Nonlinear Dynamics, 76(4), 1963–1975p. (2014) DOI:10.1007/s11071-014-1261-0

Bifurcation analysis of a nonlinear pendulum using recurrence and statistical methods: applications to fault diagnostics

C. A. K. Kwuimy, M. Samadani, C. Nataraj

The problem of maintenance of expensive and heavy systems has increased the need for powerful tools to analyze their performance. The methods of recurrence plots (RPs) and statistical measurement have been used as data-driven tools for diagnostics with no possibility of classifying the nature of defect and poor ability to localize it. In order to enhance the efficiency of the forecast, innovative approaches consist of using physics-based features to train a data-based assessment methods. This requires proper analysis of the physical system using appropriate methods. For this purpose, this paper focusses on the bifurcation dynamics of nonlinear systems using the recurrence and statistical methods. Considering the nonlinear pendulum as a model, the qualitative behavior of the system is discussed through the bifurcation diagram of some recurrence quantification analysis (RQA) parameters, namely the recurrence rate, determinism, and laminarity. These parameters are used to measure the level of complexity and transition from regular to chaotic motion and vice versa. Statistical parameters such as crest factor, skewness, and kurtosis are used to identify various bifurcation and amplitudes in the system, and to measure the orientation and the level of asymmetry. Plots of recurrence diagrams and histograms are presented to support our observations. Examples of detection of dynamic changes using these two methods are provided. The interesting results obtained in this paper show that statistical methods complement results obtained from RPs. In addition, the paper demonstrates how the RPs can be employed in conjunction with the physics-based model.

back


Creative Commons License © 2017 SOME RIGHTS RESERVED
The content of this web site is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.0 Germany License.

Please note: The abstracts of the bibliography database may underly other copyrights.

Ihr Browser versucht gerade eine Seite aus dem sogenannten Internet auszudrucken. Das Internet ist ein weltweites Netzwerk von Computern, das den Menschen ganz neue Möglichkeiten der Kommunikation bietet.

Da Politiker im Regelfall von neuen Dingen nichts verstehen, halten wir es für notwendig, sie davor zu schützen. Dies ist im beidseitigen Interesse, da unnötige Angstzustände bei Ihnen verhindert werden, ebenso wie es uns vor profilierungs- und machtsüchtigen Politikern schützt.

Sollten Sie der Meinung sein, dass Sie diese Internetseite dennoch sehen sollten, so können Sie jederzeit durch normalen Gebrauch eines Internetbrowsers darauf zugreifen. Dazu sind aber minimale Computerkenntnisse erforderlich. Sollten Sie diese nicht haben, vergessen Sie einfach dieses Internet und lassen uns in Ruhe.

Die Umgehung dieser Ausdrucksperre ist nach §95a UrhG verboten.

Mehr Informationen unter www.politiker-stopp.de.