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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 102848, 10 pages
http://dx.doi.org/10.1155/2012/102848
Research Article

Fast Detection of Weak Singularities in a Chaotic Signal Using Lorenz System and the Bisection Algorithm

1School of Electrical Engineering and Automation, Hefei University of Technology, Anhui Province, Hefei City 230009, China
2Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy

Received 1 March 2012; Accepted 1 May 2012

Academic Editor: Cristian Toma

Copyright © 2012 Tiezheng Song and Carlo Cattani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Signals with weak singularities are important for condition monitoring, fault forecasting, and medicine diagnosis. However, the weak singularity in a signal is usually hidden by strong noise. A novel fast method is proposed for detecting a weak singularity in a noised signal by determining a critical threshold towards chaos for the Lorenz system. First, a rough critical threshold value is calculated by local Lyapunov exponents with a step size 0.1. Second, the exact threshold value is calculated by the bisection algorithm. The advantage of the method will not only reduce the computation costs, but also show the weak singular signal which can be accurately identified from strong noise. When the variance of an external signal method embeds into a Lorenz system, according to the parametric equivalent relation between the Lorenz system and the original system, the critical threshold value of the parameter in a Lorenz system is determined.