Degradation modeling applied to residual lifetime prediction using functional data analysis

Sensor-based degradation signals measure the accumulation of damage of an engineering system using sensor technology. Degradation signals can be used to estimate, for example, the distribution of the remaining life of partially degraded systems and/or their components. In this paper we present a nonparametric degradation modeling framework for making inference on the evolution of degradation signals that are observed sparsely or over short intervals of times. Furthermore, an empirical Bayes approach is used to update the stochastic parameters of the degradation model in real-time using training degradation signals for online monitoring of components operating in the field. The primary application of this Bayesian framework is updating the residual lifetime up to a degradation threshold of partially degraded components. We validate our degradation modeling approach using a real-world crack growth data set as well as a case study of simulated degradation signals.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS448 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Adaptive Two-stage Stochastic Programming with an Application to Capacity Expansion Planning

Multi-stage stochastic programming is a well-established framework for sequential decision making under uncertainty by seeking policies that are fully adapted to the uncertainty. Often such flexible policies are not desirable, and the decision maker may need to commit to a set of actions for a number of planning periods. Two-stage stochastic programming might be better suited to such settings, where the decisions for all periods are made here-and-now and do not adapt to the uncertainty realized. In this paper, we propose a novel alternative approach, where the stages are not predetermined but part of the optimization problem. Each component of the decision policy has an associated revision point, a period prior to which the decision is predetermined and after which it is revised to adjust to the uncertainty realized thus far. We motivate this setting using the multi-period newsvendor problem by deriving an optimal adaptive policy. We label the proposed approach as adaptive two-stage stochastic programming and provide a generic mixed-integer programming formulation for finite stochastic processes. We show that adaptive two-stage stochastic programming is NP-hard in general. Next, we derive bounds on the value of adaptive two-stage programming in comparison to the two-stage and multi-stage approaches for a specific problem structure inspired by the capacity expansion planning problem. Since directly solving the mixed-integer linear program associated with the adaptive two-stage approach might be very costly for large instances, we propose several heuristic solution algorithms based on the bound analysis. We provide approximation guarantees for these heuristics. Finally, we present an extensive computational study on an electricity generation capacity expansion planning problem and demonstrate the computational and practical impacts of the proposed approach from various perspectives

Predicting Remaining Useful Life with Similarity-Based Priors

Prognostics is the area of research that is concerned with predicting the remaining useful life of machines and machine parts. The remaining useful life is the time during which a machine or part can be used, before it must be replaced or repaired. To create accurate predictions, predictive techniques must take external data into account on the operating conditions of the part and events that occurred during its lifetime. However, such data is often not available. Similarity-based techniques can help in such cases. They are based on the hypothesis that if a curve developed similarly to other curves up to a point, it will probably continue to do so. This paper presents a novel technique for similarity-based remaining useful life prediction. In particular, it combines Bayesian updating with priors that are based on similarity estimation. The paper shows that this technique outperforms other techniques on long-term predictions by a large margin, although other techniques still perform better on short-term predictions.</p

Residual Life Distributions from Component Degradation Signals: A Bayesian Approach

Received and accepted Real-time condition monitoring is becoming an important tool in maintenance decision-making. Condition monitoring is the process of collecting real-time sensor information from a functioning device in order to reason about the health of the device. To make effective use of condition information, it is useful to characterize a device degradation signal, a quantity computed from condition information that captures the current state of the device and provides information on how that condition is likely to evolve in the future. If properly modeled, the degradation signal can be used to compute a residual-life distribution for the device being monitored, which can the