This paper develops the uncertainty management of fault diagnosis and prognosis (FDP) in Lebesgue sampling (LS)-based framework with an application to helicopter drivetrain gearbox. In the developed LS-based FDP system, a particle filtering-based FDP algorithm, fault diagnostic model, failure prognostic model, and uncertainty management are discussed. Although uncertainty management has been developed in the traditional Riemann sampling (RS)-based FDP, it needs to be analyzed and managed in a totally different way since the working principle of LS-FDP is fundamentally different from that of RS-FDP. Inaccurate model structure and parameter, measurement noise, process noise, and unknown future loading are major contributing factors of uncertainties in LS-FDP framework. Since the noise in LS-based prognosis is a distribution on time axis while the noise in RS-based prognosis is one on fault state axis, this paper studies the transpose of noise distribution from state domain to time domain. In order to reduce the uncertainty in the prediction of remaining useful life (RUL), model noise and measurement noise terms are adjusted based on a short-term prediction with n steps and correction loop. In this scheme, the priori time distribution at the (t + n)-th Lebesgue state is predicted and stored at the t-th Lebesgue state. Then, at the (t + n)-th Lebesgue state, when the posteriori distribution becomes available, it is compared with the stored priori distribution to manage the uncertainty. The methods for uncertainty management are illustrated by a case study of the prediction of RUL of gearbox. The experimental results show that the uncertainty in the diagnosis and prognosis process of gearbox is properly managed and the confidence interval is decreased, which enhances the confidence level for decision-making and condition-based maintenance.

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