This paper presents a novel set of uncertainty measures to quantify the impact of input uncertainty on nonlinear prognosis systems. A Particle Filtering-based method is also presented that uses this set of uncertainty measures to quantify, in real time, the impact of load, environmental, and other stresses for long-term prediction. Furthermore, this work shows how these measures can be used to implement a novel feedback correction loop aimed to suggest modifications, at a system input level, with the purpose of extending the remaining useful life of a faulty nonlinear, non-Gaussian system.

Opportunities exist to apply nonlinear filtering to model-based prognostics in order to provide a systematic way of dealing with the propagation of system damage at some future time, whenever imprecise diagnostic information is obtained. Central to the prognostics problem is the ability to properly capture and manage uncertainties when predicting remaining useful life of a particular component of interest. The goal of this paper is to present a foundation for prediction and filtering of the failure process using nonlinear prognostic models and exact (finite-dimensional) filters.

In this paper, a maximum entropy-based general framework for probabilistic fatigue damage prognosis is investigated. The proposed methodology is based on an underlying physics-based crack growth model. Various uncertainties from measurements, modeling, and parameter estimations are considered to describe the stochastic process of fatigue damage accumulation. A probabilistic prognosis updating procedure based on the maximum relative entropy concept is proposed to incorporate measurement data.

Particle filters (PF) have been established as the de facto state of the art in failure prognosis, and particularly in the representation and management of uncertainty in long-term predictions when used in combination with outer feedback correction loops. This paper presents a novel Risk-Sensitive PF (RSPF) framework that complements the benefits of the classic approach, by representing the probability of rare and costly events within the formulation of the nonlinear dynamic equation that describes the evolution of the fault condition in time.