recursive least squares method

This paper presents the detection of fault prognostics in bearings with the application of extended Takagi-Sugeno fuzzy recursive least square algorithms (exTSFRLSA). The nonlinear system is decomposed into a multi-model structure, consisting of linear models that are not inherently independent, due to the fuzzy regions defined in exTSFRLSA. The exTSFRLSA was developed to tune, adjust and adapt the parameters involved in the propagation model, as it tends to update itself with the availability of new data. This method is suitable for the online identification of systems because of its unsupervised learning pattern which dwells on a mechanism cantered on rule-based evolution. Scenarios considered for the rule-based modification and upgrade are quite diverse, thereby ensuring effective comparison of measured and predicted defect size. An estimation of the remaining useful life was determined successfully with the proposed method, showing that the system performance health indicator reflects bearing degradation, and it was concluded that exTSFRLSA can be used for fault prediction of bearing where rolling element  are involved, especially while its operation is associated with fluctuating speed and load conditions