A non-Gaussian continuous state space model for asset degradation

The degradation model plays an essential role in asset life prediction and condition based maintenance. Various degradation models have been proposed. Within these models, the state space model has the ability to combine degradation data and failure event data. The state space model is also an effective approach to deal with the multiple observations and missing data issues. Using the state space degradation model, the deterioration process of assets is presented by a system state process which can be revealed by a sequence of observations. Current research largely assumes that the underlying system development process is discrete in time or states. Although some models have been developed to consider continuous time and space, these state space models are based on the Wiener process with the Gaussian assumption. This paper proposes a Gamma-based state space degradation model in order to remove the Gaussian assumption. Both condition monitoring observations and failure events are considered in the model so as to improve the accuracy of asset life prediction. A simulation study is carried out to illustrate the application procedure of the proposed model

Predicting Remaining Useful Life using Time Series Embeddings based on Recurrent Neural Networks

We consider the problem of estimating the remaining useful life (RUL) of a system or a machine from sensor data. Many approaches for RUL estimation based on sensor data make assumptions about how machines degrade. Additionally, sensor data from machines is noisy and often suffers from missing values in many practical settings. We propose Embed-RUL: a novel approach for RUL estimation from sensor data that does not rely on any degradation-trend assumptions, is robust to noise, and handles missing values. Embed-RUL utilizes a sequence-to-sequence model based on Recurrent Neural Networks (RNNs) to generate embeddings for multivariate time series subsequences. The embeddings for normal and degraded machines tend to be different, and are therefore found to be useful for RUL estimation. We show that the embeddings capture the overall pattern in the time series while filtering out the noise, so that the embeddings of two machines with similar operational behavior are close to each other, even when their sensor readings have significant and varying levels of noise content. We perform experiments on publicly available turbofan engine dataset and a proprietary real-world dataset, and demonstrate that Embed-RUL outperforms the previously reported state-of-the-art on several metrics.Comment: Presented at 2nd ML for PHM Workshop at SIGKDD 2017, Halifax, Canad

Data-driven nonparametric Li-ion battery ageing model aiming at learning from real operation data - Part B : cycling operation

Conventional Li-ion battery ageing models, such as electrochemical, semi-empirical and empirical models, require a significant amount of time and experimental resources to provide accurate predictions under realistic operating conditions. At the same time, there is significant interest from industry in the introduction of new data collection telemetry technology. This implies the forthcoming availability of a significant amount of real-world battery operation data. In this context, the development of ageing models able to learn from in-field battery operation data is an interesting solution to mitigate the need for exhaustive laboratory testing. In a series of two papers, a data-driven ageing model is developed for Li-ion batteries under the Gaussian Process framework. A special emphasis is placed on illustrating the ability of the Gaussian Process model to learn from new data observations, providing more accurate and confident predictions, and extending the operating window of the model. The first paper of the series focussed on the systematic modelling and experimental verification of cell degradation through calendar ageing. Conversantly, this second paper addresses the same research challenge when the cell is electrically cycled. A specific covariance function is composed, tailored for use in a battery ageing application. Over an extensive dataset involving 124 cells tested during more than three years, different training possibilities are contemplated in order to quantify the minimal number of laboratory tests required for the design of an accurate ageing model. A model trained with only 26 tested cells achieves an overall mean-absolute-error of 1.04% in the capacity curve prediction, after being validated under a broad window of both dynamic and static cycling temperatures, Depth-of-Discharge, middle-SOC, charging and discharging C-rates

Data-driven nonparametric Li-ion battery ageing model aiming at learning from real operation data – Part A : storage operation

Conventional Li-ion battery ageing models, such as electrochemical, semi-empirical and empirical models, require a significant amount of time and experimental resources to provide accurate predictions under realistic operating conditions. At the same time, there is significant interest from industry in the introduction of new data collection telemetry technology. This implies the forthcoming availability of a significant amount of real-world battery operation data. In this context, the development of ageing models able to learn from in-field battery operation data is an interesting solution to mitigate the need for exhaustive laboratory testing

Threshold Regression for Survival Analysis: Modeling Event Times by a Stochastic Process Reaching a Boundary

Many researchers have investigated first hitting times as models for survival data. First hitting times arise naturally in many types of stochastic processes, ranging from Wiener processes to Markov chains. In a survival context, the state of the underlying process represents the strength of an item or the health of an individual. The item fails or the individual experiences a clinical endpoint when the process reaches an adverse threshold state for the first time. The time scale can be calendar time or some other operational measure of degradation or disease progression. In many applications, the process is latent (i.e., unobservable). Threshold regression refers to first-hitting-time models with regression structures that accommodate covariate data. The parameters of the process, threshold state and time scale may depend on the covariates. This paper reviews aspects of this topic and discusses fruitful avenues for future research.Comment: Published at http://dx.doi.org/10.1214/088342306000000330 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Perturbed Inverse Gaussian Process Model with Time Varying Variance-To-Mean Ratio

International audienceThe inverse gaussian (IG) process has become a common model for reliability analysis of monotonic degradation processes. The traditional IG process model assumes that the degradation increment follows an IG distribution, and the variance-to-mean ratio (VMR) is constant with time. However, for the degradation paths of some practical applications, e.g., the GaAs laser degradation data that motivated to propose the IG process, the VMR is actually time varying. Confronted with this, we propose an IG process model with measurement errors that depend on the actual degradation level. According to different forms or parameter values of the dependence function, the VMR of the degradation paths can display different time varying patterns. The maximum likelihood estimation method is developed in a step-by-step way, combined with numerical integration method and heuristic optimization method. Finally, the GaAs laser example is revisited to illustrate the effectiveness of the proposed model, which indicates that the introduction of statistically dependent measurement error can provide better fitting results and lifetime evaluation performance