An off-online fuzzy modelling method for fault prognosis with an application

Fault prognosis plays a key role in prognostics and health management (PHM). Currently, there are many methods to predict the occurrence of a fault, but the fuzzy model has become an effective alternative owing to its advantage of using not only quantitative data but also qualitative information with fuzzy uncertainty. It is particularly useful for a dynamic system with complexity, morbidity and nonlinearity. Compared with the prediction from an offline fuzzy model, an online prediction is more desired, since we can monitor the health condition of a system and achieve fault prognosis in real time. In this paper, we develop a prediction model by firstly establishing an initial fuzzy model with offline information, then, using the online information to adjust the initial offline model in real time. The offline fuzzy model is modelled through a relevance vector machine (RVM) method and the structure of the initial fuzzy model is adjusted based on the statistical utility of a fuzzy rule using online information. The model parameters are optimized by the gradient decent (GD) algorithm. To do so, a fault prognosis algorithm is proposed on the basis of our off-online fuzzy modelling method. Finally, the proposed fuzzy modelling method and its fault prognosis algorithm are applied to a practical example. The empirical results show that our developed method has a significant improvement over the existing fuzzy modelling methods in terms of accuracy and the corresponding fault prognosis algorithm is effective.