Uncertainty Quantification in Remaining Useful Life Prediction Using First-Order Reliability Methods

Abstract

In this paper, we investigate the use of first-order reliability methods to quantify the uncertainty in the remaining useful life (RUL) estimate of components used in engineering applications. The prediction of RUL is affected by several sources of uncertainty, and it is important to systematically quantify their combined effect on the RUL prediction in order to aid risk assessment, risk mitigation, and decision-making. While sampling-based algorithms have been conventionally used for quantifying the uncertainty in RUL, analytical approaches are computationally cheaper, and sometimes they are better suited for online decision-making. Exact analytical algorithms may not be available for practical engineering applications, but effective approximations can be made using first-order reliability methods. This paper describes three first-order reliability-based methods for RUL uncertainty quantification: first-order second moment method (FOSM), the firstorder reliability method (FORM), and the inverse first-order reliability method (inverse-FORM). The inverse-FORM methodology is particularly useful in the context of online health monitoring, and this method is illustrated using the power system of an unmanned aerial vehicle, where the goal is to predict the end of discharge of a lithium-ion battery.Index Terms-Analytical algorithms, first-order reliability method, ithium-ion battery, model-based prognostics, probability distribution, remaining useful life, uncertainty.

Significance, interpretation, and quantification of uncertainty in prognostics and remaining useful life prediction

“…By repeating this calculation for multiple values of r, the entire CDF can be obtained. While this approach is an approximation, it has been proven that it can estimate the CDF with reasonable accuracy in many practical applications [16,52,80]. 3.…”

Prognostics: a literature review

“…For this reason, researchers in the past few years identified the RUL estimation task as an uncertainty propagation problem [69]. Sankararaman and Goebel [70] and Sankararaman et al [71] proposed analytical methods such as the most probable point concept and first-order reliability methods to propagate different sources of uncertainty to RUL estimation. These analytical methods are not computationally expensive as sampling methods, which make it useful for online applications.…”

Improved Dynamic Dependability Assessment Through Integration With Prognostics

“…The approach is applied to a rectifier case study comprised of a transformer, two diodes, three capacitors and an inductive load. Particle filtering is first applied to estimate the system health state and then an extended version of the first-order reliability method [68] is used to estimate the system RUL based on the ripple factor of the output current. The system degradation is modelled through the physics-offailure equations of capacitors, but the degradation models of transformers and diodes are not considered.…”