Condition-based diagnosis of mechatronic systems using a fractional calculus approach

Abstract

While fractional calculus (FC) is as old as integer calculus, its application has been mainly restricted to mathematics. However, many real systems are better described using FC equations than with integer models. FC is a suitable tool for describing systems characterised by their fractal nature, long-term memory and chaotic behaviour. It is a promising methodology for failure analysis and modelling, since the behaviour of a failing system depends on factors that increase the model’s complexity. This paper explores the proficiency of FC in modelling complex behaviour by tuning only a few parameters. This work proposes a novel two-step strategy for diagnosis, first modelling common failure conditions and, second, by comparing these models with real machine signals and using the difference to feed a computational classifier. Our proposal is validated using an electrical motor coupled with a mechanical gear reducer.

Keywords:

• intelligent maintenance
• intelligent diagnostics
• application of fractional calculus
• identification of fractional order systems

Acknowledgements

The authors acknowledge the Campinas State University – UNICAMP (Brazil), Polytechnic Institute of Porto – ISEP (Portugal) and the National Council for Scientific and Technological Development – CNPq (Brazil), for financially supporting this work, and also to Marian Lee for her help in proofreading this article.