Fuzzy transition probability: a new method for monitoring progressive faults. Part 1: the theory

This paper presents a new method for condition monitoring, especially for monitoring progressive faults such as wear and fatigue. Based on the literature survey, the existing condition monitoring methods are based on either probability or fuzzy logic. The new method, called the fuzzy transition probability (FTP), combines the transition probability (Markov process) as well as the fuzzy set. From a theoretical point of view, the new method uses the available information from the training samples to the maximum extent (finding both the transition probability and the fuzzy membership) and hence, is more effective than the existing methods. This paper is the first part of a two-part paper. It presents the basic theory and shows how to compute the transition probability from the available training samples step by step. A simple demonstration example is also included. The second part of the paper presents two practical applications: one is material tensile strength testing and the other is tool condition monitoring in boring. Based on the testing results, the new method outperforms the popular artificial neural networks. Future research and applications are also discussed. [Copyright &y& Elsevier]