CN113609685B - Bearing residual life prediction method based on optimized RVM and mixed degradation model - Google Patents

Abstract

The invention discloses a bearing residual life prediction method based on optimized RVM and a hybrid degradation model, which comprises the following steps: s1, setting and initializing parameters; s2, reconstructing a phase space; s3, training an RVM model; s4, fitting a degradation curve based on a multi-degradation model; s5, similarity measurement: calculating the similarity between a real degradation curve and a fitted degradation curve by adopting a Frechet distance; s6, judging iteration termination; s7, selecting an optimal degradation curve; s8, extrapolating a fitting curve; and S9, calculating the residual service life. The method not only improves the accuracy of the long-term prediction of the residual life of the bearing and avoids the adverse effects on the prediction performance caused by the increase of the prediction step length, the selection of parameter experience and the like, but also can be applied to the prediction research of the residual life of other parts of the rotary machine or equipment with similar mechanisms, and provides guarantee for the fault prediction and the health management of the equipment.

Description

Bearing remaining life prediction method based on optimized RVM and hybrid degradation model

Technical Field

The present invention belongs to the field of fault prediction and health management, and in particular relates to a bearing remaining life prediction method based on optimized RVM and a hybrid degradation model.

Background Art

As a key component of equipment, the safety of rolling bearings is self-evident. As an important means to ensure the safe operation of equipment, the remaining life prediction has become an important research hotspot in recent years. Usually, the operation of bearings will go through the normal stage, the degradation stage, and finally failure. Therefore, once the bearing begins to degrade, its remaining life prediction needs to be carried out.

Typically, the data-driven remaining life prediction model tracks the degradation trend through the constructed health indicators, and performs single-step or multi-step predictions starting from the set inspection time. Single-step prediction relies on historical information to make predictions, and has high prediction accuracy, but is not very practical. Based on the single step, the introduction of prediction values can construct a multi-step iterative prediction model, but the larger the prediction step, the greater the error accumulation, and the prediction accuracy is limited.

The Relevance Vector Machine (RVM) is trained and learned under the Bayesian framework. It removes irrelevant points based on the Automatic Relevance Determination (ARD) theory under the structure of prior parameters to obtain a sparse model. During the iterative learning process of sample data of the RVM model, the posterior probability distribution of most parameters will tend to zero, and the points corresponding to those non-zero parameters are called relevance vectors (RVs). Existing studies have also used support vector machines, support vector regression models, etc. for multi-step prediction, but the sparsity and nonlinear processing capabilities of RVM are more suitable for nonlinear time series prediction.

In addition, the prediction of the remaining life of bearings is also affected by the degradation model. The bearing degradation process is often described by a single exponential model. Existing research results show that the degradation model constructed by the weighted combination of exponential functions can achieve good results in the prediction of the remaining life of bearings by adjusting the weights and exponential function parameters. However, due to the influence of load changes and poor bearing installation and positioning, the bearings show the characteristics of nonlinear degradation, and the exponential model is not sufficient to describe the dynamic degradation process of the bearings. Therefore, in order to improve the accuracy of long-term remaining life prediction, it is necessary to study how to improve the bearing remaining life prediction model based on RVM.

Summary of the invention

The purpose of the present invention is to overcome the shortcomings of the prior art and provide a bearing remaining life prediction method based on optimized RVM and hybrid degradation model, which can improve the accuracy of long-term prediction of bearing remaining life, avoid the adverse effects of increased prediction step size and empirical parameter selection on prediction performance, and provide guarantee for equipment fault prediction and health management.

The objective of the present invention is achieved through the following technical solution: A bearing remaining life prediction method based on optimized RVM and hybrid degradation model comprises the following steps:

S1. Parameter setting and initialization: Set the value range of Gaussian kernel width δ _i (1≤i≤L) to [δ ₁ ,δ _L ], set its variation to Δδ, set bearing failure threshold γ; set i=1;

S2, phase space reconstruction: import the health index values from the initial degradation time to the inspection time, and construct the feature matrix and target vector;

S3, RVM model training: perform RVM regression according to the set Gaussian kernel width value to determine the correlation vector;

S4. Degradation curve fitting based on multiple degradation models: The correlation vector obtained in S3 is fitted by using a single exponential model, a double exponential model and a polynomial model, and the fitting curve parameters are determined by a nonlinear least squares regression method to obtain the degradation curve _fi ;

S5, similarity measurement: Fréchet distance is used to calculate the similarity between the true degradation curve S and the fitted degradation curve _fi ;

S6, iterative termination judgment: when δ _i >δ _L , the iteration is terminated and the next step is entered; otherwise, i＝i+1, δ _i+1 ＝δ _i +Δδ, and the process returns to step S3;

S7, selecting the optimal degradation curve: taking the fitting curve with the minimum similarity between the real degradation curve S and the fitting degradation curve _fi as the optimal fitting curve f _o ;

S8, extrapolating the fitting curve: using the parameters of the optimal fitting curve f _o to extrapolate until its health index value HI reaches the failure threshold γ, that is, reaching HI _t ≥ γ for the first time, marking the corresponding time as N _f = t;

S9. Calculate the remaining service life: The remaining service life of the bearing is the time from the inspection time to the predicted failure time _Nf .

Furthermore, the known conditions for the prediction are: bearing vibration data is obtained by a monitoring sensor, the value of the bearing health index is obtained by feature extraction, fusion and standardization, the time corresponding to the initial degradation is marked as n=1, and the current time is set as the inspection time n=N, then the bearing health index value is (HI ₁ , HI ₂ , ..., HI _n , ..., HI _N ), and these health index values are connected to form a bearing degradation curve S; the remaining service life of the bearing starting from the inspection time N is predicted.

Furthermore, the implementation process of step S2 is as follows:

Based on the obtained health values (HI ₁ ,HI ₂ ,...,HI _n ,...,HI _N ), the phase space is reconstructed to obtain the feature matrix and target vector required for RVM model training, which are expressed as follows:

为特征矩阵，

为目标向量，将目标向量记为z＝[z₁,...,z_N-m]^T，HI_n表示n时刻的健康指标数值，m为嵌入维度。In formula (1),

is the feature matrix,

is the target vector, and the target vector is recorded as z = [z ₁ , ..., z _Nm ] ^T , HI _n represents the health index value at time n, and m is the embedding dimension.

组成的集合，RVM模型旨在刻画输入特征集和目标对之间的非线性关系，即：Furthermore, the implementation process of step S3 is as follows: given the features and the target

The RVM model is designed to characterize the nonlinear relationship between the input feature set and the target pair, namely:

的高斯噪声；w＝(w₁,w₂,...,w_N)^T是权值向量；K选取高斯核函数，设定高斯核宽度δ_i，其表达式如下：Where, j = 1,…,Nm; s _noise (0,σ ² ) is a noise with a mean of 0 and a variance of

Gaussian noise; w = (w ₁ ,w ₂ ,...,w _N ) ^T is the weight vector; K selects the Gaussian kernel function and sets the Gaussian kernel width δ _i , which is expressed as follows:

Among them, || || ² represents the square of the vector norm;

The target variable z _j follows a Gaussian distribution with a mean of y(x _j ) and a variance of σ ² , that is

Assuming that _zj is independent and identically distributed, the likelihood function of the entire training sample is expressed as follows:

Wherein, Φ is the kernel function matrix, that is, Φ = [K(x,x ₁ ), K(x,x ₂ ),·, K(x,x _N )] ^T .

Use the Gaussian prior of w to avoid the overfitting problem in the above parameter optimization:

表示高斯分布；a＝(a₁,...,a_j,...,a_N)^T为超参数向量，a_j表示相对应权重w_j的精度；超参数向量a主导着模型的泛化性能；利用贝叶斯原则得到权值的后验分布：in,

represents Gaussian distribution; a＝(a ₁ ,...,a _j ,...,a _N ) ^T is the hyperparameter vector, a _j represents the accuracy of the corresponding weight w _j ; the hyperparameter vector a dominates the generalization performance of the model; the posterior distribution of the weight is obtained using the Bayesian principle:

p(z|a,σ ² ) represents the marginal likelihood estimate; the continuous sparse Bayesian learning algorithm is used to optimize the hyperparameters a and σ ² ; after the RVM model training is completed, the input x _j corresponding to the non-zero weight in the hyperparameter {a _j } is the correlation vector.

Furthermore, the specific implementation process of step S4 is as follows: after obtaining the correlation vector through the RVM model, the obtained correlation vector is fitted by curve fitting; a hybrid degradation model is formed by a single exponential model, a weighted double exponential model and a polynomial model, which is described as follows:

Wherein, HI _RV represents the correlation vector obtained by RVM model training, t represents the time corresponding to the correlation vector; a, b, c and d are unknown parameters of the degradation model, and the nonlinear least squares regression method is used to determine the unknown parameters, and the degradation model is fitted into a degradation curve, which is recorded as the degradation curve _fi .

Furthermore, the implementation process of step S5 is: for a given original degradation trajectory S, the similarity between the original degradation trajectory S and the fitted degradation curve _fi is calculated and measured by using the Fréchet distance, which is defined as follows:

表示两个任意非减连续函数，满足

表示两条曲线之间的欧式距离。Among them, ξ(x) and

represents two arbitrary non-decreasing continuous functions that satisfy

Represents the Euclidean distance between two curves.

Furthermore, the implementation process of step S7 is: obtaining L fitting degradation curves according to the setting range of Gaussian kernel width, comparing the Fréchet distances between all fitting curves and the original degradation trajectory, and taking the fitting curve with the smallest Fréchet distance value as the optimal fitting curve, that is, the optimal fitting curve is: f _o ={f _i |min(Ω(S,f _i ))}.

Furthermore, the implementation process of step S9 is as follows: when the optimal degradation trajectory exceeds the failure threshold γ for the first time, the bearing is considered to be failed; the time corresponding to the optimal trajectory crossing the failure threshold γ for the first time is recorded as N _f , and the predicted remaining life of the bearing is defined as follows:

RUL(N)＝ _Nf -N (9)

Wherein, RUL(N) represents the remaining service life of the bearing predicted at the inspection time N.

The beneficial effects of the present invention are as follows: the present invention proposes a method for predicting the remaining life of a bearing based on an optimized RVM and a hybrid degradation model. The one-dimensional time series of the bearing health index can reflect the dynamic characteristics of the original system after phase space reconstruction, and the reconstructed characteristic matrix can better reflect the relationship between the characteristic vector and the target. The phase space reconstruction is combined with the RVM regression model to extend the range of life prediction from the perspective of the characteristic space and improve the accuracy of long-term prediction. According to the sparsity analysis of the RVM model, the kernel width of the Gaussian kernel function can affect the selection of related vectors and even the generalization performance of the RVM model. At the same time, the weighted exponential model can reflect the overall degradation process of the bearing according to the trend of historical data changes, and can better reflect the nonlinear degradation characteristics of the bearing in combination with the polynomial degradation model. Therefore, multiple degradation curves can be provided by adjusting the Gaussian kernel width and the hybrid degradation model. The one closest to the known bearing degradation sample is selected as the optimal prediction curve in combination with the Fréchet distance. The remaining life evaluation result can be obtained by extrapolating this curve to the bearing failure threshold. This method not only improves the accuracy of long-term prediction of remaining life of bearings, avoids the adverse effects of increasing prediction step size and empirical parameter selection on prediction performance, but can also be applied to other components of rotating machinery or remaining life prediction research of equipment with similar mechanisms, providing guarantee for equipment fault prediction and health management.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of a method for predicting the remaining life of a bearing based on an optimized RVM and a hybrid degradation model according to the present invention;

FIG2 is a schematic diagram of prediction curve selection for bearing 1 of test set 2 in this embodiment;

FIG. 3 is a diagram showing the long-term prediction results of two prediction models for bearing 1 of test set 2 in this embodiment.

DETAILED DESCRIPTION

The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

The known conditions for prediction described in the present invention are: bearing vibration data is obtained by a monitoring sensor, and the value of the bearing health indicator (HI) is obtained by feature extraction, fusion and standardization, the time corresponding to the initial degradation is marked as n=1, and the current time is set as the inspection time n=N, then the bearing health indicator value is (HI ₁ , HI ₂ , ..., HI _n , ..., HI _N ), and these health indicator values are connected to form a bearing degradation curve S; the remaining service life of the bearing starting from the inspection time N is predicted.

As shown in FIG1 , a bearing remaining life prediction method based on optimized RVM and hybrid degradation model of the present invention comprises the following steps:

S1. Parameter setting and initialization: Set the value range of Gaussian kernel width δ _i (1≤i≤L) to [δ ₁ ,δ _L ], set its variation to Δδ, set bearing failure threshold γ; set i=1;

S2, phase space reconstruction: import the health index values from the initial degradation time to the inspection time, construct the feature matrix and target vector; the specific implementation process is: based on the obtained health values (HI ₁ ,HI ₂ ,...,HI _n ,...,HI _N ), perform phase space reconstruction to obtain the feature matrix and target vector required for RVM model training, which is expressed as follows:

为特征矩阵，

为目标向量，将目标向量记为z＝[z₁,...,z_N-m]^T，HI_n表示n时刻的健康指标数值，m为嵌入维度。In formula (1),

is the feature matrix,

is the target vector, and the target vector is recorded as z = [z ₁ , ..., z _Nm ] ^T , HI _n represents the health index value at time n, and m is the embedding dimension.

S3, RVM model training: perform RVM regression according to the set Gaussian kernel width value to determine the correlation vector;

组成的集合，RVM模型旨在刻画输入特征集和目标对之间的非线性关系，即：The specific implementation process is: given features and goals

The RVM model is designed to characterize the nonlinear relationship between the input feature set and the target pair, namely:

的高斯噪声；w＝(w₁,w₂,...,w_N)^T是权值向量；K选取高斯核函数，设定高斯核宽度δ_i，其表达式如下：Where, j = 1,…,Nm; s _noise (0,σ ² ) is a noise with a mean of 0 and a variance of

Gaussian noise; w = (w ₁ ,w ₂ ,...,w _N ) ^T is the weight vector; K selects the Gaussian kernel function and sets the Gaussian kernel width δ _i , which is expressed as follows:

Among them, || || ² represents the square of the vector norm;

The target variable z _j follows a Gaussian distribution with a mean of y(x _j ) and a variance of σ ² , that is

Assuming that _zj is independent and identically distributed, the likelihood function of the entire training sample is expressed as follows:

Wherein, Φ is the kernel function matrix, that is, Φ = [K(x,x ₁ ), K(x,x ₂ ),·, K(x,x _N )] ^T .

Use the Gaussian prior of w to avoid the overfitting problem in the above parameter optimization:

表示高斯分布；a＝(a₁,...,a_j,...,a_N)^T为超参数向量，a_j表示相对应权重w_j的精度；超参数向量a主导着模型的泛化性能；利用贝叶斯原则得到权值的后验分布：in,

represents Gaussian distribution; a＝(a ₁ ,...,a _j ,...,a _N ) ^T is the hyperparameter vector, a _j represents the accuracy of the corresponding weight w _j ; the hyperparameter vector a dominates the generalization performance of the model; the posterior distribution of the weight is obtained using the Bayesian principle:

p(z|a,σ ² ) represents the marginal likelihood estimate; the sequential sparse Bayesian learning algorithm is used to optimize the hyperparameters a and σ ² ; after the RVM model training is completed, the input x _j corresponding to the non-zero weight in the hyperparameter {a _j } is the correlation vector.

S4. Degradation curve fitting based on multiple degradation models: The correlation vector obtained in S3 is fitted by using a single exponential model, a double exponential model and a polynomial model, and the fitting curve parameters are determined by a nonlinear least squares regression method to obtain the degradation curve _fi ;

The specific implementation process is: after obtaining the correlation vector through the RVM model, the obtained correlation vector is fitted by curve fitting; the hybrid degradation model is composed of a single exponential model, a weighted double exponential model and a polynomial model, which is described as follows:

Wherein, HI _RV represents the correlation vector obtained by RVM model training, t represents the time corresponding to the correlation vector; a, b, c and d are unknown parameters of the degradation model, and the nonlinear least squares regression method is used to determine the unknown parameters, and the degradation model is fitted into a degradation curve, which is recorded as the degradation curve _fi .

S5. Similarity measurement: The Fréchet distance is used to calculate the similarity between the true degradation curve S and the fitted degradation curve _fi . The implementation process is: for a given original degradation trajectory S, the similarity between the original degradation curve S and the fitted degradation curve _fi is calculated and measured using the Fréchet distance, which is defined as follows:

表示两个任意非减连续函数，满足

表示两条曲线之间的欧式距离。Among them, ξ(x) and

represents two arbitrary non-decreasing continuous functions that satisfy

Represents the Euclidean distance between two curves.

S6, iterative termination judgment: when δ _i >δ _L , the iteration is terminated and the next step is entered; otherwise, i＝i+1, δ _i+1 ＝δ _i +Δδ, and the process returns to step S3;

S7. Select the optimal degradation curve: take the fitting curve with the minimum similarity between the real degradation curve S and the fitting degradation curve _fi as the optimal fitting curve f _o ; the implementation process is: obtain L fitting degradation curves according to the setting range of the Gaussian kernel width, compare the Fréchet distances between all the fitting curves and the original degradation trajectory, and take the fitting curve with the minimum Fréchet distance value as the optimal fitting curve, that is, the optimal fitting curve is: f _o ={ _fi |min(Ω(S, _fi ))}.

S8, extrapolating the fitting curve: using the parameters of the optimal fitting curve f _o to extrapolate until its health index value HI reaches the failure threshold γ, that is, reaching HI _t ≥ γ for the first time, marking the corresponding time as N _f = t;

S9. Calculate the remaining service life: The remaining service life of the bearing is the time between the inspection time and the predicted failure time _Nf . The implementation process is: when the optimal degradation trajectory exceeds the failure threshold γ for the first time, the bearing is considered to have failed. The time corresponding to the first crossing of the optimal trajectory through the failure threshold γ is recorded as _Nf , and the predicted remaining service life of the bearing is defined as follows:

RUL(N)＝ _Nf -N (9)

Wherein, RUL(N) represents the remaining service life of the bearing predicted at the inspection time N.

In this embodiment, Cincinnati test set 2 bearing 1 is used as an example to illustrate the implementation results. This group of experimental data sets collected a total of 984 sets of vibration signals from the start of the bearing operation to the end of the degradation experiment. The data sampling frequency in the experiment was 20kHz, 20480 data points were collected each time, and the collection time interval was 10 minutes; after the experiment, the test bearing was checked and the outer ring fault was found. Multi-domain statistical features are used to extract the bearing vibration signal features, and the bearing health index is constructed based on this. The construction content does not belong to the description of this patent, so it is not described in detail. Corresponding to the bearing data in this example, the health index shows that an initial fault occurred at time 533 (that is, the 533th group of collected data, corresponding to the time of 533×10 minutes=5330 minutes, the time marked by the vertical dotted line on the left side of Figure 2), the bearing failure threshold γ=0.66 (the position indicated by the horizontal dotted line in Figure 2), and the corresponding time is 867 (the time is 8670 minutes). The Gaussian kernel width is set to [δ ₁ ,δ _L ] = [0.005, 0.05], and the variation is Δδ = 0.005. In formula (1), the embedding dimension m = 3. It should be pointed out that the main purpose of spatially reconstructing health indicators is to obtain correlation vectors, and the main factor affecting the number of correlation vectors is the kernel width. The embedding dimension m has little effect on the correlation vectors. The "lsqcurvefit()" function in MATLAB is used to solve the parameters in formula (7).

The inspection time is set to N = 632 (the time marked by the vertical long dot-dash line in the middle of Figure 2). In Figure 2, the degradation curve described by the bearing health index is represented by a black curve; the health index values between the initial fault time 533 and the inspection time N = 632 (the range marked by the double arrows below ① in Figure 2) are used as training samples to input into the improved RVM model. For each kernel width value, the corresponding correlation vector and the fitted degradation curve _fi can be obtained, as shown in several gray curves in Figure 2. Among them, the Fréchet distance between the real degradation curve S in the range ① and the corresponding curve f _o in Figure 2 (a dark double dot-dash line in the gray curve) is the smallest, and the correlation vector corresponding to this curve is shown in the circle in Figure 3; it is used as the optimal degradation curve and extrapolated to the failure threshold γ = 0.66, and the corresponding time is N _f =817, the predicted remaining service life is RUL(632)=(817–632)×10min=1850min (corresponding to the range marked by the double arrows below ③ in Figure 2), while the actual remaining service life ActRUL(632)=(867–632)×10min=2350min (corresponding to the range marked by the double arrows below ② in Figure 2).

In order to evaluate the performance of the proposed method, the relative prediction accuracy index is introduced:

Wherein, ActRUL(N) represents the actual remaining service life of bearing N at the time of inspection, and RUL(N) represents the predicted remaining service life of bearing N at the time of inspection. When the inspection time is set to N=632, the relative prediction accuracy is 21.3%. If a double exponential degradation model is used, other settings are consistent, and the resulting predicted degradation curve is shown in FIG3 , where (a) is a mixed degradation model (the method of the present invention), and (b) is a double exponential model; its predicted remaining life is (743-632)×10 minutes=1110 minutes, which is earlier than the remaining life prediction value obtained by the present invention, and the relative prediction accuracy is 52.8%, and the prediction performance is significantly lower.

Take another inspection time, such as N = 733, the actual remaining life is ActRUL (N) = 1340 minutes, the RUL (N) obtained by the method described in the present invention is 104 × 10 minutes = 1040 minutes, and the remaining life prediction value obtained by the double exponential model is 660 minutes; if the inspection time is set to N = 833 (close to failure), the actual remaining life is ActRUL (N) = 340 minutes, the RUL (N) obtained by the method described in the present invention is 270 minutes, and the remaining life prediction value obtained by the double exponential model is 0 points. The above comparison shows that the closer to failure, the more training data is obtained, and the more accurate the prediction is. However, compared with the existing methods, the prediction method proposed by the present invention has significant improvements in long-term prediction.

Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims (5)

1. A bearing remaining life prediction method based on optimized RVM and hybrid degradation model, characterized in that it comprises the following steps: S1. Parameter setting and initialization: Set the value range of Gaussian kernel width δ _i to [δ ₁ ,δ _L ], set its variation to Δδ, set bearing failure threshold γ; set i = 1; S2, phase space reconstruction: import the health index values from the initial degradation time to the inspection time, and construct the feature matrix and target vector; The known conditions for prediction are: bearing vibration data is obtained by monitoring sensors, the value of bearing health index is obtained by feature extraction, fusion and standardization, the time corresponding to initial degradation is marked as n = 1, and the current time is set as the inspection time n = N, then the bearing health index value is (HI ₁ ,HI ₂ ,...,HI _n ,...,HI _N ), and these health index values are connected to form the bearing degradation curve S; predict the remaining service life of the bearing starting from the inspection time N; The implementation process of step S2 is: Based on the obtained health values (HI ₁ ,HI ₂ ,...,HI _n ,...,HI _N ), the phase space is reconstructed to obtain the feature matrix and target vector required for RVM model training, which are expressed as follows:

In formula (1),

is the feature matrix,

is the target vector, and the target vector is recorded as z = [z ₁ , ..., z _Nm ] ^T , HI _n represents the health index value at time n, and m is the embedding dimension; S3, RVM model training: Perform RVM regression according to the set Gaussian kernel width value to determine the relevant vector; the implementation process of step S3 is: given the features and targets

The RVM model is designed to characterize the nonlinear relationship between the input feature set and the target pair, namely:

Where, j = 1,…,Nm; s _noise (0,σ ² ) is a noise with a mean of 0 and a variance of

Gaussian noise; w = (w ₁ ,w ₂ ,...,w _N ) ^T is the weight vector; K selects the Gaussian kernel function and sets the Gaussian kernel width δ _i , which is expressed as follows:

Among them, || || ² represents the square of the vector norm; The target variable z _j follows a Gaussian distribution with a mean of y(x _j ) and a variance of σ ² , that is

Assuming that _zj is independent and identically distributed, the likelihood function of the entire training sample is expressed as follows:

Wherein, Φ is the kernel function matrix, that is, Φ = [K(x,x ₁ ), K(x,x ₂ ), ·, K(x,x _N )] ^T ; Use the Gaussian prior of w to avoid the overfitting problem in the above parameter optimization:

in,

represents Gaussian distribution; a＝(a ₁ ,...,a _j ,...,a _N ) ^T is the hyperparameter vector, a _j represents the accuracy of the corresponding weight w _j ; the hyperparameter vector a dominates the generalization performance of the model; the posterior distribution of the weight is obtained using the Bayesian principle:

p(z|a,σ ² ) represents the marginal likelihood estimate; the continuous sparse Bayesian learning algorithm is used to optimize the hyperparameters a and σ ² ; after the RVM model training is completed, the input x _j corresponding to the non-zero weight in the hyperparameter {a _j } is the correlation vector; S4. Degradation curve fitting based on multiple degradation models: The correlation vector obtained in S3 is fitted by using a single exponential model, a double exponential model and a polynomial model, and the fitting curve parameters are determined by a nonlinear least squares regression method to obtain the degradation curve _fi ; S5, similarity measurement: Fréchet distance is used to calculate the similarity between the true degradation curve S and the fitted degradation curve _fi ; S6, iterative termination judgment: when δ _i >δ _L , the iteration is terminated and the next step is entered; otherwise, i＝i+1, δ _i+1 ＝δ _i +Δδ, and the process returns to step S3; S7, selecting the optimal degradation curve: taking the fitting curve with the minimum similarity between the real degradation curve S and the fitting degradation curve _fi as the optimal fitting curve f _o ; S8, extrapolating the fitting curve: using the parameters of the optimal fitting curve f _o to extrapolate until its health index value HI reaches the failure threshold γ, that is, reaching HI _t ≥ γ for the first time, marking the corresponding time as N _f = t; S9. Calculate the remaining service life: The remaining service life of the bearing is the time from the inspection time to the predicted failure time _Nf . 2. The method for predicting the remaining life of a bearing based on the optimized RVM and the hybrid degradation model according to claim 1 is characterized in that the implementation process of step S4 is as follows: after obtaining the correlation vector through the RVM model, the obtained correlation vector is fitted by curve fitting; the hybrid degradation model is composed of a single exponential model, a weighted double exponential model and a polynomial model, which is described as follows:

Wherein, HI _RV represents the correlation vector obtained by RVM model training, t represents the time corresponding to the correlation vector; a, b, c and d are unknown parameters of the degradation model, and the nonlinear least squares regression method is used to determine the unknown parameters, and the degradation model is fitted into a degradation curve, which is recorded as the degradation curve _fi . 3. The method for predicting the remaining life of a bearing based on the optimized RVM and the hybrid degradation model according to claim 1 is characterized in that the implementation process of step S5 is: for a given original degradation trajectory S, the similarity between the original degradation trajectory S and the fitted degradation curve _fi is calculated and measured by the Fréchet distance, which is defined as follows:

Among them, ξ(x) and

represents two arbitrary non-decreasing continuous functions that satisfy

D(S(ξ(x),

Represents the Euclidean distance between two curves. 4. The method for predicting the remaining life of a bearing based on the optimized RVM and the hybrid degradation model according to claim 1 is characterized in that the implementation process of step S7 is as follows: L fitting degradation curves are obtained according to the set range of the Gaussian kernel width, the Fréchet distances between all the fitting curves and the original degradation trajectory are compared, and the fitting curve with the smallest Fréchet distance value is taken as the optimal fitting curve, that is, the optimal fitting curve is: f _o ={f _i |min(Ω(S,f _i ))}. 5. The method for predicting the remaining life of a bearing based on the optimized RVM and the hybrid degradation model according to claim 1, characterized in that the implementation process of step S9 is as follows: when the optimal degradation trajectory exceeds the failure threshold γ for the first time, the bearing is considered to be failed; the time corresponding to the first crossing of the optimal trajectory through the failure threshold γ is recorded as _Nf , and the predicted remaining life of the bearing is defined as follows: RUL(N)＝ _Nf -N (9) Wherein, RUL(N) represents the remaining service life of the bearing predicted at the inspection time N.

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