Distribution Free Prediction Interval for Uncertainty Quantification in Remaining Useful Life Prediction

Remaining useful life (RUL) prediction is an important component for system health monitoring and prognosis. Ideally, one expects the prediction algorithm to provide the complete distribution of the RUL prediction over time taking various uncertainties into account. However, the dynamic model be- ing used to characterize state estimation and future loading uncertainties is often simplified through various approximations, leading to non-credible predicted distribution. Nevertheless, certain algorithm may only provide a point estimate of the RUL, making it difficult to quantify the uncertainty of the prediction. In this paper, we focus on interval prediction with high probability that guarantees finite sample validity without the knowledge of statistical distribution of the noise. The key idea is to leverage the newly proposed conformal pre- diction framework with non-parametric conditional density estimation. Under certain regularity conditions, the proposed interval estimator converges to an oracle band at a minimax optimal rate. In addition, we apply a data driven method to automatically select the bandwidth in the kernel density estimator. We discuss practical approximations to speed up the computation. The proposed method can be used to predict the RUL interval with physics-based model in a distribution free manner. It can also be applied to assess the validity of other prognostic algorithms from experimental data. We demonstrate the effectiveness of the RUL prediction for Li-Ion batteries using both simulated and experimental data.