmented vibration signal, ensuring that the vibration signal amplitude falls within a preset numerical range.

[0057] Step Two: As Figure 2 As shown, the standardized vibration signal data obtained in step one undergoes Symmetric Point Distribution (SDP) image transformation processing to map the one-dimensional vibration signal into a two-dimensional symmetric point distribution image, generating the corresponding bearing fault SDP image dataset. Specifically, the standardized vibration signal is mapped to polar coordinate space, and the symmetric point distribution image is constructed by generating multiple sets of mirror symmetric points. The mapping relationship satisfies the following formula:

[0058]

[0059]

[0060]

[0061] Where: i represents the sampling point number; This represents the vibration amplitude at the i-th sampling point; and These represent the minimum and maximum values ​​of the vibration signal, respectively. Represents the polar radius in polar coordinates; and These represent the clockwise and counterclockwise polar angles, respectively. Indicates the number of planes of symmetry; The time interval parameter represents the generation of mirror-symmetric points; This represents the angular magnification factor, used to control the angular distribution range of symmetrical points in polar coordinate space.

[0062] Step 3: As Figure 3As shown, the polar coordinate attention mechanism is introduced into the deep residual neural network to construct a fault diagnosis model of polar coordinate attention residual network.

[0063] The polar coordinate attention mechanism constructs radial and angular feature sequences to characterize the feature distribution in different radial and angular regions by grouping and statistically analyzing the input features along both radial and angular indices. The statistical method for the radial feature sequences satisfies the following:

[0064]

[0065] in, Indicates the first The first channel in the Statistical characteristics on radial indices; This indicates the spatial location of the input feature map in channel c. eigenvalues ​​at that location and These represent the width and height of the input feature map, respectively. Indicates the total number of radial indices.

[0066] The radial index judgment function Defined as

[0067]

[0068] in, Indicates spatial location The corresponding radial index.

[0069] Similarly, by grouping and statistically analyzing the input features based on the angular index, an angular feature sequence is constructed, and the statistical method satisfies:

[0070]

[0071] in, Indicates the angular index number, This indicates the total number of angular indices.

[0072] Angular index determination function Defined as

[0073]

[0074] in, Indicates spatial location The corresponding angular index.

[0075] Based on this, the radial feature sequences are respectively... and angular feature sequences Feature mapping is performed to generate radial and angular weight sequences, whose generation relationship satisfies:

[0076]

[0077]

[0078] in, and These represent the radial weight sequence and the angular weight sequence, respectively. and The transformation function represents the mapping of sequence features and can be implemented by one-dimensional convolution, fully connected layers, or linear transformations. This represents a non-linear activation function used to limit the weights within a preset range.

[0079] A polar coordinate attention mechanism is introduced into a deep residual neural network to construct a fault diagnosis model for a polar coordinate attention residual network.

[0080] Specifically, based on the representation of the symmetrical point distribution image in polar coordinate space, the corresponding radial and angular indices are determined for each pixel position in the input features, and the correspondence between the input features and the polar coordinate indices is established. On this basis, the input features are grouped and statistically analyzed on the radial and angular indices respectively to generate radial feature sequences and angular feature sequences for characterizing the feature distribution of different radial and angular regions. Furthermore, the corresponding radial weight sequences and angular weight sequences are obtained through feature mapping.

[0081] Subsequently, based on the radial index and angular index, the input features are subjected to polar coordinate attention modulation using the radial weight sequence and angular weight sequence, and the modulation relationship satisfies:

[0082]

[0083] in This represents element-wise multiplication. This represents the features before modulation by the polar coordinate attention mechanism. This represents the features modulated by the polar coordinate attention mechanism;

[0084] like Figure 4 As shown, the features modulated by polar coordinate attention are embedded into the residual structure, and feature fusion and updating are completed through residual connections. The residual update relationship satisfies:

[0085]

[0086] in This represents the output characteristics of the residual main branch. This represents an identity mapping or a linear mapping. This represents the output characteristics of the residual block.

[0087] The residual structure is used to form the feature extraction layer of a deep residual neural network, thereby completing the construction of a polar coordinate attention residual network fault diagnosis model.

[0088] Step 4: Using the polar coordinate attention residual network fault diagnosis model constructed in Step 3 as the bearing fault diagnosis model, perform feature extraction and fault classification processing on the bearing fault SDP image obtained in Step 2, and output the corresponding rolling bearing fault diagnosis results.

[0089] Example 1: Bearing Fault Identification Based on Constant Speed ​​Operating Conditions

[0090] Under constant speed conditions, a vibration acceleration sensor is installed at the rolling bearing on the drive end to continuously collect vibration signals during bearing operation. The collected signals are segmented into fixed data lengths, and the amplitude of each segment is normalized to eliminate amplitude differences between different sampling segments. A symmetrical point distribution image is constructed from the normalized vibration signals. By generating pairs of mirror-symmetrical points in polar coordinate space, a stable and clearly structured two-dimensional image representation is formed. The generated image is then input into a residual network with a polar coordinate attention mechanism for feature learning, enabling accurate differentiation between inner ring faults, outer ring faults, and normal conditions.

[0091] Example 2: Robust Fault Diagnosis Example under Variable Speed ​​Conditions

[0092] To address the complex operating conditions of fluctuating bearing speeds, vibration signals at different speed stages were collected and processed in segments. A normalization operation was used to unify the amplitude scale at different speeds, and a time interval parameter was used to control the correlation of sampling points during the generation of symmetrical points, ensuring that the constructed symmetrical point distribution image reflects the dynamic evolution characteristics of the vibration signal. A polar coordinate attention mechanism was employed to weightedly modulate the feature distributions in the radial and angular regions, effectively suppressing interference from speed variations and improving the model's diagnostic stability under varying operating conditions.

[0093] Example 3: Early Identification of Weak Faults

[0094] In the early stages of bearing damage, the fault feature energy in the vibration signal is weak and easily masked by noise. By setting a larger angular amplification parameter, the symmetrical points are distributed more dispersedly in polar coordinate space, thereby amplifying the structural changes of subtle amplitude differences in the image. Combined with the adaptive weighting of features in different radial regions using a polar coordinate attention mechanism, the network focuses more on local region features related to early damage, achieving effective extraction of minute fault features.

[0095] Example 4: Example of Joint Diagnosis of Multiple Fault Types

[0096] For datasets containing multiple fault types, including inner rings, outer rings, and rolling elements, corresponding symmetrical point distribution images are constructed. Radial and angular indices are assigned to each pixel location using polar coordinate indices, enabling the network to distinguish the distribution differences of different faults in polar coordinate space during feature learning. By jointly modulating radial and angular attention weights, the residual network maintains its deep feature representation capabilities while improving the discriminative power between different fault modes.

[0097] Example 5: Online Monitoring and Real-time Diagnosis Example

[0098] Vibration signal acquisition, symmetrical point distribution image construction, and polar coordinate attention residual network are deployed in the online monitoring system. The system receives bearing operating vibration data in real time and completes signal segmentation and image construction according to preset rules. By dynamically modulating the real-time generated image features through the polar coordinate attention mechanism, continuous discrimination of bearing operating status is achieved, providing real-time and reliable fault diagnosis results for equipment operation and maintenance.

[0099] Evidence related to the technical effects obtained by the embodiments of the present invention.

[0100] The training and validation data used in this algorithm is a dataset of real bearing multi-state vibration signals independently collected from industrial sites. This dataset comprehensively covers signals of rolling bearings under normal operating conditions, as well as various typical fault modes such as inner ring faults, outer ring faults, rolling element faults, cage faults, and their combined faults, ensuring the model's generalization ability and diagnostic reliability in real industrial scenarios. Results are shown below. Figure 5 and Figure 6 As shown.

[0101] To verify that the model has better diagnostic efficiency in the field of bearing fault diagnosis, it was compared and validated with convolutional neural network (CNN), squeeze-excitation network (SE-Net) and visual transformer (VIT). The experimental results are shown in Table 1.

[0102]

[0103] The above embodiments fully reveal the implementation method and technical effect of the technical solution of the present invention from multiple aspects such as working condition adaptability, feature construction method and polar coordinate attention collaboration mechanism, enabling those skilled in the art to implement the present invention without creative effort.

Claims

1. A bearing fault diagnosis method based on symmetrical point distribution images, characterized in that, include: Vibration acceleration signals are collected from the rolling bearing at the drive end, and the vibration signals are segmented and normalized to obtain standardized vibration signals. The standardized vibration signal is mapped to polar coordinate space. By generating pairs of mirror symmetric points for each sampling point, a symmetric point distribution image reflecting the relationship between vibration time sequence and amplitude is constructed, and a bearing fault image dataset is formed. Based on the distribution characteristics of the symmetric point distribution image in polar coordinate space, a polar coordinate attention mechanism is constructed in a deep residual neural network. By statistically analyzing the distribution of features in the radial and angular dimensions respectively, radial weights and angular weights for modulating feature responses are generated. The features are jointly modulated using the radial and angular weights, and the modulated features are embedded into the residual structure to complete the feature update. Based on the residual characteristics modulated by polar coordinate attention, fault classification and diagnosis of rolling bearing operating conditions are realized.

2. The bearing fault diagnosis method according to claim 1, characterized in that, The vibration signal is segmented according to a preset data length, so that each segment of the vibration signal is used as an independent sample for subsequent image construction and diagnosis.

3. The bearing fault diagnosis method according to claim 1, characterized in that, The normalization process linearly maps the amplitude of each vibration signal segment to a preset numerical range, thereby eliminating the influence of differences in vibration amplitude under different sampling conditions.

4. A method for constructing a symmetrical point distribution image for bearing fault diagnosis, characterized in that, include: Each sampling point of the standardized vibration signal is mapped to a polar radius component in polar coordinate space, and the polar radius is determined by the relative position of the sampling point amplitude in the current signal segment. Based on the preset number of symmetry planes, at least one set of angular positions symmetrical about the symmetry planes is generated for each sampling point in polar coordinate space, so that the sampling points are distributed in pairs in the clockwise and counterclockwise directions; By setting the time interval parameter to control the sampling point interval relationship involved in generating symmetrical points, and by controlling the expansion range of symmetrical points in the angular direction through the angle magnification parameter, a symmetrical point distribution image reflecting the temporal evolution characteristics of vibration signals is formed.

5. The method according to claim 4, characterized in that, The time interval parameter is used to control the time correspondence between adjacent sampling points when generating symmetrical points, so as to enhance the ability to express the dynamic characteristics of vibration signals.

6. The method according to claim 4, characterized in that, The angle magnification parameter is used to adjust the dispersion of the angular distribution of symmetrical points in polar coordinate space, so as to improve the separability of different fault modes in image space.

7. A bearing fault diagnosis system based on polar coordinate attention mechanism, characterized in that, include: The signal acquisition module is used to acquire the vibration acceleration signal of the rolling bearing at the drive end; The image construction module is used to segment and normalize the acquired vibration signals, and generate bearing fault images based on the polar coordinate symmetric point distribution rules. The feature extraction module includes a deep residual network that incorporates a polar coordinate attention mechanism for feature learning of the symmetric point distribution image. The polar coordinate attention mechanism is used to generate radial weights and angular weights respectively based on the distribution of features on the radial and angular indices, and to jointly modulate the features; The fault diagnosis module is used to output bearing fault diagnosis results based on the residual features after polar coordinate attention modulation.

8. The bearing fault diagnosis system according to claim 7, characterized in that, The feature extraction module establishes a correspondence between features and polar coordinate space by determining the corresponding radial and angular indices for each spatial location in the input features.

9. The bearing fault diagnosis system according to claim 7, characterized in that, The polar coordinate attention mechanism forms a radial feature sequence by statistically analyzing the features within the region corresponding to the radial index, and forms an angular feature sequence by statistically analyzing the features within the region corresponding to the angular index.

10. The bearing fault diagnosis system according to claim 7, characterized in that, The radial weights and angular weights are generated by mapping the radial feature sequences and angular feature sequences, respectively, and the weight range is constrained by a nonlinear activation method to achieve adaptive modulation of the residual features.

Images