A bearing data augmentation method and system based on a Gaussian mixture model and a particle swarm optimization

Abstract

The application provides a bearing data expansion method and system based on a Gaussian mixture model and a particle swarm optimization, and belongs to the field of data expansion. In order to solve the problem of how to effectively expand the data set, increase the data diversity, alleviate the data scarcity, and improve the generalization ability and detection performance of the model in the existing small sample bearing defect detection, the application adopts a Gaussian mixture model (GMM) to model the original data, optimizes the parameters of the GMM through a particle swarm optimization (PSO) algorithm, generates new data points, and expands the data set. The method can effectively increase the data diversity, alleviate the data scarcity problem, 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 expansion, and in particular to a bearing data expansion method and system based on a Gaussian mixture model and particle swarm optimization. Background Art

[0002] In the field of bearing defect detection, especially in small sample sizes, the number of bearing data samples obtained is limited, and the data distribution is uneven, which poses a great challenge to model training and optimization. Traditional data expansion methods such as data augmentation 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 probabilistic model, the Gaussian mixture model (GMM) can model and sample data to generate new data points, but its parameter optimization is difficult. When processing high-dimensional data, especially when the sample size is small, the covariance matrix estimation of the GMM becomes complicated. At the same time, the variational autoencoder (VAE) is prone to blurring and distortion when generating high-resolution data, affecting the quality of the generated defects. Summary of the Invention

[0003] The technical problems to be solved by the present invention are:

[0004] In order to solve the problem of how to effectively expand the data set, increase data diversity, alleviate data scarcity, and improve the generalization ability and detection performance of the model in the existing small sample bearing defect detection.

[0005] The present invention is to solve the above technical problems using the following technical solutions:

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

[0007] S100, obtaining an original bearing data set, the data set including a plurality of sample data points, each sample data point representing a feature vector of a bearing sample, the feature vector including defect feature information of the bearing;

[0008] S200, initializing parameters of a Gaussian mixture model, wherein the parameters include a mean, a covariance matrix, and a mixture weight;

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

[0010] S400 , selecting a Gaussian distribution according to the mixing weight, and randomly sampling from the distribution to generate new data points to obtain expanded bearing data.

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

[0012] Furthermore, in step S200, it specifically includes:

[0013] In the training process of the Gaussian mixture model, the starting point of the model parameters is first set, 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;

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

[0015]

[0016] 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 the condition is N(l i ∣μ j ,Cov j ), the initial mixing weight is K is the total number of Gaussian components.

[0017] Furthermore, in step S300, the objective function of the particle swarm optimization is the likelihood function of the GMM, that is, maximizing the probability density of the data under the GMM, thereby optimizing the parameters of the GMM; specifically,

[0018] 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):

[0019]

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

[0021]

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

[0023] Furthermore, in step S400, a Gaussian distribution is selected according to the mixing weight, and new data points are randomly sampled from the distribution to generate:

[0024] l n ~N(μ j ,Σ j )(5)

[0025] 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

[0026] A bearing data expansion system based on a Gaussian mixture model and particle swarm optimization is disclosed. The system has a program module corresponding to the above steps and executes the steps in the above bearing data expansion method based on a Gaussian mixture model and particle swarm optimization during operation.

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

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] The present invention provides a bearing data expansion method and system based on a Gaussian mixture model and particle swarm optimization, which has the following beneficial effects:

[0030] Effectively expand the data set: Modeling and sampling the original data through the Gaussian mixture model can generate new data points, effectively expand the data set, increase the data volume, and alleviate the problem of data scarcity;

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

[0032] Optimize model performance: The expanded dataset can provide more training samples, enabling the model to better learn and fit the data during training, thereby improving the model's detection performance and accuracy.

[0033] Strong adaptability: This method is applicable to various types of bearing defect data, has strong adaptability and a wide range of applicability, and can meet the data expansion needs in different scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0036] Figure 3 A comparison chart of algorithms generated in an embodiment of the present invention. DETAILED DESCRIPTION

[0037] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

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

[0039] S100. Obtain an original bearing dataset. The original bearing dataset includes multiple sample data points. Each sample data point in the dataset represents a feature vector of a bearing sample and includes defect feature information of the bearing. The dataset may be preprocessed, including data normalization, noise removal, or other existing preprocessing methods, to improve data quality and model training effect.

[0040] S200, initialize the parameters of the Gaussian mixture model (GMM), including the mean, covariance matrix and mixing weight; the mean represents the center position of each Gaussian distribution, the covariance matrix represents the shape and direction of each Gaussian distribution, and the mixing weight represents the proportion of each Gaussian distribution in the overall data; the initialization parameters can be randomly generated or set based on experience to provide initial values ​​for subsequent parameter optimization, specifically including:

[0041] In the training process of Gaussian mixture model (GMM), the starting point of the model parameters is first set, 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;

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

[0043]

[0044] 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 the condition is N(l i ∣μ j ,Cov j ), the initial mixing weight is K is the total number of Gaussian components;

[0045] S300, using a particle swarm optimization algorithm to optimize the GMM parameters initialized in step S200, and using a particle swarm optimization (PSO) algorithm to optimize the GMM parameters to obtain optimal GMM parameters;

[0046] The particle swarm optimization algorithm simulates the foraging behavior of a flock of birds, treating each particle as a potential solution. The particles fly in the solution space and search for the optimal solution by iteratively updating the particle's position and velocity.

[0047] In the present invention, 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,

[0048] The mean μ generated by the expected step is optimized and the particle swarm optimization (PSO) algorithm is used to search for the optimal mean in the parameter space. This method can avoid the problem of local mean. The optimization function is shown in the following formula (2):

[0049]

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

[0051]

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

[0053] S400, select a Gaussian distribution according to the mixing weight, and randomly sample from the 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, we 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 datasets

[0056] Specific implementation scheme 2: The present invention provides a bearing data expansion system based on Gaussian mixture model and particle swarm optimization. The system has a program module corresponding to the above steps, and executes the steps in the above bearing data expansion method based on Gaussian mixture model and particle swarm optimization during operation.

[0057] The other combinations and connection relationships of this embodiment are the same as those of the first embodiment.

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

[0059] The other combinations and connection relationships of this embodiment are the same as those of the first embodiment.

[0060] Example 1

[0061] Suppose there is a bearing defect dataset containing 100 samples, each containing 10 features. The dataset has been preprocessed, and the eigenvalues ​​have been normalized to between 0 and 1. First, load the preprocessed bearing defect dataset from the data storage system, ensuring 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 three Gaussian distributions for modeling, randomly generate three 10-dimensional vectors as the initial means, set the covariance matrix to the unit matrix, indicating that the variance of each feature is 1 at the beginning and there is no correlation between the features, and set the mixing weights to [0.3, 0.3, 0.4], indicating the initial proportion of the three Gaussian distributions in the data.

[0062] Then, the particle swarm optimization (PSO) algorithm is used to optimize the parameters of the GMM. The particle swarm size is set to 50 particles, the number of iterations is set to 100, the inertia weight is set to 0.9 to control the continuity of the particle velocity, and the learning factor is set to 2 to affect the degree to which the particles learn to move towards the individual and global optimal positions. The particle swarm is initialized, and each particle represents a set of GMM parameters. The fitness value of each particle is calculated, that is, the GMM likelihood function value of the data under this set of parameters. The individual optimal position and global optimal position of each particle are updated, and the particle speed and position are adjusted according to the update formula. This process is repeated until 100 iterations are reached to obtain the optimal GMM parameters, including the mean, covariance matrix, and mixing weights. These parameters can better describe the distribution characteristics of the data.

[0063] Based on the optimized GMM parameters, 200 new 10-dimensional feature vectors were generated by sampling from three Gaussian distributions according to the mixing weights. These 200 new data points were merged with the original 100 data points to form an expanded dataset of 300 samples. Finally, the expanded dataset was used for model training, with a support vector machine (SVM) selected as the defect detection model. The SVM model was trained using the expanded dataset, and cross-validation was used to evaluate model performance. The expanded dataset increased the model's accuracy from 85% to 90%, demonstrating excellent generalization and detection performance.

[0064] Example 2

[0065] Consider a bearing defect dataset containing 50 samples, each containing 20 features, with eigenvalues ​​normalized to between -1 and 1. Similarly, load the preprocessed dataset, initialize the GMM parameters, select five Gaussian distributions for modeling, randomly generate five 20-dimensional vectors as the initial mean, set the covariance matrix to the identity matrix, and set the mixing weights to [0.2, 0.2, 0.2, 0.2]. Use the PSO algorithm to optimize the GMM parameters with a particle swarm size of 100 particles, 200 iterations, an inertia weight of 0.8, and a learning factor of 1.5. The optimization results in the optimal GMM parameters.

[0066] Based on the optimized parameters, 150 new 20-dimensional feature vectors were generated by sampling from five Gaussian distributions using a mixed weight. These vectors were then merged with the original 50 data points to form an expanded dataset of 200 samples. A random forest was selected as the defect detection model and trained on the expanded dataset. Cross-validation was used to evaluate model performance. The expanded dataset increased the model's accuracy from 80% to 88%, further demonstrating that the proposed method can effectively expand datasets of varying sizes and feature dimensions, improving both model training and detection performance.

[0067] Simulation experiment

[0068] Experimental dataset:

[0069] This study used a dataset of bearings produced by Harbin Bearing Group. The data was collected from the bearing assembly line. To ensure data quality, the experiments were conducted in a custom-built laboratory to control the light source and minimize external interference. Figure 2This article shows an example of a dataset 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 of each type were selected for the experiment.

[0070] Experimental setup:

[0071] The experiments were conducted on an Ubuntu 20.04 operating system, based on the PyTorch open-source deep learning framework, using Torch 1.8.0 and Torchvision 0.8.0. The computing resources used were an NVIDIA GeForce RTX1080 GPU with 20GB of memory. The number of data augmentations, m, was set to 40, the high-dimensionality, D, was set to 100, the low-dimensionality, d, was set to 50, and the total number of Gaussian components, K, 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, with the amount of generated data remaining the same as the original training dataset to facilitate direct comparison.

[0073] Fréchet Inception Distance (FID) (Heusel et al., 2017): This method calculates the difference between two datasets using the InceptionV3 model to assess the similarity between the generated data and the real data. Lower FID values ​​indicate more similar data distributions.

[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. It is more stable than FID, especially when working with smaller datasets. It assesses the similarity between generated data and real data in the feature space. KID can help assess the similarity of visual features between generated samples and original samples while avoiding computational instability caused by small sample sizes.

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

[0076] Diversity Score (Gurumurthy et al., 2017): Diversity Score is well-suited for assessing the diversity of generated datasets. It evaluates whether the generated data is sufficiently diverse by calculating the differences between generated samples in feature space. Diversity Score can be used to assess the dispersion of generated data across different features, ensuring that generated samples are not only similar to the original data but also exhibit a wide diversity of features, allowing the inference of new defect types.

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

[0078] Perceptual Similarity (Johnson et al., 2016): Perceptual similarity is calculated by comparing the activations of two sets of images in the VGG16 network. Smaller values ​​indicate that the images are perceptually closer and more realistic.

[0079] Experimental results:

[0080] To verify the effectiveness of the proposed model in bearing data generation, we conducted comparative experiments on various generation algorithms, including GAN (Goodfellow et al., 2020), GMVAE (Dilokthanakul et al., 2017), GVAE (Chadebec et al., 2021), VQVAE (van den Oord et al., 2017), RHVAE (Chadebec et al., 2020), and StableDiffusion (SD, Rombach et al., 2021). Table 1 lists the evaluation metrics 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 GAN and GMVAE have poor generation effects on high-dimensional small-sample bearing datasets due to insufficient potential space processing capabilities, and there are many artifacts; although GVAE introduces Riemannian geometry and random walk algorithms, there are still too many artifacts in the generated data. The data generated by VQVAE and RHVAE are of relatively good quality, but the details are still blurred. In contrast, the details generated by Stable Diffusion are better, but the overall problem of excessive background redrawing and shape distortion still exists. 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 scope of protection disclosed by the present invention is not limited thereto. Those skilled in the art of the present invention may make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will fall within the scope of protection 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 including a plurality of sample data points, each sample data point representing a feature vector of a bearing sample, the feature vector including 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; 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 of the expected steps To optimize, 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): (2)； Through the maximization step, the model parameters are updated to maximize the likelihood of the data. The update formula is as follows: (3)； (4)； The model is fitted by iteratively executing the expectation step, PSO and maximization step until the iteration termination condition is met; In the formula, the data point Belong to The responsibility of a component is , at the mean and covariance matrix The probability density function of the multivariate Gaussian distribution under ; S400 , selecting a Gaussian distribution according to the mixing 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 the model parameters is first set, including the mean , mixed weight and the covariance matrix , 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 degree of responsibility. The process is expressed as: (1)； In the formula, the data point Belong to The responsibility of a component is , at the mean and covariance matrix The probability density function of the multivariate Gaussian distribution under , the initial mixing weight is , 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, 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: (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 .

5. 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 4 above, and executes the steps of the bearing data expansion method based on Gaussian mixture model and particle swarm optimization when running.

6. 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 according to any one of claims 1 to 4 when called by a processor.

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