System health management capability strives to estimate the current and the future operating states of the system through continuous monitoring of key operating variables. Once the current and future states are estimated, this information will be used to help the dispatcher (or field commander) better respond to anticipated fault conditions, it will also help the logistician (or support crew) better prepare for maintenance actions. Estimating the current and the future operating states are commonly referred to as the diagnostic and the prognostic problems. Diagnostic and prognostic problems can be solved by two different approaches: the model-based approach and the data-based approach. The model-based approach is increasingly favored because it is able to provide more accurate estimation of these operating states, and because it is naturally extensible to the physics of failure, which has been considered a promising enhancement to the conventional prognostic technology. To apply the model-based approach more effectively to diagnostic and prognostic problems, we need to cast these problems in a unified formulation to understand the relationship between the two; furthermore, we need to integrate candidate algorithms with the problem formulation to allow sound evaluation of different solution methods. A unified formulation of the diagnostic and prognostic problems has been suggested in a paper presented at the 2005 ASME World Congress. This formulation uses a linear, time-invariant model as the foundation and expressed diagnostics and prognostics as the same threshold-checking problem. However, the formulation does not include the algorithms used in system health management. Augmenting the problem formulation with health management algorithms is the goal of this paper. This paper presents integrated mathematical formulations for several model-based methods to solve the diagnostic and prognostic problems. Each integrated formulation combines the basic problem formulation with a specific algorithm. The set of integrated formulation provides a theoretical perspective of system health management challenges.

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