Reducing Signature Models for Extended Kalman Filtering for Adaptive Prognostic Estimation

This paper presents a heuristic-based rationale for reducing the number of families of signature models used to support Extended Kalman Filtering (EKF) for Adaptive Prognostic Estimation. In Ridgetop Group's Adaptive Remaining Useful Life Estimation (TM) (ARULE (TM)) software, signature modeling is used to transform Feature Data (FD) that has been isolated and extracted from Condition-Based Data (CBD): the transformation linearizes input data before EKF processing to produce prognostic estimates after each input data point. A simplified description of EKF is presented; a rationale is given for using functional failure (operation is out-of-specification) rather than physical failure; then a rationale is provided for replacing exponential physics-of-failure models with a power function; and then it is mathematically shown that five families of power functions for representing fault-to-failure progression (FFP) signatures can be simplified and reduced to one power function. Then it is shown that a single model is sufficient to support single-failure modes with insignificant to moderate noise and non-linearity distortion - provided the level of such noise and distortion, after conditioning and mitigation, is not greater than a desired level of relative accuracy. Before and after case-study examples are presented: the examples result in prognostic estimates within ten-percent relative accuracy with at least 50-percent remaining of the maximum prognostic distance (PD). A summary and conclusion end the paper.