Uncertainty quantification in prognostics: A data driven polynomial chaos approach

Prognostic deals with predicting the possible future failure of different types of engineering systems. For the purpose of prognostics, the failure of the system is defined to be the instant when the degradation (performance) level rises above (drops below) a defined threshold. It is impossible to make a precise prediction of the remaining useful life (RUL) of a system due to many sources of uncertainties. Therefore, one has to develop a structured approach to account for the different sources of uncertainties. While some methods such as Monte Carlo/Quasi Monte Carlo can be implemented easily, its accuracy is limited and the computational cost involved is large. Recently, it was shown that UQ in prognostics with the non-intrusive polynomial chaos approach is a good choice, thanks to its accuracy and low computational cost. Unfortunately though, it requires the prior knowledge of parametric distributions. This work tackles the challenge of uncertainty quantification (UQ) in model based prognostics using the moment-based arbitrary polynomial chaos approach. The moment-based polynomial chaos is suitable for this purpose and its advantages can be summarized as: 1) UQ can be done with small computational effort in comparison to the standard Monte Carlo method. 2) It avoids the necessity to assign parametric probability distributions. 3) It can be used with arbitrary distributions with arbitrary measures, which can be specified numerically by means of a histogram or a raw data set. 4) Global sensitivity indices are available directly and can be used to identify which parameter is relatively more important than the others over the entire parameter space of the models. The method is illustrated for an example of battery resistance degradation.