Abstract
Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their integrity. It is possible to employ mathematical models to develop a deeper understanding of the acquired ultrasonic data and enhance defect imaging algorithms. In this paper, a model for the scattering of ultrasonic waves by a crack is derived in the time–frequency domain. The fractional Fourier transform (FrFT) is applied to an inhomogeneous wave equation where the forcing function is prescribed as a linear chirp, modulated by a Gaussian envelope. The homogeneous solution is found via the Born approximation which encapsulates information regarding the flaw geometry. The inhomogeneous solution is obtained via the inverse Fourier transform of a Gaussian-windowed linear chirp excitation. It is observed that, although the scattering profile of the flaw does not change, it is amplified. Thus, the theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excitation, as well as establishing a time–frequency domain framework to assist in flaw identification and classification.
Highlights
Non-destructive testing (NDT) is an umbrella term for a wide and varied group of analysis techniques used to2015 The Authors
The simple algebraic formula derived for the optimal order of the fractional Fourier transform (FrFT) of a Gaussian-windowed linear chirp exhibits an error in application to the inhomogeneous solution and does not incorporate the maximum amplitude
This paper examined the use of chirp excitation as a means of improving the signal-to-noise ratio (SNR) by increasing the amplitude of the recovered signal
Summary
Non-destructive testing (NDT) is an umbrella term for a wide and varied group of analysis techniques used to. Of particular interest to this paper are ultrasonic phased array systems, which have become increasingly popular as tools for flaw detection and characterization within the NDT industry They provide improved resolution and coverage by transmitting and receiving ultrasound signals over multiple elements, which, when fired in predefined sequences, can provide increased control of beam directivity [2]. Owing to thermal effects as the weld is forming, a spatially heterogeneous structure is formed by local fluctuations in the crystal orientation This complex internal geometry is highly scattering and results in low signal-to-noise ratio (SNR) levels, which can subsequently lead to the obscuration of defects. To combat this problem, two approaches are suggested and combined in this paper: the use of chirp excitations and the post-processing of the collected data in the time–frequency domain.
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