Guided Wave Ultrasonic Detection Method Based On Duffing Equation

Ultrasonic guided waves (UGW) have been become an important NDTmethod for long-distance pipelines, because of their superior abilities such asfast speed, wide range and so on. However, the influence of the attenuation andnoise during the propagation of the guided wave makes the defect echo signalvery weak. In order to promote the sensitivity to small defects and extend thedetection range of UGW, a new method of weak signal inspection method usingLyapunov exponents of Duffing equation was proposed in this paper. Numericaland experimental studies were carried out. The results showed the method couldfind the defect and further locate the defect. Finally, the UGW signal processingsystem was designed based on MATLAB-GUI. It could improved theoperability and validity of the proposed method.In theory, a Chaos system, for example Duffing equation, is very sensitiveon initiation condition. Let UGW signal as the initiation inputting of the Duffingequation, and thus the motion states of solution will be changed. For example, ifthe motion states was strange attractor and can be transform to limit cycle wheninputting UGW signal even polluted by strong noise. The proposed method canbe used to detect weak guided wave signal with strong noise even under thenoise levels of100%. In order to further study the feasibility of this method, thepropagation of guided wave in3m-in-length steel pipe is measuredexperimentally, and the measured signals are analyzed by the DuffingInspection System. The experimental results show that the Lyapunov exponentsof Duffing Inspection System can effectively identify small defect echo by3%loss of section area. In addition, Lyapunov Exponent can evaluate the damagelevel of defect because the Lyapunov Exponent along with the change ofpipeline section reduction is monotone decreasing when the defects are within acertain range. A time-moving window function is constructed to interceptranging signal. And then put the signals into the Duffing Inspection System tocalculating the Lyapunov Exponent. The Lyapunov Exponent curve along with the change of window function center moment is drawn and it can effectivelylocate the position of the defects.A design of The UGW signal processing system was the last innovation inthis paper. By the system, the operator need not understand the profound theoryand the program but they can do the same job. The system includes the phaseTrajectory, Lyapunov Exponent, frequency spectrum, the time-frequencyanalysis. It can greatly improve the valid of the method in practice.