A nonlinear Wiener degradation model integrating degradation data under accelerated stresses and real operating environment

Remaining useful life (RUL) prediction in real operating environment (ROE) plays an important role in condition-based maintenance. However, the life information in ROE is limited, especially for some long-life products. In such cases, accelerated degradation test (ADT) is an effective method to collect data and then the accelerated degradation data are converted to normal level of accelerated stresses through acceleration factors. However, the stresses in ROE are different from normal stresses since there are some other stresses except normal stresses, which cannot be accelerated, but still have impact on the degradation. To predict the RUL in ROE, a nonlinear Wiener degradation model is proposed based on failure mechanism invariant principle which is the precondition and requirement of an ADT and a calibration factor is introduced to calibrate the difference between ROE and normal stresses. Moreover, the unit-to-unit variability is considered in the concern model. Based upon the proposed approach, the RUL distribution is derived in closed form. The unknown parameters in the model are obtained by a new two-step method through fuzing converted degradation data in normal stresses and degradation data in ROE. Finally, the validity of the proposed model is demonstrated through several simulation data and a case study.

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Remaining useful life prediction of cylinder liner based on nonlinear degradation model

Eksploatacja i Niezawodnosc - Maintenance and Reliability ◽

10.17531/ein.2022.1.8 ◽

2021 ◽

Vol 24 (1) ◽

pp. 62-69

Author(s):

Jianxiong Kang ◽

Yanjun Lu ◽

Bin Zhao ◽

Hongbo Luo ◽

Jiacheng Meng ◽

...

Keyword(s):

Estimation Method ◽

Cylinder Liner ◽

Likelihood Estimation ◽

Remaining Useful Life ◽

Model Parameters ◽

Operational Environment ◽

Unknown Parameters ◽

Degradation Model ◽

Proposed Model ◽

Useful Life

In order to effectively monitor the wear and predict the life of cylinder liner, a nonlinear degradation model with multi-source uncertainty based on Wiener process is established to evaluate the remaining useful life (RUL) of cylinder liner wear. Due to complex service performance of cylinder liner, the uncertainty of operational environment and working conditions of cylinder liner wear are considered into the model by a random function. The probability density function (PDF) formula of RUL is derived, and the maximum likelihood estimation method is adopted to estimate the unknown parameters of PDF. Considering the evaluated parameters as the initial values, the model parameters are updated adaptively, and an adaptive PDF is obtained. Furthermore, the proposed model is compared with two classical degradation models. The results show that the proposed model has a good performance for predicting the life, and the error is within 5%. The method can provide a reference for condition monitoring of cylinder liner wear.

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Particle Filtering Based Remaining Useful Life Prediction for Electromagnetic Coil Insulation

Sensors ◽

10.3390/s21020473 ◽

2021 ◽

Vol 21 (2) ◽

pp. 473

Author(s):

Haifeng Guo ◽

Aidong Xu ◽

Kai Wang ◽

Yue Sun ◽

Xiaojia Han ◽

...

Keyword(s):

Particle Filtering ◽

Remaining Useful Life ◽

Electrical Parameters ◽

Degradation Model ◽

Accelerated Degradation ◽

Insulation Failure ◽

Electromagnetic Coils ◽

Degradation Monitoring ◽

Insulation Degradation ◽

Useful Life

Electromagnetic coils are one of the key components of many systems. Their insulation failure can have severe effects on the systems in which coils are used. This paper focuses on insulation degradation monitoring and remaining useful life (RUL) prediction of electromagnetic coils. First, insulation degradation characteristics are extracted from coil high-frequency electrical parameters. Second, health indicator is defined based on insulation degradation characteristics to indicate the health degree of coil insulation. Finally, an insulation degradation model is constructed, and coil insulation RUL prediction is performed by particle filtering. Thermal accelerated degradation experiments are performed to validate the RUL prediction performance. The proposed method presents opportunities for predictive maintenance of systems that incorporate coils.

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Bivariate Nonlinear Diffusion Degradation Process Modeling via Copula and MCMC

Mathematical Problems in Engineering ◽

10.1155/2014/510929 ◽

2014 ◽

Vol 2014 ◽

pp. 1-11 ◽

Cited By ~ 7

Author(s):

Huibing Hao ◽

Chun Su

Keyword(s):

Nonlinear Diffusion ◽

Goodness Of Fit ◽

Real Data ◽

Degradation Process ◽

Copula Function ◽

Assessment Method ◽

Unknown Parameters ◽

Degradation Data ◽

Proposed Model ◽

Frank Copula

A novel reliability assessment method for degradation product with two dependent performance characteristics (PCs) is proposed, which is different from existing work that only utilized one dimensional degradation data. In this model, the dependence of two PCs is described by the Frank copula function, and each PC is governed by a random effected nonlinear diffusion process where random effects capture the unit to unit differences. Considering that the model is so complicated and analytically intractable, Markov Chain Monte Carlo (MCMC) method is used to estimate the unknown parameters. A numerical example about LED lamp is given to demonstrate the usefulness and validity of the proposed model and method. Numerical results show that the random effected nonlinear diffusion model is very useful by checking the goodness of fit of the real data, and ignoring the dependence between PCs may result in different reliability conclusion.

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Remaining Useful Life Estimation Considering Prior Accelerated Degradation Data and Bayesian Inference for Multi-Stress Operating Conditions

International Journal of Mathematical Engineering and Management Sciences ◽

10.33889/ijmems.2021.6.1.008 ◽

2020 ◽

Vol 6 (1) ◽

pp. 103-117

Author(s):

Shah M. Limon ◽

Om Prakash Yadav

Keyword(s):

Asset Management ◽

Field Performance ◽

Degradation Process ◽

Management Plan ◽

Remaining Useful Life ◽

Operating Conditions ◽

Degradation Behavior ◽

Accelerated Degradation ◽

Degradation Data ◽

Useful Life

Prediction of remaining useful life using the field monitored performance data provides a more realistic estimate of life and helps develop a better asset management plan. The field performance can be monitored (indirectly) by observing the degradation of the quality characteristics of a product. This paper considers the gamma process to model the degradation behavior of the product characteristics. An integrated Bayesian approach is proposed to estimate the remaining useful life that considers accelerated degradation data to model degradation behavior first. The proposed approach also considers interaction effects in a multi-stress scenario impacting the degradation process. To reduces the computational complexity, posterior distributions are estimated using the MCMC simulation technique. The proposed method has been demonstrated with an LED case example and results show the superiority of Bayesian-based RUL estimation.

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Wear Calculation-Based Degradation Analysis and Modeling for Remaining Useful Life Prediction of Ball Screw

Mathematical Problems in Engineering ◽

10.1155/2018/2969854 ◽

2018 ◽

Vol 2018 ◽

pp. 1-18 ◽

Cited By ~ 1

Author(s):

Li Zhang ◽

Hongli Gao ◽

Dawei Dong ◽

Guoqiang Fu ◽

Qi Liu

Keyword(s):

Experimental Data ◽

Remaining Useful Life ◽

Ball Screw ◽

Wear Volume ◽

Degradation Model ◽

Volume Formula ◽

Proposed Model ◽

Degradation Analysis ◽

Wear Calculation ◽

Useful Life

Ball screw is a kind of precise transmission element in drive system of machine tool. In this paper, the degradation model of ball screw is proposed based on wear calculation-based degradation analysis and experimental data-based validation. At first, fatigue wear is analyzed to be the predominant degradation mode of ball screw. The wear volume formula of ball screw is derived as the function of working load and stroke number. Secondly, the degradation rate of ball screw is analyzed to be affected by the total degradation and wear rate. Based on this finding, the degradation model of ball screw is theoretically derived as an exponential model by inputting wear volume formula. Thirdly, experimental data-based cross-validation method is proposed to validate the exponential degradation model. Determination coefficients are calculated to evaluate the fitting degree between the degradation model and real degradation path. Next, run-to-failure test of ball screw is carried out to collect experimental data in different working conditions. The average determination coefficient of different working conditions is calculated as 0.7848, which indicates that the proposed model can well fit the actual degradation path. In addition, the proposed model is applied to predict remaining useful life (RUL) of the tested ball screw by using collected data. RUL is estimated in a high and stable accuracy after 168000 strokes. For further validation, comparison with linear model is performed. All results show that the exponential degradation model is reasonable and correct in reflecting the degradation process of ball screw.

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Analyzing Accelerated Degradation Data via an Inverse Gaussian Degradation Model with Random Parameters

2018 Prognostics and System Health Management Conference (PHM-Chongqing) ◽

10.1109/phm-chongqing.2018.00183 ◽

2018 ◽

Author(s):

Fei Teng ◽

Haowei Wang

Keyword(s):

Inverse Gaussian ◽

Random Parameters ◽

Degradation Model ◽

Accelerated Degradation ◽

Degradation Data

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Accelerated Degradation Process Analysis Based on the Nonlinear Wiener Process with Covariates and Random Effects

Mathematical Problems in Engineering ◽

10.1155/2016/5246108 ◽

2016 ◽

Vol 2016 ◽

pp. 1-13 ◽

Cited By ~ 4

Author(s):

Li Sun ◽

Xiaohui Gu ◽

Pu Song

Keyword(s):

Diffusion Coefficient ◽

Wiener Process ◽

Random Effects ◽

Process Analysis ◽

Likelihood Estimation ◽

Degradation Process ◽

Unknown Parameters ◽

Accelerated Degradation ◽

Degradation Data ◽

Drift Parameter

It is assumed that the drift parameter is dependent on the acceleration variables and the diffusion coefficient remains the same across the whole accelerated degradation test (ADT) in most of the literature based on Wiener process. However, the diffusion coefficient variation would also become obvious in some applications with the stress increasing. Aiming at the phenomenon, the paper concludes that both the drift parameter and the diffusion parameter depend on stress variables based on the invariance principle of failure mechanism and Nelson assumption. Accordingly, constant stress accelerated degradation process (CSADP) and step stress accelerated degradation process (SSADP) with random effects are modeled. The unknown parameters in the established model are estimated based on the property of degradation and degradation increment, separately for CASDT and SSADT, by the maximum likelihood estimation approach with measurement error. In addition, the simulation steps of accelerated degradation data are provided and simulated step stress accelerated degradation data is designed to validate the proposed model compared to other models. Finally, a case study of CSADT is conducted to demonstrate the benefits of our model in the practical engineering.

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Nonlinear Doubly Wiener Constant-Stress Accelerated Degradation Model Based on Uncertainties and Acceleration Factor Constant Principle

Applied Sciences ◽

10.3390/app11198968 ◽

2021 ◽

Vol 11 (19) ◽

pp. 8968

Author(s):

Xiaoning Wang ◽

Xiaobao Su ◽

Jinjing Wang

Keyword(s):

Applied Stress ◽

Measurement Errors ◽

Constant Stress ◽

Acceleration Factor ◽

Process Models ◽

Unknown Parameters ◽

Degradation Model ◽

Practical Applications ◽

Accelerated Degradation ◽

Factor Constant

Although Wiener process models with the consideration of uncertainties, which are nonlinearity, random effects, and measurement errors, have been developed for lifetime prediction in the accelerated degradation test (ADT), they fail to describe the real degradation process because these models assume that the drift parameter correlates with the applied stress, while the diffusion parameter is constant. This paper put forward a nonlinear doubly Wiener constant-stress accelerated degradation model, where both diffusion and drift parameters were compatible with the applied stress according to the acceleration factor constant principle. When degradation data were available, we obtained the unknown parameters by applying a maximum likelihood estimation (MLE) algorithm in the constant-stress ADT (CSADT) model taking uncertainties into account. In addition, the proposed model’s effectiveness was validated through an illustrative example, and an application to the traveling wave tube (TWT) was carried out to demonstrate the superiority of our model in practical applications.

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Stressed State of the Axisymmetric Adhesive Joint of Two Cylindrical Shells under Axial Tension

Materials Science Forum ◽

10.4028/www.scientific.net/msf.968.519 ◽

2019 ◽

Vol 968 ◽

pp. 519-527

Author(s):

S.S. Kurennov ◽

Konstantin P. Barakhov ◽

A.G. Poliakov

Keyword(s):

Stressed State ◽

Linear Equations ◽

Adhesive Layer ◽

Radial Coordinate ◽

Normal Stresses ◽

Proposed Model ◽

The Matrix ◽

Deflected Mode ◽

Axisymmetric Shells ◽

The Difference

The research of the deflected mode of the construction, composed of two coaxially-glued cylindrical pipes, is done. Pipes are considered as thin-walled axisymmetric shells, which are joined by adhesive layer of a certain thickness. The shearing stresses in the glue are considered to be constant over the thickness of the adhesive layer, and normal stresses are linearly dependent on the radial coordinate. The shearing stresses in the adhesive layer are considered to be proportional to the difference in the longitudinal displacements of the shell sides that are faced to the adhesive layer. Normal stresses are proportional to the difference in radial displacement of the shells. It is supposed that the change in the adhesive layer thickness under deformation does not affect the stress, that is, the linear model is considered. The problem of the joint deflected mode finding is reduced to the system of four ordinary differential equations relative to the radial and longitudinal displacements of the layers. The system is solved by the matrix method. Displacements of layers outside of the adherent area can be found by the classical theory of axisymmetric shells. Satisfaction of boundary conditions and conjugation conditions leads to a system of twenty two linear equations with twenty two unknown coefficients. The model problem is solved; the results are compared with the computation made by the finite element method. The tangential and normal stresses in the glue reach the maximum values at the edges of the adhesive line. It is shown that the proposed model describes the stressed state of the joint with high accuracy, and this joint has an influx of glue residues at the ends of the adhesive line but can not be applied in the absence of adhesive influxes. Because in this case, the tangential stresses due to the parity rule reach maximum values not on the edge, but at some distance from the edge of the line. As a result, the distribution of normal stresses at the edge of the line also substantially changes. Thus, the proposed model with certain restrictions has sufficient accuracy for engineering problems and can be used to solve design problems.

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