Singularity detection of 2D signals using fractal dimension analysis of scale information

Abstract

Fractal dimension (FD) analysis has been widely used in signal processing. The key issue in signal processing is the singularity detection. One of the main problems for FD analysis of signals is its susceptibility to measurement noise, likely obscuring the identification of singularities. To address this deficiency, a new physical quantity, named ‘the scale-window fractal dimension (SWFD)’, is proposed and a SWFD analysis method is formed to identify the singularities in the noisy 2D signal. With this method, the noisy 2D signal first is decomposed into sets of scale signals with the aid of 2D Gabor wavelet transforms; then SWFD estimates are calculated along every scale signals to form the FD surface. The singularities can be localized by the sudden changes in the spatial variation of the FD surface. As an application of the method, the identification of damage singularity for an experimental composite plate is performed with the mode shapes measured by a scanning laser vibrometer as the analyzed 2D signals. The results show that the SWFD analysis method has the prominent features of high accuracy of singularity localization and strong robustness to noise.