CN113609685B - Bearing residual life prediction method based on optimized RVM and mixed degradation model - Google Patents
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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
Technical Field
The invention belongs to the field of fault prediction and health management, and particularly relates to a bearing residual life prediction method based on optimized RVM and a hybrid degradation model.
Background
The safety of rolling bearings, which are critical components of the installation, is naturally self-evident. The prediction of the residual life is an important research hotspot in recent years as an important means for guaranteeing the safe operation of equipment. Typically the bearing carrier will go through a normal, degenerate phase until failure, so a residual life prediction is required once the bearing begins to degrade.
Generally, the degradation trend is tracked through the constructed health index based on the data-driven residual life prediction model, and single-step or multi-step prediction is carried out from the set inspection time. The single-step prediction relies on historical information to carry out prediction, the prediction precision is high, but the practicability is not strong. On the basis of single step, a multi-step iterative prediction model can be constructed by introducing a predicted value, but the larger the prediction step is, the larger the error accumulation is, and the prediction accuracy is limited.
A Relevance Vector Machine (RVM) performs training and learning under a Bayesian framework, and irrelevant points are removed based on an Automatic Relevance decision theory (ARD) under the structure of prior parameters, so that a sparse model is obtained. In the iterative learning process of sample data, the posterior probability distribution of most parameters of the RVM model tends to zero, and points corresponding to the non-zero parameters are called Relevance Vectors (RVs). In the existing research, multi-step prediction is carried out by using a support vector machine, a support vector regression model and the like, but the sparsity and the nonlinear processing capability of the RVM are more suitable for nonlinear time series prediction.
In addition, the bearing residual life prediction is also influenced by the degradation model. The degradation process of the bearing is mostly described by adopting a single exponential model, and the existing research results show that the degradation model constructed by the weighted combination exponential function can obtain a good effect in predicting the residual life of the bearing by adjusting the weight and the parameters of the exponential function. However, under the influence of load change, poor bearing installation positioning and the like, the bearing presents the characteristic of nonlinear degradation, and an exponential model is not enough to describe the dynamic degradation process of the bearing. Therefore, in order to improve the accuracy of the long-term remaining life prediction, it is necessary to study how to improve the RVM-based bearing remaining life prediction model.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a bearing residual life prediction method based on optimized RVM and a mixed degradation model, which can improve the accuracy of long-term prediction of the residual life of a bearing, avoid the adverse effects on the prediction performance caused by increased prediction step length, parameter experience selection and the like, and provide guarantee for fault prediction and health management of equipment.
The purpose of the invention is realized by the following technical scheme: the method for predicting the residual life of the bearing based on the optimized RVM and the hybrid degradation model comprises the following steps:
s1, parameter setting and initialization: setting the Gaussian kernel width delta i The value range of (1 is more than or equal to i and less than or equal to L) is set as [ delta [ [ delta ] 1 ,δ L ]Setting the variation as delta and setting a bearing failure threshold value gamma; let i =1;
s2, phase space reconstruction: importing health index values from the initial degradation moment to the inspection moment, and constructing a feature matrix and a target vector;
s3, training an RVM model: performing RVM regression according to the set Gaussian kernel width value to determine a correlation vector;
s4, fitting a degradation curve based on a multi-degradation model: comprehensive application sheetFitting the related vectors obtained by S3 through an exponential model, a bi-exponential model and a polynomial model, determining fitting curve parameters by adopting a nonlinear least square regression method, and obtaining a degradation curve f i ；
S5, similarity measurement: calculating a real degradation curve S and a fitted degradation curve f by using the Frechet distance i Similarity between them;
s6, iteration termination judgment: delta i >δ L When the iteration is ended, the next step is carried out; otherwise i = i +1, δ i+1 ＝δ i + Δ δ, and return to step S3;
s7, selecting an optimal degradation curve: the real degradation curve S and the fitted degradation curve f are combined i The fitted curve having the smallest similarity therebetween is used as the best fitted curve f o ；
S8, extrapolation of a fitting curve: using a best-fit curve f o Is extrapolated until its health indicator value HI reaches the failure threshold value gamma, i.e. first reaches HI t Not less than gamma, the corresponding time of the mark is N f ＝t；
S9, calculating the remaining service life: the residual service life of the bearing is from the inspection time to the predicted failure time N f The time in between.
Further, the known conditions of the prediction are: obtaining bearing vibration data by a monitoring sensor, obtaining a numerical value of a bearing health index through feature extraction, fusion and standardization, marking the time corresponding to initial degradation as N =1, setting the current time as the inspection time N = N, and then obtaining the numerical value of the bearing health index as (HI) 1 ,HI 2 ,...,HI n ,...,HI N ) The health index values are connected to form a bearing degradation curve S; the remaining service life of the bearing is predicted from the inspection time N.
Further, the implementation process of step S2 is:
in the obtained health value (HI) 1 ,HI 2 ,...,HI n ,...,HI N ) And performing phase space reconstruction on the basis to obtain a feature matrix and a target vector required by RVM model training, wherein the feature matrix and the target vector are expressed as follows:
in the formula (1), the reaction mixture is,
is a feature matrix, based on the status of the device>
For the target vector, let target vector be z = [ ] 1 ,...,z N-m ] T ，HI n And the health index value at n time is shown, and m is an embedding dimension.
Further, the implementation process of step S3 is: given characteristics and objectives
Set of constituents, the RVM model aims to characterize the non-linear relationship between the input feature set and the target pair, namely:
wherein j =1, …, N-m; s noise (0,σ 2 ) Is a mean of 0 and a variance of
Gaussian noise of (2); w = (w) 1 ,w 2 ,...,w N ) T Is a weight vector; k selects a Gaussian kernel function and sets a Gaussian kernel width delta i The expression is as follows:
wherein | | | purple hair 2 Represents the square of the vector norm;
target variable z j Obey a Gaussian distribution with a mean value of y (x) j ) Variance is σ 2 I.e. by
Let z j Independently and identically distributed, the likelihood function of the whole training sample is expressed as follows:
where Φ is the kernel function matrix, i.e., = [ K (x, x) 1 ),K(x,x 2 ),·,K(x,x N )] T 。
The overfitting problem in the above-equation parameter optimization is avoided with gaussian priors for w:
wherein,
represents a gaussian distribution; a = (a) 1 ,...,a j ,...,a N ) T Is a hyper-parametric vector, a j Represents the corresponding weight w j The accuracy of (2); the hyper-parameter vector a dominates the generalization performance of the model; and (3) obtaining posterior distribution of the weight by using a Bayes principle:
p(z|a,σ 2 ) Representing a marginal likelihood estimate; optimization of superparameters a and sigma using a successive sparse Bayesian learning algorithm 2 (ii) a After RVM model training is finished, the hyper-parameter { a j The input x corresponding to the non-zero weight in the j Is a correlation vector.
Further, the step S4 is specifically implemented as follows: after obtaining a correlation vector through an RVM model, fitting the obtained correlation vector in a curve fitting mode; the mixed degradation model is formed by a single exponential model, a weighted double exponential model and a polynomial model and is described as follows:
wherein, HI RV Representing a correlation vector obtained by RVM model training, wherein t represents the corresponding moment of the correlation vector; a. b, c and d are unknown parameters of the degradation model, the unknown parameters are determined by adopting a nonlinear least square regression method, the degradation model is fitted into a degradation curve, and the degradation curve is recorded as a degradation curve f i 。
Further, the implementation process of step S5 is: for a given original degradation track S, a degradation curve f is calculated and fitted i The similarity between the two is measured by using a Frechet distance, which is defined as follows:
wherein ξ (x) and
represents two arbitrary non-decreasing continuous functions satisfying
Representing the euclidean distance between the two curves.
Further, the implementation process of step S7 is: obtaining L fitting degradation curves according to the set range of the Gaussian kernel width, comparing the Frechet distances between all the fitting curves and the original degradation track, and taking the fitting curve with the minimum Frechet distance value as an optimal fitting curve, namely the optimal fitting curve is as follows: f. of o ＝{f i |min(Ω(S,f i ))}。
Further, the implementation process of step S9 is: when the optimal degraded track exceeds the failure threshold for the first timeγ, the bearing is considered to fail; recording the time corresponding to the first time that the optimal track passes through the failure threshold value gamma as N f The predicted remaining life of the bearing is then defined as follows:
RUL(N)＝N f -N (9)
where RUL (N) represents the predicted remaining useful life of the bearing at the inspection time N.
The invention has the beneficial effects that: the invention provides a bearing residual life prediction method based on an optimized RVM and a mixed degradation model. The one-dimensional time sequence of the bearing health index can reflect the dynamic characteristics of an original system through phase space reconstruction, a characteristic matrix obtained through reconstruction can better reflect the correlation between a characteristic vector and a target, the phase space reconstruction is combined with an RVM regression model, the service life prediction range is prolonged from the angle of a characteristic space, and the accuracy of long-term prediction is improved. According to the RVM model sparsity analysis, the kernel width of the Gaussian kernel function can influence the selection of the related vector and further the generalization performance of the RVM model. Meanwhile, the weighted index model can reflect the whole degradation process of the bearing according to the change trend of historical data, and can better reflect the nonlinear degradation characteristic of the bearing by combining with the polynomial degradation model. Therefore, a plurality of degradation curves can be provided by adjusting the Gaussian kernel width and the mixed degradation model, the closest to a known bearing degradation sample is selected as an optimal prediction curve by combining the Frechet distance, and the estimation result of the residual life can be obtained by extrapolating the optimal prediction curve to the bearing failure threshold value along the optimal prediction curve. The method improves the accuracy of long-term prediction of the residual life of the bearing, avoids adverse effects on the prediction performance caused by increase of the prediction step length, selection of parameter experience and the like, can be applied to other parts of the rotary machine or the prediction research of the residual life of equipment with similar mechanisms, and provides guarantee for fault prediction and health management of the equipment.
Drawings
FIG. 1 is a flow chart of a bearing residual life prediction method based on optimized RVM and a hybrid degradation model according to the invention;
FIG. 2 is a schematic diagram showing the selection of a prediction curve of the bearing 1 of the test set 2 in this embodiment;
fig. 3 is a long-term prediction result graph of two prediction models of the bearing 1 of the test set 2 in this embodiment.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
The known conditions for the prediction of the present invention are: obtaining bearing vibration data by a monitoring sensor, obtaining a numerical value of a bearing Health Indicator (HI for short) through feature extraction, fusion and standardization, marking the time corresponding to initial degradation as N =1, setting the current time as a checking time N = N, and then obtaining the numerical value of the bearing Health Indicator (HI) 1 ,HI 2 ,...,HI n ,...,HI N ) The health index values are connected to form a bearing degradation curve S; the remaining service life of the bearing is predicted from the inspection time N.
As shown in fig. 1, a method for predicting the residual life of a bearing based on an optimized RVM and a hybrid degradation model according to the present invention includes the following steps:
s1, parameter setting and initialization: setting the Gaussian kernel width δ i The value range of (1 is more than or equal to i and less than or equal to L) is set as [ delta [ [ delta ] 1 ,δ L ]Setting the variation as delta and setting a bearing failure threshold value gamma; let i =1;
s2, phase space reconstruction: leading in health index values from the initial degradation moment to the inspection moment, and constructing a feature matrix and a target vector; the specific implementation process is as follows: in the value of Health (HI) obtained 1 ,HI 2 ,...,HI n ,...,HI N ) And performing phase space reconstruction on the basis to obtain a feature matrix and a target vector required by RVM model training, wherein the feature matrix and the target vector are expressed as follows:
in the formula (1), the reaction mixture is,
is a feature matrix, based on the status of the device>
For the target vector, let target vector be z = [ z ] 1 ,...,z N-m ] T ，HI n And the health index value at n time is shown, and m is an embedding dimension.
S3, training an RVM model: performing RVM regression according to the set Gaussian kernel width value to determine a correlation vector;
the specific implementation process is as follows: given characteristics and objectives
Set of constituents, the RVM model aims to characterize the non-linear relationship between the input feature set and the target pair, namely:
wherein j =1, …, N-m; s noise (0,σ 2 ) Is a mean of 0 and a variance of
Gaussian noise of (2); w = (w) 1 ,w 2 ,...,w N ) T Is a weight vector; k selects a Gaussian kernel function and sets a Gaussian kernel width delta i The expression is as follows:
wherein | | | purple hair 2 Represents the square of the vector norm;
target variable z j Obeying a Gaussian distribution with a mean value of y (x) j ) Variance is σ 2 I.e. by
Let z j Independently and identically distributed, the likelihood function of the whole training sample is expressed as follows:
where Φ is the kernel function matrix, i.e., = [ K (x, x) 1 ),K(x,x 2 ),·,K(x,x N )] T 。
The overfitting problem in the above-equation parameter optimization is avoided with gaussian prior of w:
wherein,
represents a gaussian distribution; a = (a) 1 ,...,a j ,...,a N ) T Is a hyper-parametric vector, a j Represents the corresponding weight w j The accuracy of (2); the hyper-parameter vector a dominates the generalization performance of the model; and (3) obtaining posterior distribution of the weight by using a Bayes principle:
p(z|a,σ 2 ) Representing a marginal likelihood estimate; optimization of hyper-parameters a and sigma using successive sparse Bayesian learning algorithm (Sequential sparse Bayesian learning algorithm) 2 (ii) a After RVM model training is finished, the hyper-parameter { a j The input x corresponding to the non-zero weight in the j Is a correlation vector.
S4, fitting a degradation curve based on a multi-degradation model: fitting the correlation vector obtained by S3 by comprehensively using a single exponential model, a double exponential model and a polynomial model, determining fitting curve parameters by using a nonlinear least square regression method, and obtaining a degradation curve f i ；
The specific implementation process is as follows: after obtaining a correlation vector through an RVM model, fitting the obtained correlation vector in a curve fitting mode; the mixed degradation model is formed by a single exponential model, a weighted double exponential model and a polynomial model and is described as follows:
wherein, HI RV Representing a correlation vector obtained by RVM model training, wherein t represents the corresponding moment of the correlation vector; a. b, c and d are unknown parameters of the degradation model, the unknown parameters are determined by adopting a nonlinear least square regression method, the degradation model is fitted into a degradation curve, and the degradation curve is recorded as a degradation curve f i 。
S5, similarity measurement: calculating a real degradation curve S and a fitted degradation curve f by using the Frechet distance i Similarity between them; the realization process is as follows: for a given original degradation track S, a degradation curve f is calculated and fitted i The similarity between the two is measured by using a Frechet distance, which is defined as follows:
wherein ξ (x) and
represents two arbitrary non-decreasing continuous functions satisfying
Representing the euclidean distance between the two curves.
S6, iteration termination judgment: delta i >δ L When the iteration is ended, the next step is carried out; otherwise i = i +1, δ i+1 ＝δ i + Δ δ, and return to step S3;
s7, selecting an optimal degradation curve: the real degradation curve S and the fitted degradation curve f are combined i The fitted curve having the smallest similarity therebetween is used as the best fitted curve f o (ii) a The realization process is as follows: according to the width of the Gaussian kernelObtaining L fitting degradation curves in the set range of the degree, comparing the Frechet distances between all the fitting curves and the original degradation track, and taking the fitting curve with the minimum Frechet distance value as an optimal fitting curve, namely the optimal fitting curve is as follows: f. of o ＝{f i |min(Ω(S,f i ))}。
S8, extrapolation of a fitting curve: using a best-fit curve f o Is extrapolated until its health indicator value HI reaches the failure threshold value gamma, i.e. first reaches HI t Not less than gamma, the corresponding time of the mark is N f ＝t；
S9, calculating the remaining service life: the residual service life of the bearing is from the inspection time to the predicted failure time N f The time between; the realization process is as follows: when the optimal degraded track exceeds a failure threshold gamma for the first time, the bearing is considered to be failed; recording the time corresponding to the first time that the optimal track passes through the failure threshold value gamma as N f The predicted bearing residual life is then defined as follows:
RUL(N)＝N f -N (9)
where RUL (N) represents the predicted remaining useful life of the bearing at the inspection time N.
In the present embodiment, the embodiment uses the sincinatide test set 2 bearing 1 as an example to clarify the implementation results. The set of experimental data sets collected 984 sets of vibration signals in total from the beginning of the bearing run to the end of the degradation experiment. In the experiment, the data sampling frequency is 20kHz, 20480 data points are acquired each time, and the acquisition time interval is 10 minutes; the test bearings were inspected after the experiment was completed to find outer ring faults. The vibration signal characteristics of the bearing are extracted by adopting multi-domain statistical characteristics, and the health index of the bearing is constructed on the basis of the vibration signal characteristics, and the construction content does not belong to the description content of the patent and is not described in detail. For the bearing data in this example, the health indicator shows that the initial fault occurred at time 533 (i.e., the 533 th group of collected data, corresponding to time 533 × 10 =5330, and the time marked by the left vertical dotted line in fig. 2), the bearing failure threshold γ =0.66 (the position indicated by the horizontal dotted line in fig. 2), and the corresponding time 867 (time 8670). Setting the value range of the Gaussian kernel width as [ delta ] 1 ,δ L ]＝[0.005,0.05]Change ofThe amount Δ δ =0.005. The embedding dimension m =3 in formula (1). It should be noted that the main purpose of reconstructing the health indicator through the space is to obtain the correlation vector, and the main factor influencing the number of the correlation vectors is the kernel width, and the influence of the embedding dimension m on the correlation vectors is small. The parameters in equation (7) are solved using the "lsqcurvefit ()" function in MATLAB.
The examination time is set to N =632 (time marked by a long dashed line vertical to the middle in fig. 2). In fig. 2, the degradation curve described by the bearing health indicator is represented by a black curve; the health indicator value (the range indicated by the double arrow below (1) in fig. 2) between the initial fault 533 and the inspection time N =632 is input into the improved RVM model as a training sample, and a corresponding correlation vector and a fitted degradation curve f can be obtained by taking the value of each kernel width i E.g., several gray curves in FIG. 2, wherein (1) the true degradation curve S in the range is the corresponding curve f in FIG. 2 o The smallest frichet distance (one dark chain double-dashed line in the gray curve) corresponds to the correlation vector shown by the circle in fig. 3; extrapolating the optimal degradation curve to a failure threshold value gamma =0.66, wherein the corresponding time is N f =817, the predicted remaining lifetime is RUL (632) = (817-632) × 10 min =1850 min (corresponding to the range indicated by the lower double arrow in fig. 2 (3)), and the actual remaining lifetime actril (632) = (867-632) × 10 min =2350 min (corresponding to the range indicated by the lower double arrow in fig. 2 (2)).
In order to evaluate the performance of the proposed method, a relative prediction accuracy index is introduced:
where actriul (N) represents the actual remaining useful life of the bearing at inspection time N, and RUL (N) represents the predicted remaining useful life of the bearing at inspection time N. When the detection time is set to N =632, the relative prediction accuracy is 21.3%. If a double-exponential degradation model is adopted, the other settings are consistent, and the obtained prediction degradation curve is shown in fig. 3, wherein (a) is a mixed degradation model (the method of the invention), and (b) is a double-exponential model; the predicted residual life is (743-632) × 10 min =1110 min, which is earlier than the predicted residual life value obtained by the method, the relative prediction precision is 52.8%, and the prediction performance is obviously lower.
Another check moment is taken, for example, N =733, the actual remaining life is actriul (N) =1340 minutes, RUL (N) =104 × 10 minutes =1040 minutes obtained by the method described in the present invention, and the predicted value of the remaining life obtained by the double-index model is 660 minutes; if the check time N =833 is set (close to failure), the actual remaining life is actriul (N) =340 minutes, RUL (N) =270 minutes obtained by the method described in the present invention, and the predicted value of the remaining life obtained by the dual index model is 0 minute. The comparison shows that the closer to failure, the more training data are obtained, the more accurate the prediction is, but compared with the existing method, the prediction method provided by the invention is obviously improved in the aspect of long-term prediction.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.
Claims (5)
1. The method for predicting the residual life of the bearing based on the optimized RVM and the hybrid degradation model is characterized by comprising the following steps of:
s1, parameter setting and initialization: setting the Gaussian kernel width δ i Is set to [ delta ] as the value range of 1 ,δ L ]Setting the variation as delta and setting a bearing failure threshold value gamma; let i =1;
s2, reconstructing a phase space: importing health index values from the initial degradation moment to the inspection moment, and constructing a feature matrix and a target vector;
the known conditions for prediction are: obtaining bearing vibration data by a monitoring sensor, obtaining a numerical value of a bearing health index through feature extraction, fusion and standardization, marking the initial degradation corresponding time n =1, and setting the initial degradation corresponding time asThe previous moment is the checking moment N = N, and the bearing health index value is (HI) 1 ,HI 2 ,...,HI n ,...,HI N ) The health index values are connected to form a bearing degradation curve S; predicting the remaining service life of the bearing from the inspection time N;
the implementation process of the step S2 is as follows:
in the value of Health (HI) obtained 1 ,HI 2 ,...,HI n ,...,HI N ) And performing phase space reconstruction on the basis to obtain a feature matrix and a target vector required by RVM model training, wherein the feature matrix and the target vector are expressed as follows:
in the formula (1), the reaction mixture is,
is a feature matrix, based on the status of the device>
For the target vector, let target vector be z = [ ] 1 ,...,z N-m ] T ，HI n Representing the health index value at n moments, wherein m is an embedding dimension;
s3, training an RVM model: performing RVM regression according to the set Gaussian kernel width value to determine a correlation vector; the implementation process of the step S3 is as follows: given characteristics and objectives
Set of constituents, the RVM model aims to characterize the non-linear relationship between the input feature set and the target pair, namely:
wherein j =1, …, N-m; s noise (0,σ 2 ) Is a mean of 0 and a variance of
Gaussian noise of (2); w = (w) 1 ,w 2 ,...,w N ) T Is a weight vector; k selecting a Gaussian kernel function and setting the width delta of the Gaussian kernel i The expression is as follows:
wherein | | | calving 2 Represents the square of the vector norm;
target variable z j Obey a Gaussian distribution with a mean value of y (x) j ) Variance is σ 2 I.e. by
Let z j Independently and identically distributed, the likelihood function of the whole training sample is expressed as follows:
where Φ is the kernel function matrix, i.e., = [ K (x, x) 1 ),K(x,x 2 ),·,K(x,x N )] T ；
The overfitting problem in the above-equation parameter optimization is avoided with gaussian priors for w:
wherein,
represents a gaussian distribution; a = (a) 1 ,...,a j ,...,a N ) T Is a hyper-parametric vector, a j Represents the corresponding weight w j The accuracy of (2); the hyper-parameter vector a dominates the generalization performance of the model; and (3) obtaining posterior distribution of the weight by using a Bayes principle:
p(z|a,σ 2 ) Representing a marginal likelihood estimate; optimization of hyper-parameters a and sigma using a successive sparse Bayesian learning algorithm 2 (ii) a After RVM model training is finished, the hyper-parameter { a j The input x corresponding to the non-zero weight in the j Is a correlation vector;
s4, fitting a degradation curve based on a multi-degradation model: fitting the correlation vector obtained by S3 by comprehensively using a single exponential model, a double exponential model and a polynomial model, determining fitting curve parameters by using a nonlinear least square regression method, and obtaining a degradation curve f i ；
S5, similarity measurement: calculating a real degradation curve S and a fitting degradation curve f by using the Frechet distance i Similarity between them;
s6, iteration termination judgment: delta i >δ L When the iteration is ended, the next step is carried out; otherwise i = i +1, δ i+1 ＝δ i + Δ δ, and return to step S3;
s7, selecting an optimal degradation curve: the real degradation curve S and the fitted degradation curve f are combined i The fitted curve with the least similarity therebetween is used as the optimal fitted curve f o ；
S8, extrapolation of a fitting curve: using best-fit curve f o Is extrapolated until its health indicator value HI reaches the failure threshold value gamma, i.e. first reaches HI t Not less than gamma, the corresponding time of the mark is N f ＝t；
S9, calculating the remaining service life: the residual service life of the bearing is from the inspection time to the predicted failure time N f The time in between.
2. The method for predicting the residual life of the bearing based on the optimized RVM and the hybrid degradation model as claimed in claim 1, wherein the step S4 is realized by the following steps: after obtaining a correlation vector through an RVM model, fitting the obtained correlation vector in a curve fitting mode; the mixed degradation model is formed by a single exponential model, a weighted double exponential model and a polynomial model and is described as follows:
wherein, HI RV Representing a correlation vector obtained by RVM model training, wherein t represents the corresponding moment of the correlation vector; a. b, c and d are unknown parameters of the degradation model, the unknown parameters are determined by adopting a nonlinear least square regression method, the degradation model is fitted into a degradation curve, and the degradation curve is recorded as a degradation curve f i 。
3. The method for predicting the residual life of the bearing based on the optimized RVM and the hybrid degradation model as claimed in claim 1, wherein the step S5 is realized by the following steps: for a given original degradation track S, a degradation curve f is calculated and fitted i The similarity between the two is measured by using a Frechet distance, which is defined as follows:
wherein ξ (x) and
represents two arbitrary non-decreasing continuous functions, satisfies->
D(S(ξ(x),
Representing the euclidean distance between the two curves.
4. The method for predicting the residual life of the bearing based on the optimized RVM and the hybrid degradation model as claimed in claim 1, wherein the step S7 is realized by the following steps: obtaining L fitting degradation curves according to the set range of the Gaussian kernel width, comparing the Frechet distances between all the fitting curves and the original degradation track, and taking the fitting curve with the minimum Frechet distance value as an optimal fitting curve, namely the optimal fitting curve is as follows: f. of o ＝{f i |min(Ω(S,f i ))}。
5. The method for predicting the residual life of the bearing based on the optimized RVM and the hybrid degradation model as claimed in claim 1, wherein the step S9 is realized by the following steps: when the optimal degraded track exceeds a failure threshold gamma for the first time, the bearing is considered to be failed; recording the time corresponding to the first time that the optimal track passes through the failure threshold value gamma as N f The predicted bearing residual life is then defined as follows:
RUL(N)＝N f -N (9)
where RUL (N) represents the predicted remaining useful life of the bearing at the inspection time N.
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