Failure diagnosis by trajectory parallel measure on attractor

The study of chaos is attracting attention, and a wide range of academic fields is actively involved. On the other hand, Aihara (1992) proposed the term “chaos engineering” to describe the application of chaos theory for engineering purposes, and its possibilities have been demonstrated. The approaches to the engineering applications of chaos are generally classified, into two groups: (1) creative methods and (2) analytical methods. In the former, chaos conditions, consistent with the particular application, are produced in any case, and this behavior is used in a positive manner. In the latter, a phenomenon is examined to see whether it is chaotic or not, and if it is a deterministic chaos, the latent rules involved are extracted and used for a practical purpose. Applications based on the creative methods include chaos computing, chaotic memory, chaos cipher communications, chaos art, applications using chaos fluctuations, chaos circuits, non-linear engineering systems, etc. applications using the analytical methods include failure diagnosis, deterministic non-linear short-term forecasting, identifying chaos, modeling bio-chaos, etc. This paper first describes approaches of chaotic diagnosis. Next, the trajectory parallel measure method for diagnosis is described. Finally, fault diagnosis is discussed as a prospective industrial application using practical examples