CN109977552B - Equipment residual life prediction method and system considering state detection influence - Google Patents
Equipment residual life prediction method and system considering state detection influence Download PDFInfo
- Publication number
- CN109977552B CN109977552B CN201910242340.8A CN201910242340A CN109977552B CN 109977552 B CN109977552 B CN 109977552B CN 201910242340 A CN201910242340 A CN 201910242340A CN 109977552 B CN109977552 B CN 109977552B
- Authority
- CN
- China
- Prior art keywords
- model
- degradation
- state detection
- equipment
- distribution
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/04—Ageing analysis or optimisation against ageing
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Testing Of Devices, Machine Parts, Or Other Structures Thereof (AREA)
Abstract
The invention discloses a method and a system for predicting the residual service life of equipment by considering the influence of state detection. The method comprises the following steps: establishing a degradation model of the equipment; establishing a degradation model under the influence of state detection according to a degradation model of the equipment; establishing a distribution model of the residual service life of the equipment under the influence of state detection by adopting a threshold value conversion method; obtaining a state space model according to a degradation model under the influence of state detection; estimating parameters of the state space model by adopting a maximum expectation algorithm to obtain an estimated state space model; carrying out self-adaptive updating on the distribution model of the residual service life of the equipment according to the estimated state space model to obtain an updated distribution model of the residual service life of the equipment; and predicting the residual life of the equipment according to the updated distribution model of the residual life of the equipment. The invention can effectively overcome the defect that the quantitative relation between the detection activity and the degradation process is difficult to describe in the existing research.
Description
Technical Field
The invention relates to the technical field of reliability engineering, in particular to a method and a system for predicting the residual service life of equipment by considering the influence of state detection.
Background
To study the reliability and remaining life of industrial equipment and military equipment, researchers and engineers have focused on methods based on performance degradation data. With the continuous upgrade of sensors, performance degradation data (gyroscope drift, Li-ion battery capacitance, etc.) are mostly obtained by state detection techniques. However, due to technical or economic cost constraints, the state detection in practical engineering is usually not continuous, and the state detection is only performed on the equipment at some discrete time points. For some specific randomly degraded devices, the state detection may change the operational stress of the device, thereby affecting the degradation process of the device. However, the existing methods do not fully consider the influence of state detection on the equipment degradation process in the degradation modeling and residual life prediction processes.
The state detection techniques vary from device to device, and therefore, the effect of state detection on the device degradation process also varies. In fact, the state detection may both increase the operational stress of the equipment and release the operational stress of the equipment, thereby changing the original degradation process of the equipment. Taking a mechanical gyroscope in inertial navigation equipment as an example, in the long-term storage process of the inertial navigation equipment, in order to ensure that the performance index meets the use requirement, the state of the gyroscope needs to be periodically detected. These state detections require powering and warming the gyroscope, thereby introducing additional electrical stress and changing the temperature field in which the gyroscope is located. In addition, the performance degradation process of the gyroscope is affected by additional electrical stress and temperature stress introduced by state detection. For another example, Li-ion batteries are widely used in electric vehicles and hybrid electric vehicles, and similar phenomena occur in the performance of the Li-ion batteries during the use process. As an important performance indicator of Li-ion batteries, capacitance values are usually calculated based on a record of the charge/discharge process. Studies have shown that, in addition to the capacitance of the battery decreasing as it accumulates over storage time, charge/discharge cycles also accelerate the loss of capacitance, thereby consuming the life of the battery. For degradation equipment containing such state detection, the influence of the state detection must be integrated into a degradation modeling process, so that the rationality of a degradation model and the accuracy of residual life prediction are improved. For this reason, two problems need to be solved: firstly, how to describe the influence of each state detection on the equipment degradation process; and the second is how to integrate the influence of state detection into the degradation model and the residual life prediction of the equipment. The present invention assumes that the duration of a single state detection is negligible compared to the time separation between two state detections. Practical devices mostly detect at discrete points in time, so this assumption is reasonable. Meanwhile, under the common influence of factors such as equipment complexity and uncertainty in the operation process, the influence of single state detection on the equipment degradation process has certain randomness. Thus, the effect of state detection on the device degradation process can be described as a random impact in the degradation process. It should be noted that, according to whether the interval of each state detection is consistent, the state detection in the engineering can be divided into periodic state detection and random state detection. In the periodic detection, the time intervals of two adjacent detections are equal and are fixed values, but the influence of a single state detection on the equipment degradation process is random.
Disclosure of Invention
The invention aims to provide a method and a system for predicting the residual life of equipment by considering the influence of state detection, which describe the influence of single state detection on the degradation level of the equipment by adopting random impact with amplitude values obeying normal distribution and effectively overcome the defect that the quantitative relation between detection activity and the degradation process is difficult to describe in the existing research.
In order to achieve the purpose, the invention provides the following scheme:
a method of predicting remaining life of a device taking into account the effects of state detection, comprising:
establishing a self degradation model of the equipment by adopting a linear Wiener process description method;
adopting a random impact depicting single-time state detection method with amplitude values obeying normal distribution according to the self degradation model of the equipment to establish a degradation model under the influence of state detection;
establishing a distribution model of the residual service life of the equipment under the influence of state detection by adopting a threshold value conversion method;
obtaining a state space model according to the degradation model under the influence of the state detection;
estimating parameters of the state space model by adopting a maximum expectation algorithm to obtain an estimated state space model;
carrying out self-adaptive updating on the distribution model of the residual service life of the equipment according to the estimated state space model to obtain an updated distribution model of the residual service life of the equipment;
and predicting the residual life of the equipment according to the updated distribution model of the residual life of the equipment.
Optionally, the establishing of the degradation model of the device by using the linear Wiener process description method specifically includes:
establishing a self degradation model X' (t) ═ η t + sigma of the equipment by adopting a linear Wiener process description methodBB(t)
Where X' (t) is the degradation level of the device at time t, B (t) is the standard Brownian motion, η and σBThe drift coefficient and the diffusion coefficient of the Wiener process are respectively.
Optionally, the establishing a degradation model under the influence of state detection by describing a single state detection with random impact whose amplitude obeys normal distribution according to the degradation model of the device itself specifically includes:
according to the self degradation model of the equipment, random impact with amplitude values obeying normal distribution is adopted to depict single state detection, and the degradation model under the influence of state detection is established
Wherein B (t) is standard Brownian motion, η and sigmaBRespectively drift coefficient and diffusion coefficient of Wiener process,
γifor the sudden change of the equipment performance caused by the ith state detection, and then order
ξ0(t) is the time interval [0, t]Sum of the amount of change in degradation level due to internal state detection, ξ0(t) obey a normal distribution, i.e.
Wherein
Optionally, the establishing a distribution model of the remaining life of the device under the influence of the state detection by using the threshold switching method specifically includes:
establishing a distribution model of the residual service life of the equipment under the influence of state detection by adopting a threshold conversion method, wherein the distribution model comprises a probability density function model and an accumulative distribution function model;
the probability density function model is represented by the following formula:
the cumulative distribution function model is represented by:
wherein η is the drift coefficient of Wiener process, sigmaBDiffusion coefficient of Wiener Process, μklIs a time interval tk,tk+ l) average of the sum of the changes in the degradation level caused by the detection of an internal state,
is a time interval tk,tk+ l) variance of the sum of the changes in the degradation level caused by the detection of an internal state, wkIs the difference between the threshold value and the current degradation value,
to account for remaining life of the condition detection effect, ξkThe amount of change in the degradation level caused by state detection.
Optionally, obtaining a state space model according to the degradation model under the influence of the state detection specifically includes:
obtaining a state space model according to a degradation model under the influence of the state detection
Wherein, ηkThe instantaneous degradation rate detected for the device at the kth state; gamma raykFor device performance jump caused by the kth state detection, γk+1For device performance jump caused by state detection at the k +1 st time, Δ xkIncrement of the degradation state of the equipment between the kth state detection and the k +1 state detection;kfor the purpose of random utility,
individual differences, w, for characterizing the degradation rate of a devicekIn order to have a random influence,
randomness, Δ t, to describe the effect of state detection on the process of device degradationkAre time intervals.
Optionally, the adaptively updating the distribution model of the remaining lifetime of the device according to the estimated state space model to obtain an updated distribution model of the remaining lifetime of the device specifically includes:
carrying out self-adaptive updating on the distribution model of the residual service life of the equipment according to the estimated state space model to obtain an updated distribution model of the residual service life of the equipment, wherein the updated distribution model of the residual service life of the equipment comprises an updated probability density function model and an updated cumulative distribution function model;
the updated probability density function model is represented by:
the updated cumulative distribution function model is represented by:
wherein the content of the first and second substances,
i is a binary identity matrix.
While
A system for predicting remaining life of a device in consideration of influence of state detection, comprising:
the first degradation model establishing module is used for establishing a degradation model of the equipment by adopting a linear Wiener process description method;
the second degradation model establishing module is used for adopting a random impact depicting single-time state detection method with amplitude values obeying normal distribution according to the degradation model of the equipment to establish a degradation model under the influence of state detection;
the first distribution model establishing module is used for establishing a distribution model of the residual service life of the equipment under the influence of state detection by adopting a threshold value conversion method;
the first state space model determining module is used for obtaining a state space model according to the degradation model under the influence of the state detection;
the second state space model determining module is used for estimating the parameters of the state space model by adopting a maximum expectation algorithm to obtain an estimated state space model;
the second distribution model establishing module is used for carrying out self-adaptive updating on the distribution model of the residual service life of the equipment according to the estimated state space model to obtain an updated distribution model of the residual service life of the equipment;
and the prediction module is used for predicting the residual life of the equipment according to the updated distribution model of the residual life of the equipment.
Optionally, the first degradation model establishing module specifically includes:
a first degradation model establishing unit for describing by linear Wiener processThe method establishes a degradation model X' (t) ═ η t + sigma of the equipmentBB(t)，
Where X' (t) is the degradation level of the device at time t, B (t) is the standard Brownian motion, η and σBThe drift coefficient and the diffusion coefficient of the Wiener process are respectively.
Optionally, the second degradation model establishing module specifically includes:
a second degradation model establishing unit for adopting random impact with amplitude obeying normal distribution to characterize single state detection according to the degradation model of the equipment to establish the degradation model under the influence of the state detection
Wherein B (t) is standard Brownian motion, η and sigmaBRespectively drift coefficient and diffusion coefficient of Wiener process,
γifor the sudden change of the equipment performance caused by the ith state detection, and then order
ξ0(t) is the time interval [0, t]Sum of the amount of change in degradation level due to internal state detection, ξ0(t) obey a normal distribution, i.e.
Wherein
Optionally, the first distribution model establishing module specifically includes:
the device comprises a first distribution model establishing unit, a second distribution model establishing unit and a third distribution model establishing unit, wherein the first distribution model establishing unit is used for establishing a distribution model of the residual service life of the device under the influence of state detection by adopting a conversion threshold method, and the distribution model comprises a probability density function model and an accumulative distribution function model;
the probability density function model is represented by the following formula:
the cumulative distribution function model is represented by:
wherein η is the drift coefficient of Wiener process, sigmaBDiffusion coefficient of Wiener Process, μklIs a time interval tk,tk+ l) average of the sum of the changes in the degradation level caused by the detection of an internal state,
is a time interval tk,tk+ l) variance of the sum of the changes in the degradation level caused by the detection of an internal state, wkIs the difference between the threshold value and the current degradation value,
to account for remaining life of the condition detection effect, ξkThe amount of change in the degradation level caused by state detection.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects: the invention provides a method for predicting the residual life of equipment by considering the influence of state detection, which effectively overcomes the defect that the quantitative relation between detection activity and a degradation process is difficult to describe in the existing research by adopting random impact with amplitude values obeying normal distribution to characterize the influence of single state detection on the degradation level of the equipment.
Drawings
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 inventive exercise.
FIG. 1 is a flowchart of a method for predicting remaining life of a device in consideration of the effect of state detection according to an embodiment of the present invention;
FIG. 2 is performance degradation data for a gyroscope according to an embodiment of the invention;
FIG. 3 is a flowchart of an embodiment of a parameter A estimation process;
FIG. 4 is a flowchart of an exemplary embodiment of a parameter Σ estimation process;
FIG. 5 shows an exemplary parameter θ0|0The estimation process of (1);
FIG. 6 shows an embodiment of the present invention with parameter P0|0The estimation process of (1);
FIG. 7 shows parameters of an embodiment of the present invention
The estimation process of (1);
FIG. 8 shows the filtering result according to an embodiment of the present invention;
FIG. 9 is a comparison of observed and estimated values according to an embodiment of the present invention;
FIG. 10 is a probability density function of remaining life without regard to detection impact and updating parameters according to an embodiment of the present invention;
FIG. 11 is a probability density function of remaining life with consideration of detecting effects and updating parameters according to an embodiment of the present invention;
FIG. 12 is a probability density function of remaining life without considering detection effects and without updating parameters according to an embodiment of the present invention;
FIG. 13 is a probability density function for remaining life with consideration of detecting effects but without updating parameters according to an embodiment of the present invention;
FIG. 14 is a comparison of mean square error of remaining life prediction for embodiments of the present invention;
fig. 15 is a diagram of a system for predicting remaining life of a device in consideration of the influence of state detection according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a method and a system for predicting the residual life of equipment by considering the influence of state detection, which describe the influence of single state detection on the degradation level of the equipment by adopting random impact with amplitude values obeying normal distribution and effectively overcome the defect that the quantitative relation between detection activity and the degradation process is difficult to describe in the existing research.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Fig. 1 is a flowchart of a method for predicting remaining life of a device in consideration of the influence of state detection according to an embodiment of the present invention. As shown in fig. 1, a method for predicting remaining life of a device considering influence of state detection includes:
step 101: establishing a self degradation model of the equipment by adopting a linear Wiener process description method;
step 102: adopting a random impact depicting single-time state detection method with amplitude values obeying normal distribution according to the self degradation model of the equipment to establish a degradation model under the influence of state detection;
step 103: establishing a distribution model of the residual service life of the equipment under the influence of state detection by adopting a threshold value conversion method;
step 104: obtaining a state space model according to the degradation model under the influence of the state detection;
step 105: estimating parameters of the state space model by adopting a maximum expectation algorithm to obtain an estimated state space model;
step 106: carrying out self-adaptive updating on the distribution model of the residual service life of the equipment according to the estimated state space model to obtain an updated distribution model of the residual service life of the equipment;
step 107: and predicting the residual life of the equipment according to the updated distribution model of the residual life of the equipment.
establishing a self degradation model X' (t) ═ η t + sigma of the equipment by adopting a linear Wiener process description methodBB(t)
Where X' (t) is the degradation level of the device at time t, B (t) is the standard Brownian motion, η and σBThe drift coefficient and the diffusion coefficient of the Wiener process are respectively.
according to the self degradation model of the equipment, random impact with amplitude values obeying normal distribution is adopted to depict single state detection, and the degradation model under the influence of state detection is established
Wherein B (t) is standard Brownian motion, η and sigmaBRespectively drift coefficient and diffusion coefficient of Wiener process,
γifor the sudden change of the equipment performance caused by the ith state detection, and then order
ξ0(t) is the time interval [0, t]Sum of the amount of change in degradation level due to internal state detection, ξ0(t) obey a normal distribution, i.e.
Wherein
establishing a distribution model of the residual service life of the equipment under the influence of state detection by adopting a threshold conversion method, wherein the distribution model comprises a probability density function model and an accumulative distribution function model;
the probability density function model is represented by the following formula:
the cumulative distribution function model is represented by:
wherein η is the drift coefficient of Wiener process, sigmaBDiffusion coefficient of Wiener Process, μklIs a time interval tk,tk+ l) average of the sum of the changes in the degradation level caused by the detection of an internal state,
is a time interval tk,tk+ l) variance of the sum of the changes in the degradation level caused by the detection of an internal state, wkIs the difference between the threshold value and the current degradation value,
to account for remaining life of the condition detection effect, ξkThe amount of change in the degradation level caused by state detection.
obtaining a state space model according to a degradation model under the influence of the state detection
Wherein, ηkThe instantaneous degradation rate detected for the device at the kth state; gamma raykFor device performance jump caused by the kth state detection, γk+1For device performance jump caused by state detection at the k +1 st time, Δ xkIncrement of the degradation state of the equipment between the kth state detection and the k +1 state detection;kfor the purpose of random utility,
individual differences, w, for characterizing the degradation rate of a devicekIn order to have a random influence,
randomness, Δ t, to describe the effect of state detection on the process of device degradationkAre time intervals.
carrying out self-adaptive updating on the distribution model of the residual service life of the equipment according to the estimated state space model to obtain an updated distribution model of the residual service life of the equipment, wherein the updated distribution model of the residual service life of the equipment comprises an updated probability density function model and an updated cumulative distribution function model;
the updated probability density function model is represented by:
the updated cumulative distribution function model is represented by:
wherein the content of the first and second substances,
i is a binary identity matrix.
While
Because the Wiener process, namely the Wiener process has good mathematical characteristics and is widely applied in engineering, the invention constructs a degradation model of the equipment in consideration of the state detection influence based on the Wiener process. In order to more intuitively understand the degradation model of the equipment under the condition of considering the state detection influence, the condition of not considering the state detection influence is firstly researched, then the influence of each state detection is independently modeled, and the influence of the state detection is further merged into the degradation model.
Based on a degradation model when the Wiener process research does not consider the influence of state detection, the basic model is as follows:
X′(t)＝ηt+σBB(t) (1)
where X' (t) is the degradation level of the device at time t, B (t) is the standard Brownian motion, η and σBWhen the device degradation process shows a non-linear trend, it may try to convert Λ (t) through a specific time transformation to convert the non-linear degradation process into linearity, namely:
X′(Λ(t))＝ηΛ(t)+σBB(Λ(t)) (2)
and (3) linearizing the nonlinear degradation process, and still predicting the residual life by using the conclusion corresponding to the formula (1) in the converted degradation process. Therefore, the discussion is based on equation (1) herein.
To incorporate the effects of state detection into the degradation process model of the device, the effects of state detection are described herein as impulses that cause abrupt changes in the degradation level of the device. The time for each state detection is typically much less than the interval between two state detections. Therefore, each state detection time is assumed to be negligible during modeling.
It should be noted that the degradation level mutation caused by the state detection is a random variable. To simplify the model, assume that the random variables obey mean and variance, respectively, of μIAnd
is normally distributed. Simultaneously, the device performance mutation caused by the k-th state detection is gammakI.e. by
In addition, each time the state detection causes the device performance mutation set
Is independent and equally distributed normal random variable. Since periodic state detection is adopted for the equipment, assuming the detection period is h, the time interval tk,tk+s]The number of internal state detections is
Wherein
Denotes the largest integer not exceeding x, i.e.
To round the symbol down.
Based on the above description, considering the effect of state detection, the degradation process of the device can be described as:
wherein
Reissue to order
Represents a time interval [0, t]Sum of the amount of change in the level of degradation due to internal state detection ξ is known from the nature of the normal distribution0(t) obey a normal distribution, i.e.
Wherein
The case where the influence of the state detection is not considered is first studied. According to the basic characteristics of the Wiener process, under the first arrival time meaning, the service life T of the equipment obeys the random variable of inverse Gaussian distribution, and the probability density function is as follows:
the cumulative distribution function is:
where Φ (·) is the cumulative distribution function of the standard normal distribution, and w is the failure threshold preset by the device.
Similarly, the device is at tkRemaining life L of timekCan be defined as Lk＝inf{lk:x(tk+lk)≥wxkThe probability density function and the cumulative distribution function are respectively:
wherein, wkIs the difference between the threshold and the current degradation value, wk＝w-xk，xkIs the amount of degradation at the current time.
After introducing the effect of state detection, the time for the degradation process defined by equation (3) to reach the fixed threshold w can be converted into the time-varying random threshold for the random process shown by equation (1)
Also obey a normal distribution, i.e.
According to a total probability formula, the expectation of the converted failure threshold is obtained on the basis of the formulas (3) and (4), and the service life T of the equipment under the influence of state detection can be considered*The probability density function and the cumulative distribution function of (a) are respectively:
similarly, the impact of state detection on the degradation process that may exist for some period of time in the future needs to be considered in predicting the remaining life of the device. Suppose that in the time interval tk,tk+ l) in total
Secondary State detection, the amount of change in degradation level caused thereby is noted as ξk(l) Easy to know, ξk(l) Obey mean value of
Variance of
Is normally distributed. At the moment, according to the total probability formula, the residual service life of the equipment under the influence of state detection is considered
The probability density function and cumulative distribution function of the distribution are respectively:
in order to realize the self-adaptive online prediction of the residual service life of the equipment while simultaneously considering the factors such as time-varying uncertainty, random utility, state detection and the like, the degradation model needs to be improved. Meanwhile, according to engineering experience, after a series of impacts act, the degradation rate of the equipment may be increased, and the same impact has different influences on equipment with different degradation rates, here, the influence of the degradation rate and state detection of the equipment on the degradation process is described by the drift coefficient and random impact of the Wiener process, respectively, and the degradation model is improved into the form of a state space model as follows:
η thereinkThe instantaneous degradation rate of the device between the kth state detection and the k +1 state detection; Δ xkIncrement of the degradation state of the device between the kth state detection and the k +1 state detection; random variable
Individual differences, i.e., random utilities, used to characterize the rate of degradation of the device; random variable
The randomness of the impact of the state detection on the device degradation process is described. The state space model in equation (13) can be further written as
Wherein v isk＝σBB(Δtk)，yk＝Δxk，
Here, θkObey a binary normal distribution BVN (0, Σ) with a mean and variance of
Let Y1 k＝[y1,…,yk]TNext based on Y1 kAnd updating the drift coefficient and the state detection influence on line by adopting a Kalman filtering algorithm.
Step 1: state estimation
Pk|k-1＝APk-1|k-1AT+Σk；
Step 2: covariance matrix update
Wherein the content of the first and second substances,
in order to predict the value of the state one step,
for optimal predicted value of state, Kk|kFor an optimal gain matrix, Pk|k-1For covariance one-step prediction, Pk|kIt is noted that for the covariance optimum predictor,
updated state
Drift coefficient contained therein
Influence of state detection
Sum-covariance matrix Pk|kAnd meanwhile, the method is fused into the prediction result of the residual service life of the equipment. The residual life of the equipment under the influence of state detection is considered and obtained according to a total probability formula
The probability density function and the cumulative distribution function of the distribution are sequentially:
wherein the content of the first and second substances,
i is a binary identity matrix.
While
It should be noted that the remaining life results in equations (11) and (12) do not take into account the random utility of the drift coefficient, and equations (15) and (16) take into account the expectation and variance of the drift coefficient, so that online prediction of the remaining life of the device considering the influence of periodic state detection is realized.
Based on the above analysis, the parameters to be estimated include A and Sigma, in the observation equation
And initial state estimate of Kalman filter
And the estimation error variance matrix P0|0. Since the state (mean of drift coefficient and state detection influence) in the state space model is an implicit variable, the unknown parameter Θ can be estimated by using the EM algorithm.
Let us assume the cutoff tkThe state of the equipment is detected k times at all times, and the corresponding k observed values are respectively recorded as
Meanwhile, in order to simplify the symbols, all the corresponding drift coefficients, detection influence and initial values of the Kalman filtering algorithm are used as symbols
Indicating and assuming that the state detections at different times are independent of each other. Given complete data
And Y1 kThe likelihood function of the unknown parameter can be written as
Drift coefficient and detecting influence
Cannot be directly observed, which will result in
It is difficult to maximize. Thus, it is possible to use the observation data Y1 kAnd adopting an EM algorithm to realize the maximization of the log-likelihood function.
E, step E:
wherein
Obtaining a parameter estimation value for the first iteration;
and M: maximization
Obtain a new set of observations of Θ, i.e.
To calculate
The calculation of the condition expectation value is required to include:
wherein j is less than or equal to k.
Based on the state space model constructed by the equation (14), the expected value of the condition to be calculated can be calculated by a kalman method and an optimal fixed interval smoothing method.
Step 1: acquisition according to the Kalman Filter Algorithm described previously
And Pk|k；
Step 2: the following backward smoothing step is performed:
wherein S isjIs a smoothed gain matrix.
And step 3: initializing covariance matrix
Mk|k＝(I-Kkck T)Ak-1Pk-1|k-1；
Wherein M isj|k＝cov(θj,θj-1|Y1 k)。
After the RTS algorithm is executed based on the parameter estimation value of the last iteration, the required condition expectation value can be determined according to the property of the covariance matrix. Specifically, there are
Wherein, Tr represents the tracing operation on the matrix. And (3) solving the partial derivative of the formula (23) about the unknown parameter vector, enabling the result to be zero, and solving the obtained equation set to obtain the parameter estimation value of the M steps. The final result is in turn:
wherein the content of the first and second substances,
and
the result is updated for the parameter. And executing the E-step and the M-step alternately until the estimated result meets the preset algorithm termination condition, such as the maximum iteration number or parameter convergence.
Specific example 1:
gyroscopes are important components of inertial navigation systems. Inertial gyroscopes are expensive, their performance directly determines the performance of the navigation system, and degradation of the performance of the inertial devices is one of the main causes of failure of the inertial navigation system. Typically, a long term storage period is experienced before the gyroscope is installed on a missile or other single use weaponry. Under the combined action of storage environment, self material aging and other factors, the performance of the gyroscope is degraded along with the increase of storage time of the gyroscope. In order to ensure that the stored gyroscope can reach the expected performance index after being installed, the stored gyroscope is generally subjected to state detection periodically, and the state detection changes the storage environment and the working stress of the gyroscope, so that the degradation process of the gyroscope is accelerated. In order to improve the accuracy of the service life prediction of the gyroscope and provide scientific and reasonable basis for the maintenance, replacement and spare part ordering of the gyroscope, the influence of state detection on the degradation of the gyroscope must be considered.
The duration of each state detection is negligible compared to the storage time of the gyroscope. Thus, the proposed method can be used to predict the remaining lifetime of a gyroscope. The gyroscope performance degradation data used here is shown in fig. 2. FIG. 2 is performance degradation data for a gyroscope according to an embodiment of the present invention. When the first term drift of the gyroscope exceeds the threshold w ═ 0.366(°/hour), the usage requirements are no longer met, so the gyroscope fails at the 72 th observation instant. To illustrate and verify the proposed method, the parameters of the degradation model are estimated using the first 67 data and the remaining data are used to update the parameters of the model and the remaining lifetime of the gyroscope on-line.
And selecting the difference value of two adjacent state detections as an observed value of the state space model, and estimating unknown parameters by using the provided EM algorithm. The results of the parameter estimation are shown in fig. 3 to 7, respectively. FIG. 3 shows an estimation process of parameter A according to an embodiment of the present invention. FIG. 4 is a diagram illustrating an exemplary process for estimating the parameter Σ. FIG. 5 shows an exemplary parameter θ0|0The estimation process of (1). FIG. 6 shows an embodiment of the present invention with parameter P0|0The estimation process of (1). FIG. 7 shows parameters of an embodiment of the present invention
The estimation process of (1). It can be seen from the figure that after the EM algorithm iterates a certain number of steps, the parameters of the degradation model and the initial values of the kalman method both converge to corresponding values, which illustrates the effectiveness of the proposed parameter estimation method.
FIG. 8 shows the filtering result according to an embodiment of the present invention. FIG. 9 is a comparison of observed and estimated values according to an embodiment of the present invention. Using the estimated parameters A, sigma,
And an initial value θ of Kalman filtering0|0And the estimation error variance matrix P0|0Kalman filtering is operated, the obtained filtered state value and the mean value of the observed value are shown in FIGS. 8 and 9, and it can be seen that the estimated state can well describe the degradation process of the gyroscope, so that the accuracy of parameter estimation is proved. Therefore, the estimated parameters can be further utilized to realize the residual life of the gyroscopeAdaptive update of (3).
FIG. 10 is a probability density function of remaining life without regard to the detection impact and updating parameters according to an embodiment of the present invention. FIG. 11 is a probability density function of remaining life for an embodiment of the present invention in view of detecting effects and updating parameters. The probability density function and the average value of the remaining life with and without considering the influence of the state detection are shown in fig. 10 and 11. FIG. 12 is a probability density function of remaining life without considering detection effects and without updating parameters according to an embodiment of the present invention. FIG. 13 is a probability density function for remaining life with consideration of detecting effects but without updating parameters according to an embodiment of the present invention. When online updating is not performed, the obtained remaining life prediction results are respectively shown in fig. 12 and fig. 13. As is clear from the figure, considering the influence of the state detection can improve the accuracy of the remaining life prediction.
In addition, in order to quantitatively compare the residual life prediction results of different methods, the mean square error is adopted for measurement, namely:
wherein
The true remaining life of the device at the moment of the kth state detection. The mean square error of the remaining life prediction from the 67 th state detection point to the 71 th state detection point is shown in fig. 14, and IF in fig. 14 represents the detection influence.
FIG. 14 is a comparison of mean square error of remaining life prediction according to an embodiment of the present invention. As can be seen from fig. 14, considering the effect of state detection can reduce the mean square error of the remaining life prediction, while online updating of the parameters and remaining life can further reduce the estimated mean square error. Therefore, it is necessary to update the model parameters according to new observation data after introducing the influence of state detection, and the validity of the random system degradation modeling and remaining life prediction method considering state detection provided by the invention is also verified.
Fig. 15 is a diagram of a system for predicting remaining life of a device in consideration of the influence of state detection according to an embodiment of the present invention. As shown in fig. 15, a system for predicting the remaining life of a device in consideration of the influence of state detection includes:
the first degradation model establishing module 201 is used for establishing a degradation model of the equipment by adopting a linear Wiener process description method;
the second degradation model establishing module 202 is configured to establish a degradation model under the influence of state detection by adopting a random impact depicting single-time state detection method with amplitude values complying with normal distribution according to the degradation model of the device;
a first distribution model establishing module 203, configured to establish a distribution model of the remaining life of the device under the influence of state detection by using a threshold conversion method;
a first state space model determining module 204, configured to obtain a state space model according to a degradation model under the influence of the state detection;
a second state space model determining module 205, configured to estimate parameters of the state space model by using a maximum expectation algorithm, so as to obtain an estimated state space model;
a second distribution model establishing module 206, configured to perform adaptive update on the distribution model of the remaining lifetime of the device according to the estimated state space model, so as to obtain an updated distribution model of the remaining lifetime of the device;
and the prediction module is used for predicting the residual life of the equipment according to the updated distribution model of the residual life of the equipment.
The first degradation model establishing module 201 specifically includes:
a first degradation model establishing unit, configured to establish a degradation model X' (t) ═ η t + σ of the device itself by using a linear Wiener process description methodBB(t)，
Where X' (t) is the degradation level of the device at time t, B (t) is the standard Brownian motion, η and σBThe drift coefficient and the diffusion coefficient of the Wiener process are respectively.
The second degradation model establishing module 202 specifically includes:
second degradation modelingA vertical unit for adopting random impact with amplitude value obeying normal distribution to describe single state detection according to the self degradation model of the equipment and establishing the degradation model under the influence of state detection
Wherein B (t) is standard Brownian motion, η and sigmaBRespectively drift coefficient and diffusion coefficient of Wiener process,
γifor the sudden change of the equipment performance caused by the ith state detection, and then order
ξ0(t) is the time interval [0, t]Sum of the amount of change in degradation level due to internal state detection, ξ0(t) obey a normal distribution, i.e.
Wherein
The first distribution model establishing module 203 specifically includes:
the device comprises a first distribution model establishing unit, a second distribution model establishing unit and a third distribution model establishing unit, wherein the first distribution model establishing unit is used for establishing a distribution model of the residual service life of the device under the influence of state detection by adopting a conversion threshold method, and the distribution model comprises a probability density function model and an accumulative distribution function model;
the probability density function model is represented by the following formula:
the cumulative distribution function model is represented by:
wherein η is the drift coefficient of Wiener process, sigmaBDiffusion coefficient of Wiener Process, μklIs a time interval tk,tk+ l) average of the sum of the changes in the degradation level caused by the detection of an internal state,
is a time interval tk,tk+ l) variance of the sum of the changes in the degradation level caused by the detection of an internal state, wkIs the difference between the threshold value and the current degradation value,
to account for remaining life of the condition detection effect, ξkThe amount of change in the degradation level caused by state detection. The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (4)
1. A method for predicting remaining life of a device in consideration of influence of state detection, comprising:
establishing a self degradation model of the equipment by adopting a linear Wiener process description method;
adopting a random impact depicting single-time state detection method with amplitude values obeying normal distribution according to the self degradation model of the equipment to establish a degradation model under the influence of state detection;
establishing a distribution model of the residual service life of the equipment under the influence of state detection by adopting a threshold value conversion method;
obtaining a state space model according to the degradation model under the influence of the state detection;
estimating parameters of the state space model by adopting a maximum expectation algorithm to obtain an estimated state space model;
carrying out self-adaptive updating on the distribution model of the residual service life of the equipment according to the estimated state space model to obtain an updated distribution model of the residual service life of the equipment;
predicting the residual life of the equipment according to the updated distribution model of the residual life of the equipment;
the method for establishing the self degradation model of the equipment by adopting the linear Wiener process description method specifically comprises the following steps:
establishing a self degradation model X' (t) ═ η t + sigma of the equipment by adopting a linear Wiener process description methodBB(t)；
Where X' (t) is the degradation level of the device at time t, B (t) is the standard Brownian motion, η and σBRespectively the drift coefficient and the diffusion coefficient of the Wiener process;
the method comprises the following steps of describing single state detection by adopting random impact with amplitude values obeying normal distribution according to the degradation model of the equipment, and establishing the degradation model under the influence of the state detection, wherein the method specifically comprises the following steps:
according to the self degradation model of the equipment, random impact with amplitude values obeying normal distribution is adopted to depict single state detection, and the degradation model under the influence of state detection is established
Wherein B (t) is standard Brownian motion, η and sigmaBRespectively drift coefficient and diffusion coefficient of Wiener process,
γifor the sudden change of the equipment performance caused by the ith state detection, and then order
ξ0(t) is the time interval [0, t]Sum of the amount of change in degradation level due to internal state detection, ξ0(t) obey a normal distribution, i.e.
Wherein
The method for establishing the distribution model of the residual service life of the equipment under the influence of state detection by adopting the threshold switching method specifically comprises the following steps:
establishing a distribution model of the residual service life of the equipment under the influence of state detection by adopting a threshold conversion method, wherein the distribution model comprises a probability density function model and an accumulative distribution function model;
the probability density function model is represented by the following formula:
the cumulative distribution function model is represented by:
wherein η is the drift coefficient of Wiener process, sigmaBDiffusion coefficient of Wiener Process, μklIs a time interval tk,tk+ l) average of the sum of the changes in the degradation level caused by the detection of an internal state,
is a time interval tk,tk+ l) receding caused by internal state detectionVariance of sum of horizontal variations, wkIs the difference between the threshold value and the current degradation value,
to account for remaining life of the condition detection effect, ξkIs the interval [ tk,tk+ l) amount of change in the degradation level caused by detection of an internal state.
2. The method for predicting the remaining life of equipment under consideration of the influence of state detection according to claim 1, wherein obtaining a state space model according to a degradation model under the influence of state detection specifically comprises:
obtaining a state space model according to a degradation model under the influence of the state detection
Wherein, ηkThe instantaneous degradation rate detected for the device at the kth state; gamma raykThe device performance mutation, gamma, caused by the k-th state detectionk+1For device performance jump caused by state detection at the k +1 st time, Δ xkIncrement of the degradation state of the equipment between the kth state detection and the k +1 state detection;kfor the purpose of random utility,
individual differences, w, for characterizing the degradation rate of a devicekIn order to have a random influence,
randomness, Δ t, to describe the effect of state detection on the process of device degradationkAre time intervals.
3. The method according to claim 1, wherein the adaptively updating the distribution model of the remaining device lifetime according to the estimated state space model to obtain an updated distribution model of the remaining device lifetime specifically includes:
carrying out self-adaptive updating on the distribution model of the residual service life of the equipment according to the estimated state space model to obtain an updated distribution model of the residual service life of the equipment, wherein the updated distribution model of the residual service life of the equipment comprises an updated probability density function model and an updated cumulative distribution function model;
the updated probability density function model is represented by:
the updated cumulative distribution function model is represented by:
wherein the content of the first and second substances,
i is a binary identity matrix, and I is a binary identity matrix,
while
4. A system for predicting remaining life of a device in consideration of influence of state detection, comprising:
the first degradation model establishing module is used for establishing a degradation model of the equipment by adopting a linear Wiener process description method;
the second degradation model establishing module is used for adopting a random impact depicting single-time state detection method with amplitude values obeying normal distribution according to the degradation model of the equipment to establish a degradation model under the influence of state detection;
the first distribution model establishing module is used for establishing a distribution model of the residual service life of the equipment under the influence of state detection by adopting a threshold value conversion method;
the first state space model determining module is used for obtaining a state space model according to the degradation model under the influence of the state detection;
the second state space model determining module is used for estimating the parameters of the state space model by adopting a maximum expectation algorithm to obtain an estimated state space model;
the second distribution model establishing module is used for carrying out self-adaptive updating on the distribution model of the residual service life of the equipment according to the estimated state space model to obtain an updated distribution model of the residual service life of the equipment;
the prediction module is used for predicting the residual service life of the equipment according to the updated distribution model of the residual service life of the equipment;
the first degradation model establishing module specifically includes:
a first degradation model establishing unit, configured to establish a degradation model X' (t) ═ η t + σ of the device itself by using a linear Wiener process description methodBB(t)；
Where X' (t) is the degradation level of the device at time t, B (t) is the standard Brownian motion, η and σBRespectively the drift coefficient and the diffusion coefficient of the Wiener process;
the second degradation model establishing module specifically includes:
a second degradation model establishing unit for adopting random impact with amplitude obeying normal distribution to characterize single state detection according to the degradation model of the equipment to establish the degradation model under the influence of the state detection
Wherein B (t) is standard Brownian motion, η and sigmaBRespectively drift coefficient and diffusion coefficient of Wiener process,
γifor the sudden change of the equipment performance caused by the ith state detection, and then order
ξ0(t) is the time interval [0, t]Sum of the amount of change in degradation level due to internal state detection, ξ0(t) obey a normal distribution, i.e.
Wherein
The first distribution model establishing module specifically includes:
the device comprises a first distribution model establishing unit, a second distribution model establishing unit and a third distribution model establishing unit, wherein the first distribution model establishing unit is used for establishing a distribution model of the residual service life of the device under the influence of state detection by adopting a conversion threshold method, and the distribution model comprises a probability density function model and an accumulative distribution function model;
the probability density function model is represented by the following formula:
the cumulative distribution function model is represented by:
wherein η is the drift coefficient of Wiener process, sigmaBDiffusion coefficient of Wiener Process, μklIs a time interval tk,tk+ l) internal stateThe mean of the sum of the changes in the level of degradation caused is detected,
is a time interval tk,tk+ l) variance of the sum of the changes in the degradation level caused by the detection of an internal state, wkIs the difference between the threshold value and the current degradation value,
to account for remaining life of the condition detection effect, ξkIs the interval [ tk,tk+ l) amount of change in the degradation level caused by detection of an internal state.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910242340.8A CN109977552B (en) | 2019-03-28 | 2019-03-28 | Equipment residual life prediction method and system considering state detection influence |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910242340.8A CN109977552B (en) | 2019-03-28 | 2019-03-28 | Equipment residual life prediction method and system considering state detection influence |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109977552A CN109977552A (en) | 2019-07-05 |
| CN109977552B true CN109977552B (en) | 2020-09-15 |
Family
ID=67081193
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910242340.8A Active CN109977552B (en) | 2019-03-28 | 2019-03-28 | Equipment residual life prediction method and system considering state detection influence |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109977552B (en) |
Families Citing this family (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111368403B (en) * | 2020-02-24 | 2022-03-08 | 西安交通大学 | Self-adaptive non-linear degradation residual life prediction method |
| CN112949026B (en) * | 2021-01-19 | 2023-05-23 | 中国人民解放军火箭军工程大学 | Age and state dependence considered degradation equipment residual life prediction method |
| CN112906213B (en) * | 2021-02-05 | 2024-05-14 | 中国人民解放军空军工程大学 | Self-adaptive prediction method for residual life of airborne electronic equipment |
| CN113029998B (en) * | 2021-03-31 | 2024-01-09 | 河南中烟工业有限责任公司 | Method, device and equipment for measuring checking period during online infrared moisture meter |
| CN113392507A (en) * | 2021-05-25 | 2021-09-14 | 西安科技大学 | Method for predicting residual life of lithium ion power battery |
| CN114444370B (en) * | 2021-10-11 | 2023-10-10 | 崔跃芹 | Method and device for predicting accumulated loss life of rechargeable battery by considering operation conditions, electronic equipment and readable storage medium |
| CN115979310B (en) * | 2023-03-20 | 2023-07-07 | 中国人民解放军火箭军工程大学 | Inertial navigation system performance degradation evaluation method, system, electronic equipment and medium |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107862134A (en) * | 2017-11-06 | 2018-03-30 | 河南科技大学 | A kind of Wiener process reliability analysis methods for considering autocorrelation measurement error |
| CN108549769A (en) * | 2018-04-13 | 2018-09-18 | 中国人民解放军火箭军工程大学 | A kind of maintenance of equipment method for predicting residual useful life and system |
| CN109214109A (en) * | 2018-09-27 | 2019-01-15 | 广东石油化工学院 | A kind of predicting residual useful life verification method of landification equipment rotating machinery |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US9310426B2 (en) * | 2012-09-25 | 2016-04-12 | Globalfoundries Inc. | On-going reliability monitoring of integrated circuit chips in the field |
| US10539621B2 (en) * | 2017-08-02 | 2020-01-21 | Total Solar International | Method and apparatus for identifying a battery model |
-
2019
- 2019-03-28 CN CN201910242340.8A patent/CN109977552B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107862134A (en) * | 2017-11-06 | 2018-03-30 | 河南科技大学 | A kind of Wiener process reliability analysis methods for considering autocorrelation measurement error |
| CN108549769A (en) * | 2018-04-13 | 2018-09-18 | 中国人民解放军火箭军工程大学 | A kind of maintenance of equipment method for predicting residual useful life and system |
| CN109214109A (en) * | 2018-09-27 | 2019-01-15 | 广东石油化工学院 | A kind of predicting residual useful life verification method of landification equipment rotating machinery |
Non-Patent Citations (2)
| Title |
|---|
| A Wiener-process一based degradation model with a recursive filter algorithm for remaining useful life estimation;Xiao-Sheng Si;《Mechanical Systems and Signal Processing》;20130228;第219-237页 * |
| 多阶段随机退化设备剩余寿命预测方法;张正新;《系统工程学报》;20170228;第1-7页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109977552A (en) | 2019-07-05 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN109977552B (en) | Equipment residual life prediction method and system considering state detection influence | |
| CN204269785U (en) | For calculating the system of battery state of charge | |
| CN107145645B (en) | Method for predicting residual life of non-stationary degradation process with uncertain impact | |
| CN107145720B (en) | Method for predicting residual life of equipment under combined action of continuous degradation and unknown impact | |
| JP5944291B2 (en) | Battery parameter estimation apparatus and method | |
| Liang et al. | Cyber attacks on AC state estimation: Unobservability and physical consequences | |
| US20170244256A1 (en) | Modeling a change in battery degradation | |
| CN104459560A (en) | Method for predicting remaining service life of lithium battery based on wavelet denoising and relevant vector machine | |
| US10346758B2 (en) | System analysis device and system analysis method | |
| KR20160146032A (en) | Method and device to estimate state of battery | |
| CN104007390A (en) | Battery state of charge tracking, equivalent circuit selection and benchmarking | |
| CN109829136B (en) | Method and system for predicting residual life of degradation equipment with random jump | |
| CN106933618B (en) | System upgrade evaluation method based on system parameter correlation coefficient | |
| KR20170134193A (en) | Method for estimating state of charge of battery and apparatus for impelmeing the method | |
| Bockrath et al. | State of charge estimation using recurrent neural networks with long short-term memory for lithium-ion batteries | |
| CN112949026A (en) | Age and state dependence considered degradation equipment residual life prediction method | |
| CN115453376A (en) | State monitoring method and system for power battery of electric automobile and electric automobile | |
| CN115979310A (en) | Inertial navigation system performance degradation evaluation method and system, electronic device and medium | |
| JP2017015594A (en) | Battery, power supply management device, and power supply management method | |
| WO2022229611A1 (en) | Health monitoring of electrochemical energy supply elements | |
| CN108228959A (en) | Using the method for Random censorship estimating system virtual condition and using its wave filter | |
| CN114254555A (en) | Deep learning-based counteraction wheel fault detection and health assessment system and method | |
| CN110866325B (en) | Method for predicting imperfect maintenance of residual life of equipment based on indirect monitoring data | |
| Pola et al. | Particle-filtering-based state-of-health estimation and end-of-life prognosis for lithium-ion batteries at operation temperature | |
| CN116736174B (en) | Method, apparatus, computer device and storage medium for predicting remaining life of battery |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |