FRACTAL DIMENSION BASED SIGNAL PROCESSING TECHNIQUE AND ITS USE FOR NONDESTRUCTIVE TESTING

摘要

Fractal dimension based signal processing technique has been extensively applied to various fields, but using the method to characterize discrete time domain ultrasonic signals reflecting defects and any other structural/material inhomogeneities has not been fully investigated. The aim of our study is to investigate the fractal features of the ultrasonic echoes with fractal dimensions and the implement in NDT (nondestructive testing). In order to obtain faithful representation of fractal dimensions, two improved fractal dimension algorithms, box-counting method and R/S (range/standard deviation) method, are presented and with their capability evaluated by two kinds of fractal signals, FBM (fractal Bronian motion) and WM (Weierstrass - Mandelbrot); and a new method to guarantee the feasibility of calculated fractal dimensions is proposed based on the analysis of the above simulated results. Then the fractal dimensions of ultrasonic signals measured from pipeline sample, carbon steel and aluminum specimens have been calculated and statistically analyzed to find the fractal properties of the ultrasonic signals. The experimental results show that ultrasonic signals have the scale-invariant property that the fractal set possessed; the fractal dimension can indicate the complexity and irregularity degree of waveform of 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. Our study reveals the potentiality of the technique for defect testing and material microstructure assessment by ultrasonic echoes.