^{a}, Khac Tuan Huynh

^{b}, Yves Langeron

^{c}, and Antoine Grall

^{d}

^{a}yufei.gong@utt.fr

^{b}tuan.huynh@utt.fr

^{c}yves.langeron@utt.fr

^{d}antoine.grall@utt.fr

Prognosis is a key task in the health management of deteriorating dynamic systems. Our aim is to develop an efficient approach to predict the remaining useful lifetime of a feedback control system subject to stochastic hidden damage and proportional-integral-differential controller. The damage gradually degrades the system performance over time, and eventually leads to a random failure. The high complexity of feedback control system makes the hidden damage inaccessible by direct condition monitoring techniques. We thus consider the system as a black-box, use the inputoutput to construct its transfer function, and define the associated maximum gain as the system degradation index. Due to the fault tolerance of feedback control system, it is impossible to describe the evolution of degradation index as common stochastic processes, and hence classical remaining useful lifetime prognosis approaches based on probabilistic computations are no longer applicable. To bypass this obstacle, a learning approach is proposed with the assumption that degradation data and associated failure times of similar systems are additionally available. Using such data, we characterize the system remaining useful lifetime by a Birnbaum-Saunders distribution and learn its parameters as piecewise polynomials of degradation indices. Therefore, we can infer the remaining useful lifetime distribution of the considered feedback control system from any known current degradation. Numerous numerical experiments confirm the effectiveness of the proposed method.