Xiao-Sheng Si

Remaining useful life estimation - A review on the statistical data driven approaches

Remaining useful life (RUL) is the useful life left on an asset at a particular time of operation. Its estimation is central to condition based maintenance and prognostics and health management. RUL is typically random and unknown, and as such it must be estimated from available sources of information such as the information obtained in condition and health monitoring. The research on how to best estimate the RUL has gained popularity recently due to the rapid advances in condition and health monitoring techniques. However, due to its complicated relationship with observable health information, there is no such best approach which can be used universally to achieve the best estimate. As such this paper reviews the recent modeling developments for estimating the RUL. The review is centred on statistical data driven approaches which rely only on available past observed data and statistical models. The approaches are classified into two broad types of models, that is, models that rely on directly observed state information of the asset, and those do not. We systematically review the models and approaches reported in the literature and finally highlight future research challenges.

Remaining Useful Life Estimation Based on a Nonlinear Diffusion Degradation Process

Remaining useful life estimation is central to the prognostics and health management of systems, particularly for safety-critical systems, and systems that are very expensive. We present a non-linear model to estimate the remaining useful life of a system based on monitored degradation signals. A diffusion process with a nonlinear drift coefficient with a constant threshold was transformed to a linear model with a variable threshold to characterize the dynamics and nonlinearity of the degradation process. This new diffusion process contrasts sharply with existing models that use a linear drift, and also with models that use a linear drift based on transformed data that were originally nonlinear. Both existing models are based on a constant threshold. To estimate the remaining useful life, an analytical approximation to the distribution of the first hitting time of the diffusion process crossing a threshold level is obtained in a closed form by a time-space transformation under a mild assumption. The unknown parameters in the established model are estimated using the maximum likelihood estimation approach, and goodness of fit measures are applied. The usefulness of the proposed model is demonstrated by several real-world examples. The results reveal that considering nonlinearity in the degradation process can significantly improve the accuracy of remaining useful life estimation.

A degradation path-dependent approach for remaining useful life estimation with an exact and closed-form solution

Remaining useful life (RUL) estimation is regarded as one of the most central components in prognostics and health management (PHM). Accurate RUL estimation can enable failure prevention in a more controllable manner in that effective maintenance can be executed in appropriate time to correct impending faults. In this paper we consider the problem of estimating the RUL from observed degradation data for a general system. A degradation path-dependent approach for RUL estimation is presented through the combination of Bayesian updating and expectation maximization (EM) algorithm. The use of both Bayesian updating and EM algorithm to update the model parameters and RUL distribution at the time obtaining a newly observed data is a novel contribution of this paper, which makes the estimated RUL depend on the observed degradation data history. As two specific cases, a linear degradation model and an exponential-based degradation model are considered to illustrate the implementation of our presented approach. A major contribution under these two special cases is that our approach can obtain an exact and closed-form RUL distribution respectively, and the moment of the obtained RUL distribution from our presented approach exists. This contrasts sharply with the approximated results obtained in the literature for the same cases. To our knowledge, the RUL estimation approach presented in this paper for the two special cases is the only one that can provide an exact and closed-form RUL distribution utilizing the monitoring history. Finally, numerical examples for RUL estimation and a practical case study for condition-based replacement decision making with comparison to a previously reported approach are provided to substantiate the superiority of the proposed model.

Estimating Remaining Useful Life With Three-Source Variability in Degradation Modeling

The use of the observed degradation data of a system can help to estimate its remaining useful life (RUL). However, the degradation progression of the system is typically stochastic, and thus the RUL is also a random variable, resulting in the difficulty to estimate the RUL with certainty. In general, there are three sources of variability contributing to the uncertainty of the estimated RUL: 1) temporal variability, 2) unit-to-unit variability, and 3) measurement variability. In this paper, we present a relatively general degradation model based on a Wiener process. In the presented model, the above three-source variability is simultaneously characterized to incorporate the effect of three-source variability into RUL estimation. By constructing a state-space model, the posterior distributions of the underlying degradation state and random effect parameter, which are correlated, are estimated by employing the Kalman filtering technique. Further, the analytical forms of not only the probability distribution but also the mean and variance of the estimated RUL are derived, and can be real-time updated in line with the arrivals of new degradation observations. We also investigate the issues regarding the identifiability problem in parameter estimation of the presented model, and establish the according results. For verifying the presented approach, a case study for gyros in an inertial platform is provided, and the results indicate that considering three-source variability can improve the modeling fitting and the accuracy of the estimated RUL.

A maintenance optimization model for mission-oriented systems based on Wiener degradation

Over the past few decades, condition-based maintenance (CBM) has attracted many researchers because of its effectiveness and practical significance. This paper deals with mission-oriented systems subject to gradual degradation modeled by a Wiener stochastic process within the context of CBM. For a mission-oriented system, the mission usually has constraints on availability/reliability, the opportunity for maintenance actions, and the monitoring type (continuous or discrete). Furthermore, in practice, a mission-oriented system may undertake some preventive maintenance (PM) and after such PM, the system may return to an intermediate state between an as-good-as new state and an as-bad-as old state, i.e., the PM is not perfect and only partially restores the system. However, very few CBM models integrated these mission constraints together with an imperfect nature of the PM into the course of optimizing the PM policy. This paper develops a model to optimize the PM policy in terms of the maintenance related cost jointly considering the mission constraints and the imperfect PM nature. A numerical example is presented to demonstrate the proposed model. The comparison with the simulated results and the sensitivity analysis show the usefulness of the optimization model for mission-oriented system maintenance presented in this paper.

An Adaptive Prognostic Approach via Nonlinear Degradation Modeling: Application to Battery Data

Remaining useful life (RUL) estimation via degradation modeling is considered as one of the most central components in prognostics and health management. Current RUL estimation studies mainly focus on linear stochastic models, and the results under nonlinear models are relatively limited in literature. Even in nonlinear degradation modeling, the estimated RUL is aimed at a population of systems of the same type or depend only on the current degradation observation. In this paper, an adaptive and nonlinear prognostic model is presented to estimate RUL using a systems history of the observed data to date. Specifically, a general nonlinear stochastic process with a time-dependent drift coefficient is first adopted to characterize the dynamics and nonlinearity of the degradation process. In order to render the RUL estimation depending on the degradation history to date, a state-space model is constructed, and Kalman filtering is applied to update one key parameter in the drifting function through treating this parameter as an unobserved state variable. To update the hidden state and other parameters in the state-space model simultaneously and recursively, the expectation maximization algorithm is used in conjunction with Kalman smoother to achieve this aim. The probability density function of the estimated RUL is derived with an explicit form, and some commonly used results under linear models turn out to be its special cases. Finally, the implementation of the presented approach is illustrated by numerical simulations, and an application for estimating the RUL of lithium-ion batteries is used to demonstrate the superiority of the method.

An Additive Wiener Process-Based Prognostic Model for Hybrid Deteriorating Systems

Hybrid deteriorating systems, which are made up of both linear and nonlinear degradation parts, are often encountered in engineering practice, such as gyroscopes which are frequently utilized in ships, aircraft, and weapon systems. However, little reported literature can be found addressing the degradation modeling for a system of this type. This paper proposes a general degradation modeling framework for hybrid deteriorating systems by employing an additive Wiener process model that consists of a linear degradation part and a nonlinear part. Furthermore, we derive the analytical solution of the remaining useful life distribution approximately for the presented model. For a specific system in service, the posterior estimates of the stochastic parameters in the model are updated recursively by using the condition monitoring observations based on a Bayesian framework with the consideration that the stochastic parameters in the linear and nonlinear deteriorating parts are correlated. Thereafter, the posterior distribution of stochastic parameters is used to update in real-time the distribution of the remaining useful life where the uncertainties in the estimated stochastic parameters are incorporated. Finally, a numerical example and a practical case study are provided to verify the effectiveness of the proposed method. Compared with two existing methods in literature, our proposed degradation modeling method increases the one-step prediction accuracy slightly in terms of mean squared error, but gains significant improvements in the estimated remaining useful life.

A New Prediction Model Based on Belief Rule Base for System's Behavior Prediction

In engineering practice, a systems behavior constantly changes over time. To predict the behavior of a complex engineering system, a model can be built and trained using historical data. This paper addresses the forecasting problems with a belief rule base (BRB) to trace and predict system performance in a more interpretable and transparent way. More precisely, it extends the BRB method to handle a systems behavior prediction, and a new prediction model based on BRB is presented, which can model and analyze prediction problems using not only numerical data but human judgmental information as well. The proposed forecasting model includes some unknown parameters that can be manually tuned and trained. To build an effective BRB forecasting model, a multiple-objective optimization model is provided to locally train the BRB prediction model by minimizing the mean square error (MSE). Finally, a practical case study is provided to illustrate the detailed implementation procedures and examine the feasibility of the proposed approach in engineering application. Furthermore, the comparative studies with other state-of-the-art prediction methods are carried out. It is shown that the proposed model is effective and can generate better prediction in terms of accuracy, as well as comprehensibility.

System reliability prediction model based on evidential reasoning algorithm with nonlinear optimization

In this paper, a novel reliability prediction technique based on the evidential reasoning (ER) algorithm is developed and applied to forecast reliability in turbocharger engine systems. The focus of this study is to examine the feasibility and validity of the ER algorithm in systems reliability prediction by comparing it with some existing approaches. To determine the parameters of the proposed model accurately, some nonlinear optimization models are investigated to search for the optimal parameters of forecasting model by minimizing the mean square error (MSE) criterion. Finally, a numerical example is provided to demonstrate the detailed implementation procedures. The experimental results show that the prediction performance of the ER-based prediction model outperforms several existing methods in terms of prediction accuracy or speed.

A Residual Storage Life Prediction Approach for Systems With Operation State Switches

This paper concerns the problem of predicting residual storage life for a class of highly critical systems with operation state switches between the working state and storage state. A success of estimating the residual storage life for such systems depends heavily on incorporating their two main characteristics: 1) system operation process could experience a number of state transitions between the working state and storage state; and 2) systems degradation depends on its operation states. Toward this end, we present a novel degradation model to account for the dependency of the degradation process on the systems operation states, where a two-state continuous-time homogeneous Markov process is used to approximate the switches between the working state and storage state. Using the monitored degradation data during the working state and the available system operation information, the parameters in the presented model can be estimated/updated under Bayesian paradigm. Then, the posterior probabilistic law of the number of state transitions and their transition times are derived, and further, the formulation for the predicted residual storage life distribution is established by considering the possible state transitions in the future. To be solvable, a numerical solution algorithm is provided to calculate the distribution of the predicted residual storage life. Finally, we demonstrate the proposed approach by a case study for gyroscopes.