Spline cell-based hidden Markov approach for singular time series forecasting in performance degradation trend analysis

Performance degradation trend analysis (PDTA) using time series is often applied to estimate the remaining useful life (RUL) of a system or device in reliability assessment. Singularity arising in the degradation data, however, frequently give rise to a bad decline in prediction accuracy of time series, which is a great challenge for prediction of degradation time series data. To address this issue, a new approach based on spline hidden Markov model is proposed in this paper. This method takes the cubic non-polynomial spline as the output prediction cell of a weighed hidden Markov model (HMM). According to the restrictions and properties of cubic non-polynomial splines, its second derivative at each degradation data point can be calculated to form a series of observation frames by using a sliding window method, and then a weighed HMM is used to forecast the observation sequence in order to obtain the last two values of second derivative to reconstruct the spline function. Furthermore, an application to a real electronic system involving with singularities is presented to demonstrate the prediction ability of the proposed method and assess its accuracy.