Defect detection of pipes using Lyapunov dimension of Duffing oscillator based on ultrasonic guided waves

Abstract

This study proposes a novel small defect detection approach for steel pipes using the Lyapunov dimension (D) of the Duffing chaotic system based on ultrasonic guided waves. In this paper, inspection model is constructed by inputting the measured guided wave signal into the Duffing equation as the external turbulent driving force term and thenDis calculated. The properties of the Duffing system's noise immunity are first demonstrated theoretically based on the Lyapunov exponents. By comparingDof the Duffing inspection system between the conditions of the inputted pure noise and the guided wave signal, the amplitude of the periodic force (F), the important parameter of the Duffing inspection system, could be determined. The values of other parameters of the Duffing inspection system are subsequently determined according to the numerical investigation. Furthermore, a time-moving window function is constructed to scan along the measured signal to locate the defect. And the small defect echo signal polluted by the noise is illustrated to prove the availability of the proposed method. Both numerical and experimental results show that the proposed approach can be used to improve the sensitivity of small defect detection and locate the small defect in pipes.