Asymmetric epsilon-Support Vectors Regression for Remaining Useful Life Distribution Estimation

Estimating the remaining useful life (RUL) of industrial components is essential in predictive maintenance practice. In real-world applications, both aleatoric uncertainties (e.g., randomness due to uncontrollable factors) and epistemic uncertainties (e.g., ignorance about the model correctness) exist. Therefore, uncertainty quantification is expected to be associated with the point estimation, i.e., an estimation of the RUL probability density function (PDF) is necessary. However, existing data-driven methods which can give a probabilistic estimation of RUL have limitations when applying to real-world industrial systems: statistical methods often rely on certain assumptions on the degradation process; probabilistic machine learning methods usually have large complexity and need some prior knowledge on the parameter distribution and/or likelihood model. In this paper, we seek to design an effective model-free approach to estimate RUL distribution with few assumptions, when prior knowledge on the system is not available. The basic idea is to incorporate asymmetric epsilon-support vector regression (epsilon-SVR) into the framework of restricted regression quantiles (RRQ), to approximate mutually uncrossed quantile curves of RUL. Then, for a given input vector, among all distributions that fit the estimated monotone quantiles, a robust RUL probability density could be selected as the final estimation. We apply SVR as the basic learning machine due to its solid theoretical foundation and ability to process small training sets and multi-dimensional data. The effectiveness of our proposed method is validated by numerical experiments on a dataset of turbofan engines. It has the potential to be applied in RUL distribution estimations for increasingly complex industrial systems whose mechanism is hard to be understood completely.