CN112231925A - Residual life prediction method considering state dependence time lag - Google Patents

Residual life prediction method considering state dependence time lag Download PDF

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CN112231925A
CN112231925A CN202011159533.6A CN202011159533A CN112231925A CN 112231925 A CN112231925 A CN 112231925A CN 202011159533 A CN202011159533 A CN 202011159533A CN 112231925 A CN112231925 A CN 112231925A
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time lag
state
degradation
residual life
time
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周东华
席霄鹏
纪洪泉
钟麦英
高明
王建东
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Shandong University of Science and Technology
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Abstract

The invention discloses a residual life prediction method considering state dependence time lag, and belongs to the field of prediction and health management. The invention comprises the following steps: inputting a group of degradation data, and initializing a state-dependent time lag structure and parameters of a degradation model; resampling original data based on discretization model description under an implicit Euler format; estimating unknown parameters by utilizing a maximum likelihood algorithm; reducing the complexity of first-arrival time analysis by combining a wiener process transformation theory, and simulating a future degradation track by a one-step extrapolation method to further obtain an approximate analytical solution of the remaining life distribution; and finally, outputting the residual life distribution at each monitoring moment. The method is suitable for processing the fractal degradation process with the time-varying hysteresis effect, and is mainly applied to corrosion analysis and maintenance of the furnace wall and the cooling wall of the large-scale blast furnace.

Description

Residual life prediction method considering state dependence time lag
Technical Field
The invention belongs to the field of prediction and health management, and particularly relates to a residual life prediction method considering state dependence time lag.
Background
Remaining life is generally defined as the time remaining until the degradation process first reaches a failure threshold, and can be optimized by estimating its mathematical expectation or probability distribution. For complex industrial processes such as iron making, oil refining and the like, establishing a reasonable degradation model based on monitoring data is an important basis for predicting the residual service life of the system.
In recent years, a fractal Brown motion-driven degradation modeling method provides a new idea for solving the problem of residual life prediction of a non-Markov process, and is concerned by a plurality of experts and scholars (Zhang, 2017; Wang, 2020; Song, 2020). On the basis of Brownian motion, long-term and short-term memory effects are introduced by fractal Brownian motion and an expansion form of the fractal Brownian motion, statistical correlation between a historical degradation state and a future evolution trend is constructed, and compared with a traditional random walk process, the fractal Brownian motion and an expansion form are more suitable for describing biased diffusion characteristics of performance variables such as the temperature of a furnace wall and a cooling wall of a large-scale blast furnace.
However, most of the existing methods ignore the potential hysteresis effect when performing the degradation analysis. Unlike global long-term short-term memory effects in the full life cycle, the time lag is more focused on reflecting the local dependency of the degenerated state in the neighbor interval. It is noted that only some time-lag system life prediction studies adopt an artificial intelligence method to weaken the markov characteristic of the degradation process, and a more intuitive time-lag model is not established (Zhang, 2015; Liu, 2016; Rai, 2017). In particular, the above method generally assumes that the time lag is constant, and cannot cope with the situation that the time lag is time-varying and related to the current state under the unstable working condition. This problem can be attributed to a type of state-dependent time lag problem, i.e., the degree of lag in the rate of change of the degradation rate needs to be dynamically adjusted according to real-time data.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a residual life prediction method considering state dependence time lag, and a nonlinear fractal degradation model covering state dependence and a hysteresis effect at the same time is constructed, wherein a non-uniform diffusion link is represented by fractal Brownian motion. Because the model does not meet infinite separability, a series of approximate transformations are made to the original degradation process in the weak convergence meaning, and the analytic probability distribution of the residual service life is further deduced. The method has good prediction performance for the industrial equipment erosion and aging process with complex mechanism and state depending on time lag and specific fractal characteristics.
In order to achieve the purpose, the invention adopts the following technical scheme:
a residual life prediction method considering state-dependent time lag is characterized in that the residual life of industrial equipment is predicted, and the method comprises the following steps:
step 1: inputting a set of target device degradation data of length N x1,x2,…,xNSetting an initial value to be zero, and initializing a maximum time lag T according to the following state-dependent time lag model structure:
Figure BDA0002743775840000021
where t is the monitoring time, η is the drift coefficient, ξ is the nonlinear coefficient, σ is the diffusion coefficient, B is the time of flightH(T) is a standard fractal Brownian motion with a Herster index of H, Ts(x (t)) is a time-lag function, and has x (t) e [0, ∞);
step 2: discretizing the state-dependent time lag model in an implicit Euler format, wherein the discretization expression form is as follows:
Figure BDA0002743775840000022
wherein the content of the first and second substances,
Figure BDA0002743775840000023
Figure BDA0002743775840000024
where k is the serial number of the discrete monitoring instant, a is the weighting factor, p is the resampling interval, n is the serial number of the resampling instant,
Figure BDA0002743775840000025
tau is the original sampling interval and is,
Figure BDA0002743775840000026
y1:NΔis a re-sampling of the samples of the sample,
Figure BDA0002743775840000027
a (-) is a non-linear drift function,
Figure BDA0002743775840000028
εnand
Figure BDA0002743775840000029
is Gaussian noise,. epsilonn～N(0,ρ)，
Figure BDA00027437758400000210
h (-) is a scale function of the fractal diffusion term under weak convergence condition, I{·}Is an illustrative function, H is a Hurst exponent, Γ (·) is a Gamma function, s, r, m, c, J, χ, and
Figure BDA00027437758400000212
is an internal variable used to solve for h (·);
and step 3: calling a maximum likelihood solution of a Nelder-Mead simplex search model unknown parameter set theta ═ { eta, xi, sigma, H }:
Figure BDA00027437758400000211
Figure BDA0002743775840000031
and 4, step 4: at tkGenerating M simulated degradation tracks at a time
Figure BDA0002743775840000032
Based on the wiener process transformation theory, the probability density function of the remaining life is expressed as:
Figure BDA0002743775840000033
wherein lkIt is the remaining life that is the life of the battery,
Figure BDA0002743775840000034
Figure BDA0002743775840000035
Figure BDA0002743775840000036
wherein the content of the first and second substances,
Figure BDA0002743775840000037
is a failure threshold;
and 5: and finally outputting the residual life estimation result value of the target equipment at each monitoring moment.
Preferably, the industrial equipment is mechanism-oriented complex industrial equipment with state dependent time lag and specific fractal characteristics.
Preferably, the industrial equipment includes, but is not limited to, blast furnace walls, cooling walls.
The invention has the following beneficial technical effects:
the core advantage of the invention is that the state-dependent time lag is integrated into the fractal degradation modeling principle by the method, and the problem that a complex time lag system is difficult to effectively characterize by the traditional method is solved. The method highlights the time-varying time-lag characteristic of the degradation process by introducing a quantitative description of the historical state lag effect, and the prediction precision is high. Particularly, the method and the device can also give a reasonable residual life estimation result aiming at the industrial process that the internal and external working environments tend to be in an unstable state. The invention is mainly applied to corrosion analysis and maintenance of the furnace wall and the cooling wall of the large-scale blast furnace.
Drawings
FIG. 1 is a flow chart of the present invention for implementing a residual life prediction for a time-lag system;
FIG. 2 is a degradation trace generated by simulation of example 2;
fig. 3 is the estimation result of the remaining life distribution of example 2.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
Example 1
The method solves the problem of residual life prediction of a complex time delay system based on a fractal degradation model with state dependent time delay, and the estimated residual life distribution can provide sufficient decision support for the prediction and maintenance technology of industrial equipment. As shown in FIG. 1, the specific steps of the invention for realizing the residual life prediction of the time-lag system of the blast furnace wall are as follows:
1) inputting a group of blast furnace wall degradation data { x with the length of N1,x2,…,xNSetting an initial value to be zero, and initializing a maximum time lag T according to the following state-dependent time lag model structure:
Figure BDA0002743775840000041
where t is the monitoring time, η is the drift coefficient, ξ is the nonlinear coefficient, σ is the diffusion coefficient, B is the time of flightH(T) is a standard fractal Brownian motion with a Herster index of H, Ts(x (t)) is a time-lag function, and has x (t) e [0, ∞);
2) and combining a weak convergence criterion of fractal Brownian motion to give a discretization expression form of the model in an implicit Euler format:
Figure BDA0002743775840000042
wherein the content of the first and second substances,
Figure BDA0002743775840000043
Figure BDA0002743775840000044
where k is the serial number of the discrete monitoring instant, a is the weighting factor, p is the resampling interval, n is the serial number of the resampling instant,
Figure BDA0002743775840000045
tau is the original sampling interval and is,
Figure BDA0002743775840000046
y1:NΔis a re-sampling of the samples of the sample,
Figure BDA0002743775840000047
a (-) is a non-linear drift function,
Figure BDA0002743775840000048
εnand
Figure BDA0002743775840000049
is Gaussian noise,. epsilonn～N(0,ρ)，
Figure BDA00027437758400000410
h (-) is a scale function of the fractal diffusion term under weak convergence condition, I{·}Is an illustrative function, H is a Hurst exponent, Γ (·) is a Gamma function, s, r, m, c, J, χ, and
Figure BDA0002743775840000059
is an internal variable used to solve for h (·);
3) invoking the Nelder-Mead simplex search model maximum likelihood solution of unknown parameter set Θ ═ { η, ξ, σ, H } corresponds to the minimization problem as follows:
Figure BDA0002743775840000051
wherein the content of the first and second substances,
Figure BDA0002743775840000052
4) at tkGenerating M simulated degradation tracks at a time
Figure BDA0002743775840000053
Based on wiener process transformation theory, the probability density function of remaining life can be expressed as:
Figure BDA0002743775840000054
wherein lkIt is the remaining life that is the life of the battery,
Figure BDA0002743775840000055
Figure BDA0002743775840000056
Figure BDA0002743775840000057
wherein the content of the first and second substances,
Figure BDA0002743775840000058
is a failure threshold;
5) and outputting the residual service life distribution of the blast furnace wall at each monitoring moment.
Example 2
The residual life prediction effect of the method is verified through a numerical simulation example, and the simulation environment is as follows:
model: intel Core i5-5200U (CPU 2.20Ghz, 8.00GB RAM);
operating the system: windows 7;
software: MATLAB R2018 b.
Description of simulation procedure:
1) initializing a state-dependent time lag model structure according to formula (1), setting the maximum time lag to be 0.5, and setting the rest model parameters as: η ═ 1.4, ξ ═ 0.1, σ ═ 0.2, and H ═ 0.7;
2) based on the discretization model given by formula (2) to formula (4), let a be 0.5, ρ be 0.01, τ be 0.1, and N be 200, the generated raw data and the resampled data in the implicit euler format are as shown in fig. 2, and the failure threshold is shown as fig. 2
Figure BDA0002743775840000061
The failure time is tN＝20；
3) And (3) seeking a maximum likelihood solution of theta by using the formula (5) and the formula (6), wherein the identification result is as follows:
Figure BDA0002743775840000062
Figure BDA0002743775840000063
it is worth noting that the Nelder-Mead simplex method cannot guarantee that the result of the multidimensional search can be converged to the global optimal solution certainly, and is only suitable for the situation with lower dimensionality;
4) and (5) taking M as 1000, simulating a future degradation track by a one-step extrapolation method, and solving t by combining the formula (7) and the formula (10)kDistribution of remaining life at time fk(lk) With specific results as shown in fig. 3, it can be seen that the estimated probability density function can track the true value of the remaining lifetime as a whole, i.e. effectively extract the state-dependent time lag induced randomnessUncertainty, thus verifying the feasibility of the proposed method;
5) and outputting the residual life distribution at each monitoring moment for making a subsequent prediction maintenance strategy.
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.

Claims (3)

1. A residual life prediction method considering state-dependent time lag is characterized in that the residual life of industrial equipment is predicted, and the method comprises the following steps:
step 1: inputting a set of target device degradation data of length N x1,x2,…,xNSetting an initial value to be zero, and initializing a maximum time lag T according to the following state-dependent time lag model structure:
Figure FDA0002743775830000011
where t is the monitoring time, η is the drift coefficient, ξ is the nonlinear coefficient, σ is the diffusion coefficient, B is the time of flightH(T) is a standard fractal Brownian motion with a Herster index of H, Ts(x (t)) is a time-lag function, and has x (t) e [0, ∞);
step 2: discretizing the state-dependent time lag model in an implicit Euler format, wherein the discretization expression form is as follows:
Figure FDA0002743775830000012
wherein the content of the first and second substances,
Figure FDA0002743775830000013
Figure FDA0002743775830000014
where k is the serial number of the discrete monitoring instant, a is the weighting factor, p is the resampling interval, n is the serial number of the resampling instant,
Figure FDA0002743775830000015
tau is the original sampling interval and is,
Figure FDA0002743775830000016
y1:NΔis a re-sampling of the samples of the sample,
Figure FDA0002743775830000017
a (-) is a non-linear drift function,
Figure FDA0002743775830000018
εnand
Figure FDA0002743775830000019
is Gaussian noise,. epsilonn～N(0,ρ)，
Figure FDA00027437758300000110
h (-) is a scale function of the fractal diffusion term under weak convergence condition, I{·}Is an illustrative function, H is a Hurst exponent, Γ (·) is a Gamma function, s, r, m, c, J, χ, and
Figure FDA00027437758300000111
is an internal variable used to solve for h (·);
and step 3: calling a maximum likelihood solution of a Nelder-Mead simplex search model unknown parameter set theta ═ { eta, xi, sigma, H }:
Figure FDA0002743775830000021
Figure FDA0002743775830000022
and 4, step 4: at tkGenerating M simulated degradation tracks at a time
Figure FDA0002743775830000023
Based on the wiener process transformation theory, the probability density function of the remaining life is expressed as:
Figure FDA0002743775830000024
wherein lkIt is the remaining life that is the life of the battery,
Figure FDA0002743775830000025
Figure FDA0002743775830000026
Figure FDA0002743775830000027
wherein the content of the first and second substances,
Figure FDA0002743775830000028
is a failure threshold;
and 5: and finally outputting the residual life estimation result value of the target equipment at each monitoring moment.
2. The method for predicting the remaining life by considering the state-dependent time lag as claimed in claim 1, wherein the industrial equipment is an industrial equipment which is complex in mechanism and has the state-dependent time lag and a specific fractal characteristic.
3. The method of claim 1, wherein the industrial equipment includes, but is not limited to, blast furnace walls, cooling walls.
CN202011159533.6A 2020-10-27 2020-10-27 Residual life prediction method considering state dependence time lag Pending CN112231925A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112949026A (en) * 2021-01-19 2021-06-11 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

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112949026A (en) * 2021-01-19 2021-06-11 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
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

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Application publication date: 20210115