A Review of Phase Space Topology Methods for Vibration-Based Fault Diagnostics in Nonlinear Systems
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ORIGINAL PAPER
A Review of Phase Space Topology Methods for Vibration‑Based Fault Diagnostics in Nonlinear Systems T. Haj Mohamad1 · Foad Nazari1 · C. Nataraj1 Received: 23 January 2019 / Revised: 2 May 2019 / Accepted: 9 June 2019 © The Author(s) 2019, corrected publication 2019
Abstract Background In general, diagnostics can be defined as the procedure of mapping the information obtained in the measurement space to the presence and magnitude of faults in the fault space. These measurements, and especially their nonlinear features, have the potential to be exploited to detect changes in dynamics due to the faults. Purpose We have been developing some interesting techniques for fault diagnostics with gratifying results. Methods These techniques are fundamentally based on extracting appropriate features of nonlinear dynamical behavior of dynamic systems. In particular, this paper provides an overview of a technique we have developed called Phase Space Topology (PST), which has so far displayed remarkable effectiveness in unearthing faults in machinery. Applications to bearing, gear and crack diagnostics are briefly discussed. Keywords Phase Space Topology · Bearing diagnostics · Gear fault diagnostics · Crack detection · Machine learning
Introduction Fault diagnostics of practical systems is a very important problem that needs to be solved robustly to be able to make giant leaps in reliability and safety. Diagnostics is essentially an epistemological problem that requires us to make intelligent inferences based on data, which could be derived from empirical observations or computer models, and are often incomplete, noisy and uncertain. Although there is a rich and varied literature,1 we feel that many of the diagnostic techniques in use are quite ad hoc and heuristic, resulting in lack of general applicability. This paper presents innovative and rigorous techniques involving the nonlinear characteristics in a computational intelligence setting to diagnose changes in complex systems. Our approach consists of developing diagnostic methods * T. Haj Mohamad [email protected] http://vcads.org
using a combination of nonlinear dynamic analysis and computational intelligence techniques. In this paper, several applications are chosen with sufficient generality to demonstrate applicability to a host of disciplines. The theoretical approaches are validated using data from fault simulators at Villanova University and Case Western University; we also validate our algorithms using experimental data from practical machinery provided by United Technologies Research Center (UTRC, USA) and Federal University of Uberlândia (Brazil). The rest of the paper is organized as follows. Section 2 describes a family of methods that were originated and derived by our team called Phase Space Topology (PST). In Sect. 3, we present a recent development in PST using an example of bearing defect analysis. Section 4 summarizes some of the applications that were investigated to generalize the applicability of our developed methods. Finall
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