Model-based prognostics approaches use domain knowledge about a system and its failure modes through the use of physics-based models. Model-based prognosis is generally divided into two sequential problems: a joint state-parameter estimation problem, in which, using the model, the health of a system or component is determined based on the observations; and a prediction problem, in which, using the model, the state-parameter distribution is simulated forward in time to compute end of life and remaining useful life. The first problem is typically solved through the use of a state observer, or filter. The choice of filter depends on the assumptions that may be made about the system, and on the desired algorithm performance. In this paper, we review three separate filters for the solution to the first problem: the Daum filter, an exact nonlinear filter; the unscented Kalman filter, which approximates nonlinearities through the use of a deterministic sampling method known as the unscented transform; and the particle filter, which approximates the state distribution using a finite set of discrete, weighted samples, called particles. Using a centrifugal pump as a case study, we conduct a number of simulation-based experiments investigating the performance of the different algorithms as applied to prognostics.

Prognostics has taken center stage in Condition Based Maintenance (CBM) where it is desired to estimate Remaining Useful Life (RUL) of a system so that remedial measures may be taken in advance to avoid catastrophic events or unwanted downtimes. Validation of such predictions is an important but difficult proposition and a lack of appropriate evaluation methods renders prognostics meaningless. Evaluation methods currently used in the research community are not standardized and in many cases do not sufficiently assess key performance aspects expected out of a prognostics algorithm. In this paper we introduce several new evaluation metrics tailored for prognostics and show that they can effectively evaluate various algorithms as compared to other conventional metrics. Four prognostic algorithms, Relevance Vector Machine (RVM), Gaussian Process Regression (GPR), Artificial Neural Network (ANN), and Polynomial Regression (PR), are compared. These algorithms vary in complexity and their ability to manage uncertainty around predicted estimates. Results show that the new metrics rank these algorithms in a different manner; depending on the requirements and constraints suitable metrics may be chosen. Beyond these results, this paper offers ideas about how metrics suitable to prognostics may be designed so that the evaluation procedure can be standardized.

Prognostics is an emerging concept in condition basedmaintenance(CBM)ofcriticalsystems.Alongwith developing the fundamentals of being able to confidently predict Remaining Useful Life (RUL), the technology calls for fielded applications as it inches towards maturation. This requires a stringent performance evaluation so that the significance of the concept can be fully exploited. Currently, prognostics concepts lack standard definitions and suffer from ambiguous and inconsistent interpretations. This lack of standards is in part due to the varied end-user requirements for different applications, time scales, available information, domain dynamics, etc. to name a few issues. Instead, the research community has used a variety of metrics based largely on convenience with respect to their respective requirements. Very little attention has been focused on establishing a common ground to compare different efforts. This paper surveys the metrics that are already used for prognostics in a variety of domains including medicine, nuclear, automotive, aerospace, and electronics. It also considers other domains that involve prediction-related tasks, such as weather and finance. Differences and similarities between these domains and health maintenancehave been analyzed to help understand what performance evaluation methods may or may not be borrowed. Further, these metrics have been categorized in several ways that may be useful in deciding upon a suitable subset for a specific application. Some important prognostic concepts have been defined using a notational framework that enables interpretation of different metrics coherently. Last, but not the least, a list of metrics has been suggested to assess critical aspects of RUL predictions before they are fielded in real applications.

With recent advancements in prognostics methodologies there has been a significant interest in maturing Prognostics and Health Management (PHM) to increase its technology readiness level for onboard deployments. Active research is underway both in industry and academia to address shortcomings in availability of run-to-failure data, accelerated aging environments, real-time prognostics algorithms, uncertainty representation and management (URM) techniques, prognostics performance evaluation, etc., to name a few. At this juncture it is highly desirable to close the loop by connecting the high level customer requirements for mission planning and execution to performance specifications for prognostics methodologies at the lower technical level. This calls for integrating the pragmatics of safety, reliability, cost, and real-time viability into the prognostics methodologies to establish a connection between top-down and bottom-up approaches currently pursued in the PHM community. In this paper we identify key areas that must be addressed to bridge these gaps and provide an overview of how these areas have been addressed in part at various levels. We also discuss on how these issues can be further developed into a comprehensive and more coherent portfolio of technologies that will ultimately lead to specifying guidelines for prognostics performance.

In situations where the cost/benefit analysis of using physics-based damage propagation algorithms is not favorable and when sufficient test data are available that map out the damage space, one can employ data-driven approaches. In this investigation, we evaluate different algorithms for their suitability in those circumstances. We are interested in assessing the trade-off that arises from the ability to support uncertainty management, and the accuracy of the predictions. We compare here a Relevance Vector Machine (RVM), Gaussian Process Regression (GPR), and a Neural Network-based approach and employ them on relatively sparse training sets with very high noise content. Results show that while all methods can provide remaining life estimates although different damage estimates of the data (diagnostic output) changes the outcome considerably. In addition, we found that there is a need for performance metrics that provide a comprehensive and objective assessment of prognostics algorithm performance.

**Abstract** Prognostics solutions for mission critical systems require a comprehensive methodology for proactively detecting and isolating failures, recommending and guiding condition-based maintenance actions, and estimating in real time the remaining useful life of critical components and associated subsystems. A major challenge has been to extend the benefits of prognostics to include computer servers and other electronic components. The key enabler for prognostics capabilities is monitoring time series signals relating to the health of executing components and subsystems. Time series signals are processed in real time using pattern recognition for proactive anomaly detection and for remaining useful life estimation. Examples will be presented of the use of pattern recognition techniques for early detection of a number of mechanisms that are known to cause failures in electronic systems, including: environmental issues; software aging; degraded or failed sensors; degradation of hardware components; degradation of mechanical, electronic, and optical interconnects. Prognostics pattern classification is helping to substantially increase component reliability margins and system availability goals while reducing costly sources of "no trouble found" events that have become a significant warranty-cost issue. **Bios** Aleksey Urmanov is a research scientist at Sun Microsystems. He earned his doctoral degree in Nuclear Engineering at the University of Tennessee in 2002. Dr. Urmanov's research activities are centered around his interest in pattern recognition, statistical learning theory and ill-posed problems in engineering. His most recent activities at Sun focus on developing health monitoring and prognostics methods for EP-enabled computer servers. He is a founder and an Editor of the Journal of Pattern Recognition Research. Anton Bougaev holds a M.S. and a Ph.D. degrees in Nuclear Engineering from Purdue University. Before joining Sun Microsystems Inc. in 2007, he was a lecturer in Nuclear Engineering Department and a member of Applied Intelligent Systems Laboratory (AISL), of Purdue University, West Lafayette, USA. Dr. Bougaev is a founder and the Editor-in-Chief of the Journal of Pattern Recognition Research. His current focus is in reliability physics with emphasis on complex system analysis and the physics of failures which are based on the data driven pattern recognition techniques.

It is an inescapable truth that no matter how well a system is designed it will degrade, and if degrading parts are not repaired or replaced the system will fail. Avoiding the expense and safety risks associated with system failures is certainly a top priority in many systems; however, there is also a strong motivation not to be overly cautious in the design and maintenance of systems, due to the expense of maintenance and the undesirable sacrifices in performance and cost effectiveness incurred when systems are over designed for safety. This paper describes an analytical process that starts with the derivation of an expression to evaluate the desirability of future control outcomes, and eventually produces control routines that use uncertain prognostic information to optimize derived risk metrics. A case study on the design of fault-adaptive control for a skid-steered robot will illustrate some of the fundamental challenges of prognostics-based control design.

Model-based diagnosis typically uses analytical redundancy to compare predictions from a model against observations from the system being diagnosed. However this approach does not work very well when it is not feasible to create analytic relations describing all the observed data, e.g., for vibration data which is usually sampled at very high rates and requires very detailed finite element models to describe its behavior. In such cases, features (in time and frequency domains) that contain diagnostic information are extracted from the data. Since this is a computationally intensive process, it is not efficient to extract all the features all the time. In this paper we present an approach that combines the analytic model-based and feature-driven diagnosis approaches. The analytic approach is used to reduce the set of possible faults and then features are chosen to best distinguish among the remaining faults. We describe an implementation of this approach on the Flyable Electro-mechanical Actuator (FLEA) test bed.

Failure prognosis - as a natural extension to the fault detection and isolation (FDI) problem - has become a key issue in a world where the economic impact of system reliability and cost-effective operation of critical assets is steadily increasing. Failure prognostic algorithms aim to characterize the evolution of incipient fault conditions in complex dynamic processes, thus allowing to estimate of the remaining useful life (RUL) of subsystems and components. Several examples can be used here to illustrate the range of possible applications for these algorithms: electro-mechanical systems, continuous-time manufacturing processes, structural damage analysis, and even fault tolerant software architectures. Most of them have in common the fact that they are highly complex, nonlinear, and affected by large-grain uncertainty. We introduce in this chapter an integrated failure prognosis architecture that is applicable to a variety of aircraft systems and industrial processes. We are targeting a specific rotorcraft system as a prototypical testbed for proof-of-concept. The overall architecture consists of an on-board and an off-board module for eventual on-platformimplementation purposes.

A remaining useful life prediction algorithm and degradation model for electrolytic capacitors is presented. Electrolytic capacitors are used in several applications ranging from power supplies on critical avionics equipment to power drivers for electro-mechanical actuators. These devices are known for their low reliability and given their criticality in electronics subsystems they are a good candidate for component level prognostics and health management research. Prognostics provides a way to assess remaining useful life of a capacitor based on its current state of health and its anticipated future usage and operational conditions. In particular, experimental results of an accelerated aging test under electrical stresses are presented. The capacitors used in this test form the basis for a remaining life prediction algorithm where a model of the degradation process is suggested. This preliminary remaining life prediction algorithm serves as a demonstration of how prognostics methodologies could be used for electrolytic capacitors.