Accelerating uncertainty propagation in power laws for prognostics and health management

This paper proposes a sampling-based approach for uncertainty propagation in scalar power laws. The methodology takes advantage of the properties of stochastic calculus, and outperforms the standard Monte Carlo integration in terms of speed of computation. Three sources of uncertainty are considered; (i) modeling error arising from regressions on historical data, (ii) uncertainty or ignorance on the power law parameters, i.e., constant and exponent, and (iii) initial condition defined through probability density functions. The method is applied to an existing scenario extracted from literature in the area of prognostics and health management, and is then compared against state-of-the-art Monte Carlo integration based on Euler's forward method. The results show that the accuracy of the proposed uncertainty propagation method is virtually identical to Euler's integration. However, the presented approach is orders of magnitude faster than the integration via Euler's forward method when computing the first hitting time of a threshold. This translates into faster computation of the first hitting time distribution, which is one of the key elements of prognostics and health management.