Investigation of Stochastic Differential Models and a Recursive Nonlinear Filtering Approach for Fusion-Prognostics

Electronics-rich systems perform important societal functions in diverse fields. Failures in such systems can cause loss of revenue and lives, e.g., the Xian MA-60 propeller plane that crashed into sea leaving 27 people dead in May 2011, or the failure in a point-of-sale information verification system that can result in loss of sales worth $5,000,000/min. These failures and unplanned downtime could be prevented if these systems could be made self-cognizant, i.e., if they could self-assess performance, estimate their remaining useful life (RUL), and adaptively make decisions for mitigating risks. However, this has been difficult to achieve because of a lack of understanding of the interactions between system parameters and application environments and their effect on system degradation. In order to address these issues, Pecht (Pecht, 2010; Cheng & Pecht, 2009) introduced the fusion prognostics approach. This approach first defines a degradation model that takes into account the presence of multiple failure mechanisms, varying environmental conditions, unit-to-unit uncertainty, and the uncertainty (temporal) associated with the progression of degradation. Existing degradation models for electronic systems simply aggregate the degradation of critical components and fail to consider the unit-to-unit variability. In these models environmental effects are mostly addressed from an accelerated testing perspective, which helps to analyze only a specific type of degradation (Gu, 2009; Alam, 2010; Kwon, 2010). Recent variants of these models that account for unitto-unit uncertainty and the time-varying environmental effects have failed to account for temporal uncertainty (Gebraeel, 2008 & 2009). And few of the reported models consider degradation as a result of both wearout and overstress mechanisms (Kharoufeh, 2006; Shetty, 2008; Rangan, 2008). Another challenge has been the identification of appropriate RUL estimation techniques. Recently, Unscented Kalman (Tian, 2011) and Particle Filters (Orchard 2007; Zio, 2011) have been receiving a lot of attention for this purpose (Saha, 2009). However, degradation is a continuous process, and these techniques require the degradation to be a discrete process. It is generally assumed that the degradation is Gaussian in nature and there exists a predetermined failure threshold. However, it has been proven that the degradation process can have a skewed distribution and that there does not always exist a predetermined threshold. Thus, modeling errors and assumptions about the degradation process contribute to uncertainty in estimation. Thus, there is a need for new techniques to improve the confidence level of RUL estimates. Also, it is desirable to make the RUL estimates in a recursive manner and identify the possible failure mechanisms from the predicted degradation state. In this work, the focus is on developing a generic fusion prognostics approach that will allow systems to self-assess performance and recursively estimate RUL. For this generic fusion prognostics approach we have the following goals: a) To define a mathematical model that best describes the dynamic nature of system degradation and b) To construct a recursive algorithm for the defined model that uses only the previous estimate of the RUL and the latest observations to make a new estimate of the RUL. Initially, we investigate the use of stochastic differential equations (SDEs) for modeling system degradation. The states of the model are defined using the parameters reflecting system response and their behavior with respect to time and usage. The effects of wearout and overstress mechanisms are included by decomposing the degradation process into two subprocesses. Based on the investigation, the algebraic and geometric structure of the SDE representing system degradation will be defined. For the autonomous functioning of the system, recursive and optimal nonlinear filtering equations are derived to estimate future health states. For computational feasibility, the finite dimensional form of the filtering equations will be derived from optimal filtering equations by using concepts from nonlinear systems, the theory of Lie algebra, and recent insights gained from particle filters.