Wiener Process Model Research Articles

Bayesian information fusion method for reliability analysis with failure‐time data and degradation data

AbstractDegradation data and failure‐time data are two types of data commonly used in reliability analysis. Both types of data are collected from different sources for reliability analysis of complex products. For highly reliable products, however, it is often difficult to collect sufficient useful data for reliability analysis with high accuracy, which poses the challenge for small sample size problems, that is, single‐type data with few samples. In this paper, three novel Bayesian information fusion models are first proposed to characterize the inherent relationship between the failure‐time data and the degradation data, and further to integrate the heterogeneous data to obtain accurate reliability analysis results under small sample size. Then, a model selection method is developed to choose appropriate model from the Wiener process, gamma process, and IG process models. Finally, the reliability analysis is completed based on the parameter estimation of the Bayesian information fusion model with the aid of the MCMC method. An industrial example is presented to demonstrate the effectiveness of the proposed Bayesian information fusion method.

Reliability estimation from two types of accelerated testing data based on an artificial neural network supported Wiener process

Considering the powerful ability of artificial neural network on data fitting, we have combined it with Wiener process in reliability estimation, while the previously published artificial neural network supported Wiener process based reliability estimation method only can utilize degradation testing data under normal use stress. However, the accelerated degradation tests and accelerated life tests are always performed to shorten the testing time. Hence, based on a general log-linear form acceleration model, we develop the artificial neural network supported Wiener process model into an accelerated testing model to utilize the accelerated testing data and improve the reliability estimating accuracy. Furthermore, the corresponding model training and parameter inferencing approaches are also constructed to apply the proposed model in reliability estimation. A simulation experiment and a case study on stress relaxation dataset are performed to verify the effectiveness of the proposed method. It is concluded that, the proposed method shows superiorities on population evaluation and individual predictions comparing the other methods, considering the accuracies of degradation modeling, life and reliability estimations. As a result, it is more suitable and practical than the previously published approaches.

A new class of mechanism-equivalence-based Wiener process models for reliability analysis

It is quite common to see that a unit of a product with a higher degradation rate also presents a more prominent dispersion. This phenomenon has motivated studies on developing new degradation models. In particular, a variety of Wiener process models have been developed by correlating the drift parameter and the diffusion parameter based on the statistical features of data. However, no insightful explanations are provided for such interesting correlations. In this article, degradation mechanism equivalence is first introduced based on the acceleration factor invariant principle, and the correlation between degradation rate and variation is explained using basic principles. Then, mechanism-equivalence-based Wiener process models, including a basic model and a random-effects model, are proposed to characterize such degradation behavior of a product. Analytical solutions for both point estimation and interval estimation of unknown model parameters are obtained using the maximum likelihood estimation method and an expectation–maximization algorithm. An extension of the proposed model that is able to handle accelerated degradation tests is developed. A simulation study and two real-world applications are provided to illustrate the effectiveness of the proposed models in product reliability estimation based on degradation data.

An adaptive and generalized Wiener process model with a recursive filtering algorithm for remaining useful life estimation

In this paper, we propose a generalized Wiener process-based degradation model with an adaptive drift to characterize the degradation behavior exhibiting nonlinearity, temporal uncertainty, item-to-item variability, and time-varying degradation. A recursive Bayesian filtering algorithm is derived to update the drift distribution. The expectation-maximization algorithm is utilized to estimate all other model parameters online whenever a new degradation measurement from the system under consideration is available without requiring population-based degradation data from identical systems in the same batch. This renders both the hidden drift and model parameters adaptive to the newly acquired degradation data. An analytical approximation to the RUL distribution considering the uncertainty of the hidden drift is derived in a closed form which is proved to encompass some existing formulae as its special cases. A numerical example is provided to illustrate the implementation procedure of the proposed RUL estimation method, and a practical milling dataset is adopted to testify to the superior performance of the proposed method against previous similar methods in remaining useful life estimation.

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

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.

Degradation modeling considering unit-to-unit heterogeneity-A general model and comparative study

The performance of units in the same batch can exhibit considerable heterogeneity due to the variation in the raw materials and fluctuation in the manufacturing process. For products suffering performance degradation in their use, such heterogeneity often results in an increase in the dispersion of the degradation paths of units in a population. The degradation rate of products can be unit-specific and often treated as random effects. This paper develops a novel random-effects Wiener process model to account for the unit-to-unit heterogeneity in the degradation, where the generalized inverse Gaussian (GIG) distribution is used to model the unit-specific degradation rate. The GIG distribution is a very general distribution with broad applications, which includes the inverse Gaussian (IG) distribution and the Gamma distribution as special cases. We investigate the model properties and develop an expectation maximization (EM) algorithm for parameter estimation. By comparing the proposed model with existing models on two real degradation datasets of the infrared LEDs and the GaAs lasers, we show that the proposed model is quite effective for degradation modeling with heterogeneous rates.

Reliability analysis for a system experiencing dependent degradation processes and random shocks based on a nonlinear Wiener process model

Complex systems usually fail due to competing failure modes caused by multiple degradation processes (i.e., soft failures) and random shocks (i.e., hard failures). The dependence of these competing failure modes, including the one among the degradation processes and the one between degradation and random shocks, must be considered in reliability analysis. In this paper, a more general reliability model that takes into account such complex dependence is developed based on a nonlinear Wiener process model and time-varying copula method. First, the nonlinear Wiener process model is used to characterize the degradation behavior of the system. Then, the impact of random shocks on the increments and rate of a degradation process along with the impact of the degradation process on random shocks are investigated. The role of the time-varying copula method is to characterize the dependence among multiple failure processes. A numerical example and a real application on a type of MEMS oscillator are provided to illustrate the use of the proposed mathematical model in practice, and a sensitivity analysis is conducted to gain insights into the impact of key parameters of random shocks on system reliability.

Life Prediction of Residual Current Device Based on Wiener Process with GM (1, 1) Model

Residual current device (RCD), the critical equipment to protect the safety of electrical users, are known to experience performance degrade over time during their use lifetime. Therefore, in order to promptly replace the RCD before failure, it is very important to predict its lifetime. In order to predict the remaining life of the RCD, a constant‐stress accelerated degradation test (CSADT) and a combination prediction model are proposed. First, the CSADT is conducted with temperature as the acceleration stress and the residual operating current as degradation characteristic. Then, based on the prediction result of pseudo failure life, a combination model of Wiener process and GM (1, 1) model is given. Finally, the remaining life of the RCD under normal use environment is extrapolated. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

On multivariate copula modeling of dependent degradation processes

Multivariate degradation processes have been observed in many engineering systems. Most existing multivariate degradation modeling techniques, such as multivariate general path models or multivariate Wiener process models, assume an underlying Gaussian dependence structure. Unfortunately, in reality, the dependencies among degradation processes are often nonlinear, asymmetric and greatly tail-skewed, and thus limit the usefulness of the conventional modeling techniques in practice. To overcome these limitations, in this paper, we develop a copula-based multivariate modeling framework. Three fundamental copula classes are applied to model the complex dependence structure among correlated degradation processes. Statistical inference and model selection techniques, including two graphical diagnostic tools, a test of independence and a goodness-of-fit test, are employed to identify the best model. The advantages of the proposed modeling framework are demonstrated through simulation studies. And we also discuss the effect of ignoring tail dependence on system failure probability assessment. Finally, the applications of the copula-based multivariate degradation models on both system reliability evaluation and remaining useful life prediction are provided. The proposed methodology is illustrated using a numerical example.

A hybrid prognostic method based on gated recurrent unit network and an adaptive Wiener process model considering measurement errors

Remaining useful life (RUL) prediction is fundamental to prognostics and health management (PHM). Considering the advantages of both model-based and data-driven prognostic approaches, this paper develops a hybrid prognostic method for machinery degradation. First, a 3σ criterion-based algorithm is introduced to detect the initial timepoint of degradation. Second, gated recurrent unit (GRU) network is utilized to learn the degradation characteristics based on the available data and thereby predict the long-term degradation trend by a multi-prediction procedure. Then, an adaptive Wiener process model considering measurement errors is constructed. The states of this model consisting of the drift rate and the underlying degradation value are updated adaptively based on the monitored observations and the predictions by GRU using a Kalman filtering algorithm. The predicted values of the RUL can be determined according to the underlying degradation and the failure threshold. Finally, to account for the drift adaptivity in the future degradation, exponentially weighted average method is adopted to aggregate the estimated drift sequence from the current time until failure for the derivation of real-time RUL distributions. The effectiveness and superiority are illustrated by a simulation study and an application to rolling element bearings.

A nonlinear-drift-driven Wiener process model for remaining useful life estimation considering three sources of variability

The estimation of remaining useful life (RUL) for a degrading system has gained increasing attention both in academia and in industry for decades. In this study, a nonlinear-drift-driven Wiener process model considering three common sources of uncertainty is constructed by an age-dependent state-space model for the RUL estimation of degrading systems. Analytical expressions approximating the probability distribution function of RUL of the above-described model are derived for both online estimation and offline estimation scenarios. It is shown that the derived expressions are more general and cover the simplified cases discussed in previous woks. A model parameter estimation method is proposed based on unbalanced historical degradation measurements, and a down-sampling strategy is introduced to avert the underflow issue. The prognostic performance of the proposed method against previous similar works under the online and offline estimation scenarios is demonstrated on two publicly available datasets by comparisons in terms of three prognostic metrics and the probabilistic distribution of RUL at different condition monitoring points. The results show that it is necessary to include the nonlinear degradation characteristics and the three sources of uncertainty into the RUL estimation especially for the offline estimation scenario.

Optimum degradation test plan under model mis-specification for Wiener and gamma processes

Degradation tests have been used for the purpose of assessing reliability information. In this paper, we consider a degradation test design problem under a statistical model mis-specification scenario. The Wiener and gamma processes are considered in this research. A gamma process is suitable for describing degradation paths that exhibit monotone behavior. However, if one fits a Wiener process model to the data, the resulting statistical inferences may be affected. Tsai, Tseng, and Balakrishnan studied the effect on the estimated mean time to failure. However, the experimental design problem was not discussed. A lack of the explicit functional form of the estimation variances makes it difficult to find degradation plans that can improve test efficiency. In this paper, functional forms of optimal degradation test plans are proposed under model mis-specification. Furthermore, a weighted ratio objective function considering the prior probability of the true model is used to find robust test plans for practical use. The results from a numerical example show that, by using an appropriate degradation test plan, the estimation variance can be reduced, and the test efficiency can be improved. A simulation study is conducted to investigate the performance of the parameter estimates when the sample size is small.

An Improved Random Effects Wiener Process Accelerated Degradation Test Model for Lithium-Ion Battery

For the accelerated degradation test (ADT) of lithium-ion battery, the degradation path models are usually applied with the fixed parameters. To optimize the degradation path models, so many battery cells are required for the ADT models based on the degradation path. However, for some lithium-ion batteries with long cycle life and high reliability, the samples are limited due to experimental cost constraints. Meanwhile, owing to the differences in raw materials and manufacturing processes, it is easy to observe variations among the degradation path of lithium-ion battery cells. Fortunately, Wiener process model considering the individual difference can express the variations and be modeled with limited samples for lithium-ion battery. Motivated by this issue, an improved method with random effects Wiener process (REWP) is proposed in this article. First, to verify the degradation process following the Wiener process, the Shapiro-Wilk test is carried out on the basis of a significance level of 0.05. Second, we analyze the varieties of every lithium-ion battery cell. To select a suitable Wiener process model, we apply the coefficient of variation as a measure of random parameters selection for Wiener process. Meanwhile, the maximum likelihood estimation (MLE) is used to optimize parameters of the proposed model. Next, the three different REWP models and general Wiener process model are compared. Finally, to demonstrate the proposed method, the lithium-ion battery cells used for a spacecraft in low Earth orbit (LEO) are conducted for ADTs. The results suggest that the REWP model has a better performance for assessing reliability of lithium-ion battery with long cycle life.

OSS Effort Expense Optimization Based on Wiener Process Model and GA

Various open source software are managed by using several bug tracking systems. In particular, the open source software extends to the cloud service and edge computing. Recently, OSF Edge Computing Group is launched by OpenStack. There are big data behind the internet services such as cloud and edge computing. Then, it is important to consider the impact of big data in order to assess the reliability of open source software. Various optimal software release problems have been proposed by specific researchers. In the typical optimal software release problems, the cost parameters are defined as the known parameter. However, it is difficult to decide the cost parameter because of the uncertainty. The purpose of our research is to estimate the effort parameters included in our models. In this paper, we propose an estimation method of effort parameter by using the genetic algorithm. Then, we show the estimation method in section 3. Moreover, we analyze actual data to show numerical examples for the estimation method of effort parameter. As the research results, we found that the OSS managers would be able to comprehend the human resources required before the OSS project in advance by using our method.

Reliability modeling and analysis for systems governed by multiple competing failures processes

Due to that the operating environment is becoming more and more complex and rigorous, the multiple competing failure modes for the reliability system is much commonly seen. In order to improve the system performance, a sensor-based degradation calibration policy (SBDC policy) is presented in this paper. The model considers the competing failure process which is described by the soft and hard failure modes. In detail, the soft failures occur when the degradation of the system exceeds the failure threshold, and the hard failures are caused by the same shock process. We use the Wiener process model to describe the soft failure and the shock process to describe the catastrophic failure. Meanwhile, in the shock process, the damage associated with the system is normal distributed which is related to the duration of the adjacent shocks. This extended model with calibrations has a good application value for the corresponding complex reliability systems which are subject to the dependent competing failure modes. By the model in this article, the system reliability and safety can be improved and the risk of the abrupt damage shall be reduced as the circumstance changes.

A novel online method for predicting the remaining useful life of lithium-ion batteries considering random variable discharge current

Lithium-ion batteries are widely used in many electronic and electrical devices, and accurately predicting their remaining useful life is essential to ensure the safe and reliable operation of the systems. The discharge current of lithium-ion batteries in the actual environment changes randomly during one charge and discharge cycle, and the randomly changing current has a greater impact on battery life. Existing prediction methods rarely take this into account. Therefore, this paper proposes a new method for predicting the remaining useful life of lithium-ion batteries with variable discharge current. First, the battery aging experiment under variable discharge current is designed by simulating the operation state of batteries and capacity data is collected. Secondly, a novel two-stage Wiener process model is established to describe the differences in the degradation characteristics of lithium-ion batteries at different stages. Finally, the unscented particle filtering algorithm is introduced so that all parameters in the model and the remaining useful life distribution of lithium-ion batteries are adaptively updated with the latest on-line measurements. The experimental results demonstrate that the proposed method can achieve more accurate and robust results compared with the two previous methods, which verifies the effectiveness and robustness of the proposed method.

Two-stage physics-based Wiener process models for online RUL prediction in field vibration data

Due to most failure mechanisms, such as fatigue crack growth and fatigue spall, the degradation process of rotating machinery commonly exhibits two-stage features in engineering practice. Other minor factors are also the key issues affecting the health evolution process, including the component structure, assembly accuracy, and working environment. Ignoring such a mechanism may lead to imprecise in degradation modeling, life prognostic, and ultimately lead to safety risk. Besides, achieving high accuracy of prognostic emphasizes the influence of random effect in the degradation process. The contribution of this study lies in addressing this issue by proposing two-stage physics-based Wiener process models integrating: (a) fatigue crack mechanism and crack growth law, and (b) other minor factors. A general prognostic framework is formulated by jointly employing the online change point detection, parameter estimation, and remaining useful life (RUL) prediction, which has good statistic inference and applicability in two general nonlinear systems, i.e., power-law and exponential-law. A joint implement of offline two-step parameter estimation method and the online Bayesian update method is executed, making full advantage of historical and in-service data, based on which the RUL prediction transcends into an imperative PHM module. A practical case study on the vibration dataset of wheel treads demonstrates the practically implement ability of the proposed method in achieving high accuracy of RUL prediction.

Degradation analysis on high-cycle bending fatigue for woven SiC/SiC composites based on Wiener process model

A comprehensive investigation of degradation analysis under high-cycle bending fatigue (HCBF) loading for composite materials was conducted based on the Wiener process model. Degradation data are generated by conducting the probabilistic progressive damage analysis of composite materials considering the variability of material properties including mechanical properties and strength. Based on the degradation data, the Wiener process model is established with the power time transformation function and linear time-scale functions. The HCBF tests of composite cantilever beam specimen (CBS) and turbine guide vane (TGV) are conducted to evaluate the degradation process of composite materials. Compared with the experimental data and Monte Carlo simulation (MCS) method, the proposed methodology has the promising potentials to improve computational efficiency with acceptable computational accuracy for the CBSs. As for the TGV, the maximum relative errors for mean fatigue life are within 17.89%, while the degradation tendency from experiments is similar to the simulated degradation curves, verifying the rationality of the proposed method based on Wiener process model. Moreover, reliability analysis is conducted based on the stochastic degradation process, which can be used to determine whether the performance of the structure meets the design requirement.

A novel degradation-rate-volatility related effect Wiener process model with its extension to accelerated ageing data analysis

For some materials, positive correlations between degradation rate and volatility are common observations affecting health evolution processes, referred as degradation-rate-volatility related effect. Ignoring such correlations may weaken the stability and precision of prognosis outcomes, ultimately misleading maintenance decision-makings. However, few attempts explore physical integrations of rate-volatility correlations, while quantify the correlation pattern polluted by random effect. Besides, achieving high accuracy of degradation modeling emphasizes the influence of systematic error. We address such technical challenges by constructing a Wiener-based degradation model integrating: (a) time-variant drift and diffusion coefficients linked by a linear function and (b) a systematic error term independent of process variances. Joint statistical inference employing expectation maximization (EM) is executed, based on which the analytical structure of RUL distribution is constructed. We further extend the prognosis approach to accelerated ageing test (AAT) by incorporating the stress-acceleration models. A case study on degradation data of 3S-60 silicon rubber states the superior performance of the proposed approach in reducing fitting error of degradation trajectory as well as improving the RUL prediction accuracy.

Centralized Maintenance Time Prediction Algorithm for Freight Train Wheels Based on Remaining Useful Life Prediction

Many freight trains for special lines have in common the characteristics of a fixed group. Centralized Condition-Based Maintenance (CCBM) of key components, on the same freight train, can reduce maintenance costs and enhance transportation efficiency. To this end, an optimization algorithm based on the nonlinear Wiener process is proposed, for the prediction of the train wheels Remaining Useful Life (RUL) and the centralized maintenance timing. First, Hodrick–Prescott (HP) filtering algorithm is employed to process the raw monitoring data of wheel tread wear, extracting its trend components. Then, a nonlinear Wiener process model is constructed. Model parameters are calculated with a maximum likelihood estimation and the general deterioration parameters of wheel tread wear are obtained. Then, the updating algorithm for the drift coefficient is deduced using Bayesian formula. The online updating of the model is realized, based on individual wheel monitoring data, while a probability density function of individual wheel RUL is obtained. A prediction method of RUL for centralized maintenance is proposed, based on two set thresholds: “maintenance limit” and “the ratio of limit-arriving.” Meanwhile, a CCBM timing prediction algorithm is proposed, based on the expectation distribution of individual wheel RUL. Finally, the model is validated using a 500-day online monitoring data on a fixed group, consisting of 54 freight train cars. The validation result shows that the model can predict the wheels RUL of the train for CCBM. The proposed method can be used to predict the maintenance timing when there is a large number of components under the same working conditions and following the same path of degradation.