Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2012, Article ID 102848, 10 pages doi:10.1155/2012/102848 Research Article Fast Detection of Weak Singularities in a Chaotic Signal Using Lorenz System and the Bisection Algorithm Tiezheng Song 1 and Carlo Cattani 2 1 School of Electrical Engineering and Automation, Hefei University of Technology, Anhui Province, Hefei City 230009, China 2 Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy Correspondence should be addressed to Tiezheng Song, stzhefei@126.com Received 1 March 2012; Accepted 1 May 2012 Academic Editor: Cristian Toma Copyright q 2012 T. Song and C. 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. 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. 1. Introduction In engineering, most weak singular information often is submerged into strong signals, such as the peaks, the discontinuities, and so forth. Moreover, when the some weak singular points are magnified slowly with time, at the moment when the fault occurs, the output signals usually contain jump points that are often singular points. Therefore, weak singular detection has played an important role in condition monitoring, fault forecast and medicine diagnosis 1, 2. For example, some weak singular vibration signals in machine processes are important for fault forecasting. The weak-signal detection is a central problem in the general field of signal processing and the use of chaos theory in weak-signal detection, and it is also a topic of interest in chaos