Event recognition via singularity detection using wavelet transform decomposition and thresholding*

摘要

1. Introduction In recent years, event recognition has emerged as a multiple-area problem solving method1. An event is always recognized if there exists any deviation from the standard normal. For example, the damage occurs in the event of melting of a metallic piece at far below its melting point is identified as abnormality or deviation from the standard normal. In case of any spectral analysis, throughtout the region of interest the occurrence of peaks is the events of absorption of full energy. In the context of event recognition, singularity analysis plays a major role. The deviation from the standard normal is termed as the singularity of the signal that represents the event under consideration; Mathematically, for a complex function, it is well known that singularity of a function at any specified point within the domain and range of means the function is not analytic at that point. For a complex function, pole type and essential singularity exists. One pioneering work2 studied the detection of the singularities of local homogeneous functions from the phase of wavelet transforms. Wavelets are useful in many different fields of science and engineering. Examples include decomposition and reconstruction of visual data and detections of edges and singularities2,3. Singularities of a signal can be characterized by the modulus of their wavelet transforms4,5. Singularities and irregular structures often carry the most important information in signals.It is important for singularity detection of vibration signals to mechanical fault diagnosis. The interesting information for many signals is given by transient phenomenon such as peaks. In physics, it is also important to study the occurrence of an unusual event to infer the behavior of the system about the