Semi-tensor product-based fuzzy relation matrix technique for gear system state forecasting

Abstract

Multiple-variable fuzzy prediction systems are usually difficult for modeling due to their complicated fuzzy reasoning structures and propositions. To tackle this challenge, a hierarchical fuzzy state modeling technique is proposed in this work to construct fuzzy relation matrices (FRM) with reduced dimensions (orders), for system state forecasting. In processing, firstly, the FRM with high dimensions is decomposed into several lower-dimensional FRM models. Secondly, using the semi-tensor product, a fuzzy logic framework is developed to reduce the number of fuzzy rules. The proposed hierarchical fuzzy model is also implemented for gear system health state forecasting, where system parameters are trained to improve the fuzzy reasoning accuracy. The effectiveness of the proposed hierarchical FRM modeling and system identification techniques is verified by experimental tests.