CN111368403B - Self-adaptive non-linear degradation residual life prediction method - Google Patents

Self-adaptive non-linear degradation residual life prediction method Download PDF

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CN111368403B
CN111368403B CN202010113783.XA CN202010113783A CN111368403B CN 111368403 B CN111368403 B CN 111368403B CN 202010113783 A CN202010113783 A CN 202010113783A CN 111368403 B CN111368403 B CN 111368403B
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訾艳阳
江山
王宇
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Xian Jiaotong University
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Abstract

An adaptive non-linear degradation remaining life prediction method comprises the following steps: establishing a nonlinear degradation state space equation, and performing forward prediction based on equipment health indexes; obtaining posterior estimation of hidden variables in the nonlinear degradation state space equation according to a forward prediction result, updating initial parameters and a noise matrix in the nonlinear degradation state space equation by adopting an expectation-maximization-based algorithm, substituting the updated parameters and the posterior estimation result into the equation to obtain overrun time, and taking the difference value between the overrun time and the current time as a residual life prediction value; and when newly acquired equipment observation data are obtained each time, the process is repeated, the initial parameters and the noise matrix in the equation are updated each time new observation data are obtained, and the predicted value of the residual service life at the current moment is obtained. The invention fully considers the individual difference, degradation randomness and measurement error in the nonlinear degradation process of the equipment and ensures higher residual life prediction accuracy.

Description

Self-adaptive non-linear degradation residual life prediction method
Technical Field
The invention belongs to the field of equipment fault prediction and health management, and particularly relates to a self-adaptive nonlinear degradation residual life prediction method.
Background
With the continuous and deep industrialization process and the development of information technology, the utility and importance of the equipment failure prediction and health management (Prognostics and health management) technology are increasingly highlighted. The residual life prediction is used as the core of equipment failure prediction and health management, and the prediction precision and the algorithm robustness of the residual life prediction are of great significance for saving the production cost of enterprises and reducing safety accidents. Therefore, the method carries out fault prediction and health management on important equipment, further provides effective guidance for safety production and operation maintenance of enterprises, and is a research hotspot in the field of reliability engineering all the time.
At present, in the field of residual life prediction method research, most research works are based on a linearized stochastic model or a Wiener incremental stochastic model. However, in engineering practice, the degradation process of the complex electromechanical device often has nonlinear characteristics, the prediction result of a linear or interval linear model can deviate under strong nonlinearity, the residual life prediction of the nonlinear degradation device by using monitoring information in the existing nonlinear residual life prediction method can only partially reflect the degradation state of the device, and the individual difference, degradation randomness and measurement uncertainty of the device are not fully considered, so that the existing residual life prediction of the nonlinear degradation device has the problems of low precision and poor robustness. How to improve the residual life prediction accuracy and the algorithm robustness of the nonlinear equipment is a problem to be solved.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a self-adaptive nonlinear degradation residual life prediction method, which not only solves the problems of poor prediction precision deviation and robustness brought by the traditional linear residual life prediction method, but also fully considers the factors of individual difference, degradation randomness, measurement uncertainty and the like in the nonlinear degradation process of equipment, explores a novel Bayesian inference updating paradigm based on a nonlinear filtering technology, and provides an effective tool for improving the prediction precision of the nonlinear degradation residual life of the equipment.
The invention is realized by the following technical scheme:
a self-adaptive non-linear degradation residual life prediction method comprises the following steps:
(1) establishing a nonlinear degradation state space equation, wherein the nonlinear degradation state space equation comprises a state transition equation and an observation equation; taking the health state of the equipment as a hidden variable of a state transition equation and taking the health index of the equipment as an observation variable of an observation equation;
(2) forward prediction is carried out by utilizing the nonlinear degradation state space equation constructed in the step (1) and adopting an unscented Kalman filtering algorithm based on equipment health indexes;
(3) combining the forward prediction result in the step (2), performing backward smoothing by adopting an unscented Kalman smoothing algorithm containing covariance smoothing to obtain a backward smoothing result, and obtaining posterior estimation of hidden variables in a nonlinear degradation state space equation according to the backward smoothing result;
(4) updating initial parameters and a noise matrix in a nonlinear state space equation by adopting an expectation-maximization-based algorithm according to the posterior estimation result obtained in the step (3), substituting the updated parameters and the posterior estimation result into the nonlinear degradation state space equation to obtain the overrun time, and taking the difference value between the overrun time and the current time as a predicted value of the residual life;
(5) and (4) repeating the steps (2) to (4) each time newly acquired equipment observation data is obtained, updating initial parameters and a noise matrix in the nonlinear state space equation each time new observation data is obtained, and obtaining a predicted value of the residual life at the current moment.
The invention is further improved in that the nonlinear degradation state space equation established in the step (1) is as follows:
xk+1＝f(xk,uk)+v
yk＝h(xk,uk)+vy
wherein xkIs the equipment health index, k is the time stamp, f is the state transition function, h is the observation function, v and vyNoise matrices for the state equation and the measurement equation, respectively.
The further improvement of the invention is that in the step (3), an improved unscented kalman filter smoothing algorithm including covariance smoothing is adopted, and the specific flow of obtaining a backward smoothing result is as follows:
step 3.1, sequence of forward prediction results calculated in step 2
Figure BDA0002390859810000031
And noise sequence
Figure BDA0002390859810000032
Where the subscript 1: T represents the sequence of time 1 to time T, the value of k at time
Figure BDA0002390859810000033
And
Figure BDA0002390859810000034
performing unscented Kalman filtering forward one-step prediction, wherein k belongs to {0: T }, k is subjected to descending order dereferencing from T to obtain a forward one-step prediction result, and generating sampling particles through symmetric sampling according to the forward one-step prediction result
Figure BDA0002390859810000035
And particle weight { Wi-1Where i denotes different sample generating particles, according to which the particles are sampled
Figure BDA0002390859810000036
And particle weight { Wi-1And calculating to obtain a predicted value at the k +1 moment
Figure BDA0002390859810000037
Step 3.2, predicting the value according to the k +1 moment
Figure BDA0002390859810000038
Calculating a noise matrix and covariance at the k +1 moment;
step 3.3, calculating the smooth gain D at the k moment according to the noise matrix and the covariance at the k +1 momentk：
Step 3.4, initializing a hidden variable covariance smooth value at the time T;
step 3.5, smoothing the gain D according to the k momentkAnd initializing the hidden variable covariance smooth value at the T moment, and performing iterative backward smoothing calculation to obtain a backward smoothing result.
The invention has the further improvement that the step 3.2 comprises the following specific processes:
Figure BDA0002390859810000039
Figure BDA00023908598100000310
wherein
Figure BDA00023908598100000311
Is a k +1 time noise matrix, Ck+1Is the covariance at time k +1,
Figure BDA00023908598100000312
for forward prediction of the result sequence
Figure BDA00023908598100000313
The value of time k.
A further development of the invention is that, in step 3.3,
Figure BDA00023908598100000314
the invention has the further improvement that the step 3.4 comprises the following specific processes:
Figure BDA00023908598100000315
wherein, I is an identity matrix,
Figure BDA00023908598100000316
and kappaTCovariance and filter gain at time T, M, in the sequence of forward prediction results from step (2)T|TThe covariance smooth value of the hidden variable at the time T;
Figure BDA0002390859810000041
Figure BDA0002390859810000042
Figure BDA0002390859810000043
wherein xk|T、Pk|T、Mk|TBased on the current time T respectivelySmoothing results of the k-time hidden variable mean, the variance and the covariance, wherein k | T represents a smoothing value based on the current time T and k;
the backward smoothing results are:
Ex(xk)＝xk|T
Figure BDA00023908598100000410
Ex(xk-1xk)＝xk|Txk-1|T+Mk|T
wherein E isx(xk) The mean expectation of the hidden variable at time k,
Figure BDA0002390859810000044
mean the latent variable variance expectation at time k, Ex(xk-1xk) Representing the hidden variable covariance expectation at time k.
The further improvement of the invention is that the initial parameters and the noise matrix of the state space equation are updated by adopting an expectation-maximization-based algorithm in the step (4), and the updating expression is as follows:
Figure BDA0002390859810000045
Figure BDA0002390859810000046
Figure BDA0002390859810000047
Figure BDA0002390859810000048
wherein the content of the first and second substances,
Figure BDA0002390859810000049
initial value, initial variance, state transition equation noise matrix and observation equation noise matrix of the nonlinear degradation state space equation, E (h (x) respectivelyj) Expected for observation.
Compared with the prior art, the invention has the following beneficial technical effects:
according to the method, the equipment health index is utilized to construct a nonlinear degradation state space equation, so that the degradation process of the equipment is more reasonably depicted, and errors caused by a traditional residual life prediction method based on a linear simplified model are avoided; the unscented Kalman filtering method is adopted to drive the forward data of the model, so that the method has the characteristics of faster calculation, calculation resource saving and strong application instantaneity; the improved unscented Kalman smoothing algorithm is adopted to carry out backward smoothing on the hidden variable when new observation data are obtained, so that the posterior estimation of complete initial parameters and a noise matrix can be obtained, and the method has the characteristics of quickness and feasibility; by adopting a parameter updating strategy based on an expectation maximization algorithm, when new observation data are obtained each time, model initial parameters and a noise matrix are updated in a self-adaptive mode according to historical data, individual differences, degradation randomness and measurement errors in the degradation process of equipment are fully considered, and the prediction accuracy of the model can be effectively improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
FIG. 1 is a flow chart of a self-adaptive non-linear degradation remaining life prediction method based on unscented Kalman filtering according to the present invention;
FIG. 2 is a diagram of measuring the life cycle vibration waveform of the bearing according to the embodiment of the present invention.
FIG. 3 is a trend tracking chart of the health index of the bearing in the embodiment of the invention.
Fig. 4 is an enlarged view of fig. 3 at block.
FIG. 5 is a diagram illustrating a predicted residual life of a bearing according to an embodiment of the present invention.
FIG. 6 is a diagram illustrating an error of the prediction of the residual life of the bearing according to the embodiment of the present invention.
Detailed Description
The present invention will now be described in further detail with reference to specific examples, which are intended to be illustrative, but not limiting, of the invention.
Referring to fig. 1, the invention provides a self-adaptive non-linear degradation residual life prediction method based on unscented kalman filtering technology, which comprises the following steps of constructing a device non-linear degradation model; acquiring equipment operation data in real time, calculating equipment health indexes each time the operation data is acquired, and performing forward prediction by using unscented Kalman filtering; carrying out backward smoothing on the basis of forward prediction by utilizing an improved unscented Kalman smoothing algorithm containing covariance smoothing to obtain an implicit variable mean, variance and covariance posterior estimation; combining the obtained forward prediction result and the posterior estimation result, updating the initial parameters and the noise matrix by using an expectation maximization method, substituting the updated result into a nonlinear model, and calculating a predicted value of the residual life based on an overrun threshold; and when new observation data are obtained each time, the step of updating the initial parameters and the noise matrix by using the unscented Kalman filtering forward prediction to expectation maximization method is repeatedly carried out, the predicted value of the residual life is obtained, and the initial parameters and the noise matrix are updated.
The invention utilizes real-time operation data to predict the non-linear degradation residual life of equipment and is implemented according to the following specific steps:
(1) constructing a device nonlinear degradation model
Firstly, selecting a proper nonlinear degradation state space equation according to a degradation mechanism of nonlinear degradation equipment; the nonlinear degradation state space equation comprises a state transition equation and an observation equation; taking the health state of the equipment as a hidden variable of a state transition equation and taking the health index of the equipment as an observation variable of an observation equation;
specifically, the corresponding nonlinear degradation state space equation is selected according to the working state and degradation mechanism of the equipment, such as corrosion dominance or the like.
Then, considering individual difference, degradation randomness and measurement uncertainty of the nonlinear degradation equipment; and taking the implicit health state of the equipment as an implicit variable of a state transition equation, and taking the health index of the equipment calculated by utilizing the actual measured value as an observation variable of an observation equation. The equipment health index is calculated through equipment observation data obtained in real time, selection can be performed according to different equipment and working environments, and how to calculate is a known technology in the field.
The established nonlinear degradation state space equation is as follows:
xk+1＝f(xk,uk)+v
yk＝h(xk,uk)+vy
wherein xkThe index k is a time stamp, f is a state transition function, h is an observation function, the form of h is determined by different degradation tracks, v and v are equipment health indexesyNoise matrices for the state equation and the measurement equation, respectively. The model takes the initial parameters and the noise matrix as self-adaptive updatable parameters, and fully considers the influences of individual difference, degradation randomness and measurement errors of equipment.
The initial value of the established nonlinear degradation state space equation reflects the individual difference of equipment, the variance of the state transition equation reflects degradation randomness, and the variance of the measurement equation reflects measurement uncertainty.
(2) Model forward prediction
Firstly, acquiring real-time equipment operation data, and calculating to obtain an equipment health index value at the current moment according to the acquired real-time equipment operation data;
then, substituting the calculated equipment health index value into a nonlinear degradation state space equation, and performing model driving by using an unscented Kalman filtering algorithm to obtain a forward prediction result; the forward prediction result comprises a sequence
Figure BDA0002390859810000071
And noise sequence
Figure BDA0002390859810000072
(3) Model backward smoothing
Combining the forward prediction result obtained in the step (2), based on newly obtained equipment observation data, utilizing an unscented Kalman smoothing algorithm containing covariance smoothing to carry out backward smoothing on the model, and obtaining the posterior estimation of the hidden variable in the nonlinear degradation state space equation;
the specific process of obtaining the backward smoothing result by adopting the improved unscented Kalman filtering smoothing algorithm containing covariance smoothing is as follows:
step 3.1, sequence of forward prediction results calculated in step 2
Figure BDA0002390859810000073
And noise sequence
Figure BDA0002390859810000074
Where the subscript 1: T represents the sequence of time 1 to time T, the value of k at time
Figure BDA0002390859810000075
And
Figure BDA0002390859810000076
performing unscented Kalman filtering forward one-step prediction (wherein k belongs to {0: T }, k is a value in descending order from T, k is a variable and T is a constant) to obtain a forward one-step prediction result, and generating sampling particles by symmetric sampling according to the forward one-step prediction result
Figure BDA0002390859810000077
And particle weight { Wi-1Where i denotes different sample generating particles, according to which the particles are sampled
Figure BDA0002390859810000078
And particle weight { Wi-1And calculating to obtain a predicted value at the k +1 moment
Figure BDA0002390859810000079
Step 3.2, calculating a noise matrix and covariance at the moment k + 1:
Figure BDA0002390859810000081
Figure BDA0002390859810000082
wherein
Figure BDA0002390859810000083
Is a k +1 time noise matrix, Ck+1Is the covariance at time k +1,
Figure BDA0002390859810000084
for the forward prediction result sequence obtained in step (2)
Figure BDA0002390859810000085
The value of time k.
Step 3.3, calculating the smooth gain D at the moment kk：
Figure BDA0002390859810000086
Step 3.4, initializing the hidden variable covariance smooth value at the T moment:
Figure BDA0002390859810000087
wherein, I is an identity matrix,
Figure BDA0002390859810000088
and kappaTRespectively, the covariance of T time in the forward prediction result sequence obtained in step (2) (the covariance is the covariance between the hidden variable and the observed variable)And filter gain, MT|TThe covariance smooth value of the hidden variable at the time T;
step 3.5, iterative backward smoothing calculation:
Figure BDA0002390859810000089
Figure BDA00023908598100000810
Figure BDA00023908598100000811
wherein xk|T、Pk|T、Mk|TRespectively based on the mean value, the variance and the covariance smoothing result of the hidden variables at the time k of the current time T, wherein k | T represents that k starts to take the value from T-1 to 0 for the smoothing value at the past time k based on the current time T, and when k takes T-1, Mk|TIs MT|T。
The backward smoothing results are:
Ex(xk)＝xk|T
Figure BDA00023908598100000812
Ex(xk-1xk)＝xk|Txk-1|T+Mk|T
wherein E isx(xk) The mean expectation of the hidden variable at time k,
Figure BDA0002390859810000091
mean the latent variable variance expectation at time k, Ex(xk-1xk) Representing the hidden variable covariance expectation at time k.
(4) Initial parameter and noise matrix update
Firstly, updating initial parameters and a noise matrix by using an expectation-maximization algorithm according to a backward smoothing result obtained in the step (3). The update expression is:
Figure BDA0002390859810000092
Figure BDA0002390859810000093
Figure BDA0002390859810000094
Figure BDA0002390859810000095
wherein the content of the first and second substances,
Figure BDA0002390859810000096
respectively an initial value, an initial variance, a state transition equation noise matrix and an observation equation noise matrix of the nonlinear degradation state space equation, Ex(h(xk) For observation expectations, the expression of which is determined by the established observation equation.
Then, substituting the updated initial parameters and the noise matrix into a nonlinear degradation state space equation for prediction, and taking the first breakthrough of the safety threshold of the equipment health index as the overrun time;
and finally, taking the difference value between the overrun time and the current time as a predicted value of the residual life of the equipment.
(5) Model iterative driving
And (3) repeating the steps (2) to (4) after new observation data are obtained each time, obtaining a predicted value of the residual life and continuously updating the initial parameters and the noise matrix when new observation data are obtained each time, so as to realize real-time residual life prediction.
The following gives a specific application example process, and at the same time, the effectiveness of the invention in engineering application is verified.
In this example, the tested bearing was subjected to a full-life accelerated degradation test on a PRONOSTIA accelerated degradation test platform. In the bearing degradation process, vibration acceleration signals are collected through an acceleration sensor and are collected every 10 s. For safety reasons, it is defined that the degradation experiment was stopped when the peak to peak vibration value exceeded 20g, at which point the bearing was deemed to be completely failed, and the measured full life cycle vibration waveform of the bearing is shown in fig. 2.
By utilizing the method, the self-adaptive non-linear degradation residual life prediction method of the bearing comprises the following steps:
(1) constructing a non-linear degradation model
The exponential degradation model is a typical process for describing degradation accumulation, and is widely applied to degradation modeling of equipment corrosion, bearing fatigue wear and the like, so the example adopts the exponential degradation model to describe the degradation process of the bearing:
ak+1＝ak+v
yk＝ak exp(bt)+vy
wherein a isk+1＝ak+ v is the equation of state transition, a denotes the change in bearing hidden health, yk＝ak exp(bt)+vyThe bearing health index is an observation equation and is calculated by using actually measured data, and since the effective value of the vibration signal can represent the energy of the vibration signal, the effective value is selected as the bearing health index in the example and is subjected to smoothing treatment. b is a nonlinear parameter, b can be obtained by searching through an optimization method when the model is subjected to expectation maximization updating, and the algorithm of matlab library function 'fmisearch' is used for calculation in the embodiment. v, vyAnd the variance of the state transition equation and the observation equation is expressed and used for describing the randomness and the measurement error of the bearing degradation, and each initial value of the state space equation is used for describing the individual difference of the bearing degradation.
(2) Model forward prediction
Acquiring real-time operation data of equipment, and calculating to obtain an effective value of a bearing vibration signal at the current moment; substituting the calculated bearing vibration signal effective value into a state space equation, and performing model driving by using unscented Kalman filtering to obtain a model forward prediction result;
(3) model backward smoothing
Calculating an effective value of newly acquired observation data by combining the forward prediction result of the model obtained in the step (2), and performing backward smoothing on the model by using an improved unscented Kalman smoothing algorithm containing covariance smoothing to acquire the posterior estimation of the hidden variable in the nonlinear degradation state space equation;
(4) initial parameter and noise matrix update
Firstly, combining the forward prediction and backward smoothing results obtained in the step (3) and the step (2), and updating an initial parameter and a noise matrix by using an expectation-maximization algorithm.
Then, substituting the updated initial parameters and the noise matrix into a nonlinear degradation state space equation for prediction, and taking the first breakthrough of the safety threshold of the bearing health index as the overrun time, wherein in the embodiment, the safety threshold of the bearing health index is 1.95;
and finally, taking the difference value between the overrun time and the current time as a predicted value of the residual life of the equipment.
(5) Model iterative driving
After new observation data are obtained each time, repeating the steps (2) to (4), obtaining a residual life prediction value, continuously updating the initial parameters and the noise matrix, and predicting the residual life in real time, wherein in the example, the updating expression of each parameter of the exponential nonlinear degradation model is as follows:
Figure BDA0002390859810000111
Figure BDA0002390859810000112
Figure BDA0002390859810000113
Figure BDA0002390859810000114
wherein the content of the first and second substances,
Figure BDA0002390859810000115
the initial value and the initial variance of the hidden variable are obtained,
Figure BDA0002390859810000116
in order to be a state-transition noise matrix,
Figure BDA0002390859810000117
to measure the noise matrix.
In order to verify the effectiveness of the invention, a traditional particle filtering method is selected for comparison. The bearing degradation trajectory tracking of different methods is shown in fig. 3 and 4, and as can be seen from fig. 3 and 4, compared with the traditional particle filtering method, the adaptive unscented kalman filter method provided by the invention can more accurately track the equipment degradation process, and has higher tracking precision. The prediction results of the residual life of the bearings in different methods are shown in fig. 5, and as can be seen from fig. 5, the predicted value of the residual life of the adaptive unscented kalman filter method provided by the invention is more suitable for the actual residual life, the fluctuation is smaller, and the robustness of the algorithm is strong. The residual life prediction error of the bearing of the different methods is shown in fig. 6. As can be seen from fig. 6, the prediction accuracy of the residual life of the adaptive unscented kalman filter method provided by the present invention is higher, and the absolute average error is only 2.5135 (the absolute average error of the conventional particle filter method is 17.9189).
Compared with other traditional methods, the self-adaptive non-linear degradation residual life prediction method provided by the invention effectively avoids errors caused by linear simplification, can self-adaptively adjust the initial parameters and the noise matrix, fully considers the individual difference, degradation randomness and measurement errors in the non-linear degradation process of the equipment, ensures higher residual life prediction accuracy, and verifies the robustness and effectiveness of the algorithm.

Claims (6)

1. A self-adaptive non-linear degradation residual life prediction method is characterized by comprising the following steps:
(1) establishing a nonlinear degradation state space equation, wherein the nonlinear degradation state space equation comprises a state transition equation and an observation equation; taking the health state of the equipment as a hidden variable of a state transition equation and taking the health index of the equipment as an observation variable of an observation equation;
(2) forward prediction is carried out by utilizing the nonlinear degradation state space equation constructed in the step (1) and adopting an unscented Kalman filtering algorithm based on equipment health indexes;
(3) combining the forward prediction result in the step (2), performing backward smoothing by adopting an unscented Kalman smoothing algorithm containing covariance smoothing to obtain a backward smoothing result, and obtaining posterior estimation of hidden variables in a nonlinear degradation state space equation according to the backward smoothing result; the specific flow of obtaining the backward smoothing result by adopting the improved unscented Kalman filtering smoothing algorithm containing covariance smoothing is as follows:
step 3.1, sequence of forward prediction results calculated in step 2
Figure FDA0003478903140000011
And noise sequence
Figure FDA0003478903140000012
Where the subscript 1: T represents the sequence of time 1 to time T, the value of k at time
Figure FDA0003478903140000013
And
Figure FDA0003478903140000014
performing unscented Kalman filtering forward one-step prediction, wherein k belongs to {0: T }, k is subjected to descending order dereferencing from T to obtain a forward one-step prediction result, and generating sampling particles through symmetric sampling according to the forward one-step prediction result
Figure FDA0003478903140000015
And particle weightWi-1Where i denotes different sample generating particles, according to which the particles are sampled
Figure FDA0003478903140000016
And particle weight { Wi-1And calculating to obtain a predicted value at the k +1 moment
Figure FDA0003478903140000017
Step 3.2, predicting the value according to the k +1 moment
Figure FDA0003478903140000018
Calculating a noise matrix and covariance at the k +1 moment;
step 3.3, calculating the smooth gain D at the k moment according to the noise matrix and the covariance at the k +1 momentk：
Step 3.4, initializing a hidden variable covariance smooth value at the time T;
step 3.5, smoothing the gain D according to the k momentkInitializing a hidden variable covariance smooth value at the time T, and performing iterative backward smoothing calculation to obtain a backward smoothing result; (4) updating initial parameters and a noise matrix in a nonlinear state space equation by adopting an expectation-maximization-based algorithm according to the posterior estimation result obtained in the step (3), substituting the updated parameters and the posterior estimation result into the nonlinear degradation state space equation to obtain the overrun time, and taking the difference value between the overrun time and the current time as a predicted value of the residual life;
(5) and (4) repeating the steps (2) to (4) each time newly acquired equipment observation data is obtained, updating initial parameters and a noise matrix in the nonlinear state space equation each time new observation data is obtained, and obtaining a predicted value of the residual life at the current moment.
2. The adaptive non-linear degradation remaining life prediction method according to claim 1, wherein the non-linear degradation state space equation established in step (1) is as follows:
xk+1＝f(xk,uk)+v
yk＝h(xk,uk)+vy
wherein xkIs the equipment health index, k is the time stamp, f is the state transition function, h is the observation function, v and vyNoise matrices for the state equation and the measurement equation, respectively.
3. The method for predicting the remaining life of the adaptive nonlinear degradation according to claim 1, wherein the specific process of the step 3.2 is as follows:
Figure FDA0003478903140000021
Figure FDA0003478903140000022
wherein
Figure FDA0003478903140000023
Is a k +1 time noise matrix, Ck+1Is the covariance at time k +1,
Figure FDA0003478903140000024
for forward prediction of the result sequence
Figure FDA0003478903140000025
The value of time k.
4. An adaptive non-linear degradation remaining life prediction method according to claim 3, characterized in that, in step 3.3,
Figure FDA0003478903140000026
5. the adaptive non-linear degradation remaining life prediction method according to claim 4, wherein the specific process of step 3.4 is as follows:
Figure FDA0003478903140000027
wherein, I is an identity matrix,
Figure FDA0003478903140000028
and kappaTCovariance and filter gain at time T, M, in the sequence of forward prediction results from step (2)T|TThe covariance smooth value of the hidden variable at the time T;
Figure FDA0003478903140000031
Figure FDA0003478903140000032
Figure FDA0003478903140000033
wherein xk|T、Pk|T、Mk|TRespectively based on the k time hidden variable mean value, the variance and the covariance smoothing result of the current time T, wherein k | T represents the smoothing value based on the current time T time k;
the backward smoothing results are:
Ex(xk)＝xk|T
Figure FDA0003478903140000034
Ex(xk-1xk)＝xk|Txk-1|T+Mk|T
wherein E isx(xk) The mean expectation of the hidden variable at time k,
Figure FDA0003478903140000035
mean the latent variable variance expectation at time k, Ex(xk-1xk) Representing the hidden variable covariance expectation at time k.
6. The adaptive non-linear degradation remaining life prediction method according to claim 1, wherein the updating of the initial parameters and the noise matrix of the state space equation by the expectation-maximization-based algorithm in step (4) is performed by:
Figure FDA0003478903140000036
Figure FDA0003478903140000037
Figure FDA0003478903140000038
Figure FDA0003478903140000039
wherein the content of the first and second substances,
Figure FDA00034789031400000310
respectively an initial value, an initial variance, a state transition equation noise matrix and an observation equation noise matrix of the nonlinear degradation state space equation, Ex(h(xk) Is expected to be observed).
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