A novel health indicator based on the Lyapunov exponent, a probabilistic self-organizing map, and the Gini-Simpson index for calculating the RUL of bearings

Abstract

Abstract The estimation of the remaining useful life (RUL) of rolling element bearings has been an area of excessive research over the past few decades. Time-series forecasting approaches are the most popular methods for calculating the RUL of bearings. However, there exist two key challenges in predicting the RUL using time-series forecasting. The first is the development of an accurate health indicator (HI) that can indicate bearing degradation i.e. the developed HI must be capable of tracking the early and critical degradation stages in bearings. The second is the determination of a suitable failure threshold for the HI time-series. The HIs for different bearings fluctuate at different levels at the time of failure and consequently, it becomes difficult to set a definite failure threshold for them. To overcome these problems, a novel HI is proposed in this paper. First, the vibration signals acquired from the bearings are subjected to the feature extraction process. For this purpose, chaotic features determined using the Lyapunov exponent are utilized. Then, feature samples extracted under healthy bearing conditions are used to train probabilistic self-organizing map (p-SOM) algorithm. Finally, the trained p-SOM model is tested against the monitored feature samples to construct the HI. This HI has a major advantage in that it lies in a specific range from [0–1] and therefore allows for the selection of precise limits for defining bearing failure. Once the HI has been determined, a state-space model is employed to forecast the HI up to pre-set failure thresholds and subsequently compute the RUL of the bearings. The proposed technique is validated on publicly-available benchmark datasets. The experimental results confirm that the suggested HI is effective in predicting damage growth as well as forecasting the RUL of bearings. Further, it outperforms the traditional health indicator i.e. SOM-based-minimum quantization error (MQE).