A fractal-dimension-based signal-processing technique and its use for nondestructive testing

A fractal-dimension-based signal-processing technique has been extensively applied to various fields, but the use of the method to characterize discrete time-domain ultrasonic signals reflecting defects and any other structural-material inhomogeneities has not been fully investigated. The fractal features of the ultrasonic echoes with fractal dimensions and their implementation in nondestructive testing are investigated. In order to obtain a faithful representation of the fractal dimensions, two improved fractal dimension algorithms are presented: the box-counting method and the R/S (range/standard deviation) method. Their capabilities are evaluated with two kinds of fractal signals: the FBM (fractal Brownian motion) and WM (Weierstrass-Mandelbrot) signals. A new method to guarantee the feasibility of the calculated fractal dimensions is proposed on the basis of the analysis of the results simulated above. Then, the fractal dimensions of ultrasonic signals measured from a pipeline sample and from carbon-steel and aluminum specimens are calculated and statistically analyzed to find the fractal properties of the ultrasonic signals. The experimental results show that ultrasonic signals have the property of scale invariance that the fractal set possessed. The fractal dimension is indicative of the complexity and degree of irregularity of the waveform of an ultrasonic signal. The fractal dimensions of ultrasonic signals from various defects and microstructures are found to possess solid distribution intervals, which can be used to identify the presence of defects and the features of materials. The potential of the technique for testing defects and assessing the microstructure of materials via the use of ultrasonic echoes is revealed. The text was submitted by the authors in English.