Health state recognition method based on image statistical characteristics

Abstract

The invention relates to a health state recognition method based on image statistical characteristics. Comprising the following steps of: firstly, acquiring an original vibration signal of a bearing by using a sensor, converting the original vibration signal into a time-frequency domain color image by adopting short-time Fourier transform, and then converting the time-frequency domain color image into a grayscale image by using grayscale transform; secondly, extracting six types of image statistical characteristics from the grayscale image, wherein the six types of image statistical characteristics comprise a mean value, a variance, a contrast ratio, correlation, energy and homogeneity; then, six types of image statistical features are used as input, and a fusion feature vector is output through a designed stability-enhanced sparse PCA (Principal Component Analysis) module; and finally, performing health state recognition on the fused feature vector by using a state change detection function. The method is good in recognition effect and high in industrial scene adaptability, and provides high-precision and high-reliability technical support for predictive maintenance of equipment; the method is high in calculation efficiency, good in real-time performance and high in robustness, unification of precision, efficiency and robustness is achieved, and the method is very suitable for online real-time monitoring application in engineering practice.

Description

Technical Field

[0001] This invention relates to the fields of fault prediction and health management, and in particular to a health status recognition method based on image statistical features. Background Technology

[0002] In the Industrial Internet of Things (IIoT) environment, sensing devices are essentially "sensory systems" deployed on mechanical equipment, responsible for collecting various signals from the physical world, such as temperature, pressure, sound, and vibration, and converting them into electrical or digital signals that can be transmitted, stored, and analyzed. In the field of bearing condition monitoring, the most commonly used and effective sensing device is the accelerometer. Bearing vibration signals are collected through accelerometers, the core of which is converting mechanical vibration into electrical signals to obtain the equipment's operating status. As a common core moving component, the health status of bearings is crucial to the overall operational safety of equipment. Accurately identifying the bearing's operating status is essential for improving the accuracy of remaining life prediction and is a vital foundation for subsequent remaining life prediction.

[0003] The document with publication number "CN202510213776.X" proposes a "method for identifying the condition of large bearings by dynamic interaction and fusion of features from multiple sensors and multiple domains." It mainly achieves dynamic interaction and fusion of features from multiple sensors and multiple domains through a multi-level improved graph neural network, improving the accuracy and reliability of the results and filling a technological gap in the identification of the health condition of large bearings. However, the following problems exist: 1. The multi-level improved graph neural network model has a complex structure and large parameter scale, requiring high computational resources; 2. The model training time is long, making it difficult to meet real-time detection requirements; 3. The model's generalization ability is insufficient, and its adaptability to different working conditions (such as speed and load changes) is weak.

[0004] The document with publication number "CN202110671228.3" proposes a "Bearing Health Status Recognition Method Based on Multi-View Attention Network". It primarily trains and identifies the status of bearings by inputting multi-channel data into a deep residual network with an attention module, ensuring the effectiveness and accuracy of the features. However, it has significant drawbacks: 1. The multi-view attention network needs to process multi-dimensional data simultaneously, and the deep residual network has numerous node parameters, resulting in extremely high hardware computing power requirements for the model; 2. It relies on large-scale labeled data for model training, leading to long iterative optimization cycles and making it difficult to meet the rapid deployment needs of industrial scenarios; 3. It has poor cross-scenario adaptability, as the features learned by the model are strongly bound to operating conditions such as rotational speed and load during training, resulting in a significant decrease in recognition accuracy when operating conditions change.

[0005] The document with publication number "CN104408698B" proposes a "QR code image illumination equalization method based on compressed sensing". The core of this method is to perform a "hard truncation" soft thresholding operation on the Fourier domain spectrum signal to achieve image restoration and output an illuminated QR code image. However, it has prominent problems: 1. Although there is no deep neural network, the compressed sensing framework contains complex calculations such as Fourier transform, construction of uncorrelated sampling matrices and FISTA iterative optimization. It requires point-by-point thresholding and iterative updates of the two-dimensional image spectrum. The data processing scale is large and the process is cumbersome under high-resolution images, resulting in an imbalance between processing complexity and real-time requirements; 2. The scene adaptability and generalization ability are weak. The soft threshold parameter setting and spectrum restoration logic are highly adapted to the "QR code uneven illumination" scenario. The threshold needs to be manually adjusted and iteratively attenuated according to fixed illumination interference (e.g., T = T × 0.9). When facing QR codes with different intensities / types of illumination interference or different resolutions, the preset strategy is difficult to adapt and the parameters need to be readjusted.

[0006] The common problems of the above patents are: 1. Imbalance between model complexity and efficiency requirements: They all use deep neural networks with complex structures, resulting in a large number of parameters and nodes, and high resource dependence; 2. Weak scene adaptability and generalization ability: They are highly dependent on working conditions, and the features learned by the model are strongly bound to the training scene, lacking the ability to adapt to changing working conditions. Summary of the Invention

[0007] To address the problems of high resource dependence, weak generalization ability, and poor adaptability to varying working conditions in existing complex neural network-based methods, this invention proposes a health status recognition method based on image statistical features.

[0008] To achieve the above objectives, the present invention provides the following technical solution: a health status recognition method based on image statistical features, comprising the following steps:

[0009] Step 1: Using the original vibration signal of the bearing acquired by the sensor, the original vibration signal is converted into a time-frequency domain color image by short-time Fourier transform, and then the time-frequency domain color image is converted into a grayscale image by grayscale transform.

[0010] Step 2: Extract six types of image statistical features from the grayscale image: mean, variance, contrast, correlation, energy, and homogeneity;

[0011] Step 3: Take the six types of image statistical features as input, pass them through the designed stability-enhanced sparse PCA module, and output the fused feature vector;

[0012] Step 4: Use the state change detection function to identify the fused feature vector and identify the end time of the healthy state.

[0013] Furthermore, in step one above, the grayscale transformation uses a weighted summation method to convert the RGB three-channel information into a single-channel grayscale value.

[0014] Furthermore, in step two above, six types of image statistical features are extracted from the grayscale image based on the grayscale co-occurrence matrix, using the following specific formula:

[0015] Suppose a grayscale image I is an M×N matrix, where M is the number of rows and N is the number of columns, and I(i,j) represents the grayscale value of the pixel in the i-th row and j-th column. Then the mean μ of the image is calculated as follows:

[0016]

[0017] Image variance σ 2 The calculation is as follows:

[0018]

[0019] The formula for calculating contrast is:

[0020]

[0021] Where, N g P(i,j) is the number of gray levels, and P(i,j) is the element in the i-th row and j-th column of the gray-level co-occurrence matrix.

[0022] The formula for calculating correlation is:

[0023]

[0024] Where, μ i and μ j These are the mean of the rows and columns of the gray-level co-occurrence matrix, respectively, σ i and σ j These are the standard deviations of the rows and columns of the gray-level co-occurrence matrix, respectively.

[0025] The formula for calculating Energy:

[0026]

[0027] The formula for calculating homogeneity is:

[0028]

[0029] Furthermore, step three above specifically includes the following sub-steps:

[0030] 3.1 The stability-enhanced sparse PCA method adopts a dual initialization strategy of fixed random seed and weight vector normalization in the initialization stage;

[0031] 3.2 Perform standardization preprocessing on the six types of features obtained in step two to obtain standardized feature vectors;

[0032] 3.3 Design the core optimization part of the sparse PCA method with enhanced stability, complete feature fusion, and obtain the optimal weight matrix after the end of the iteration rounds;

[0033] 3.4 The optimal weight matrix and the standardized eigenvectors are used to calculate the fused eigenvectors, resulting in a fused eigenvector that condenses the core information.

[0034] Furthermore, the specific sub-steps of step 3.3 above include:

[0035] 3.3.1 Calculate the projection score, gradient, and regularization term based on the current load vector, and initially update the weights. The specific sub-steps are as follows:

[0036] 3.3.1.1 Calculate the sample projection score based on the current load vector v:

[0037] First, define the optimization objective function with elastic net constraints as follows:

[0038]

[0039] Where v is the load vector, λ1 is the L1 regularization coefficient, λ2 is the L2 regularization coefficient, and v T ∑v is the variance maximization term, and λ1||v||1 is the Lasso penalty term, which induces sparsity. This is a ridge regression penalty item, enhancing stability;

[0040] During the iteration process, the sample projection score α is first calculated based on the current load vector v. j =Z·v, and then complete the gradient calculation and initial update through the following steps:

[0041] 3.3.1.2 Calculating the gradient molecule: based on the projection score α j Given the eigenvector Z, calculate the gradient numerator using the following formula:

[0042] numerator = Z T ·α j (11)

[0043] Where numerator is the gradient numerator, which is equivalent to the scaled form of the product of the covariance matrix ∑ and the current load vector v;

[0044] 3.3.1.3 Calculating the Regularization Denominator: Combining the variance term of the projected score with the L1 regularization coefficient, construct the regularization denominator using the following formula:

[0045] denominator = α j T ·α j +λ1 (12)

[0046] Where denominator is the regularization denominator, α j T ·α j λ1 is the variance term of the sample projection, and λ1 is the L1 regularization coefficient.

[0047] 3.3.1.4 Preliminary Weight Update: The load vector is initially updated by using the ratio of the gradient numerator to the regularization denominator. This preserves the optimization information of the gradient direction while achieving the weight decay effect of L2 regularization through the denominator term, laying the foundation for subsequent sparsity operations. The formula is:

[0048] v temp =numerator / denominator (13)

[0049] Among them, v temp To initially update the load vector;

[0050] 3.3.2 Update to v temp Explicit sparsity processing is performed to obtain the soft thresholding operator, the formula of which is:

[0051]

[0052] in, It is a threshold term; v temp It is the updated load vector, S λ (v temp ) is the soft-thresholded load vector, sign(v temp ) is the symbolic function (v) temp When >0, it is 1, v temp When <0, it is -1, v temp =0 is 0);

[0053] 3.3.3 Weight vector normalization and division-by-zero protection mechanism;

[0054] Weight vector normalization and the division-by-zero protection mechanism are subsequent supplements and robustness enhancements to the soft thresholding operator. The soft thresholding operator provides the processing object for weight vector normalization, while the division-by-zero protection mechanism serves as a fallback for extreme cases of the soft thresholding operator (such as when all vector components are 0). The specific execution flow is as follows:

[0055] First, calculate the soft-thresholded load vector S. λ (v temp First, determine the norm of S; second, perform branching based on the norm result. If the norm is greater than the minimum value, then...λ (v temp Normalize the expression as shown in formula (15). If the norm is not greater than the minimum value, then directly let v new =0, to avoid numerical anomalies caused by dividing by zero;

[0056]

[0057] Among them, v new This is the updated load vector. For the soft thresholding operator, ∑v temp v is the product of the covariance matrix and the initial updated load vector. temp For the initial update of the load vector, |·|2 is the L2 norm.

[0058] Furthermore, in step 3.4 above, the process of calculating the fused feature vector is as follows:

[0059] Based on the optimal weight matrix W selected in step 3.3 new The standardized feature vector Z is multiplied by the optimal weight matrix to obtain the fused feature vector that condenses the core information. The calculation formula is as follows:

[0060] s = Z·W new (18)

[0061] Where s is the fused feature vector, Z is the standardized bearing feature vector, and W new The optimal weight matrix for sparse PCA output with enhanced stability.

[0062] Furthermore, in step four above, assume there is a data sequence {x1, x2, ..., x...} n}, where each x i Let x be a real number. Define a function f(x) to predict the starting point of degradation, as shown in formula (19):

[0063]

[0064] Where x represents the characteristic value at different times;

[0065] Define a state change detection function g(x) i ,x i+1 To identify state change points, the formula is shown in (20):

[0066]

[0067] Compared with the prior art, the beneficial effects of the present invention are:

[0068] 1. This invention introduces a dual initialization strategy combining a fixed random seed and a normalized weight vector. During the iterative optimization phase, it employs "expanded iteration count (500 times) + tightened tolerance (10... -6 The convergence mechanism of "" solves the problem of unstable results in traditional sparse PCA. This design ensures consistency in different experimental scenarios and provides a foundation for the standardized application of the algorithm in engineering practice.

[0069] 2. The innovative soft thresholding operation incorporated into the weight update process of this invention significantly improves its adaptability to industrial scenarios: This invention focuses on "bearing feature fusion and core information purification," targeting the feature load vector (i.e., the weight vector of the six statistical features of the bearing), and calculates S through a "gradient shrinkage" method. λ (v temp ) = sign(v temp )·max(|v temp The algorithm, using the formula |-λ,0), explicitly sets the weights of redundant features below a threshold to 0 and shrinks the weights of key features above a threshold towards 0. This upgrades the "indirect regularization constraint" relied upon by traditional sparse methods to "direct sparsity intervention," significantly improving the sparsity and interpretability of the fused features and solving the problems of feature redundancy and ambiguous physical meaning in traditional methods. Furthermore, this invention additionally designs a division-by-zero protection mechanism (to avoid numerical anomalies when the weight vector approaches zero and ensure stable algorithm operation) and a square-form definition of reconstruction error (to amplify changes in early-stage minor degradation features of bearings and improve fault sensitivity). This significantly enhances the robustness of the algorithm in complex industrial environments, making it more suitable for the engineering needs of early fault diagnosis of critical equipment such as bearings, and providing high-precision and high-reliability technical support for predictive maintenance of equipment.

[0070] 3. This invention uses a state change detection function, which is logically intuitive and highly interpretable, g(x i ,x i+1 =1 directly corresponds to the behavior of the feature vector crossing the zero point, and the physical meaning is clear; at the same time, this method only needs to compare the signs of two adjacent moments, and the computational complexity is O(1), which is computationally efficient and has good real-time performance, making it very suitable for online real-time monitoring systems; in addition, this function is not sensitive to the overall translation of the feature sequence, and only focuses on the position change of its relative to the zero point, which can effectively avoid false alarms caused by slow environmental drift, and has high robustness.

[0071] 4. This method employs L1 and L2 regularization in conjunction with soft thresholding to design a stable sparse PCA feature fusion framework. It is further enhanced by a fixed random seed and weight vector normalization initialization strategy, along with fine-grained convergence control through "iteration expansion + tolerance tightening." Finally, it completes identification through an efficient state detection function based on sign change. Its core advantage lies in achieving a balance between accuracy, efficiency, and robustness: the synergistic effect of dual regularization and soft thresholding significantly improves the accuracy and interpretability of feature selection; stable initialization and a fine-grained convergence mechanism ensure the consistency and stability of the algorithm under different experiments and complex data; and efficient sign change detection enables the system to possess excellent real-time response capabilities, quickly and accurately identifying changes in bearing health status. It also exhibits good robustness to environmental drift and other disturbances, making it highly suitable for online real-time monitoring applications in engineering practice. Attached Figure Description

[0072] Figure 1 This is the overall flowchart of this method;

[0073] Figure 2 This is a diagram of the original vibration signal obtained using this method.

[0074] Figure 3 The six types of image statistical features proposed in this method are as follows: Figure 3 (a) is the mean. Figure 3 (b) represents the variance. Figure 3 (c) represents the contrast. Figure 3 (d) represents correlation. Figure 3 (e) represents energy. Figure 3 (f) indicates homogeneity;

[0075] Figure 4 This is a graph showing the sparse PCA results of this method;

[0076] Figure 5 This is a diagram showing the state recognition results of this method; Detailed Implementation

[0077] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0078] This invention proposes a health status recognition method based on image statistical features. By converting bearing vibration signals into images and extracting statistical features, and combining them with sparse PCA for feature fusion, this method aims to solve the problems of high resource dependence, long training cycle and weak generalization ability of existing methods based on complex neural networks. It achieves accurate identification of bearing status change points and provides a reliable basis for subsequent remaining life prediction.

[0079] See Figure 1This invention provides a health status recognition method based on image statistical features, comprising the following steps: First, using the original vibration signal of the bearing acquired by the sensor, the original vibration signal is converted into a time-frequency domain color image using short-time Fourier transform, and then the time-frequency domain color image is converted into a grayscale image using grayscale transform; Second, six types of image statistical features are extracted from the grayscale image: mean, variance, contrast, correlation, energy, and homogeneity; Then, the six types of image statistical features are used as input, and after passing through a designed stability-enhanced sparse PCA module, a fused feature vector is output; Finally, a state change detection function is used to identify the health status of the fused feature vector.

[0080] Based on the above ideas, this invention provides a health status recognition method based on image statistical features, the specific implementation steps of which are as follows:

[0081] Step 1: Using the original vibration signal of the bearing acquired by the sensor, the original vibration signal is converted into a time-frequency domain color image using short-time Fourier transform, and then the time-frequency domain color image is converted into a grayscale image using grayscale transform. The specific sub-steps are as follows:

[0082] The "original vibration signal of the bearing" referred to in this invention comes from the bearing dataset of Xi'an Jiaotong University.

[0083] 1.1 The vibration signal is converted into a time-frequency domain color image using the Short-Time Fourier Transform (STFT). STFT is a time-frequency analysis method developed from Fourier Transform, which is suitable for the time-frequency characteristic analysis of non-stationary signals, thereby revealing the frequency component changes of the signal in different time periods.

[0084] For any L 2 The vibration signal x(t) in the interval (R) has an STFT defined as:

[0085]

[0086] Where x(τ) is the original signal, w(τ-t) is a window function used to truncate a local portion of the signal, and e -j2πfτ It is a short-time Fourier transform kernel. The parameters of the STFT are set as follows: window length of 256, number of overlapping samples of 128, and windowing function of Hamming window.

[0087] See Figure 2 , Figure 2 The original vibration signal of bearing Bearing1_1 is displayed. It fluctuates around the zero mean line. In the early stage, the waveform is flat, the amplitude is uniform and the noise is weak. In the later stage, the fluctuation amplitude increases, intermittent sharp pulses appear and periodic interference occurs, which intuitively reflects the change of bearing from healthy operation to degradation.

[0088] 1.2 Use grayscale transformation to convert time-frequency domain color images into grayscale images.

[0089] Grayscale transformation (GT) is a fundamental operation in digital image processing, aiming to redistribute pixel grayscale values ​​through mathematical mapping functions to optimize image quality or highlight specific features. This invention employs a typical color-to-grayscale conversion technique, essentially a linear weighted transformation based on the characteristics of human vision. This method uses the International Telecommunication Union (ITU-R) BT.601 standard weighting coefficients (R: 0.2989, G: 0.5870, B: 0.1140) to convert RGB three-channel information into single-channel grayscale values ​​through weighted summation, thus obtaining a grayscale image and simplifying the feature extraction process. The specific formula is as follows:

[0090] I gray =0.2989·R+0.5870·G+0.1140·B (2)

[0091] In this diagram, R represents the red channel, G represents the green channel, and B represents the blue channel.

[0092] Step 2: Extract six types of image statistical features from the grayscale image: mean, variance, contrast, correlation, energy, and homogeneity;

[0093] The image statistical features extracted in this invention include mean, variance, contrast, correlation, energy, and homogeneity. The grayscale image is converted into a gray-level co-occurrence matrix (GLCM), which describes the spatial relationship of pixel grayscale values ​​in the image. Image statistical features are calculated based on this matrix. Assuming the grayscale image I is an M×N matrix, where M is the number of rows and N is the number of columns, and I(i,j) represents the grayscale value of the pixel in the i-th row and j-th column, the mean μ of the image is calculated as follows:

[0094]

[0095] Image variance σ 2 The calculation is as follows:

[0096]

[0097] Contrast is a metric that measures local variation in an image. Images with high contrast exhibit a wider range of pixel value variations, meaning there is a greater difference between bright and dark areas. The formula for calculating contrast is:

[0098]

[0099] Where, N gP(i,j) is the number of gray levels, and P(i,j) is the element in the i-th row and j-th column of the gray-level co-occurrence matrix.

[0100] Correlation measures the degree of linear dependence of gray levels in an image, that is, the correlation between the gray values ​​of pixel pairs in an image. It describes the regularity and directionality of image texture. High correlation indicates that the image texture has strong regularity and directionality; low correlation indicates that the image texture is relatively random. The formula for calculating correlation is:

[0101]

[0102] Where, μ i and μ j These are the mean of the rows and columns of the gray-level co-occurrence matrix, respectively, σ i and σ j These are the standard deviations of the rows and columns of the gray-level co-occurrence matrix, respectively.

[0103] Energy, also known as the second moment of the angle, reflects the uniformity of gray-level distribution and the fineness of texture in an image. A higher energy value indicates a more concentrated distribution of gray-level values ​​and a finer texture; a lower energy value indicates a more dispersed distribution of gray-level values ​​and a coarser texture. The formula for calculating Energy is:

[0104]

[0105] Homogeneity measures the similarity of gray values ​​in an image, emphasizing the importance of elements on the diagonal of the gray-level co-occurrence matrix. Higher homogeneity indicates more similar gray values ​​among adjacent pixels, resulting in a smoother image texture; lower homogeneity indicates greater differences in gray values ​​among adjacent pixels, leading to a more complex image texture. The formula for calculating homogeneity is:

[0106] See Figure 3 , Figure 3 This paper presents six types of image statistical features of bearing Bearing1_1; and visualizes and analyzes six types of feature indicators (energy, correlation, contrast, variance, mean, and homogeneity) of bearing Bearing1_1's entire life cycle data. Each indicator exhibits a physically meaningful and differentiated evolutionary pattern. From the perspective of the changes in bearing's life cycle characteristics, the six types of indicators collaboratively reflect the evolution of operating status from different dimensions: see [link to relevant documentation]. Figure 3 (a) The mean value continued to rise. In the early stage (first 80-90 sampling points), it increased slowly with wear. In the middle stage (90-130 sampling points), it increased rapidly due to periodic impacts. In the later stage, it remained at a high level due to stable abnormal vibration sources. See also Figure 3(b) The variance initially remained stable at a high level (in the first 70-80 sampling points, with strong vibration dispersion), then dropped sharply in the middle stage (80-110 sampling points) due to increased clearance and roller eccentricity leading to a homogenization of vibration modes, before approaching a stable low value in the later stage; see also Figure 3 (c) The contrast ratio continuously increases, initially slowly with microscopic damage (first 60 sampling points), then rapidly increases due to fault expansion (60-120 sampling points), and finally remains high with fluctuations; see also Figure 3 (d) The correlation initially remained high and stable (approaching 1 in the first 50-70 sampling points), then dropped sharply due to a change in vibration mode caused by the fault (70-100 sampling points), and continued to decline in the later stages due to structural damage; see also Figure 3 (e) The energy exhibits a trend of "slow decay - sharp drop - stable low value". In the early stage (first 60 sampling points), it is slowly dissipated due to normal wear; in the middle stage (60-100 sampling points), it decreases rapidly due to microcracks and lubrication failure; and in the later stage (after 100 sampling points), it approaches stability due to severe deterioration. See also Figure 3 (f) Homogeneity continuously decreases. Initially (first 70-80 sampling points), it is close to 1 (uniform vibration). In the middle stage (80-120 sampling points), it drops rapidly due to local faults (inner ring scratches). In the later stage, it remains at a low value due to failure. The six types of indicators corroborate each other, jointly outlining the complete degradation path of the bearing from healthy operation to serious failure.

[0107] Step 3: Input the six types of image statistical features, process them through the designed stability-enhanced sparse PCA module, and output the fused feature vector. This includes the following sub-steps:

[0108] 3.1 The stability-enhanced sparse PCA method adopts the following strategy in the initialization phase:

[0109] This invention presents a stability-enhanced sparse PCA method designed using a dual initialization strategy of fixed random seed and normalized weight vector. Compared to traditional sparse PCA methods, the improvement lies in abandoning the single mode of relying solely on random initial weight generation. Instead, it adds a consistency constraint of "fixed random seed" and a standardization constraint of "normalized weight vector." The former ensures that the generation benchmark of initial weights is completely consistent under different experiments and data input scenarios, avoiding initial state fluctuations caused by differences in random seeds. The latter eliminates the optimization starting point deviation caused by uneven initial weight magnitudes by normalizing the initial weight vector to a unit magnitude. Therefore, it solves the problem of result fluctuations caused by initialization randomness in traditional sparse PCA from the source.

[0110] This embodiment sets the iteration count expansion (500) and the convergence shrinkage error (10). -6 );

[0111] 3.2 Perform standardization preprocessing on the six types of features extracted in step two to obtain the standardized feature vectors:

[0112] The standardization preprocessing eliminates dimensional differences between different features through a centralization operation; the specific formula is as follows:

[0113] Z = X - μ (9)

[0114] Where X is the feature vector, μ is the feature mean vector, and Z is the standardized feature vector.

[0115] 3.3 The core optimization part of the sparse PCA method with enhanced stability is designed to complete feature fusion and obtain the optimal weight matrix after the iteration rounds. This includes the following sub-steps:

[0116] Step 3.3.1 For the standardized feature vector obtained in step 3.2, calculate the projection score based on the current load vector, and iteratively obtain the optimal load vector that fits the elastic net constraint.

[0117] This step reconstructs the traditional variance maximization objective into a convex optimization problem with Elastic Net constraints. L1 regularization is used to impose a sparsity penalty on the feature weights (to suppress redundant feature weights), and L2 regularization constrains the weight magnitudes (to avoid overfitting and enhance stability). The specific sub-steps are as follows:

[0118] 3.3.1.1 Calculate the sample projection score based on the current load vector v:

[0119] First, define the optimization objective function with elastic net constraints as follows:

[0120]

[0121] Where v is the load vector, λ1 is the L1 regularization coefficient, λ2 is the L2 regularization coefficient, and v T ∑v is the variance maximization term, and λ1||v||1 is the Lasso penalty term, which induces sparsity. It is a ridge regression penalty term, which enhances stability. The optimization objective function of formula (10) provides a theoretical basis and constraint direction for the gradient calculation of formula (11) and the regularization denominator calculation of formula (12).

[0122] Then, iterative optimization is performed vector-by-load optimization: during the iteration process, the sample projection score α is calculated based on the current load vector v to be optimized. j =Z·v (where Z is the eigenvector after standardization in step 3.2).

[0123] 3.3.1.2 Calculating the gradient molecule: based on the projection score α j Given the eigenvector Z, calculate the gradient numerator using the following formula:

[0124] numerator = Z T ·α j (11)

[0125] Here, numerator is the gradient numerator, which is equivalent to the scaled form of the product of the covariance matrix ∑ and the current load vector v, and directly reflects the gradient direction of the "maximize variance" objective.

[0126] 3.3.1.3 Calculating the Regularization Denominator: Combining the variance term of the projected score with the L1 regularization coefficient, construct the regularization denominator using the following formula:

[0127] denominator = α j T ·α j +λ1 (12)

[0128] Where denominator is the regularization denominator, α j T ·α j λ1 is the variance term of the sample projection and L1 regularization coefficient. The denominator fusion achieves a balance between "variance maximization" and "sparse constraints", while implicitly containing the weight decay effect of L2 regularization.

[0129] 3.3.1.4 Preliminary Weight Update: The load vector is initially updated by using the ratio of the gradient numerator to the regularization denominator. This preserves the optimization information of the gradient direction while achieving the weight decay effect of L2 regularization through the denominator term, laying the foundation for subsequent sparsity operations. The formula is:

[0130] v temp =numerator / denominator (13)

[0131] Among them, v temp This is for the initial update of the load vector.

[0132] Step 3.3.2 Preliminary update of the load vector v in Step 3.3.1 temp Through the innovative incorporation of a soft thresholding operation, an explicitly sparsified load vector is obtained, namely the soft thresholding operator S. λ (v temp This operation, by actively truncating minute weight values, upgrades "indirect regularization constraints" to "direct sparsity intervention," explicitly preserving key features strongly correlated with bearing health. The soft thresholding operator formula is:

[0133]

[0134] in, It is a threshold term, determined by the L1 regularization coefficient λ1, L2 regularization coefficient λ2, and projection score α in the elastic net constraints. j Jointly decided; v temp It is the updated load vector, S λ (v temp ) is the soft-thresholded load vector, sign(v temp ) is the symbolic function (v) temp When >0, it is 1, v temp When <0, it is -1, v temp =0 when it is 0). This operation not only achieves the sparsification of the load vector, but also enhances the stability of the sparsity process through linkage with the L2 term, which is consistent with the optimization objective of formula (10).

[0135] Step 3.3.3 Explicitly sparsifying the load vector S from Step 3.3.2 λ (v temp After normalizing the weight vector and using a divide-by-zero protection mechanism, the robustly enhanced final updated load vector v is obtained. new .

[0136] Weight vector normalization and the division-by-zero protection mechanism are subsequent supplements and robustness enhancements to the soft thresholding operator. The soft thresholding operator provides the processing object for weight vector normalization, while the division-by-zero protection mechanism serves as a fallback for extreme cases of the soft thresholding operator (such as when all vector components are 0). The specific execution flow is as follows:

[0137] First, calculate the soft-thresholded load vector S. λ (v temp First, determine the norm of S; second, perform branching based on the norm result. If the norm is greater than the minimum value (e.g., 10^-10), then... λ (v temp Normalize the expression as shown in formula (15). If the norm is not greater than the minimum value, then directly let v new =0, to avoid numerical anomalies caused by dividing by zero.

[0138]

[0139] Among them, v new This is the updated load vector. For the soft thresholding operator, ∑v temp v is the product of the covariance matrix and the initial update load vector (equivalent to the gradient numerator in step 3.3.1.2). temp For the initial update of the load vector, |·|2 is the L2 norm.

[0140] Step 3.3.4 Robust Enhancement of Step 3.3.3: Final Update of Load Vector v newAfter the newly added square form reconstruction error calculation, the iterative monitoring index err, which reflects the feature representation effect, is obtained. This index amplifies small errors to further ensure the robustness of the algorithm, while enhancing the sensitivity to early bearing degradation, and providing accurate data support for iterative convergence judgment.

[0141] Using the squared form of reconstruction error as an iterative monitoring indicator, this quantifies the difference between the original feature vector and the reconstructed matrix from the weight matrix, reflecting the current weight matrix's representation effect on the features. The formula is as follows:

[0142]

[0143] Where W is the current weight matrix (composed of the v values ​​of each principal component). new Composition), ||·|| F It is the Frobenius norm, and its squared form can amplify small errors and enhance sensitivity to feature changes. err is the reconstruction error of the current iteration.

[0144] Step 3.3.5: The iterative monitoring index err from step 3.3.4 is combined with the weight matrix W of the current and historical iterations. new W old After "expanding the number of iterations (maximum 500 times) + tightening the tolerance (10) -6 The convergence mechanism of ")" obtains the algorithm convergence judgment result. This mechanism provides sufficient optimization space for complex feature data, and at the same time improves the fusion accuracy through tolerance tightening, ensuring that the optimal weight matrix output at the end of the iteration meets the core requirements of "accurate representation + stability and reliability".

[0145] The convergence of the algorithm is determined by calculating the difference between the weight matrices before and after the iteration. The specific formula is as follows:

[0146] ΔW=||W new -W old || F (17)

[0147] Among them, W old W is the weight matrix at the start of the current iteration round. new The weight matrix obtained after the current iteration (updated in step 3.3.3). ΔW is the Frobenius norm difference of the weight matrix. Convergence criterion: If ΔW < 10... -6 If the number of iterations reaches 500, stop the iteration and set the current W... new Use this as the optimal weight matrix; otherwise, return to 3.3.1 to continue the iteration.

[0148] 3.4 The optimal weight matrix W in step 3.3.5 newThe fused feature vector s, which condenses the core information, is obtained by performing a fusion feature vector calculation operation on the standardized feature vector Z obtained in step 3.2. The calculation formula is as follows:

[0149] s = Z·W new (18)

[0150] Where s is the fusion feature vector (each row corresponds to the fusion feature of one sample, and each column corresponds to the feature contribution of one principal component), Z is the standardized bearing feature vector, and W is the fusion feature vector. new The optimal weight matrix for sparse PCA output with enhanced stability.

[0151] Step 4: Use the state change detection function to identify the fused feature vector and identify the end time of the healthy state.

[0152] The essence of health status identification is to classify each value in a data sequence according to its sign (positive or negative) to identify points of state change. Specifically, elements greater than 0 are marked as 1, elements less than 0 are marked as 0, and points where 0 changes to 1 or 1 changes to 0 represent state transitions.

[0153] Suppose we have a data sequence {x1, x2, ..., x} n}, where each x i Let x be a real number. Define a function f(x) to predict the starting point of degradation, as shown in formula (19):

[0154]

[0155] Where x is the characteristic value at different times.

[0156] Define a state change detection function g(x) i ,x i+1 To identify state change points, the formula is shown in (20):

[0157]

[0158] Based on the image statistical feature-based health status recognition method provided in this embodiment of the invention, the starting point prediction of different bearings is performed, and the numerical prediction results are shown in Table 1. The bearing dataset of Xi'an Jiaotong University includes 3 types of working conditions, with 5 bearings in each type of working condition, namely Bearing1_1, Bearing1_2, Bearing1_3, Bearing1_4, Bearing1_5; Bearing2_1, Bearing2_2, Bearing2_3, Bearing2_4, Bearing2_5; Bearing3_1, Bearing3_2, Bearing3_3, Bearing3_4, Bearing3_5.

[0159] Table 1. Starting point prediction for different datasets

[0160]

[0161] See Figure 4 , Figure 4 One result is shown, representing the sparse PCA results for bearing Bearing1_1. The black curve represents the time-series trend of the SPCA fusion characteristics, reflecting the continuous evolution of the bearing's condition. The black horizontal line represents the state abrupt change line. After the starting point, the "continuous increase + intensified fluctuation" of the vibration amplitude corresponds to the rapid development of internal bearing faults, necessitating the initiation of remaining life prediction.

[0162] See Figure 5 , Figure 5 The status identification results of bearing Bearing1_1 are displayed, and... Figure 2 As can be seen from the comparison, the health status identification method of the present invention is accurate; the black waveform in the figure represents the vibration amplitude time sequence of the bearing throughout its entire life cycle, intuitively presenting the changes in signal energy; the black vertical line represents the "life prediction starting point" corresponding to the trend change detection graph, accurately locating the critical moment when the vibration signal changes from "stable small fluctuations" to "high frequency impact".

[0163] The above description is a specific illustration of the present invention, and not a limitation thereof. Those skilled in the art can make various equivalent technical solutions without departing from the scope of the present invention; therefore, all equivalent technical solutions should be included within the protection scope of the present invention.

Claims

1. A health state recognition method based on image statistical features, characterized in that: The method comprises the following steps: Step one, using the sensor to collect the original vibration signal of the bearing, using short-time Fourier transform to convert the original vibration signal into a time-frequency domain color image, and using gray scale transformation to convert the time-frequency domain color image into a gray scale image; Step two, extracting six types of image statistical features: mean, variance, contrast, correlation, energy and homogeneity from the gray scale image; Step three, taking the six types of image statistical features as input, and outputting a fusion feature vector through the designed stability-enhanced sparse PCA module; Step four, using a state change detection function to identify the fusion feature vector, and identifying the end time of the healthy state.

2. The health state recognition method based on image statistical features according to claim 1, characterized in that: In step one, the gray scale transformation adopts a weighted summation method to convert the RGB three-channel information into a single-channel gray scale value. 3.The health state recognition method based on image statistical features according to claim 1, characterized in that: In step two, six types of image statistical features are extracted from the gray scale image according to the gray scale co-occurrence matrix, and the specific formula is as follows: Assume that the gray scale image I is an M×N matrix, where M is the number of rows of the image, N is the number of columns of the image, and I(i,j) represents the pixel gray scale value of the i-th row and j-th column in the image. Then the calculation of the mean μ of the image is: The variance σ of the image 2 is calculated as: The calculation formula of the contrast Contrast is: where N g is the number of gray levels, and P(i,j) is the element in the i-th row and j-th column of the GLCM. The calculation formula of the correlation Correlation is: where μ i and μ j are the mean of the GLCM row and column, respectively, and σ i and σ j are the standard deviation of the GLCM row and column, respectively. The calculation formula of the energy Energy is: The calculation formula of the homogeneity Homogeneity is:

4. The health state recognition method based on image statistical features according to claim 1, characterized in that: In step three, the following sub-steps are included: 3.1 The stability-enhanced sparse PCA method initialization stage adopts a double initialization strategy of fixed random seed and weight vector unitization for design; 3.2 Standardization preprocessing is performed on the six types of image statistical features obtained in step two to obtain a standardized feature vector; 3.3 The core optimization part of the stability-enhanced sparse PCA method is designed to complete feature fusion, and the optimal weight matrix is obtained after the iteration round is completed; 3.4 The optimal weight matrix and the standardized feature vector are subjected to fusion feature vector calculation operation to obtain a fusion feature vector that condenses the core information.

5. The health state recognition method based on image statistical features according to claim 4, characterized in that: The specific sub-steps of step 3.3 include: 3.3.1 Based on the current load vector, the projection score, gradient and regularization term are calculated and the weight is preliminarily updated, and the specific sub-steps are as follows: 3.3.1.1 Calculate the sample projection score according to the current load vector v: First, define the optimization objective function with elastic net constraint as follows: where v is the load vector, λ1is the L1 regularization coefficient, λ2is the L2 regularization coefficient, v T ∑v is the variance maximization term, λ1||v||1is the Lasso penalty term, inducing sparsity, is the ridge regression penalty term, enhancing stability; During the iteration, first the sample projection score a is computed from the current load vector v j = Z - v, and the gradient computation and preliminary update is done by the following steps: 3.3.1.2 Compute gradient molecules: based on projection scores a j With the eigenvector Z, compute gradient molecules, formula is: numerator = Z T • a j (11) Where numerator is the gradient numerator, which is equivalent to the scaling form of the product of the covariance matrix ∑ and the current load vector v; 3.3.1.3 Calculate the regularization denominator: combine the variance term of the projection score and the L1 regularization coefficient to construct the regularization denominator, and the formula is as follows: denominatro = a j T • a j + l1 (12) wherein denominator is the regularization denominator, a j T • a j is the variance term of sample projection, and λ1is the L1 regularization coefficient; 3.3.1.4 Preliminary weight update: through the ratio of the gradient numerator and the regularization denominator, the load vector is preliminarily updated, which not only retains the optimization information in the gradient direction, but also realizes the weight attenuation effect of L2 regularization through the denominator term, laying a foundation for subsequent sparse operation; The formula is as follows: v temp = numerator / denominator (13) where v temp is the preliminary updated load vector; 3.3.2 On the updated v temp The explicit sparse processing is performed to obtain a soft threshold operator, and a formula is as follows: wherein is a threshold term; v temp is an updated payload vector, S λ (v temp ) is a soft thresholded payload vector, sign(v temp ) is a sign function (1 for v temp > 0, -1 for v temp < 0, and 0 for v temp = 0); 3.3.3 Weight vector unitization and zero division protection mechanism; The weight vector unitization and the division by zero protection mechanism are the follow-up supplement and robustness enhancement links of the soft thresholding operator operation. The soft thresholding operator provides the processing object for the weight vector unitization, and the division by zero protection mechanism is the bottom line for the extreme case of the soft thresholding operator. The specific execution process is as follows: First, the norm of the soft-thresholded load vector S λ (v temp ) is calculated; second, based on the norm result, a branch is determined, if the norm is greater than a minimum value, the S λ (v temp ) is normalized, as shown in equation (15), if the norm is not greater than the minimum value, v new = 0 is directly set to avoid numerical anomalies caused by division by zero; where v new is the updated load vector, is the soft thresholding operator, ∑v temp is the product of the covariance matrix and the preliminary updated load vector, v temp is the preliminary updated load vector, |·|2 is the L2 norm.

6. The health state recognition method based on image statistical features according to claim 5, characterized in that: In step 3.4, the process of calculating the fusion feature vector is: The optimal weight matrix W screened out based on step 3.3 new The normalized feature vector Z is multiplied by the optimal weight matrix to obtain a fusion feature vector of condensed core information, and the calculation formula is: s = Z - W new (18) where s is the fused feature vector, Z is the normalized bearing feature vector, W new is the optimal weight matrix for the stability enhanced sparse PCA output.

7. The health state recognition method based on image statistical features according to claim 1, characterized in that: In step four, it is assumed that there is a data sequence {x1,x2,…,x} n }, where each x i Let x be a real number. Define a function f(x) to predict the starting point of degradation, as shown in formula (19): Wherein, x is the feature value at different times; Define a state change detection function g(x i ,x i+1 ) to identify state change points, as shown in equation (20):

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