Bearing health index construction method and system based on adaptive Gaussian mixture model

Abstract

The invention discloses a bearing health index construction method and system based on an adaptive Gaussian mixture model, and the method comprises the steps: carrying out the sampling of the detection data of the operation condition of a full-life work cycle of a bearing, and obtaining a data set; extracting data from the data set to obtain a feature data set; performing an AP clustering algorithm on the feature data set to obtain a sub-Gaussian component number of a GMM model; substituting the sub-Gaussian fraction into a GMM probability density definition formula, and carrying out iterative updating on the sub-Gaussian fraction by utilizing an EM algorithm until the number of iterations is reached, so as to obtain a GMM parameter model; carrying out dimension reduction on the GMM parameter model to output health indexes, and carrying out normalization on the health indexes to generate final health indexes; the method has the advantages that the stability and the accuracy of the clustering calculation result are improved, and the generated health index is relatively accurate.

Description

Technical Field

[0001] The present invention relates to the technical field of rolling bearing life prediction health index construction, and particularly relates to a method and system for constructing a bearing health index based on an adaptive Gaussian mixture model. Background Art

[0002] Bearings are key components of typical rotating machinery such as generators, turbines, rotary compressors, and transmission gearboxes, and are widely used in many fields such as aviation, aerospace, chemical industry, and manufacturing. In actual use, the degradation or failure of bearings may lead to unexpected failures of mechanical systems, and may even cause significant economic losses and casualties. Research shows that bearing failures and damages account for about 45% - 55% of mechanical failures. Therefore, it is necessary to conduct in-depth research on the failure of rolling bearings of mechanical equipment and carry out failure early warning. Extracting degradation characteristic information from bearing vibration signals and constructing it into an index for describing the bearing health is called a health indicator (Health Indicator, HI). The bearing health index is a self-comparative evaluation method, which eliminates the influence of assembly and external environment on the state evaluation. The construction of the bearing health index will directly affect the decision-maker's grasp of the actual situation in actual use.

[0003] Traditional methods for constructing bearing health indexes mostly rely on single-dimensional characteristic parameters and describe the bearing degradation trend through one-dimensional curves. However, in actual scenarios, the degradation process of bearings is often accompanied by complex non-linear characteristic changes. Single characteristics are easily interfered by external factors and it is difficult to comprehensively characterize the degradation information of different stages of bearings. Such methods ignore the influence of factors such as different working scenarios, assembly differences, and instantaneous impacts during bearing operation on the feature distribution, resulting in poor robustness of the constructed bearing health indexes. Although some studies adopt multi-feature fusion technology to reduce redundancy, traditional linear dimensionality reduction methods have inherent limitations in modeling changes over time and are difficult to capture the dynamic relationship between characteristic parameters and the equipment degradation process, resulting in disadvantages such as losing key state information.

[0004] At present, health assessment methods based on probability models have been developed and popularized. For example, the GMM method based on probability distribution modeling can more accurately represent the characteristic parameters of bearing degradation by establishing the joint probability distribution of multivariate Gaussian components and distinguish normal and abnormal states in index construction. However, the traditional Gaussian mixture model (GMM) method still has disadvantages. For example, in the Gaussian mixture probability density model disclosed in an improved CHSMM rolling bearing remaining life prediction method disclosed in Chinese Patent Publication No. CN108776017A, the number of sub-Gaussian components needs to be preset in advance, relying on past data and traditional experience, which cannot be accurately preset for variable actual scenarios. Moreover, when fusing high-dimensional features, the degradation trend constraint is not introduced, resulting in errors in the accuracy of actual prediction and reducing the rationality of life prediction. In the establishment and calculation of the Gaussian mixture model, the deficiencies of traditional clustering algorithms in initialization sensitivity and convergence stability further restrict the performance of the GMM model, ultimately leading to inaccurate health indicators generated based on the above defects. Summary of the Invention

[0005] The technical problem to be solved by the present invention is that in the GMM modeling process of the existing technology for constructing bearing health indicators, the number of Gaussian components cannot be accurately preset, ultimately resulting in inaccurate health indicators generated.

[0006] The present invention solves the above technical problems through the following technical means: A method for constructing bearing health indicators based on an adaptive Gaussian mixture model, including:

[0007] S1. Sampling the detection data of the operating conditions of the bearing throughout its life cycle to obtain a data set;

[0008] S2. Extracting data from the data set to obtain a feature data set;

[0009] S3. Using the AP clustering algorithm for the feature data set to obtain the number of sub-Gaussian components of the GMM model;

[0010] S4. Substituting the number of sub-Gaussian components into the GMM probability density definition formula and iteratively updating it using the EM algorithm until the number of iterations is reached to obtain the GMM parameter model;

[0011] S5. Reducing the dimension of the GMM parameter model to output a health indicator, and normalizing the health indicator to generate the final health indicator.

[0012] Beneficial effects: The present invention uses the AP clustering algorithm to automatically determine the number of GMM sub-Gaussian components, which can solve the disadvantage that the parameters in the traditional Gaussian mixture model need to be preset, reduce subsequent related manual losses, improve the stability and accuracy of the clustering calculation results, and ultimately generate relatively accurate health indicators.

[0013] Furthermore, S2 includes:

[0014] S201. Calculate the monotonicity calculation result of the data set by taking the absolute value of the difference between the number of data points that increase relative to the previous point and the number of data points that decrease relative to the previous point in the data set, and then dividing by the difference between the sequence length of the data set and 1.

[0015] S202. Calculate the time correlation calculation result of the current data point in the data set by dividing the covariance between the current data point and its acquisition time by the difference between the standard deviation of each data point and the standard deviation of the acquisition time corresponding to each data point.

[0016] S203. Add the monotonicity calculation result and the time correlation calculation result of the current data point and divide by 2 to obtain the characteristic factor. Extract the data points in the data set whose characteristic factor values are greater than the set threshold as the characteristic data set.

[0017] Further, S3 includes:

[0018] The process of the AP clustering algorithm is to take the negative Euclidean distance between the i-th element and the j-th element in the characteristic data set as the element in the i-th row and j-th column of the similarity matrix. Set a parameter P, which is the diagonal element of the similarity matrix and is initialized to the median value of the similarity matrix. Set the maximum number of iterations. In each iteration process, calculate the attractiveness matrix according to the similarity matrix, calculate the membership matrix according to the attractiveness matrix, and use the damping factor to decay the attractiveness matrix and the membership matrix respectively. Iterate repeatedly. After the iteration is completed, add the attractiveness matrix and the membership matrix to obtain the decision matrix. The samples in the decision matrix that are greater than 0 are the clustering center points, and the number of clustering center points is used as the number of sub-Gaussian components. After each round of clustering by the AP clustering algorithm, calculate the BWP index. If the BWP index decreases compared with the previous round, lower the parameter P, otherwise increase the parameter P, and perform the next round of clustering until a stable number of clusters is generated. This stable number of clusters is used as the final number of sub-Gaussian components. The BWP index is the average value obtained by summing the difference between the minimum inter-class distance and the average intra-class distance of each sample in each class divided by the sum of the two.

[0019] Further, S4 includes:

[0020] The sub-Gaussian component number is the number of Gaussian components. Substitute the feature dataset, the sub-Gaussian component number, the mean vectors of the Gaussian components, and the covariance matrices of the Gaussian components into the GMM probability density definition formula, and use the EM algorithm to calculate the posterior probability that each data point belongs to each Gaussian component. Use this posterior probability to calculate the covariance matrix of the Gaussian components to update the covariance matrix of the Gaussian components, and substitute the updated covariance matrix of the Gaussian components into the GMM probability density definition formula, and iterate continuously until the number of iterations is reached. Substitute the finally calculated covariance matrix of the Gaussian components into the GMM probability density definition formula to obtain the GMM parameter model.

[0021] Further, S5 includes:

[0022] Calculate the posterior probability that each data point in the feature dataset belongs to each Gaussian component for the GMM parameter model to obtain a posterior probability matrix. At the same time, calculate the Spearman rank correlation coefficient of each data point in the feature dataset, filter out the data points whose Spearman rank correlation coefficient is greater than or equal to the preset value, calculate the posterior probability that it belongs to each Gaussian component, and obtain the filtered posterior probability matrix; perform Z-score normalization on the filtered posterior probability matrix to obtain a normalized matrix, calculate the covariance matrix of the normalized matrix, perform eigenvalue decomposition on it using the PCA principal component analysis method, take the eigenvector corresponding to the largest eigenvalue as the projection direction, project the covariance matrix of the normalized matrix, obtain a health index, and normalize the health index to generate the final health index.

[0023] The present invention also provides a bearing health index construction system based on an adaptive Gaussian mixture model, including:

[0024] A data acquisition module for sampling the detection data of the operating conditions of the bearing during the entire life cycle to obtain a dataset;

[0025] A data extraction module for extracting data from the dataset to obtain a feature dataset;

[0026] A Gaussian component acquisition module for obtaining the sub-Gaussian component number of the GMM model for the feature dataset using the AP clustering algorithm;

[0027] A Gaussian model construction module for substituting the sub-Gaussian component number into the GMM probability density definition formula and iteratively updating it using the EM algorithm until the number of iterations is reached to obtain the GMM parameter model;

[0028] A health index generation module for outputting a health index by reducing the dimension of the GMM parameter model and normalizing the health index to generate the final health index.

[0029] Further, the data extraction module is further used for:

[0030] S201. Calculate the monotonicity calculation result of the data set by taking the absolute value of the difference between the number of data points that rise relative to the previous point and the number of data points that fall relative to the previous point in the data set, and then dividing it by the difference between the sequence length of the data set and 1.

[0031] S202. Calculate the time correlation calculation result of the current data point in the data set by dividing the covariance between the current data point and its acquisition time by the difference between the standard deviation of each data point and the standard deviation of the acquisition time corresponding to each data point.

[0032] S203. Add the monotonicity calculation result and the time correlation calculation result of the current data point and divide by 2 to obtain the characteristic factor. Extract the data points in the data set whose characteristic factor values are greater than the set threshold as the characteristic data set.

[0033] Furthermore, the Gaussian component acquisition module is also used for:

[0034] The process of the AP clustering algorithm is to use the negative Euclidean distance between the i-th element and the j-th element in the characteristic data set as the element in the i-th row and j-th column of the similarity matrix. Set a parameter P, which is the diagonal element of the similarity matrix and is initialized to the median of the similarity matrix. Set the maximum number of iterations. In each iteration, calculate the attractiveness matrix according to the similarity matrix, calculate the membership matrix according to the attractiveness matrix, and use the damping factor to decay the attractiveness matrix and the membership matrix respectively. Iterate repeatedly. After the iteration is completed, add the attractiveness matrix and the membership matrix to obtain the decision matrix. The samples in the decision matrix greater than 0 are the clustering center points, and the number of clustering center points is used as the number of sub-Gaussian components. After each round of clustering of the AP clustering algorithm, calculate the BWP index. If the BWP index decreases compared with the previous round, lower the parameter P, otherwise increase the parameter P, and perform the next round of clustering until a stable number of clusters is generated. This stable number of clusters is used as the final number of sub-Gaussian components. The BWP index is the average value obtained by summing the difference between the minimum inter-class distance and the average intra-class distance of each sample in each class divided by the sum of the two.

[0035] Furthermore, the Gaussian model construction module is also used for:

[0036] The number of sub-Gaussian components is the number of Gaussian components. Substitute the characteristic data set, the number of sub-Gaussian components, the mean vector of the Gaussian components, and the covariance matrix of the Gaussian components into the GMM probability density definition formula. Use the EM algorithm to calculate the posterior probability of each data point belonging to each Gaussian component. Use this posterior probability to calculate the covariance matrix of the Gaussian components to update the covariance matrix of the Gaussian components, and substitute the updated covariance matrix of the Gaussian components into the GMM probability density definition formula. Iterate continuously until the number of iterations is reached. Substitute the finally calculated covariance matrix of the Gaussian components into the GMM probability density definition formula to obtain the GMM parameter model.

[0037] Further, the health index generation module is further configured to:

[0038] Calculate the posterior probability of each data point in the feature dataset belonging to each Gaussian component for the GMM parameter model to obtain a posterior probability matrix. At the same time, calculate the Spearman rank correlation coefficient of each data point in the feature dataset, filter out the data points with a Spearman rank correlation coefficient greater than or equal to a preset value, calculate its posterior probability of belonging to each Gaussian component, and obtain a filtered posterior probability matrix; perform Z-score normalization on the filtered posterior probability matrix to obtain a normalized matrix, calculate the covariance matrix of the normalized matrix, perform eigen-decomposition on it using the PCA principal component analysis method, take the eigenvector corresponding to the largest eigenvalue as the projection direction, project the covariance matrix of the normalized matrix, obtain a health index, and normalize the health index to generate a final health index.

[0039] The advantages of the present invention are as follows:

[0040] (1) The present invention uses an improved AP clustering algorithm to automatically determine the number of GMM sub-components, which can solve the drawback that the parameters in the traditional Gaussian mixture model need to be preset, reduce subsequent related manual losses, and the subsequent model can dynamically adjust the clustering number through data-driven, and is more adaptable to the complex and variable bearing degradation data distribution in practical applications. In the establishment and calculation of the model, the improved AP clustering algorithm can enhance stability, construct an iterative optimization mechanism including a momentum damping coefficient, combine with the BWP quantization evaluation system, establish a dynamic adjustment strategy in the model, avoid problems such as interference and oscillation, and improve the stability and accuracy of the clustering calculation results, so that the finally generated health index is relatively accurate.

[0041] (2) The present invention also uses the feature fusion of various parameters of the degradation trend to improve the robustness of the constructed index, and introduces a feature index with high correlation based on the Spearman rank correlation coefficient screening. Combining the methods of Z-score normalization and PCA dimensionality reduction can achieve the standardization and simplicity of index establishment, screen the features with a Spearman rank correlation coefficient greater than or equal to a preset value as parameters, eliminate noise interference and inaccurate non-monotonic components, ensure that the correlation between the health index and the time parameter meets the requirements, avoid fluctuation interference, and solve the parameter redundancy and corresponding interference problems in traditional multi-feature fusion. In actual calculation, standardization processing is performed to eliminate the unit difference of parameters, so that the index has unified comparability under different sensor data or working conditions, and enhances the universality of the model in practical applications.

[0042] (3) The present invention can perform end-to-end automation in the whole process of modeling, reduce the dependence on experts, and achieve end-to-end automation from feature extraction, clustering to index generation. After being put into use, it can reduce subjective intervention, without relying on fault mechanism knowledge or manual experience to set parameters, and is applicable to data-driven scenarios. In theory, the computing efficiency is improved and the convergence is optimized. The convergence condition design of the improved AP clustering is used, combined with the parameter update of the EM algorithm. In the calculation, the damping factor and the change amount threshold converge quickly. The damping factor and the change amount threshold control the number of iterations, reduce the computing time, and meet the real-time monitoring requirements in actual production work. The global optimal approximation is achieved. The EM algorithm theory guarantees the parameter convergence, avoids the traditional gradient descent falling into the local optimum, and improves the model accuracy. Finally, the health index is normalized, that is, the index is unified in the interval [0, 1], and the general threshold and evaluation criteria of the model are set. The normalization of the index can simplify the setting of the alarm threshold. For example, when the health index HI > 0.8, maintenance is triggered. In the actual work scenario, it is applicable to the unified supervision and control of multiple devices. For observers, the smooth and monotonic health index curve is convenient for maintenance personnel to intuitively judge the degradation stage, which is beneficial for maintenance personnel to intuitively judge whether equipment maintenance is needed according to the health index (such as when the health index HI > 0.8, maintenance is triggered), and supports the visualization and accuracy of decision-making. Description of the Drawings

[0043] Figure 1 It is a flowchart of the method for constructing a bearing health index based on an adaptive Gaussian mixture model disclosed in an embodiment of the present invention;

[0044] Figure 2 It is a flowchart of obtaining the initial value of the GMM model by using the Ap clustering algorithm in the method for constructing a bearing health index based on an adaptive Gaussian mixture model disclosed in an embodiment of the present invention;

[0045] Figure 3 It is a flowchart of optimizing the GMM model by using the EM algorithm in the method for constructing a bearing health index based on an adaptive Gaussian mixture model disclosed in an embodiment of the present invention;

[0046] Figure 4 It is a flowchart of using PCA to extract the index f describing the bearing health in the method for constructing a bearing health index based on an adaptive Gaussian mixture model disclosed in an embodiment of the present invention. Detailed Embodiments

[0047] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0048] Example 1

[0049] like Figure 1 As shown, an embodiment of the present invention provides a method for constructing a bearing health index based on an adaptive Gaussian mixture model, comprising the following steps:

[0050] S1. Utilize various sensors to detect the operating conditions of the bearing throughout its entire working life cycle, sample the detection data, and obtain a series of sampled data sets X = {x1, x2, x3...}, where x1 represents the first sampling sequence in the data set, i.e., the data point described below. This data point is a data sequence under a certain operating condition sampled over a period of time.

[0051] S2. Extract data from the data set to obtain a feature data set. The detailed process is as follows: The method for extracting the feature data set can be set according to actual needs. The present invention uses the method of calculating the monotonicity and time correlation of each data set indicator to determine whether the data set is characteristic.

[0052] Monotonicity calculation formula:

[0053]

[0054] Among them, x up is the number of data points in the data set that rise relative to the previous point, x dowm M is the number of data points in the data set that fall relative to the previous point, and N is the length of the data sequence. x is the monotonicity calculation result of the data set.

[0055] Time correlation calculation formula:

[0056]

[0057] Among them, cov(x,t) is the covariance of a data point in the data set and the sampling time series of the data point, σ x , σ t They are the standard deviation of the data series corresponding to a data point and the time series corresponding to the data point.

[0058] The feature data set selection is determined according to the following formula:

[0059]

[0060] Let D be the characteristic factor. The larger the characteristic factor, the more representative its characteristics are. Extract the data points with the value of the characteristic factor greater than the set threshold as the characteristic data set Y = {y1, y2, y3...}, where y1 is the first data point in the characteristic data set, and this data point is the operating condition data within a certain period of time.

[0061] S3. Use the AP clustering algorithm for the characteristic data set to obtain the number of sub-Gaussian components of the GMM model; the process of the AP clustering algorithm is to take the negative Euclidean distance between the i-th element and the j-th element in the characteristic data set as the element in the i-th row and j-th column of the similarity matrix, set a parameter P, which is the diagonal element of the similarity matrix, and the initial value is the median of the similarity matrix; set the maximum number of iterations; in each iteration process, calculate the attractiveness matrix according to the similarity matrix, calculate the membership matrix according to the attractiveness matrix, and use the damping factor to decay the attractiveness matrix and the membership matrix respectively, and iterate repeatedly. After the iteration is completed, add the attractiveness matrix and the membership matrix to obtain the decision matrix. The samples greater than 0 in the decision matrix are the clustering centers, and the number of clustering centers is used as the number of sub-Gaussian components; after each round of clustering of the AP clustering algorithm, calculate the BWP index. If the BWP index decreases compared with the previous round, lower the parameter P, otherwise increase the parameter P, and perform the next round of clustering until a stable number of clusters is generated, and this stable number of clusters is used as the final number of sub-Gaussian components; the BWP index is the average value obtained by summing the difference between the minimum inter-class distance and the average intra-class distance of each sample in each class divided by the sum of the two. As Figure 2 shown, the detailed formula calculation process is as follows:

[0062] Calculate the negative Euclidean distance between the extracted characteristic data sets as the similarity matrix and input it into the AP clustering algorithm:

[0063] S(i,j) = -||y i -y j || 2

[0064] where S(i,j) represents the similarity between point i and point j; y i , y j are samples in the characteristic data set Y.

[0065] In the AP clustering algorithm, a parameter value p also needs to be set, that is, the diagonal element S(t,t) of the similarity matrix S(i,j), which indicates the tendency of each data point to be a clustering center. The higher the parameter value, the more clustering centers are generated. Usually, it is set to the median of the similarity matrix. The initial parameter value of the present invention is taken as the median of the similarity matrix.

[0066] Selection of updating the clustering center by passing through two matrices between data points:

[0067]

[0068] Among them, R n+1 (i, j) is the attraction matrix, indicating the degree to which point j is suitable as the clustering center of point i after the (n + 1)-th iteration; A n+1 (i, j) is the membership matrix, indicating the suitability of point j to select point i as the clustering center after the (n + 1)-th iteration. To prevent oscillation, a damping factor λ (default is 0.5) is introduced to attenuate the attraction matrix and the membership matrix, so as to adjust the convergence speed and improve the iteration stability:

[0069] X new = λ * X old + (1 - λ) * X new

[0070] Among them, X old 、X new are respectively substituted with the results of the previous and current iterations of the attraction matrix to obtain the updated result of the current iteration result. The iterative update of the membership matrix also uses the above formula.

[0071] Through the above calculation formula for iteration, R n+1 (i, j) and A n+1 (i, j) values are repeatedly updated.

[0072] After meeting the convergence condition, the iteration is completed, and the decision matrix C(i, j) is calculated. The samples with positive values on the diagonal of the decision matrix are the clustering center points. From this, the number of sub-Gaussian components can be obtained. The relevant formula of the decision matrix is as follows:

[0073] C n (i, j) = R n (i, j) + A n (i, j)

[0074] C n (k, k) = R n (k, k) + A n (k, k) > 0

[0075] Among them, C n (i, j) is the decision matrix for point j to be the clustering center of point i after the n-th iteration, C n (k, k) is the diagonal element of the decision matrix, and the sample with C n (k, k) being positive is the clustering center point.

[0076] The number of all sample points that meet the above conditions is the clustering number, that is, the number of sub-Gaussian components, denoted as K.

[0077] The convergence condition can be set as the number of iterations or the threshold of the degree of change. In the present invention, the threshold ε of the change amount is set to judge whether the algorithm converges. The convergence condition set by the threshold of the degree of change is as follows:

[0078] max{|R n+1 (i,j)-R n (i,j)|}<ε

[0079] max{|A n+1 (i,j)-A n (i,j)|}<ε

[0080] For the evaluation of the clustering effect, the present invention designs an improved AP clustering iteration method based on between-within part (BWP). The specific operation is as follows:

[0081] The between-class and within-class distances after clustering are evaluated by the BWP index, and the value range is [-1, 1]. The larger the value, the better the clustering effect. The BWP index can be calculated by the following formula.

[0082]

[0083] Among them, n represents the total number of samples; K represents the number of clusters; n j represents the number of samples in the j-th class; b d (j,i), w d (j,i) represent the minimum between-class distance and the average within-class distance of the i-th sample in the j-th class respectively. b d (j,i), w d (j,i) can be calculated by the following formulas respectively.

[0084]

[0085] In the formula: n k represents the number of samples in the k-th class; represents the p-th sample in the k-th class; represents the i-th sample in the j-th class.

[0086] After each round of clustering, the BWP index is calculated to adjust the parameter value p. If the BWP index decreases compared with the previous round, the parameter value p is lowered; otherwise, the parameter value p is increased until a stable number of clusters is generated. Compared with the initial value selection of the traditional GMM model, the AP clustering algorithm does not require manual presetting of the number of sub-Gaussian components. While ensuring the stability of the results, it is more suitable for complex data distributions. The BWP index is used to judge the AP clustering effect, improving the clustering quality, and the obtained number of sub-Gaussian components is more characteristic.

[0087] S4. Substitute the sub-Gaussian component scores into the GMM probability density definition formula and use the EM algorithm to iteratively update them until the number of iterations is reached to obtain the GMM parameter model; as Figure 3 shown, the detailed process is as follows:

[0088] Construct a GMM probability density distribution model, and use the feature data set Y = {y1, y2, y3...} obtained in S2 as input and substitute it into the GMM probability distribution model. The probability density definition of the constructed GMM is as follows:

[0089]

[0090] where: θ = (α1,…,α K ; μ1,…,μ K ; ξ1,…ξ k ); K represents the number of Gaussian components (obtained from S3 above); α k represents the weight of the k-th Gaussian component, satisfying μ k ∈R d×d represents the mean vector of the k-th Gaussian component; ξ k represents the covariance matrix of the k-th Gaussian component; N(y i |μ k ,ξ k ) represents the probability density function of the k-th Gaussian component,

[0091] where, the calculation formula of N(y i |μ k ,ξ k ) is as follows:

[0092]

[0093] where, d represents the dimension of the sample, referring to the number of features each sample has. For example, for hardness and crack length, then d = 2 at this time.

[0094] In the existing parameter solving methods of the Gaussian mixture model, the traditional method usually adopts maximum likelihood estimation. However, due to the existence of latent variables, it may be difficult in directly optimizing the likelihood function and other aspects, resulting in the need to combine more complex methods, such as using gradient descent or Newton's method. And combining too many methods may lead to inconsistent parameters and complex calculations, especially it will become difficult to solve in the case of high-dimensional data or more components. Therefore, the present invention uses the EM algorithm to optimize the parameter solving of the GMM, that is, iteratively solve the parameters through the E step and the M step to avoid directly solving the function. Specifically, in the E step, calculate the posterior probability that each data point belongs to its respective Gaussian model according to the current parameters:

[0095]

[0096] Avoid information loss caused by hard assignment by soft - assigning the attribution probabilities of data points to multiple components.

[0097] The M - step updates the parameters to maximize the log - likelihood:

[0098]

[0099] Update the weight α k :

[0100]

[0101] Update the mean vector μ k :

[0102] <s

[0103] The above process can be summarized as: Assume that the data is composed of multiple Gaussian distributions. Each Gaussian distribution represents a subclass or component. The model describes the data distribution by estimating the parameters (mean, covariance, mixing coefficient) of each Gaussian component and synthesizes them into a probability density. θ=(α1,…,α K ; μ1,…,μ K ; ξ1,…ξ k ) is the set of parameters to be solved. The overall solution process is an update process. The weight α k is initially initialized, for example, equal to 1 / k, and then approximates the actual value with iteration. For example, in the (n + 1)-th iteration, first calculate the posterior probability, then calculate the weight and mean vector according to the posterior probability. The covariance matrix of the (n + 1)-th iteration can be obtained using the weight, mean vector, and posterior probability after the (n + 1)-th iteration. Thus, the parameter update has an analytical solution, without a complex optimization process and with high computational efficiency. Repeatedly iterate the E - step and M - step until the final parameters converge, and then a GMM parameter model can be established. Through the EM algorithm, the robustness of the GMM model for estimating parameters is improved, the computational complexity is reduced, the theoretical convergence is guaranteed, and the risk of local optima is reduced.

[0104] S5. The GMM parameter model reduces the dimension to output health indicators, and normalizes the health indicators to generate the final health indicators; as Figure 4 shown, the detailed process is as follows:

[0105] After the adaptive GMM modeling is completed in S4, although the model can describe different health states of the bearing through probability distributions, the high-dimensional posterior probability matrix (with dimensions of the number of samples n × the number of Gaussian components K) still cannot be directly used as a health indicator. Existing traditional methods generally directly select the probability of a certain component or perform a simple weighted average, but this will ignore the co-variation between components and the monotonicity requirement of the degradation trend. Therefore, the present invention proposes a PCA fusion method based on the Spearman's rank correlation coefficient (ρ s ).

[0106] The posterior probability γ ik represents the probability that the sample y i belongs to the k-th Gaussian component, and its value range is [0, 1], and it satisfies Each Gaussian component corresponds to a potential health state of the bearing (such as a healthy state, early wear, severe fault, etc.). Therefore, γ ik can be regarded as the probability projection of the sample in the state space. For the optimized GMM parameter model, calculate the posterior probability that each sample y i belongs to each Gaussian component:

[0107]

[0108] Obtain the posterior probability matrix Γ ∈ R n×K , which characterizes the membership degree of the sample under different health states.

[0109] The GMM parameter model describes the working state of the bearing through the probability distributions of multiple sub-Gaussian components, but not all sub-components are related to the degradation process. Some components may represent noise interference, instantaneous shocks, or non-monotonic transition states. Adding these components during analysis will affect the quality of the constructed health indicator.

[0110] To strengthen the monotonicity of the degradation trend of the health indicator and screen the GMM components that are significantly correlated with time (or the degree of degradation), the Spearman's rank correlation coefficient (Spearman's rank correlation coefficient, ρ s ) is introduced, and the calculation formula is as follows:

[0111]

[0112] Where: d i is the rank difference between the time series and the feature series; n is the number of samples. Among them, rank(γ ik ) represents the rank of sample i in the posterior probability of component k (the position after sorting from small to large). rank(t i ) represents the time label ti The rank in the time tags of all samples in the dataset. For duplicate values, the average rank is calculated.

[0113] Dynamic optimization based on correlation can be adopted here. Sort the samples in descending order of the absolute value of d i and sequentially remove the first k samples. Calculate ρs after each removal, record the change trend, and select the critical point where ρs significantly increases and begins to converge as the threshold. (For example, if the original ρs = 0.7, ρs = 0.85 after removing the first 5 samples, and ρs changes little after removing the sixth sample, then select the situation of removing the first 5 samples). In this embodiment, high-correlation features satisfying |ρ s |≥0.8 are selected as effective features through the above dynamic optimization method, and the filtered matrix is obtained:

[0114] Γ filtered ∈R n×K′ (K′≤K)

[0115] For the above matrix, if the maximum likelihood estimation is directly performed on the original probability values, components with higher numerical ranges (such as the healthy component) will dominate the calculation of the above covariance matrix, resulting in the principal component direction being biased towards these components. Therefore, some components with low values but obvious trends (such as the early fault component) may be ignored. Standardization, on the other hand, ensures a fair evaluation of the influence proportion of all components by unifying the numerical scales of each component.

[0116] Perform Z-score standardization on Γ filtered to eliminate the influence of dimensions:

[0117]

[0118] where γ′ ik is the standardized posterior probability of the i-th sample on the k-th Gaussian component, and γ ik is the original posterior probability value, representing the probability that the i-th sample belongs to the k-th Gaussian component. μ k is the mean of the posterior probabilities in the k-th column, σ k is the standard deviation of the posterior probabilities in the k-th column, and n is the total number of samples. After the above standardization process, the standardized matrix Γ′ is obtained.

[0119] Through PCA orthogonal transformation, the high-dimensional posterior probability space can be mapped to a low-dimensional space, and the projection direction with the maximum variance can be found in a mathematical sense. Here, it is characterized as mining the dominant mode of the probability distribution evolution during the bearing degradation process. Among them, the first principal component direction w1 corresponds to the direction with the most significant change in the probability distribution during the bearing degradation process, which can be interpreted as the degradation-sensitive direction in engineering. The specific steps are as follows:

[0120] Calculate the covariance matrix:

[0121]

[0122] Among them, Γ′ is the standardized matrix, and the covariance matrix C reflects the linear correlation between the components.

[0123] PCA calculates the covariance matrix C of the standardized posterior probability matrix Γ′ and performs eigendecomposition on it:

[0124] C=WΛW T

[0125] Among them, Λ=diag(λ1,λ2,...,λ K′ ) are the eigenvalues arranged in descending order, representing the variance contribution of each principal component direction; W = [w1, w2, ..., w K′ ] is an orthogonal eigenvector matrix, each column corresponds to a principal component direction.

[0126] Take the eigenvector w1 corresponding to the maximum eigenvalue λ1, whose direction is the projection direction with the largest data variance, that is:

[0127]

[0128] The sign and magnitude of the weights in the first principal component direction, w1, reveal the synergistic effect of different Gaussian components in the degradation process. For components with positive weights whose probability increases with degradation (such as fault components), larger weights indicate a stronger positive contribution to degradation. For components with negative weights whose probability decreases with degradation (such as healthy components), larger absolute weights indicate a more significant reverse driving effect of health loss on degradation.

[0129] The direction of w1 can be viewed as a degradation trajectory in probability space. The evolution of a bearing from healthy to faulty is essentially the shift of the posterior probability from the healthy component to the faulty component. w1 projects this shift into a one-dimensional index f, achieving linear quantification of the degradation process. This is the engineering significance of degradation-sensitive directions.

[0130] The principal component direction w1 of PCA is learned based on the standardized posterior probability matrix of the training set. k ,σ k ) will cause the calculation of the covariance matrix to deviate from the training set distribution, and the physical meaning of the principal component direction w1 (degradation-sensitive direction) will be destroyed, which will cause the health indicator f to lose consistency across devices and make it impossible to compare degradation rates horizontally.

[0131] Standardization can solve this problem from a mathematical perspective. By standardizing, the dimension differences between devices are eliminated, making the PCA model transferable. For new bearing data, the mean μ of the training set can be used directly. kand standard deviation σ k Perform standardization and then project onto the trained w1 to achieve real-time health monitoring.

[0132] The health index f is the linear projection of the standardized posterior probability matrix Γ′ in the direction of the first principal component w1. Its essence is to compress the high-dimensional probability distribution (K′ - dimensional) into a one-dimensional space, retaining the degradation-sensitive information with the largest variance, and its evolution trend directly reflects the dominant state transition pattern during the bearing degradation process.

[0133] Perform Min - Max normalization on the health index f obtained by PCA projection to generate the final health index (HealthIndex, HI). The specific steps are as follows:

[0134]

[0135] where HI is the health index value of the i - th sample, and the value range after normalization is [0, 1]; f min is the minimum value of f for all samples in the training set; f max is the maximum value of f for all samples in the training set.

[0136] It should be noted that if the direction of f has been corrected before normalization (such as f← - f), the corrected f needs to be used to calculate HI:

[0137]

[0138] f new is the corrected f. For f new directly use the max(f) and min(f) of the training set for normalization.

[0139] Map f of any scale to [0, 1] to eliminate the difference in numerical range and facilitate setting a general alarm threshold.

[0140] Plot the time - function curve of HI, observe its functional relationship with time, and compare it with the actual bearing life degradation curve to check the response of HI to faults: whether a slight degradation leads to a moderate decrease in HI (such as 5% - 10%).

[0141] The present invention solves the problem of improving the method for constructing health indicators in the prediction of rolling bearing life. Specifically, as Figure 1As shown in the figure, by obtaining the detection data set of the full-life working conditions of the rolling bearing, monotonicity and time correlation tests are respectively carried out on each characteristic quantity in the data set to obtain an effective characteristic data set; then the obtained characteristic data set is transformed into a similarity matrix form and brought into the improved AP clustering algorithm. Through continuous iteration of the attraction matrix and the membership matrix, the number of clusters is obtained. After each iteration, the BMP index test is carried out to adjust the reference parameter and re-iterate. When the number of clusters is stable, the initial iteration value of the GMM model is obtained; a GMM probability distribution model is constructed, and the characteristic data set obtained in S2 is used as the input and brought into the distribution function; under the EM algorithm, through the E-step and the M-step respectively, the iterative update of the parameters is realized to obtain a stable GMM model. After completing the adaptive GMM modeling, the posterior probability of each sub-Gaussian component is calculated to obtain a posterior probability matrix; the Spearman rank correlation coefficient is introduced to judge each sub-Gaussian component, and the features with high correlation are taken as effective features to obtain the screened matrix. Then standardization is carried out to eliminate the influence of dimensions. The covariance matrix is calculated, and its eigen-decomposition is carried out, and then the eigenvector corresponding to the largest eigenvalue is taken to obtain the health index parameter; normalization is carried out to obtain the bearing life health index HI.

[0142] Through the above technical solutions, the present invention adopts an adaptive Gaussian model designed using the improved AP clustering convergence condition, and combines the EM algorithm to realize parameter update, so that it does not need to set initial parameters artificially and maintains high convergence stability. The PCA using Z-score standardization is used to realize data dimensionality reduction, omitting invalid noise components, and fully balancing the influence contributions of each sub-Gaussian component to the main component, and a health index HI that can characterize the bearing life is obtained. Thus, the degradation process of the bearing can be intuitively described. This method is widely applicable to application scenarios with sufficient data volume and missing failure mechanisms, and can realize intelligent monitoring without the intervention of failure mechanisms or expert experience, and can effectively improve the accuracy and robustness of classification. Through the feature extraction of vibration signals, the transformation from low information volume to high information volume is completed, but there is still redundancy between each feature index. Excessive redundancy will reduce the model accuracy. Therefore, the present invention uses the PCA method to fuse the dimensional feature values of the bearing vibration signals, minimizing information loss, and a health index construction method that can adapt to data distribution, balance trend stability and state discrimination, providing a reliable basis for bearing intelligent operation and maintenance.

[0143] Embodiment 2

[0144] Based on Embodiment 1, Embodiment 2 of the present invention further provides a bearing health index construction system based on an adaptive Gaussian mixture model, including:

[0145] A data acquisition module, configured to sample the detection data of the operating conditions of the bearing during the full-life working cycle to obtain a data set;

[0146] A data extraction module, configured to extract data from a dataset to obtain a feature dataset;

[0147] A Gaussian component acquisition module, configured to use the AP clustering algorithm on the feature dataset to obtain the number of sub-Gaussian components of the GMM model;

[0148] A Gaussian model construction module, configured to substitute the number of sub-Gaussian components into the GMM probability density definition formula and use the EM algorithm to iteratively update it until the number of iterations is reached, to obtain the GMM parameter model;

[0149] A health index generation module, configured to perform dimensionality reduction on the GMM parameter model to output a health index, and normalize the health index to generate a final health index.

[0150] Specifically, the data extraction module is further configured to:

[0151] S201. Obtain the monotonicity calculation result of the dataset by taking the absolute value after dividing the number of data points that rise relative to the previous point in the dataset minus the number of data points that fall relative to the previous point by the difference between the sequence length of the dataset and 1;

[0152] S202. Obtain the time correlation calculation result of the current data point in the dataset by dividing the covariance between the current data point and its acquisition time by the difference between the standard deviation of each data point and the standard deviation of the acquisition time corresponding to each data point;

[0153] S203. Add the monotonicity calculation result and the time correlation calculation result of the current data point and divide by 2 to obtain a characteristic factor, and extract the data points in the dataset whose characteristic factor values are greater than a set threshold as the feature dataset.

[0154] Specifically, the Gaussian component acquisition module is further configured to:

[0155] The process of the AP clustering algorithm is to use the negative Euclidean distance between the i-th element and the j-th element in the feature data set as the element in the i-th row and j-th column of the similarity matrix. Set a parameter P, which is the diagonal element of the similarity matrix and is initialized to the median value of the similarity matrix. Set the maximum number of iterations. In each iteration, calculate the attractiveness matrix according to the similarity matrix, calculate the membership matrix according to the attractiveness matrix, and use the damping factor to decay the attractiveness matrix and the membership matrix respectively. Iterate repeatedly. After the iteration is completed, add the attractiveness matrix and the membership matrix to obtain the decision matrix. The samples with values greater than 0 in the decision matrix are the clustering center points, and the number of clustering center points is used as the number of sub-Gaussian components. After each round of clustering of the AP clustering algorithm, calculate the BWP index. If the BWP index decreases compared with the previous round, lower the parameter P; otherwise, increase the parameter P and perform the next round of clustering until a stable number of clusters is generated, and this stable number of clusters is used as the final number of sub-Gaussian components. The BWP index is the average value obtained by summing the difference between the minimum inter-class distance and the average intra-class distance of each sample in each class divided by the sum of the two.

[0156] Specifically, the Gaussian model construction module is also used for:

[0157] The number of sub-Gaussian components is the number of Gaussian components. Substitute the feature data set, the number of sub-Gaussian components, the mean vector of the Gaussian components, and the covariance matrix of the Gaussian components into the GMM probability density definition formula, and use the EM algorithm to calculate the posterior probability of each data point belonging to each Gaussian component. Use this posterior probability to calculate the covariance matrix of the Gaussian components to update the covariance matrix of the Gaussian components, and substitute the updated covariance matrix of the Gaussian components into the GMM probability density definition formula. Iterate continuously until the number of iterations is reached. Substitute the finally calculated covariance matrix of the Gaussian components into the GMM probability density definition formula to obtain the GMM parameter model.

[0158] Specifically, the health index generation module is also used for:

[0159] Calculate the posterior probability of each data point in the feature data set belonging to each Gaussian component for the GMM parameter model to obtain the posterior probability matrix. At the same time, calculate the Spearman rank correlation coefficient of each data point in the feature data set, screen the data points with Spearman rank correlation coefficients greater than or equal to the preset value, calculate their posterior probabilities belonging to each Gaussian component, and obtain the screened posterior probability matrix. Perform Z-score normalization on the screened posterior probability matrix to obtain the normalized matrix, calculate the covariance matrix of the normalized matrix, perform eigen-decomposition on it using the PCA principal component analysis method, take the eigenvector corresponding to the largest eigenvalue as the projection direction, project the covariance matrix of the normalized matrix, obtain the health index, and normalize the health index to generate the final health index.

[0160] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for constructing a bearing health index based on an adaptive Gaussian mixture model, characterized in that, Including: S1. Sampling the detection data of the operating conditions during the whole life cycle of the bearing to obtain a data set; S2. Extracting data from the data set to obtain a feature data set; S3. Using the AP clustering algorithm for the feature data set to obtain the number of sub-Gaussian components of the GMM model; S4. Substituting the number of sub-Gaussian components into the GMM probability density definition formula and using the EM algorithm to iteratively update it until the number of iterations is reached to obtain the GMM parameter model; S5. Reducing the dimension of the GMM parameter model to output a health index, and normalizing the health index to generate the final health index.

2. The method for constructing a bearing health index based on an adaptive Gaussian mixture model according to claim 1, wherein S2 Including: S201. Using the number of data points that rise relative to the previous point in the data set minus the number of data points that fall relative to the previous point, dividing by the difference between the sequence length of the data set and 1, and then taking the absolute value to obtain the monotonicity calculation result of the data set; S202. Dividing the covariance between the current data point in the data set and its acquisition time by the difference between the standard deviation of each data point and the standard deviation of the acquisition time corresponding to each data point to obtain the time correlation calculation result of the current data point; S203. Adding the monotonicity calculation result and the time correlation calculation result of the current data point and dividing by 2 to obtain a characteristic factor, and extracting the data points in the data set whose characteristic factor values are greater than the set threshold as the feature data set.

3. The method for constructing a bearing health index based on an adaptive Gaussian mixture model according to claim 1, characterized in that S3 Including: The process of the AP clustering algorithm is to take the negative Euclidean distance between the i-th element and the j-th element in the feature data set as the element in the i-th row and j-th column of the similarity matrix. Set a parameter P, which is the diagonal element of the similarity matrix, and the initial value is the median of the similarity matrix; set the maximum number of iterations; in each iteration process, calculate the attractiveness matrix according to the similarity matrix, calculate the membership matrix according to the attractiveness matrix, and use the damping factor to decay the attractiveness matrix and the membership matrix respectively, and iterate repeatedly. After the iteration is completed, add the attractiveness matrix and the membership matrix to obtain the decision matrix. The samples greater than 0 in the decision matrix are the clustering center points, and the number of clustering center points is used as the number of sub-Gaussian components; after each round of clustering of the AP clustering algorithm, calculate the BWP index. If the BWP index decreases compared with the previous round, lower the parameter P, otherwise increase the parameter P, and perform the next round of clustering until a stable number of clusters is generated, and this stable number of clusters is used as the final number of sub-Gaussian components; the BWP index is the average value obtained by summing the difference between the minimum inter-class distance and the average intra-class distance of each sample in each class divided by the sum of the two.

4. The method for constructing a bearing health index based on an adaptive Gaussian mixture model according to claim 1, wherein S4 Including: The number of sub-Gaussian components is the number of Gaussian components. Substitute the feature data set, the number of sub-Gaussian components, the mean vector of the Gaussian components, and the covariance matrix of the Gaussian components into the GMM probability density definition formula, use the EM algorithm to calculate the posterior probability that each data point belongs to each Gaussian component, use this posterior probability to calculate the covariance matrix of the Gaussian components to update the covariance matrix of the Gaussian components, and substitute the updated covariance matrix of the Gaussian components into the GMM probability density definition formula, and iterate continuously until the number of iterations is reached. Substitute the finally calculated covariance matrix of the Gaussian components into the GMM probability density definition formula to obtain the GMM parameter model.

5. The method for constructing a bearing health index based on an adaptive Gaussian mixture model according to claim 1, wherein S5 Including: Calculate the posterior probability that each data point in the feature dataset belongs to each Gaussian component for the GMM parameter model to obtain a posterior probability matrix. At the same time, calculate the Spearman rank correlation coefficient of each data point in the feature dataset, filter out the data points whose Spearman rank correlation coefficient is greater than or equal to the preset value, calculate the posterior probability that they belong to each Gaussian component, and obtain the filtered posterior probability matrix; perform Z-score normalization on the filtered posterior probability matrix to obtain a normalized matrix, calculate the covariance matrix of the normalized matrix, perform eigen-decomposition on it using the PCA principal component analysis method, take the eigenvector corresponding to the largest eigenvalue as the projection direction, project the covariance matrix of the normalized matrix, obtain a health index, and normalize the health index to generate the final health index.

6. A bearing health index construction system based on an adaptive Gaussian mixture model, characterized in that, Including: A data acquisition module, which is used to sample the detection data of the operating conditions of the bearing throughout its life cycle to obtain a dataset; A data extraction module, which is used to extract data from the dataset to obtain a feature dataset; A Gaussian component acquisition module, which is used to obtain the number of sub-Gaussian components of the GMM model for the feature dataset using the AP clustering algorithm; A Gaussian model construction module, which is used to substitute the number of sub-Gaussian components into the GMM probability density definition formula and use the EM algorithm to iteratively update it until the number of iterations is reached to obtain a GMM parameter model; A health index generation module, which is used to output a health index by dimensionality reduction of the GMM parameter model and normalize the health index to generate the final health index.

7. The bearing health index construction system based on the adaptive Gaussian mixture model according to claim 6, characterized in that, The data extraction module is also used for: S201. Use the number of data points that rise relative to the previous point in the dataset minus the number of data points that fall relative to the previous point, divide by the difference between the sequence length of the dataset and 1, and then take the absolute value to obtain the monotonicity calculation result of the dataset; S202. Divide the covariance between the current data point in the dataset and its acquisition time by the difference between the standard deviation of each data point and the standard deviation of the acquisition time corresponding to each data point to obtain the time correlation calculation result of the current data point; S203. Add the monotonicity calculation result and the time correlation calculation result of the current data point and divide by 2 to obtain a characteristic factor, and extract the data points in the dataset whose characteristic factor value is greater than the set threshold as the feature dataset.

8. The bearing health index construction system based on an adaptive Gaussian mixture model according to claim 6, characterized in that, The Gaussian component acquisition module is also used for: The process of the AP clustering algorithm is to use the negative Euclidean distance between the i-th element and the j-th element in the feature dataset as the element in the i-th row and j-th column of the similarity matrix, set a parameter P, which is the diagonal element of the similarity matrix, and the initial situation is the median of the similarity matrix; Set the maximum number of iterations; in each iteration, calculate the attraction matrix according to the similarity matrix, calculate the membership matrix according to the attraction matrix, use the damping factor to decay the attraction matrix and the membership matrix respectively, iterate repeatedly, and after the iteration is completed, add the attraction matrix and the membership matrix to obtain the decision matrix. The samples in the decision matrix greater than 0 are the cluster centers, and the number of cluster centers is used as the number of sub-Gaussian components; after each round of clustering by the AP clustering algorithm, calculate the BWP index. If the BWP index decreases compared with the previous round, lower the parameter P, otherwise increase the parameter P, and perform the next round of clustering until a stable number of clusters is generated, and this stable number of clusters is used as the final number of sub-Gaussian components; the BWP index is the average value obtained by summing the difference between the minimum inter-class distance and the average intra-class distance of each sample in each class divided by the sum of the two.

9. The bearing health index construction system based on the adaptive Gaussian mixture model according to claim 6, wherein The Gaussian model construction module is also used for: The number of sub-Gaussian components is the number of Gaussian components. Substitute the feature data set, the number of sub-Gaussian components, the mean vector of the Gaussian components, and the covariance matrix of the Gaussian components into the GMM probability density definition formula, use the EM algorithm to calculate the posterior probability of each data point belonging to each Gaussian component, use this posterior probability to calculate the covariance matrix of the Gaussian components to update the covariance matrix of the Gaussian components, and substitute the updated covariance matrix of the Gaussian components into the GMM probability density definition formula, iterate continuously until the number of iterations is reached, and substitute the finally calculated covariance matrix of the Gaussian components into the GMM probability density definition formula to obtain the GMM parameter model.

10. The bearing health index construction system based on the adaptive Gaussian mixture model according to claim 6, characterized in that, The health index generation module is also used for: Calculate the posterior probability of each data point in the feature data set belonging to each Gaussian component for the GMM parameter model to obtain the posterior probability matrix. At the same time, calculate the Spearman rank correlation coefficient of each data point in the feature data set, screen the data points with the Spearman rank correlation coefficient greater than or equal to the preset value, calculate their posterior probability of belonging to each Gaussian component, and obtain the screened posterior probability matrix; perform Z-score standardization on the screened posterior probability matrix to obtain the standardized matrix, calculate the covariance matrix of the standardized matrix, perform eigenvalue decomposition on it using the PCA principal component analysis method, take the eigenvector corresponding to the largest eigenvalue as the projection direction, project the covariance matrix of the standardized matrix, obtain the health index, and normalize the health index to generate the final health index.

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