A Copula Based Sampling Method for Residual Life Prediction of Engineering Systems Under Uncertainty

The success of health prognostics of engineering systems will allow engineers to shift the traditional breakdown and time based maintenance to the state-of-art predictive and condition-based maintenance. Performing the right type of maintenance activity at the right time will minimize maintenance costs and the downtime of engineering systems. However, techniques and methodologies for health prognostics are typically application-specific. This paper aims at developing a generic real time sensor-based prognostic methodology for predicting residual life of engineering systems by modeling explicit relationship between the failure time and the time realizations at different degradation levels. Specifically, a Copula based sampling method is proposed with four technical components for off-line training and on-line life prediction. First of all, degradation signals are pre-processed to have non-decreasing degradation data sets. Next, degradation data sets are dicretized into a certain number of degradation levels with associated time realizations. Then, explicit statistical dependence modeling between the failure time and the time realizations at different degradation levels is conducted using the Bayesian Copula approach and the semi-Copula model. Finally, probability density function of the failure time and the residual life are efficiently predicted using the sampling method provided that we know some true time realizations at a certain number of degradation levels. Residual life predictions of electric cooling fans are employed to demonstrate the proposed method.