Methodology on Establishing Multivariate Failure Thresholds for Improved Remaining Useful Life Prediction in PHM

Prognostics and Health Management (PHM) methodologies and techniques have been much widely studied in the academia and practiced by the industry in recent years. Prognostic approaches commonly try to establish the relationship between Remaining Useful Life (RUL) and a single variable or health indicator (HI) which can be obtained from multi-sensor fusion or data-driven models. However, simply relying on a single variable could reduce RUL prediction robustness when it is less representative of the system health conditions. Taking multiple variables into consideration for RUL prediction, quantifying operating risks and determining multivariate failure threshold is essential yet rarely studied. Generally, there are three major challenges that limit the practicality of this topic. 1) How to determine the multivariate failure threshold? 2) How to quantify operation risks based on multiple variables? 3) How to make reliable extrapolations of future conditions? To address these questions, this paper proposes 1) a novel copula model to determine multivariate failure threshold, and 2) a Maximum Likelihood Estimation enhanced similarity-based Particle Filter (MLE-SMPF) to predict future system conditions. In the proposed methodology, the health assessment is firstly performed to obtain HI trajectory. The copula risk quantification model is then trained by two variables HI and life. The proposed copula model can easily include multiple variables compared with our previously published approach using bivariate Weibull Distribution[1]. Afterward, MLE-SMPF is used to extrapolate future HI for testing data. The prediction capability is further improved compared with [2] by introducing MLE for Particle Filter transition function parameter initialization. Finally, the system RUL is determined from the failure threshold which is obtained according to the quantified operation risk. The proposed methodology is validated on the C-MAPSS data from the PHM data competition 2008 hosted by PHM society. The result outperforms most of the benchmarks from recent publications. The proposed methodology is easy to transfer to other potential machine prognostic applications.