A method and system for dimensionality enhancement of bearing data based on radial basis function interpolation

Abstract

This invention provides a method and system for dimensionality enhancement of bearing data based on radial basis function interpolation, belonging to the field of data dimensionality enhancement. To address the challenge of effectively enhancing dimensionality-reduced data in small-sample bearing defect detection, restoring the high-dimensional feature structure of the data, preserving the relationships between features, providing richer feature information for model training, and improving the model's detection performance and generalization ability, this invention proposes a dimensionality enhancement module based on radial basis functions to ensure complete restoration of the dimensionality-reduced data. This module achieves accurate feature restoration and diversity recovery, generating more realistic data and reducing artifacts. The invention employs radial basis function interpolation technology to enhance the dimensionality of the reduced data, restoring the high-dimensional feature structure of the data, preserving the relationships between features, providing richer feature information for model training, and improving the model's detection performance and generalization ability.

Description

Technical Field

[0001] This invention relates to the field of data dimensionality enhancement technology, and more specifically, to a method and system for enhancing bearing data dimensionality based on radial basis function interpolation. Background Technology

[0002] In the field of bearing defect detection, especially with small sample sizes, the acquired bearing data is often high-dimensional and the number of samples is limited. To reduce data dimensionality and computational costs, dimensionality reduction is typically performed. However, dimensionality reduction inevitably results in the loss of some feature information, disrupting the high-dimensional feature structure of the data and weakening the relationships between features. This makes it difficult for the model to fully learn the complex features of the data during subsequent model training, affecting the model's detection performance and generalization ability. Traditional dimensionality enhancement methods, such as linear interpolation, have limitations in handling nonlinear feature relationships and cannot effectively recover the high-dimensional feature structure of the data. Summary of the Invention

[0003] The technical problem to be solved by this invention is:

[0004] To address the challenge of effectively upscaling reduced-dimensional data in small-sample bearing defect detection, restoring the high-dimensional feature structure of the data, preserving the relationships between features, providing richer feature information for model training, and improving the model's detection performance and generalization ability.

[0005] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0006] This invention provides a method for dimensionality enhancement of bearing data based on radial basis function interpolation, comprising the following steps:

[0007] S100. Obtain the dimensionality-reduced bearing dataset, which contains multiple low-dimensional data points, each data point representing a low-dimensional feature vector of a bearing sample.

[0008] S200. Calculate the Euclidean distance: calculate the Euclidean distance from each point to be interpolated to each known low-dimensional data point, and obtain a distance matrix.

[0009] S300. Process the radial basis function. The distance matrix obtained in step S200 is fed into the radial basis function for processing to obtain a weight matrix.

[0010] S400. Normalize the weight matrix obtained in step S300 so that the sum of each row is 1, and obtain the normalized weight matrix.

[0011] S500, Dimensional Upgrading Data Calculation: Multiply the normalized weight matrix with the original high-dimensional data to obtain the upgraded high-dimensional dataset.

[0012] Furthermore, in step S100, the bearing dataset is processed using manifold approximation and projection dimensionality reduction methods.

[0013] Furthermore, the manifold approximation and projection dimensionality reduction methods include the following processes:

[0014] S110. The encoder maps the input high-dimensional data to the latent space to obtain the latent representation. The high-dimensional data h generated by the encoder is then processed. i The data points are preprocessed in a D-dimensional space. The distances between these data points are calculated, and the connection count of each data point is adjusted based on a preset number of nearest neighbors to determine its nearest neighbor. A high-dimensional adjacency graph is constructed based on similarity calculations, where edges represent the similarity between data points. The similarity s... ij The calculation is as follows:

[0015]

[0016] In the formula, d(h) i ,h j ) is a high-dimensional data point h i and h j The distance between them, ρ i It is point h i The distance to the nearest neighbor, σ i It is a smoothing parameter that adjusts the similarity weights;

[0017] S120. High-dimensional data is mapped to an initial low-dimensional space through spectral embedding; first, the similarity ws between high-dimensional data points is calculated. ij Then, construct the similarity matrix W, calculate the degree matrix D, and combine it with the identity matrix I to construct the Laplacian matrix La:

[0018]

[0019] Performing eigenvalue decomposition on the Laplacian matrix La yields the eigenvector v. k and its corresponding eigenvalue λ k Select the eigenvectors corresponding to the first d smallest non-zero eigenvalues ​​to form matrix V. d In low-dimensional space, the initial data point l i The representation is through V d The i-th row of the matrix is ​​represented as:

[0020] Lav k =λ k v k V d =[v1,v2...,v d ],l i =V d[i,:] (3)

[0021] S130. In low-dimensional space, a low-dimensional adjacency graph is constructed by calculating the similarity between data points; low-dimensional data points l i With l j The similarity between them is represented as:

[0022] u ij =(1+a·d(l) i ,l j ) 2b ) -1 (4)

[0023] In the formula, a and b are positive hyperparameters, and d(l i ,l j ) is the midpoint of the low-dimensional space l i and l j The distance between them;

[0024] S140. Optimization is achieved by minimizing the cross-entropy between high-dimensional and low-dimensional similarities. The objective function L is:

[0025]

[0026] S150. During the optimization process, stochastic gradient descent is used to minimize the loss function, thereby adjusting the low-dimensional embedding to obtain the optimal low-dimensional dataset. Where d is the dimension after dimensionality reduction of the data, in order to better reflect the structural characteristics of high-dimensional data.

[0027] Further, in step S200, the calculation of each point l to be interpolated is performed. ni To each known low-dimensional data point l j The Euclidean distance yields an m×n distance matrix D = [d ij ], where d ij =||l ni -l j ||.

[0028] Further, in step S300, the obtained weight matrix is ​​an m×n weight matrix R = [r ij ],in θ is the set shape parameter.

[0029] Further, in step S400, the obtained normalized weight matrix is ​​R. n =[r nij ],in

[0030] Furthermore, in step S500, an m×D matrix H is obtained after the upscaling data is calculated. n=[h ni ]in

[0031]

[0032] A bearing data dimensionality enhancement system based on radial basis function interpolation is provided. The system has program modules corresponding to the above steps and executes the steps in the bearing data dimensionality enhancement method based on radial basis function interpolation during runtime.

[0033] A computer-readable storage medium storing a computer program configured to, when invoked by a processor, implement steps of a bearing data dimensionality-upgrading method based on radial basis function interpolation.

[0034] Compared with the prior art, the beneficial effects of the present invention are:

[0035] This invention discloses a method and system for dimensionality enhancement of bearing data based on radial basis function interpolation, which has the following beneficial effects:

[0036] Restoring high-dimensional feature structure: Radial basis function interpolation can effectively restore the high-dimensional feature structure of the dimensionality-reduced data, preserve the relationship between features, and make the data closer to the original high-dimensional data distribution;

[0037] Provides rich feature information: The upgraded dataset contains more feature information, which can provide more comprehensive and accurate feature representation for model training, thereby improving the model's learning effect and detection performance;

[0038] Improving model generalization ability: The recovered high-dimensional feature structure helps the model better understand and learn the complex feature relationships of the data, thereby improving the model's generalization ability and adaptability in practical applications;

[0039] High adaptability: This method is applicable to various types of bearing data, has strong adaptability and wide applicability, and can meet the data dimensionality upgrade needs in different scenarios; Attached Figure Description

[0040] Figure 1 This is a flowchart of a bearing data dimensionality enhancement method based on radial basis function interpolation in an embodiment of the present invention;

[0041] Figure 2 This is an example of bearing defect data in an embodiment of the present invention;

[0042] Figure 3 This is a comparison chart of dimensionality reduction methods in the embodiments of the present invention;

[0043] Figure 4 This is a box plot of the FID index results for the dimensionality reduction effect in this embodiment of the invention;

[0044] Figure 5 This is a box plot of the IS index results for the dimensionality reduction effect in this embodiment of the invention;

[0045] Figure 6 This is a comparison chart of the dimension-scaling functions in an embodiment of the present invention;

[0046] Figure 7 This is a comparison chart of the test results of the dimension-scaling function in an embodiment of the present invention. Detailed Implementation

[0047] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0048] Specific Implementation Plan 1: Combining Figure 1 As shown, this invention provides a method for dimensionality enhancement of bearing data based on radial basis function interpolation, comprising the following steps:

[0049] S100. Obtain the dimensionality-reduced bearing dataset, which contains multiple low-dimensional data points, each representing a low-dimensional feature vector of a bearing sample. The dataset can be processed by the Unified Manifold Approximation and Projection (UMAP) dimensionality reduction method, resulting in lower dimensionality and more concentrated feature information.

[0050] In other words, the high-dimensional data generated by the encoder is effectively reduced in dimensionality by the data dimensionality reduction module, while preserving the similarity of high-dimensional features and transforming it into a low-dimensional space; UMAP constructs a high-dimensional adjacency graph by calculating the similarity between data points and maps the data to the low-dimensional space through spectral embedding; for example, the high-dimensional data generated by the encoder is placed in a D-dimensional space for preprocessing, and the number of connections of each data point is adjusted by calculating the distance between data points and based on the preset number of nearest neighbors to determine its nearest neighbor data point;

[0051] This process significantly reduces data dimensionality, minimizes interference from redundant background information, and enhances feature discriminative power, thereby improving the model's learning efficiency. Dimensionality reduction also provides an efficient foundation for subsequent data augmentation steps, making the augmentation process more accurate and efficient. Specifically, this includes...

[0052] S110, Transfer the high-dimensional data h generated by the encoder... i The data points are preprocessed in a D-dimensional space. The distances between these data points are calculated, and the connection count of each data point is adjusted based on a preset number of nearest neighbors to determine its nearest neighbor. A high-dimensional adjacency graph is constructed based on similarity calculations, where edges represent the similarity between data points. The similarity s... ij The calculation is as follows:

[0053]

[0054] In the formula, d(h) i ,h j ) is a high-dimensional data point h i and h j The distance between them, ρ i It is point h i The distance to the nearest neighbor, σ i It is a smoothing parameter that adjusts the similarity weights;

[0055] S120. High-dimensional data is mapped to an initial low-dimensional space through spectral embedding; first, the similarity ws between high-dimensional data points is calculated. ij Then, construct the similarity matrix W, calculate the degree matrix D, and combine it with the identity matrix I to construct the Laplacian matrix La:

[0056]

[0057] Performing eigenvalue decomposition on the Laplacian matrix La yields the eigenvector v. k and its corresponding eigenvalue λ k Select the eigenvectors corresponding to the first d smallest non-zero eigenvalues ​​to form matrix V. d In low-dimensional space, the initial data point l i The representation is through V d The i-th row of the matrix is ​​represented as:

[0058] Lav k =λ k v k V d =[v1,v2...,v d ],l i =V d [i,:] (3)

[0059] S130. In low-dimensional space, a low-dimensional adjacency graph is constructed by calculating the similarity between data points; low-dimensional data points l i With l j The similarity between them can be represented as:

[0060] u ij =(1+a·d(l) i ,l j ) 2b ) -1 (4)

[0061] In the formula, a and b are positive hyperparameters, and d(l i ,l j ) is the midpoint of the low-dimensional space l i and l j The distance between them;

[0062] S140. To preserve the structural features of the high-dimensional adjacency graph as much as possible, optimization is ultimately achieved by minimizing the cross-entropy between the high-dimensional and low-dimensional similarities. The objective function L is:

[0063]

[0064] S150. During the optimization process, stochastic gradient descent (SGD) is used to minimize the loss function, thereby adjusting the low-dimensional embedding to obtain the optimal low-dimensional dataset. Where d is the dimension after dimensionality reduction of the data, in order to better reflect the structural characteristics of high-dimensional data;

[0065] S200. Calculate the Euclidean distance for each point l to be interpolated. ni To each known low-dimensional data point l j The Euclidean distance yields an m×n distance matrix D = [d ij ], where d ij =||l ni -l j Euclidean distance is a common method for measuring the difference between two data points. By calculating the distance matrix, we can understand the similarity and spatial relationship between the data points to be upgraded and the known data points, providing a basis for subsequent radial basis function interpolation.

[0066] S300. Process the radial basis function: Input the distance matrix obtained in step S200 into the radial basis function (RBF) for processing, to obtain an m×n weight matrix R = [r ij ],in θ is a set shape parameter, which is set to 2 in this invention;

[0067] Radial basis functions are radially symmetric functions centered at the origin, possessing excellent interpolation performance and nonlinear mapping capabilities. In this invention, radial basis functions are used to process the distance matrix, transforming distance information into weight information. The magnitude of the weights reflects the similarity and spatial proximity between the data points to be upgraded and the known data points.

[0068] S400. Normalize the weight matrix obtained in step S300 so that the sum of each row is 1, thus obtaining the normalized weight matrix R. n =[r nij ],in

[0069] Normalization can ensure the rationality and consistency of weights, making the weight distribution of each data point to be upgraded more balanced, and avoiding deviations in interpolation results due to excessively large or small weights.

[0070] S500, Dimensionality Upgrading Calculation: Multiply the normalized weight matrix by the original high-dimensional data to obtain the upgraded high-dimensional dataset, represented as an m×D matrix H. n =[h ni ]in Recover the high-dimensional feature structure of the data;

[0071] In this way, dimensional data points can be mapped back to a higher-dimensional space while preserving the relationships between features, providing richer feature information for model training. The upgraded dataset can better reflect the original feature distribution and structural characteristics of the data, which helps improve the detection performance and generalization ability of the model.

[0072] Specific Implementation Scheme 2: The present invention provides a bearing data dimensionality enhancement system based on radial basis function interpolation. This system has a program module corresponding to the above steps, and executes the steps in the bearing data dimensionality enhancement method based on radial basis function interpolation described above when running.

[0073] The other combinations and connections in this implementation scheme are the same as in Specific Implementation Scheme 1.

[0074] Specific Implementation Scheme 3: The present invention provides a computer-readable storage medium storing a computer program configured to implement, when called by a processor, the steps of a bearing data dimensionality-upgrading method based on radial basis function interpolation.

[0075] The other combinations and connections in this implementation scheme are the same as in Specific Implementation Scheme 1.

[0076] Simulation Experiment

[0077] Experimental dataset:

[0078] This study used a dataset of bearings produced by Harbin Bearing Group. The data was collected from the bearing production line, and to ensure data quality, the experiment was conducted in a custom-designed experimental shed to control the light source and reduce external interference. Figure 2 An example dataset is shown, containing the following types: Outer Surface Normal (ON), Outer Surface Rust (OR), Outer Surface Scratch (OS), Side Surface Normal (SN), and Side Surface Scratch (SS). Forty representative samples were selected from each type for experiments.

[0079] Experimental setup:

[0080] The experiment was conducted on Ubuntu 20.04, based on the PyTorch open-source deep learning framework, using Torch 1.8.0 and Torchvision 0.8.0. The experimental setup included an NVIDIA GeForce RTX 1080 GPU with 20GB of RAM. In the experiment, the number of data augmentations (m) was 40, the high-dimensional dimension (D) was set to 100, the low-dimensional dimension (d) was set to 50, and the total number of Gaussian components (K) used was 10.

[0081] Dimensionality Reduction Module Comparison Experiment

[0082] The comparative experiment of dimensionality reduction modules aims to evaluate the impact of different dimensionality reduction methods on the quality of the generated data. Four methods were tested: direct dimensionality reduction, PCA dimensionality reduction, t-SNE dimensionality reduction, and the dimensionality reduction method presented in this paper, while keeping other modules unchanged. Figure 3 The paper presents some data generated by different dimensionality reduction methods. It is clear that the data generated by the dimensionality reduction method in this paper has clearer details, fewer artifacts, and higher overall quality.

[0083] The evaluation results of the FID and IS indices in the dimensionality reduction process were obtained through Figure 4 and Figure 5 The box plot is shown below. Different colored scatter points represent the results of different dimensionality reduction methods. Each box contains 50% of the data points, and the median and mean of each group are also indicated in the plot. The dimensionality reduction method of this invention performs best in terms of median, mean, and overall FID and IS, indicating that the generated data after dimensionality reduction using this invention has higher quality and diversity. Furthermore, the smaller box height of the algorithm in the plot indicates better stability and concentration of the generated data.

[0084] Comparison Experiment of Upgrading Modules

[0085] The dimensionality upgrade module comparison tested the effectiveness of different functions in the data dimensionality upgrade module while ensuring the consistency of the expanded data after each dimensionality reduction method. Eight functions were tested, namely multivariate quadratic, inverse multivariate quadratic, linear, quintic, Gaussian, thin plate spline, inverse quadratic, and cubic functions, and the generated results were evaluated.

[0086] like Figure 6The paper demonstrates that after the dimensionality reduction module of this invention, representative data were generated using different dimensionality-upgrading functions. It can be seen that inverse multivariate quadratic functions and multivariate quadratic functions perform excellently in terms of data quality after dimensionality upgrading. They not only effectively restore and decode data with multiple features sampled by the data augmentation module, but also generate defective combinations not present in the original data. Furthermore, these combinations of defective features appear very natural, without the chaotic situation seen in the thin-plate spline interpolation data shown in the figure, nor the artifacts caused by the abrupt feature fusion resulting from Gaussian function dimensionality upgrading shown in the figure. These results indicate that the use of multivariate quadratic functions is highly effective on this small sample dataset.

[0087] like Figure 7 The results of the FID index for different functions of the dimensionality reduction module are shown in the figure. It can be clearly seen from the figure that multivariate quadratic, inverse multivariate quadratic, linear and quintic functions all have good results. In particular, the data generated by dimensionality reduction using multivariate quadratic functions is not only of high quality, but can also adapt to a variety of different dimensionality reduction methods.

[0088] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for dimensionality enhancement of bearing data based on radial basis function interpolation, characterized in that, Includes the following steps: S100. Obtain the dimensionality-reduced bearing dataset, which contains multiple low-dimensional data points, each data point representing a low-dimensional feature vector of a bearing sample. S200. Calculate the Euclidean distance. Calculate the Euclidean distance from each point to be interpolated to each known low-dimensional data point to obtain a distance matrix. S300. Process the radial basis function. Input the distance matrix obtained in step S200 into the radial basis function for processing to obtain a weight matrix. S400. Normalize the weight matrix obtained in step S300 so that the sum of each row is 1, and obtain the normalized weight matrix. S500, Dimensional Upgrading Data Calculation: Multiply the normalized weight matrix with the original high-dimensional data to obtain the upgraded high-dimensional dataset.

2. The bearing data dimensionality enhancement method based on radial basis function interpolation according to claim 1, characterized in that: In step S100, the bearing dataset is processed using manifold approximation and projection dimensionality reduction methods.

3. The bearing data dimensionality enhancement method based on radial basis function interpolation according to claim 2, characterized in that: The processing steps of manifold approximation and projection dimensionality reduction methods include, S110. The encoder maps the input high-dimensional data to the latent space to obtain the latent representation. The high-dimensional data h generated by the encoder is then processed. i The data points are preprocessed in a D-dimensional space. The distances between these data points are calculated, and the connection count of each data point is adjusted based on a preset number of nearest neighbors to determine its nearest neighbor. A high-dimensional adjacency graph is constructed based on similarity calculations, where edges represent the similarity between data points. The similarity s... ij The calculation is as follows: In the formula, d(h) i ,h j ) is a high-dimensional data point h i and h j The distance between them, ρ i It is point h i The distance to the nearest neighbor, σ i It is a smoothing parameter that adjusts the similarity weights; S120. High-dimensional data is mapped to an initial low-dimensional space through spectral embedding; first, the similarity ws between high-dimensional data points is calculated. ij Then, construct the similarity matrix W, calculate the degree matrix D, and combine it with the identity matrix I to construct the Laplacian matrix La: Performing eigenvalue decomposition on the Laplacian matrix La yields the eigenvector v. k and its corresponding eigenvalue λ k Select the eigenvectors corresponding to the first d smallest non-zero eigenvalues ​​to form matrix V. d In low-dimensional space, the initial data point l i The representation is through V d The i-th row of the matrix is ​​represented as: Lav k =λ k v k ,V d =[v1,v2...,v d ],l i =V d [i,:] (3) S130. In low-dimensional space, a low-dimensional adjacency graph is constructed by calculating the similarity between data points; low-dimensional data points l i With l j The similarity between them is represented as: u ij =(1+a·d(l i ,l j ) 2b ) -1 (4) In the formula, a and b are positive hyperparameters, and d(l i ,l j ) is the midpoint of the low-dimensional space l i and l j The distance between them; S140. Optimization is achieved by minimizing the cross-entropy between high-dimensional and low-dimensional similarities. The objective function L is: S150. During the optimization process, stochastic gradient descent is used to minimize the loss function, thereby adjusting the low-dimensional embedding to obtain the optimal low-dimensional dataset. Where d is the dimension after dimensionality reduction of the data, in order to better reflect the structural characteristics of high-dimensional data.

4. The bearing data dimensionality enhancement method based on radial basis function interpolation according to claim 3, characterized in that: In step S200, the point l to be interpolated is calculated. ni To each known low-dimensional data point l j The Euclidean distance yields an m×n distance matrix D = [d ij ], where d ij =||l ni -l j ||.

5. The bearing data dimensionality enhancement method based on radial basis function interpolation according to claim 4, characterized in that: In step S300, the obtained weight matrix is ​​an m×n weight matrix R = [r ij ],in θ is the set shape parameter.

6. The bearing data dimensionality enhancement method based on radial basis function interpolation according to claim 5, characterized in that: In step S400, the normalized weight matrix obtained is R. n =[r nij ],in 7. The bearing data dimensionality enhancement method based on radial basis function interpolation according to claim 6, characterized in that: In step S500, an m×D matrix H is obtained after the upscaling data is calculated. n =[h ni ]in 8. A bearing data dimensionality enhancement system based on radial basis function interpolation, characterized in that: The system has a program module corresponding to the steps of any one of claims 1-7 above, and executes the steps in the bearing data dimensionality upgrade method based on radial basis function interpolation described above when running.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program configured to, when invoked by a processor, implement the steps of the bearing data dimensionality-upgrading method based on radial basis function interpolation as described in any one of claims 1-7.

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