CN113158471B - Degradation equipment residual life prediction method considering measurement uncertainty - Google Patents
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Abstract
The invention discloses a degraded equipment residual life prediction method considering measurement uncertainty, which comprises the following steps of: s1: collecting discrete measurement time points and degradation amount sets of degradation equipment, and establishing a performance degradation model; s2: according to the performance degradation model, performing parameter estimation on the performance degradation model; s3: and predicting the residual life based on the performance degradation model and the parameter estimation result. The invention provides a self-adaptive degradation equipment residual life prediction method considering measurement uncertainty, which fully considers the error condition of equipment characteristic extraction in the degradation process aiming at the degradation randomness of actual equipment in the degradation process, not only can accurately predict and analyze the residual life of the equipment, but also can be used as an effective analysis tool in the life cycle.
Description
Technical Field
The invention belongs to the technical field of reliability engineering, and particularly relates to a method for predicting the residual life of degradation equipment by considering measurement uncertainty.
Background
With the continuous development of production technology, modern industrial equipment is developing towards large-scale, complicated and intelligent. However, large and complex industrial equipment is affected by various environmental factors during long-term operation, and the performance of the equipment is changed correspondingly. Over time, and reaching a certain threshold, equipment damage occurs, manifested as a change in the output parameters of the equipment, such as deterioration of component performance, wear of mechanical components and aging of insulating materials. To a certain extent, the device will eventually fail. Once an accident occurs due to such a malfunction, the loss of personnel and property and even environmental damage is often immeasurable. If the life of the equipment can be monitored and evaluated at an early stage of performance degradation to determine the optimal time for equipment maintenance and to make a corresponding maintenance plan, this may improve the reliability of the equipment, reduce the risk of equipment operation, and reduce the operating costs. Therefore, an evolution model of the degradation rule is established through the measurement data of the equipment degradation, and the residual service life (RUL) prediction of the equipment is further realized, and is the basis and core content of the Prediction and Health Management (PHM). The service life prediction result provides scientific basis for maintenance decision and spare part replacement.
In engineering practice, it is often impractical or expensive to accurately measure the hidden degradation state of a device. Furthermore, measurement data obtained by sensor state monitoring relating to the implicit degradation state of a device is inevitably affected by factors such as noise, interference and unreasonable measuring instruments. In this case, the measurement data obtained are not reasonable and only partially reflect the state of degradation of the device. In order to describe the influence of measurement uncertainty and accurately describe the degradation condition of the equipment, a relation between a potential degradation state and uncertain measurement data needs to be established.
In practice, based on the adaptive Wiener process framework, a degradation model is built that takes into account uncertainty measurements. Further based on logarithmic transformation and inverse Gaussian characteristics, an analytic form of the device life distribution of the adaptive Wiener process by considering uncertain measurement is derived theoretically, and an analytic solution of the residual life is derived. Therefore, the residual life prediction of the random degradation equipment considering the uncertain measurement self-adaptive Wiener process is obtained, and the accuracy of the residual life prediction is improved.
Disclosure of Invention
The invention aims to solve the problem of residual life prediction and provides a method for predicting the residual life of degradation equipment by considering measurement uncertainty.
The technical scheme of the invention is as follows: a degraded equipment residual life prediction method considering measurement uncertainty comprises the following steps:
s1: collecting discrete measurement time points and a degradation amount set of degradation equipment, and establishing a performance degradation model;
s2: according to the performance degradation model, performing parameter estimation on the performance degradation model;
s3: and predicting the residual life based on the performance degradation model and the parameter estimation result.
Further, step S1 comprises the following sub-steps:
s11: collecting discrete measurement time points 0= t of degradation equipment 0 <t 1 <…<t i And a set of degeneration amounts Y 1:i ＝{y 1 ,y 2 ,…,y i Get the corresponding degradation state set X 1:i ＝{x 1 ,x 2 ,…,x i In which y 1 ,y 2 ,…,y i Represents t 1 ,…,t i Amount of degradation, x, of time-of-day degraded device 1 ,x 2 ,…,x i Denotes t 1 ,…,t i Momentarily degrading a degradation state of the device;
s12: establishing a set of degenerate states X 1:i ＝{x 1 ,x 2 ,…,x i And the set of degeneration amounts Y 1:i ＝{y 1 ,y 2 ,…,y i The performance degradation equation y between i ＝x i +ε i As a model of performance degradation, where ε i Represents t i Random measurement error of time of day.
Further, step S2 comprises the following sub-steps:
s21: according to the performance degradation model, the unknown parameter theta = (k) 2 ,σ 2 ,γ 2 V, α) establishes a likelihood function l (θ | Y) of the degraded device, where k 2 Expressing the square, σ, of the diffusion coefficient of the adaptive drift term 2 Square of diffusion coefficient, gamma, representing adaptive Wiener 2 A variance representing a measurement error, v represents a drift coefficient, α represents a time exponential power of the nonlinear degradation, and Y represents monitoring data considering measurement uncertainty;
s22: k is obtained in turn from the likelihood function l (theta | Y) of the degraded device 2 、σ 2 、γ 2 And a maximum likelihood function of v and a profile likelihood function l (k, σ, γ, α | Y, v) of α, where Y represents measurement data of the degraded device corresponding to the unknown parameter θ, k represents an adaptive drift term diffusion coefficient, σ represents an adaptive Wiener diffusion coefficient, and γ represents a measurement error;
s23: using a multidimensional search method according to k 2 、σ 2 、γ 2 And a section likelihood function l (k, sigma, gamma, alpha | Y, v) of alpha and a maximum likelihood function of v are obtained, and k is obtained in turn 2 ,σ 2 ,γ 2 And maximum likelihood estimation values of alpha and v, completing parameter estimation.
Further, in step S21, the expression of the likelihood function l (θ | Y) of the degeneration apparatus is:
wherein theta represents an unknown parameter, Y represents monitoring data considering measurement uncertainty, N represents the number of degraded devices, M represents the number of monitoring points of one degraded device, and Y represents the number of monitoring points of one degraded device i Representing monitored data of a certain plant, sigma representing Y i V denotes the drift coefficient, S i Representing two monitoring point time intervals;
in step S22, the maximum likelihood function of the drift coefficient v is expressed as:
in step S22, k 2 、σ 2 、γ 2 The expression of the profile likelihood function l (k, σ, γ, α | Y, v) of sum α is:
wherein k represents the diffusion coefficient of the adaptive drift term, sigma represents the diffusion coefficient of the adaptive Wiener, and gamma 2 Indicating the variance of the measurement error, Y i Representing monitoring data of a certain plant, sigma i Represents Y i Variance of (c), Ω i Representing Y without consideration of adaptive Wiener i The variance of (c).
Further, step S3 comprises the following sub-steps:
s31: at discrete measurement time points 0= t 0 <t 1 <…<t i In accordance with the performance degradation equation y i ＝x i +ε i Set of degraded states X 1:i ＝{x 1 ,x 2 ,…,x i The performance degradation model is transformed according to the estimation result of the parameters;
s32: and (5) estimating the degradation state according to the transformed performance degradation model by using a Kalman filtering algorithm to finish the service life prediction.
Further, in step S31, the calculation formula for transforming the performance degradation model is as follows:
wherein x is i Representing discrete measurement times t i Degraded state of degraded device, x i-1 Representing discrete measurement times t i-1 Degradation state of a degraded device, v denotes the drift coefficient, Δ S i Representing the time interval of non-linear degradation, eta representing the noise term due to the time-varying uncertainty of the degradation process, y i Representing the monitored data, epsilon, taking into account measurement errors i Indicating a measurement error.
Further, in step S32, a Kalman filter algorithm is used to perform degradation state estimation, and the degradation state estimation is updated in the degradation state estimation process, where a calculation formula of the degradation state estimation is:
wherein,
representing a set Y of through-degradations 1:i For the degraded state x i Estimated expectation, P i|i Representing a set Y of pass through degradation quantities 1:i For degradation state x i The variance of the estimate is determined by the variance of the estimate,
representing the last step through a set of degeneration metricsY of the formula 1:i For the degraded state x i Estimated expectation, P i|i-1 Set Y of passing degradation quantity representing the last step 1:i For degradation state x i The estimated variance, K (i) represents the filter gain,
is shown at t i-1 Mean value of the estimated values of the time-of-day monitoring data, v represents the drift coefficient, Δ S i Representing the non-linear degradation time interval, y (i) representing the monitored data taking into account measurement errors, gamma 2 Representing the variance of the measurement error, P i-1|i-1 Is shown at t i-1 Variance, pi, of the estimated value of the time-of-day monitoring data i Represents the variance of the noise term η;
the calculation formula for updating is as follows:
P i|i ＝(1-K(i))P i|i-1 。
further, in step S32, a specific method for predicting the remaining life includes: the time at which the degraded state estimation result first reaches the predetermined failure threshold is taken as the remaining life start time of the degraded device.
The invention has the beneficial effects that: the invention provides a self-adaptive degraded equipment residual life prediction method considering measurement uncertainty, which fully considers the error condition of characteristic extraction of equipment in the degradation process aiming at the degradation randomness of actual equipment in the degradation process, not only can accurately predict and analyze the residual life of the equipment, but also can be used as an effective analysis tool in the life cycle, and provides a powerful theoretical basis for maintenance management decisions such as equipment spare part ordering, and the like, thereby realizing efficient and reasonable equipment management and avoiding waste, and further having good engineering application value.
Drawings
FIG. 1 is a flow chart of a method of predicting remaining life;
FIG. 2 is a diagram illustrating the capacity degradation process of four lithium batteries;
FIG. 3 is a diagram of lithium battery degradation fitting effects under two methods;
FIG. 4 is a probability density distribution diagram of the remaining life of the lithium battery under two methods;
FIG. 5 is a graph of absolute error of remaining life prediction for two methods;
FIG. 6 is a graph of relative error in residual life prediction for two methods;
fig. 7 is a diagram of the residual life prediction mean square error of two methods.
Detailed Description
The embodiments of the present invention will be further described with reference to the accompanying drawings.
Before describing specific embodiments of the present invention, in order to make the solution of the present invention more clear and complete, the definitions of abbreviations and key terms appearing in the present invention will be explained:
wiener process: an adaptive wiener process.
As shown in fig. 1, the present invention provides a method for predicting the remaining life of a degraded device considering measurement uncertainty, comprising the steps of:
s1: collecting discrete measurement time points and degradation amount sets of degradation equipment, and establishing a performance degradation model;
s2: according to the performance degradation model, performing parameter estimation on the performance degradation model;
s3: and predicting the residual life based on the performance degradation model and the parameter estimation result.
In an embodiment of the present invention, step S1 includes the following sub-steps:
s11: collecting discrete measurement time points 0= t of a degraded device 0 <t 1 <…<t i And a set of degeneration amounts Y 1:i ＝{y 1 ,y 2 ,…,y i Get the corresponding degradation state set X 1:i ＝{x 1 ,x 2 ,…,x i In which y 1 ,y 2 ,…,y i Denotes t 1 ,…,t i Amount of degradation, x, of time-of-day degraded device 1 ,x 2 ,…,x i Represents t 1 ,…,t i Momentarily degrading a degradation state of the device;
s12: establishing a set of degenerate states X 1:i ＝{x 1 ,x 2 ,…,x i And degenerationSet of quantities Y 1:i ＝{y 1 ,y 2 ,…,y i The performance degradation equation y between i ＝x i +ε i As a model of performance degradation, where ε i Denotes t i Random measurement error of time of day.
In an embodiment of the present invention, step S2 includes the following sub-steps:
s21: according to the performance degradation model, the unknown parameter theta = (k) 2 ,σ 2 ,γ 2 V, α) establishes a likelihood function l (θ | Y) of the degraded device, where k is 2 Expressing the square, σ, of the diffusion coefficient of the adaptive drift term 2 Square of diffusion coefficient, gamma, representing adaptive Wiener 2 A variance representing a measurement error, v represents a drift coefficient, α represents a time exponential power of the nonlinear degradation, and Y represents monitoring data considering measurement uncertainty;
s22: k is obtained in turn from the likelihood function l (theta | Y) of the degraded device 2 、σ 2 、γ 2 And a maximum likelihood function of v and a profile likelihood function l (k, σ, γ, α | Y, v) of α, where Y represents measurement data of the degraded device corresponding to the unknown parameter θ, k represents an adaptive drift term diffusion coefficient, σ represents a diffusion coefficient of an adaptive Wiener, and γ represents a measurement error;
s23: using a multidimensional search method according to k 2 、σ 2 、γ 2 And a section likelihood function l (k, sigma, gamma, alpha | Y, v) of alpha and a maximum likelihood function of v are obtained, and k is obtained in turn 2 ,σ 2 ,γ 2 And maximum likelihood estimation values of alpha and v, completing parameter estimation.
In the embodiment of the present invention, in the step S21, the expression of the likelihood function l (θ | Y) of the degeneration apparatus is:
wherein theta represents an unknown parameter, Y represents monitoring data considering measurement uncertainty, N represents the number of degraded devices, M represents the number of monitoring points of one degraded device, and Y represents the number of monitoring points of one degraded device i Indicates a certainMonitoring data of the plant, Σ representing Y i V denotes the drift coefficient, S i Representing two monitoring point time intervals;
in step S22, the maximum likelihood function of the drift coefficient v is expressed as:
in step S22, k 2 、σ 2 、γ 2 The expression of the profile likelihood function l (k, σ, γ, α | Y, v) of and α is:
wherein k represents the diffusion coefficient of the adaptive drift term, sigma represents the diffusion coefficient of the adaptive Wiener, and gamma 2 Variance, Y, representing measurement error i Representing monitoring data of a plant, sigma i Represents Y i Variance of (c), Ω i Representing Y without considering adaptive Wiener i The variance of (c).
In an embodiment of the present invention, step S3 includes the following sub-steps:
s31: at discrete measurement time points 0= t 0 <t 1 <…<t i In accordance with the performance degradation equation y i ＝x i +ε i Set of degraded states X 1:i ＝{x 1 ,x 2 ,…,x i The performance degradation model is transformed according to the estimation result of the parameters;
s32: and estimating the degradation state according to the transformed performance degradation model by using a Kalman filtering algorithm to finish the service life prediction.
In the embodiment of the present invention, in step S31, a calculation formula for transforming the performance degradation model is as follows:
wherein x is i Representing discrete measurement times t i Degraded state of degraded device, x i-1 Representing discrete measurement times t i-1 Degradation state of a degraded device, v denotes the drift coefficient, Δ S i Representing the time interval of non-linear degradation, eta representing the noise term due to the time-varying uncertainty of the degradation process, y i Representing the monitored data, e, taking into account measurement errors i Indicating a measurement error.
In the embodiment of the present invention, in step S32, a Kalman filter algorithm is used to perform degradation state estimation, and the degradation state estimation is updated in the degradation state estimation process, where the calculation formula of the degradation state estimation is:
K(i)＝P i|i-1 (P i|i-1 +γ 2 ) -1
P i|i-1 ＝P i-1|i-1 +π i
wherein,
representing a set Y of through-degradations 1:i For degradation state x i Estimated expectation, P i|i Representing a set Y of through-degradations 1:i For the degraded state x i The variance of the estimate is determined by the variance of the estimate,
representing the last step by a set of degradation values Y 1:i For degradation state x i Estimated expectation, P i|i-1 Representing the last step by a set of degradation values Y 1:i For the degraded state x i The variance of the estimate, K (i) represents the filter gain,
is shown at t i-1 Mean value of the estimated values of the time-of-day monitoring data, v represents the drift coefficient, Δ S i Representing the non-linear degradation time interval, y (i) representing the monitored data taking into account measurement errors, gamma 2 Variance, P, representing measurement error i-1|i-1 Is shown at t i-1 Variance, pi, of the estimated value of the time-of-day monitoring data i Represents the variance of the noise term η;
the calculation formula for updating is as follows:
P i|i ＝(1-K(i))P i|i-1 。
in the embodiment of the present invention, in step S32, a specific method for predicting the remaining life is as follows: the time at which the degraded state estimation result first reaches the predetermined failure threshold is taken as the remaining life start time of the degraded device.
Detailed Description
The method of the present invention is verified below for lithium battery capacity degradation data with measurement uncertainty. The data set was obtained by a charge-discharge experiment at room temperature, and the state information (including capacity) of the battery was recorded as a function of charge-discharge cycles. Due to a complex aging mechanism, the capacity of the lithium battery may decrease with charge and discharge cycles. Fig. 2 shows the deterioration of four battery packs #5, #6, #7 and #18 of the space agency of america, and it can be seen from the graph that the capacity of each cell is in a downward trend with a period of time. Monitoring the degradation data Y due to the influence of measurement uncertainty 1:i May exceed the failure threshold before the actual failure time.
A. Establishing a performance degradation model capable of describing an adaptive Wiener process for a device considering measurement uncertainty
In engineering practice, it is often impractical or expensive to accurately measure the hidden degradation state of a device. Furthermore, measurement data obtained by sensor state monitoring relating to the implicit degradation state of a device is inevitably affected by factors such as noise, interference and unreasonable measuring instruments. In this case, the measurement data obtained are not reasonable and only partially reflect the state of degradation of the device. To describe the effect of measurement uncertainty, it may be considered to establish a relationship between the potential degradation state and the uncertain measurement data.
1) Stochastic regression process modeling taking into account measurement uncertainty
The degradation model based on the adaptive Wiener process is a typical nonlinear random model for describing the random degradation of equipment, and the model is widely applied to degradation modeling of mechanical wear, corrosion and the like. In general, the degradation model { X (t), t ≧ 0} based on Wiener process can be described as:
where v (t) is the drift rate over time following the Wiener process, v 0 >0 is the initial drift rate, k is the diffusion coefficient of the adaptive drift, and W (t) is the standard Brownian motion independent of B (t). S (t; α) is a function with a parameter α that monotonically increases over time. For the case where there is measurement uncertainty in the degradation process, a degradation model between the potential degradation state and the uncertain measurement data is established based on equation (45) and the monitored data in the degradation process. Specifically, it can be expressed as:
Y(t)＝X(t)+ε，(2)
where ε is the random measurement error, and ε is assumed to be an independent identically distributed Gaussian distribution with ε -N (0, γ) at any time t 2 ). Further assuming that ε and B (t) are independent of each other, the above assumptions are widely used in the fields of degradation modeling and lifetime estimation.
2) Definition of remaining Life
To enable remaining life estimation, the life of the device is defined by the concept of the first arrival time of a random degradation process. In other words, once the random degradation process first reaches a predetermined failure threshold, the device is considered to be invalid and requires maintenance to be reused. According to the first arrival time concept, the lifetime of a device can be defined as:
T＝inf{t:X(t)≥w|X(0)<w}，(3)
where w is a preset fault threshold, typically determined by some industry standard, such as amplitude and gyroscope drift.
Based on the above, under the above framework, the main objective of the present invention is to realize the prediction of the remaining life of the service equipment based on the real-time monitoring degradation data, and to realize the update of the remaining life distribution after acquiring new degradation monitoring data. Assume that the discrete monitoring time point at which the degradation measurement data is acquired is 0= t 0 <t 1 <…<t i Let y i ＝Y(t i ) Represents t i The amount of degradation at that time. Thus, by time t i May be represented as Y 1:i ＝{y 1 ,y 2 ,…,y i X, the set of corresponding degradation states 1:i ＝{x 1 ,x 2 ,…,x i In which x i ＝X(t i ). T can be further represented by the formula (2) i The measurement equation at a time is described as y i ＝x i +ε i In which epsilon i Is an independent, identically distributed implementation of epsilon.
L i ＝inf{l i >0:X(l i +t i )≥w}，(4)
Corresponding to the remaining life L i Respectively as a probability density function and a cumulative distribution function of
And
B. parameter estimation
To realize the unknown parameter θ = (k) of the degradation model 2 ,σ 2 ,γ 2 V, α) using maximum likelihood estimation, assuming that there are N measurement devices and the measurement time of the ith device is t 1 ,t 2 ,…t M And the corresponding measured data is { Y } i (t j )＝y i,j I =1,2, \8230, N, j =1,2, \8230, M }. As can be seen from equation (2), the ith device is at t j The measurement of the time of day can be expressed as
Wherein epsilon i,j Is a measurement error and has epsilon i,j ～N(0,γ 2 )。
For convenience, the measured data of the ith device is taken as an example, and the likelihood function corresponding to the measured data is studied. Let t = (t) 1 ,t 2 ,…,t M )'，y i ＝y i,j J =1,2, \8230M, knowing y from the independence assumption and the independent incremental nature of the standard Brown ian motion i Is multivariate normally distributed, and has the following mean and variance characteristics:
where D and Q are both an M matrix, I M Is a M th The order identity matrix is specifically as follows:
thus for the measurement data of the ith device, there are
y i ～N(u,k 2 D+σ 2 Q+γ 2 I M )，(8)
The likelihood function for all the measurement data Y corresponding to theta is
Further, for equation (9), the first partial derivative with respect to v is obtained, having
k 2 ,σ 2 ,γ 2 And α with respect to vHas a section likelihood function of maximum likelihood estimation value of
Based on this, k 2 ,σ 2 ,γ 2 The maximum likelihood estimation value of the sum α can be obtained by the maximum profile function formula (11) by a multidimensional search method. Then, k is put 2 ,σ 2 ,γ 2 And the maximum likelihood estimate of α is substituted back into equation (10) to obtain the maximum likelihood estimate of v, as shown in table 1.
TABLE 1
C. Residual life prediction considering measurement uncertainty effects
First only the potential degradation process { X (t), t ≧ 0} is considered. To incorporate the current degradation state and subsequent update mechanism for remaining life prediction, assume that the system is at t i With the time still operating normally, the potential degradation state is X (t) i )＝x i (x i <w). Therefore, for l ≧ t i Given x i From t, according to Markov property of Wiener process i The time-starting degeneration process has a time-varying trajectory
In this case, if l is a random process { X (l), l ≧ t i The first arrival time of, then l-t according to the formula (4) of remaining life i Corresponds to t i The remaining life of the device. Therefore, the transformation t = l-t is adopted for equation (12) i Wherein t is>0, then the degradation process { X (t), t ≧ 0} becomes:
thus, t i The remaining lifetime of the moment is equal to the random process
First pass through threshold w i ＝w-x i In which time
And is
That is, at t i At the moment of time, the time of day,
wherein
The noise component can be approximated as a standard Brownian motion B 0 (psi (t)), the details are as follows
To deduce
It is required to first obtain
But in order to push out
It is necessary to prove that the stochastic process is still a standard Brownian motion process, and this conclusion is warranted by the following reasoning.
Introduction 1: given t i Random process { D (t), t ≧ 0} (where for any t ≧ 0, D (t) = B (t + t) i )-B(t i ) Is still a standard Brownian motion process, where { B (t), t ≧ 0} is the standard Brownian motion.
According to the correlation theory of the random process, the time that the Wiener process reaches a certain fixed threshold for the first time obeys the inverse gaussian distribution. The foregoing derivation can prove that
Still a Wiener process. Thus, given the current degradation state x i (x i W) or less, the distribution of the conditional residual life
This can be achieved by the following conclusion.
Theorem 1: for the remaining life defined by the degradation models (11) and (14), the current time t is given i Degraded state x of i (x i W) for t i The conditional remaining life distribution at the time is concluded by:
the above conclusions only consider the potential degeneration process
And the predicted remaining life depends only on the current degradation state x i . In order to realize the residual life prediction under the uncertain measurement state, Y is firstly needed to be based on 1:i Estimating the degradation state x of a device i And their distribution to characterize the effect of measurement uncertainty on state estimation.
To estimate the degradation state of the device, the degradation state equation and the measurement equation are converted into discrete time equations at the monitoring instants. Then at discrete time points t i I =1,2, \8230, the above transformed degradation model can be obtained:
wherein
Its variance
ε i Is ε at t i The implementation of the moments, and thus further of η -N (0, π) i ) And ε i ～N(0,γ 2 )。
From the established model (17), an estimation of the potential degradation state can be achieved using Kalman filtering techniques. First, define
And p i|i ＝var(x i |Y 1:i ) Respectively by measuring Y 1:i For the degraded state x i Estimated expectation and variance. In addition, define
And p i|i-1 ＝var(x i |Y 1:i-1 ) The expectation and variance of the one-step prediction, respectively. Thus, at t i The time of day, the Kalman filter based potential degradation state estimation and update process is as follows:
and (3) state estimation:
and (3) updating the variance:
P i|i ＝(1-K(i))P i|i-1 ，(19)
applying the above Kalman Filter Algorithm, based on Y 1:i Implicit degradation state x of i The a posteriori estimate of (d) is subject to a Gaussian distribution and can be expressed as
In this case, due to the measurement uncertainty, the estimation of the degradation state also has an uncertainty, from which the posterior distribution is distributedx i |v,Y 1:i A description is given. To incorporate the above uncertainty of the degradation estimate into the remaining life prediction, there is thus
Further, the following conclusion is given to calculate the integral in equation (20).
2, leading: given the current degradation state x i And all measurements of Y 1:i Is provided with
The integration problem in equation (20) can be analyzed by the total probability equation based on theorem 1 and theorem 2, and the following predicted remaining life under uncertain measurement is obtained.
Theorem 2: for the remaining life defined in the degradation models (11) and (14), given the current time t i All uncertain measurements of Y 1:i With respect to t i The following conclusion is reached in the prediction of the remaining life at the time:
wherein,
according to the estimated parameter values, the device remaining life distribution of the adaptive Wiener process considering uncertain measurement can be obtained.
In order to verify the effectiveness of the method for predicting the residual life result, the adaptive Wiener process method without considering the measurement uncertainty is defined as method 1, meanwhile, the adaptive Wiener process method considering the measurement uncertainty is defined as method 2, and the method is favorable for number 5 lithium battery monitoring data to perform prediction verification and comparison.
(1) Residual life prediction result comparison of adaptive Wiener process considering measurement uncertainty
The results of the degradation prediction fitting effect and the remaining life prediction obtained by the two methods according to the test data are shown in fig. 3 and 4. From fig. 3, it can be seen that the fitting effect of method 2 is better than that of method 1. FIG. 4 shows that the probability density function of the residual life predicted by the method 2 can well cover the true value of the residual life, and the predicted mean value is close to the actual residual life at each monitoring point, and the result is obviously superior to the predicted result of the method 1.
(2) Relative error comparison of the two methods
In order to verify that the method can improve the accuracy of the RUL prediction, the RUL absolute error and the relative error of two model predictions and the mean square error corresponding to each monitoring point are provided. As can be seen from fig. 5, 6 and 7, the absolute error, mean square error and relative error of method 2 are relatively smaller than those of method 1. The mean square error of method 1 will experience some large fluctuations due to fluctuations in the degraded data. In contrast, the method 2 proposed herein considers the influence of measurement uncertainty of degraded data, effectively avoids large fluctuation of the mean square error of RUL prediction, and exhibits better stability.
The working principle and the process of the invention are as follows: the invention belongs to the technical field of reliability engineering, and relates to a method for predicting the residual life of self-adaptive degradation equipment by considering measurement uncertainty. The method comprises the following steps: establishing a performance degradation model of a self-adaptive Wiener process capable of describing equipment considering measurement uncertainty; estimating model parameters and remaining life distribution parameters; predicting the remaining life of a randomly degraded device of an adaptive Wiener process that accounts for measurement uncertainty.
The invention has the beneficial effects that: the invention provides a self-adaptive degraded equipment residual life prediction method considering measurement uncertainty, which fully considers the error condition of characteristic extraction of equipment in the degradation process aiming at the degradation randomness of actual equipment in the degradation process, not only can accurately predict and analyze the residual life of the equipment, but also can be used as an effective analysis tool in the life cycle, and provides a powerful theoretical basis for maintenance management decisions such as equipment spare part ordering, and the like, thereby realizing efficient and reasonable equipment management and avoiding waste, and further having good engineering application value.
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 (6)
1. A degraded device remaining life prediction method considering measurement uncertainty, comprising the steps of:
s1: collecting discrete measurement time points and a degradation amount set of degradation equipment, and establishing a performance degradation model;
s2: according to the performance degradation model, performing parameter estimation on the performance degradation model;
s3: predicting the residual life based on the performance degradation model and the parameter estimation result;
the step S2 comprises the following substeps:
s21: according to the performance degradation model, the unknown parameter theta = (k) 2 ,σ 2 ,γ 2 V, α) establishes a likelihood function l (θ | Y) of the degraded device, where k 2 Expressing the square, σ, of the diffusion coefficient of the adaptive drift term 2 Square of diffusion coefficient, gamma, representing adaptive Wiener 2 A variance representing a measurement error, v represents a drift coefficient, α represents a time exponential power of the nonlinear degradation, and Y represents monitoring data considering measurement uncertainty;
s22: k is obtained in turn from the likelihood function l (theta | Y) of the degraded device 2 、σ 2 、γ 2 And a maximum likelihood function of v and a cross-sectional likelihood function l (k, σ, γ, α | Y, v) of α, where Y represents the number of measurements of the degraded device corresponding to the unknown parameter θAccording to the method, k represents the diffusion coefficient of the adaptive drift term, sigma represents the diffusion coefficient of the adaptive Wiener, and gamma represents the measurement error;
s23: using a multidimensional search method according to k 2 、σ 2 、γ 2 And a section likelihood function l (k, sigma, gamma, alpha | Y, v) of alpha and a maximum likelihood function of v are obtained, and k is obtained in sequence 2 ,σ 2 ,γ 2 And the maximum likelihood estimated values of alpha and v to complete parameter estimation;
in step S21, the expression of the likelihood function l (θ | Y) of the degeneration device is:
wherein theta represents an unknown parameter, Y represents monitoring data considering measurement uncertainty, N represents the number of degraded devices, M represents the number of monitoring points of one degraded device, and Y represents the number of monitoring points of one degraded device i Representing monitored data of a certain plant, sigma representing Y i V denotes the drift coefficient, S i Representing two monitoring point time intervals;
in step S22, the maximum likelihood function of the drift coefficient v has the expression:
in said step S22, k 2 、σ 2 、γ 2 The expression of the profile likelihood function l (k, σ, γ, α | Y, v) of sum α is:
wherein k represents the diffusion coefficient of the adaptive drift term, sigma represents the diffusion coefficient of the adaptive Wiener, and gamma 2 Indicating the variance of the measurement error, Y i Representing monitoring data of a certain plant, sigma i Represents Y i Variance of (d), omega i Representing irrespective of adaptationsWiener time Y i The variance of (c).
2. The method of predicting the remaining life of a degraded device considering the measurement uncertainty according to claim 1, characterized in that said step S1 comprises the substeps of:
s11: collecting discrete measurement time points 0= t of degradation equipment 0 <t 1 <…<t i And a set of degeneration amounts Y 1:i ＝{y 1 ,y 2 ,…,y i Get the corresponding degradation state set X 1:i ＝{x 1 ,x 2 ,…,x i In which y 1 ,y 2 ,…,y i Represents t 1 ,…,t i Amount of degradation, x, of time-of-day degraded device 1 ,x 2 ,…,x i Denotes t 1 ,…,t i Momentarily degrading a degradation state of the device;
s12: establishing a set of degenerate states X 1:i ＝{x 1 ,x 2 ,…,x i And the set of degeneration amounts Y 1:i ＝{y 1 ,y 2 ,…,y i The performance degradation equation y between i ＝x i +ε i As a model of performance degradation, where ε i Denotes t i Random measurement error of time of day.
3. The method of predicting the remaining life of a degraded device considering the measurement uncertainty according to claim 1, wherein the step S3 comprises the substeps of:
s31: at discrete measurement time points 0= t 0 <t 1 <…<t i In accordance with the performance degradation equation y i ＝x i +ε i Set of degraded states X 1:i ＝{x 1 ,x 2 ,…,x i The performance degradation model is transformed according to the estimation result of the parameters;
s32: and estimating the degradation state according to the transformed performance degradation model by using a Kalman filtering algorithm to finish the service life prediction.
4. The method of predicting remaining life of degradation equipment considering measurement uncertainty as set forth in claim 3, wherein the calculation formula for transforming the performance degradation model in step S31 is:
wherein x is i Representing discrete measurement times t i Degraded state of degraded device, x i-1 Representing discrete measurement times t i-1 Degradation state of a degraded device, v denotes the drift coefficient, Δ S i Representing the time interval of non-linear degradation, eta representing the noise term due to the time-varying uncertainty of the degradation process, y i Representing the monitored data, e, taking into account measurement errors i Indicating a measurement error.
5. The method of claim 3, wherein in step S32, a Kalman filtering algorithm is used to perform degradation state estimation and update the degradation state estimation, and the degradation state estimation is calculated by the following formula:
K(i)＝P i|i-1 (P i|i-1 +γ 2 ) -1
P i|i-1 ＝P i-1|i-1 +π i
wherein,
representing a set Y of through-degradations 1:i For the degraded state x i Estimated expectation, P i|i Representing a set Y of through-degradations 1:i For degradation state x i The variance of the estimate is determined by the variance of the estimate,
set Y of passing degradation quantity representing the last step 1:i For the degraded state x i Estimated expectation, P i|i-1 Representing the last step by a set of degradation values Y 1:i For the degraded state x i The variance of the estimate, K (i) represents the filter gain,
is shown at t i-1 Mean value of the estimated values of the time-of-day monitoring data, v represents the drift coefficient, Δ S i Representing the non-linear degradation time interval, y (i) representing the monitored data taking into account measurement errors, γ 2 Representing the variance of the measurement error, P i-1|i-1 Is shown at t i-1 Variance, pi, of the estimated value of the time-of-day monitoring data i Represents the variance of the noise term η;
the calculation formula for updating is as follows:
P i|i ＝(1-K(i))P i|i-1 。
6. the method for predicting the remaining life of a degradation device considering the measurement uncertainty as claimed in claim 3, wherein the specific method for predicting the remaining life in step S32 is as follows: the time at which the degraded state estimation result first reaches the predetermined failure threshold is taken as the remaining life start time of the degraded device.
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