Bearing data expansion method and system based on Gaussian mixture model and particle swarm optimization

Abstract

The invention provides a bearing data expansion method and system based on a Gaussian mixture model and particle swarm optimization, and belongs to the field of data expansion. The objective of the invention is to solve the problem of how to effectively expand a data set, increase data diversity, relieve data scarcity and improve generalization ability and detection performance of a model in existing small sample bearing defect detection. According to the method, a Gaussian mixture model (GMM) is adopted for modeling original data, parameters of the GMM are optimized through a particle swarm optimization (PSO) algorithm, new data points are generated, and a data set is expanded. The method can effectively increase the data diversity, alleviate the problem of data scarcity, and improve the generalization ability and detection performance of the model.

Description

Technical Field

[0001] The present invention relates to the technical field of data augmentation, and more particularly, to a bearing data augmentation method and system based on Gaussian mixture model and particle swarm optimization. Background Art

[0002] In the field of bearing defect detection, especially in the case of small samples, the number of obtained bearing data samples is limited and the data distribution is uneven, which brings great challenges to the training and optimization of models. Traditional data augmentation methods such as data enhancement and interpolation can increase the amount of data to a certain extent, but it is difficult to effectively solve the problems of uneven data distribution and insufficient feature diversity. As a probability model, the Gaussian mixture model (GMM) can model and sample data to generate new data points, but its parameter optimization has certain difficulties. When dealing with high-dimensional data, especially when the sample size is small, the covariance matrix estimation of GMM becomes complex. At the same time, the variational autoencoder (VAE) is prone to blur and distortion in high-resolution data generation, affecting the quality of generated defects. Summary of the Invention

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

[0004] To solve the problem of how to effectively augment the dataset, increase data diversity, alleviate data scarcity, improve the generalization ability and detection performance of the model in the existing small-sample bearing defect detection.

[0005] The technical solution adopted by the present invention to solve the above technical problems:

[0006] The present invention provides a bearing data augmentation method based on Gaussian mixture model and particle swarm optimization, including the following steps:

[0007] S100. Obtain the original bearing dataset, which contains multiple sample data points, and each sample data point represents the feature vector of a bearing sample, and the feature vector contains the defect feature information of the bearing;

[0008] S200. Initialize the parameters of the Gaussian mixture model, and the parameters include the mean, covariance matrix and mixing weights;

[0009] S300. Use the particle swarm optimization algorithm to optimize the GMM parameters initialized in step S200 to obtain the optimal GMM parameters;

[0010] S400. Select a Gaussian distribution according to the mixing weights and randomly sample from this distribution to generate new data points to obtain the augmented bearing data.

[0011] Further, in step S100, the original bearing data is preprocessed, including data standardization and noise removal.

[0012] Further, in step S200, specifically,

[0013] During the training process of the Gaussian mixture model, first set the starting points of the model parameters, including the mean μ j , the mixing weight φ j and the covariance matrix Cov j , and add a small regularization term while initializing the covariance matrix;

[0014] Then, enter the expectation step to calculate the probability that the data point belongs to each component, that is, the responsibility degree w ij This process is expressed as:

[0015]

[0016] In the formula, the responsibility degree of the data point l i belonging to the j-th component is w ij , and the probability density function of the multivariate Gaussian distribution under the mean μ j and the covariance matrix Cov j is N(l i ∣μ j ,Cov j ), and the initial mixing weight is K is the total number of Gaussian components.

[0017] Further, in step S300, the objective function of the particle swarm optimization is the likelihood function of the GMM, that is, to maximize the probability density of the data under the GMM, so as to optimize the parameters of the GMM; specifically,

[0018] Optimize the mean μ generated by the expectation step, and use the particle swarm optimization algorithm to search for the optimal mean in the parameter space. The optimization function is shown in the following formula (2):

[0019]

[0020] Through the maximization step, update the model parameters to maximize the likelihood of the data. The update formula is as follows:

[0021]

[0022] By iteratively executing the expectation step, PSO, and maximization step until the iteration termination condition is met, the model is fitted.

[0023] Further, in step S400, select the Gaussian distribution according to the mixing weight, and randomly sample from this distribution to generate new data points as:

[0024] l n ~N(μ j ,Σ j )(5)

[0025] Use the known n d-dimensional original data sets to estimate the parameters of the GMM for generating m interpolated d-dimensional low-dimensional data sets

[0026] A bearing data augmentation system based on Gaussian mixture model and particle swarm optimization, the system has program modules corresponding to the above steps, and executes the steps in the above bearing data augmentation method based on Gaussian mixture model and particle swarm optimization when running.

[0027] A computer-readable storage medium, the computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of the bearing data augmentation method based on Gaussian mixture model and particle swarm optimization when called by a processor.

[0028] Compared with the prior art, the beneficial effects of the present invention are:

[0029] The bearing data augmentation method and system based on Gaussian mixture model and particle swarm optimization of the present invention have the following beneficial effects:

[0030] Effectively augment the data set: By modeling and sampling the original data with the Gaussian mixture model, new data points can be generated, effectively augmenting the data set, increasing the amount of data, and alleviating the problem of data scarcity;

[0031] Improve data diversity: The generated data points can cover a wider range of data distribution, increase the diversity of data, enable the model to learn richer feature information, and improve the generalization ability of the model;

[0032] Optimize the model performance: The augmented data set can provide more training samples, enabling the model to better learn and fit the data during training, and improving the detection performance and accuracy of the model;

[0033] Strong adaptability: This method is applicable to various types of bearing defect data, has strong adaptability and a wide range of applications, and can meet the data augmentation requirements in different scenarios. Brief Description of the Drawings

[0034] Figure 1 is a flowchart of a bearing data augmentation method based on Gaussian mixture model and particle swarm optimization in an embodiment of the present invention;

[0035] Figure 2 is a legend of bearing defect data in an embodiment of the present invention;

[0036] Figure 3 This is the comparison graph of the generation algorithm in the embodiments of the present invention. Specific embodiments

[0037] To make the above objects, features, and advantages of the present invention more obvious and understandable, the following detailed description of the specific embodiments of the present invention will be given in conjunction with the accompanying drawings.

[0038] Specific implementation plan one: Combine Figure 1 As shown, the present invention provides a bearing data augmentation method based on a Gaussian mixture model and particle swarm optimization, including the following steps:

[0039] S100. Obtain the original bearing data set. The original bearing data set contains multiple sample data points. Each sample data point in the data set represents the feature vector of a bearing sample and contains the defect feature information of the bearing. The data set can be preprocessed, including data standardization, noise removal, or other existing preprocessing means, to improve the quality of the data and the training effect of the model.

[0040] S200. Initialize the parameters of the Gaussian mixture model (GMM), including the mean, covariance matrix, and mixing weights. The mean represents the central position of each Gaussian distribution, the covariance matrix represents the shape and direction of each Gaussian distribution, and the mixing weights represent the proportion of each Gaussian distribution in the overall data. The initialization parameters can be generated randomly or set based on experience to provide initial values for subsequent parameter optimization. Specifically,

[0041] During the training process of the Gaussian mixture model (GMM), first set the starting points of the model parameters, including the mean μ j , the mixing weight φ j , and the covariance matrix Cov j , and add a small regularization term while initializing the covariance matrix.

[0042] Then, enter the expectation step, that is, calculate the probability that the data point belongs to each component, that is, the responsibility degree w ij This process can be expressed as:

[0043]

[0044] In the formula, the responsibility degree of the data point l i belonging to the jth component is w ij , and the probability density function of the multivariate Gaussian distribution under the mean μ j and the covariance matrix Cov j is N(l i ∣μ j , Cov j ), and the initial mixing weight is K is the total number of Gaussian components;

[0045] S300. Optimize the GMM parameters after the initialization in step S200 using the particle swarm optimization algorithm. Use the particle swarm optimization (PSO) algorithm to optimize the parameters of the GMM to obtain the optimal GMM parameters;

[0046] The particle swarm optimization algorithm simulates the foraging behavior of a bird flock. Each particle is regarded as a potential solution. The particles fly in the solution space and search for the optimal solution by iteratively updating the positions and velocities of the particles;

[0047] In the present invention, the objective function of the particle swarm optimization is the likelihood function of the GMM, that is, to maximize the probability density of the data under the GMM, thereby optimizing the parameters of the GMM; specifically,

[0048] Optimize the mean μ generated in the expectation step. Use the particle swarm optimization (PSO) algorithm to search for the optimal mean in the parameter space. This way can avoid the problem of local means; the optimization function is shown in the following formula (2):

[0049]

[0050] Through the maximization step, update the model parameters to maximize the likelihood of the data. The update formula is as follows:

[0051]

[0052] By iteratively executing the expectation step, PSO, and maximization step until the iteration termination condition is satisfied, the model can be fitted;

[0053] S400. Select a Gaussian distribution according to the mixing weights and randomly sample from this distribution to generate new data points, which can be expressed as:

[0054] l n ~N(μ j ,Σ j )(5)

[0055] Through the above steps, first use the known n d-dimensional original data sets to estimate the parameters of the GMM. These parameters are then used to generate m interpolated d-dimensional low-dimensional data sets

[0056] Specific implementation method two: A bearing data augmentation system based on a Gaussian mixture model and particle swarm optimization according to the present invention. This system has program modules corresponding to the above steps and executes the steps in the above bearing data augmentation method based on a Gaussian mixture model and particle swarm optimization when running.

[0057] Other combinations and connection relationships in this implementation scheme are the same as those in the first specific implementation scheme.

[0058] Specific implementation scheme three: A computer-readable storage medium of the present invention, the computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of the bearing data augmentation method based on the Gaussian mixture model and particle swarm optimization when called by a processor.

[0059] Other combinations and connection relationships in this implementation scheme are the same as those in the first specific implementation scheme.

[0060] Example 1

[0061] Suppose there is a bearing defect data set containing 100 samples, and each sample contains 10 features. The data set has been preprocessed, and the feature values have been normalized to between 0 and 1. First, load the preprocessed bearing defect data set from the data storage system to ensure that the data format is correct, and each sample is a 10-dimensional feature vector. Next, initialize the parameters of the Gaussian mixture model (GMM), select 3 Gaussian distributions for modeling, randomly generate 3 10-dimensional vectors as the initial means, set the covariance matrix as the identity matrix, indicating that the variances of each feature are 1 initially and there is no correlation between features, and the mixing weights are set to [0.3, 0.3, 0.4], indicating the initial proportions of the 3 Gaussian distributions in the data.

[0062] Then, use the particle swarm optimization (PSO) algorithm to optimize the parameters of the GMM. Set the particle swarm size to 50 particles, the number of iterations to 100 times, the inertia weight to 0.9 to control the continuity of the particle velocity, and the learning factor to 2 to affect the learning degree of the particles towards the individual optimal and global optimal positions. Initialize the particle swarm, each particle represents a set of GMM parameters, calculate the fitness value of each particle, that is, the GMM likelihood function value of the data under this set of parameters. Update the individual optimal position and global optimal position of each particle, adjust the velocity and position of the particles according to the update formula, and repeat this process until 100 iterations are reached to obtain the optimal GMM parameters, including the mean, covariance matrix, and mixing weights, which can better describe the distribution characteristics of the data.

[0063] According to the optimized GMM parameters, sample from 3 Gaussian distributions according to the mixing weights to generate 200 new 10-dimensional feature vectors. Combine the generated 200 new data points with the original 100 data points to form an expanded data set, with a total of 300 samples. Finally, use the expanded data set for model training, and select the support vector machine (SVM) as the defect detection model. Use the expanded data set to train the SVM model, and adopt the cross-validation method to evaluate the model performance. The expanded data set increases the accuracy of the model from the original 85% to 90%, showing good generalization ability and detection performance.

[0064] Example 2

[0065] Suppose there is a bearing defect data set containing 50 samples, each sample contains 20 features, and the feature values are standardized to between -1 and 1. Similarly, load the preprocessed data set, initialize the GMM parameters, select 5 Gaussian distributions for modeling, randomly generate 5 20-dimensional vectors as the initial means, the covariance matrix is the identity matrix, and the mixing weights are set to [0.2, 0.2, 0.2, 0.2, 0.2]. Use the PSO algorithm to optimize the GMM parameters, the particle swarm size is 100 particles, the number of iterations is 200 times, the inertia weight is 0.8, and the learning factor is 1.5. After optimization, the optimal GMM parameters are obtained.

[0066] According to the optimized parameters, sample 150 new 20-dimensional feature vectors from 5 Gaussian distributions according to the mixing weights, combine them with the original 50 data points to form an expanded data set, with a total of 200 samples. Select the Random Forest as the defect detection model, use the expanded data set for training, and adopt cross-validation to evaluate the model performance. The expanded data set increases the accuracy of the model from the original 80% to 88%, further proving that the method of the present invention can effectively expand the data set on data sets of different scales and feature dimensions, and improve the training effect and detection performance of the model.

[0067] Simulation experiment

[0068] Experimental data set:

[0069] This study uses the bearing data set produced by Harbin Bearing Group. The data is collected from the bearing production line. To ensure the data quality, the experiment is carried out in a customized experimental shed to control the light source and reduce external interference. Figure 2Shows an example of the dataset, which contains the following types: Outer Surface Normal (ON), Outer Surface Rust (OR), Outer Surface Scratch (OS), Side Surface Normal (SN), and Side Surface Scratch (SS). 40 representative samples were selected from each type for the experiment.

[0070] Experimental setup:

[0071] The experiment was conducted on the Ubuntu 20.04 operating system, based on the PyTorch open-source deep learning framework, using versions Torch1.8.0 and Torchvision 0.8.0. The computational resources configured for the experiment were an NVIDIA GeForce RTX1080 GPU with 20 GB of memory. In the experiment, the data augmentation quantity m was 40, the high dimension D was set to 100, the low dimension d was set to 50, and the total number of Gaussian components K used was 10.

[0072] To evaluate the data generated by different datasets and dimensionality reduction methods, this study used six evaluation metrics. Eight sets of experiments were conducted for each dataset and dimensionality reduction method, and the amount of generated data was kept consistent with the original training dataset for direct comparison.

[0073] Fréchet Inception Distance (FID) (Heusel et al., 2017): Calculates the difference between two datasets through the InceptionV3 model to evaluate the similarity between the generated data and the real data. The lower the FID value, the more similar the data distributions are.

[0074] Kernel Inception Distance (KID) (Binkowski et al., 2018): KID is a metric for evaluating the quality of generated data suitable for small-sample datasets, which is more stable than FID, especially when dealing with smaller-scale datasets. It evaluates the similarity between the generated data and the real data in the feature space. KID can help evaluate the similarity of the generated samples and the original samples in terms of visual features, while avoiding computational instability problems caused by small samples.

[0075] Inception Score (IS) (Salimans et al., 2016): Evaluates the quality and diversity of the generated images based on the probability distribution of the classifier output. The higher the IS value, the better the quality and diversity of the generated data.

[0076] Diversity Score (Gurumurthy et al., 2017): The Diversity Score is very suitable for evaluating the diversity of the generated dataset. It evaluates whether the generated data is diverse enough by calculating the differences between the generated samples in the feature space. The Diversity Score can be used to evaluate the dispersion degree of the generated data among different features, ensuring that the generated samples are not only similar to the original data but also have a wide diversity in features, thus deducing new defect types.

[0077] Precision and Recall for Distributions (PRD) (Sajjadi et al., 2018): Evaluate the quality of the generated model through precision and recall, and use the Fβ score (β = 0.8 in this paper) to measure the overall performance of the model, especially when the class distribution is imbalanced.

[0078] Perceptual Similarity (Johnson et al., 2016): Calculate the perceptual similarity by comparing the activations of two groups of images in the VGG16 network. The smaller the value, the closer the images are perceptually and the higher the authenticity.

[0079] Experimental Results:

[0080] To verify the effectiveness of the model of the present invention in bearing data generation, we conducted comparative experiments on a variety of generation algorithms, including GAN (Goodfellow et al., 2020), GMVAE (Dilokthanakul et al., 2017), GVAE (Chadebec, C et al., 2021), VQVAE (van den Oord et al., 2017), RHVAE (Chadebec, C et al., 2020), and StableDiffusion (SD, Rombach et al., 2021). Table 1 lists the evaluation index results of each generation network, including FID (↓), KID (↓), IS (↑), DS (↑), Fβ (↑), and PS (↓).

[0081]

[0082] Table 1 Comparative simulation experiments of the method of the present invention under different algorithms

[0083] By observing Table 1 and Figure 3From the simulation experiment results, it can be seen that due to insufficient latent space processing capabilities, GAN and GMVAE have poor generation effects on the high-dimensional small-sample bearing dataset, with many artifacts; although GVAE introduces Riemannian geometry and random walk algorithms, there are still too many artifacts in the generated data. The data quality generated by VQVAE and RHVAE is relatively good, but there are still blurs in the details. In contrast, the details generated by Stable Diffusion are better, but there are still problems of excessive background redrawing and shape distortion overall. The model of the present invention performs best in terms of authenticity, detail retention, and artifact control.

[0084] Although the present invention is disclosed as above, the protection scope of the present invention is not limited thereto. Those skilled in the art of the present invention can make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will all fall within the protection scope of the present invention.

Claims

1. A bearing data expansion method based on Gaussian mixture model and particle swarm optimization, characterized in that: The following steps are involved: S100, obtaining an original bearing data set, the data set comprising a plurality of sample data points, each sample data point representing a feature vector of a bearing sample, the feature vector comprising defect feature information of the bearing; S200, initializing parameters of a Gaussian mixture model, wherein the parameters include a mean, a covariance matrix, and a mixture weight; S300, using a particle swarm optimization algorithm to optimize the GMM parameters initialized in step S200 to obtain optimal GMM parameters; S400, selecting a Gaussian distribution according to the mixed weight, and randomly sampling from the distribution to generate new data points to obtain expanded bearing data.

2. The bearing data expansion method based on Gaussian mixture model and particle swarm optimization according to claim 1, characterized in that: In step S100, the original bearing data is preprocessed, including data standardization and noise removal.

3. The bearing data expansion method based on Gaussian mixture model and particle swarm optimization according to claim 1, characterized in that: In step S200, specifically including: In the training process of Gaussian mixture model, the starting point of model parameters is set first, including the mean μ j , mixed weight φ j And the covariance matrix Cov j , and add a small regularization term while initializing the covariance matrix; Then, we proceed to the expectation step to calculate the probability that the data point belongs to each component, i.e., the responsibility w ij The process is expressed as: In the formula, data point l i The responsibility degree of the jth component is w ij , at the mean μ j and the covariance matrix Cov j The probability density function of the multivariate Gaussian distribution under is N(l i ∣μ j ,Cov j ), the initial mixing weight is K is the total number of Gaussian components.

4. The bearing data expansion method based on Gaussian mixture model and particle swarm optimization according to claim 3 is characterized in that: In step S300, the objective function of particle swarm optimization is the likelihood function of GMM, that is, maximizing the probability density of data under GMM, thereby optimizing the parameters of GMM; specifically, The mean μ generated by the expected step is optimized, and the particle swarm optimization algorithm is used to search for the optimal mean in the parameter space. The optimization function is shown in the following formula (2): Through the maximization step, the model parameters are updated to maximize the likelihood of the data. The update formula is as follows: The model is fitted by iteratively executing the expectation step, PSO and maximization step until the iteration termination condition is met.

5. The bearing data expansion method based on Gaussian mixture model and particle swarm optimization according to claim 4, characterized in that: In step S400, a Gaussian distribution is selected according to the mixing weight, and new data points are randomly sampled from the distribution as follows: l n ~N(μ j ,S j (5) Using a known n d dimensional original dataset To estimate the parameters of GMM, used to generate m interpolated d-dimensional low-dimensional data sets 6. A bearing data expansion system based on Gaussian mixture model and particle swarm optimization, characterized by: The system has a program module corresponding to the steps of any one of claims 1 to 5, and executes the steps of the bearing data expansion method based on Gaussian mixture model and particle swarm optimization when running.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of the bearing data expansion method based on Gaussian mixture model and particle swarm optimization described in any one of claims 1 to 5 when called by a processor.

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