Defects or flaws in highly loaded structures have a significant impact on the structural integrity. Early inspection of faults can reduce the likelihood of occurrence of potential disasters and limit the damaging effects of destructions. According to our previous work, a novel approach called as Quantitative Detection of Fourier Transform (QDFT) using guided ultrasonic waves is developed in this paper for efficiently detecting defects in pipeline structures. Details of this fast method consist of three steps: First, an in-house finite element code has been developed to calculate reflection coefficients of guided waves travelling in the pipe. Then, based on boundary integral equations and Fourier transform of space-wavenumber domain, theoretical formulations of the quantitative detection are derived as a function of wavenumber using Born approximation. This lays a solid foundation for QDFT method, in which a reference model in a problem with a known defect is utilized to effectively evaluate the unknown defects. Finally, the location and shape of the unknown defect are reconstructed using signal processing for noise removal. Several examples are presented to demonstrate the correctness and efficiency of the proposed methodology. It is concluded that the general two-dimensional surface defects can be detected with high level of accuracy by this fast approach.
The Rayleigh wave has been frequently applied in geological seismic inspection and ultrasonic non-destructive testing, due to its low attenuation and dispersion. A thorough and effective utilization of Rayleigh wave requires better understanding of its scattering phenomenon. The paper analyzes the scattering of Rayleigh wave at the canyon-shaped flaws on the surface, both in forward and inverse aspects. Firstly, we suggest a modified boundary element method (BEM) incorporating the far-field displacement patterns into the traditional BEM equation set. Results show that the modified BEM is an efficient and accurate approach for calculating far-field reflection coefficients. Secondly, we propose an inverse reconstruction procedure for the flaw shape using reflection coefficients of Rayleigh wave. By theoretical deduction, it can be proved that the objective function of flaw depth d(x 1) is approximately expressed as an inverse Fourier transform of reflection coefficients in wavenumber domain. Numerical examples are given by substituting the reflection coefficients obtained from the forward analysis into the inversion algorithm, and good agreements are shown between the reconstructed flaw images and the geometric characteristics of the actual flaws.
Torsional guided waves have been widely utilized to inspect surface corrosion in pipelines due to their simple displacement behavior and the ability of long-range transmission. Especially, the torsional mode T(0,1), which is the first order of torsional guided waves, plays the irreplaceable position and role, mainly because of its non-dispersion characteristic property. However, one of the most pressing challenges faced in modern quality inspection is to detect surface defects in pipelines with a high level of accuracy. Taking into account this situation, a quantitative reconstruction method using the torsional guided wave T(0,1) is proposed in this paper. The methodology for defect reconstruction consists of three steps. Firstly, reflection coefficients of the guided wave T(0,1) scattered by different sizes of axisymmetric defects are calculated using the developed hybrid finite element method (HFEM). Then, applying the boundary integral equation and Born approximation, Fourier transform of the surface defect profile can be analytically derived as the correlative product of reflection coefficients of torsional guided wave T(0,1) and the fundamental solution of the intact pipeline in frequency domain. Finally, reconstruction of defects is precisely performed by inverse Fourier transform of the product in the frequency domain. Numerical experiments show that the proposed approach is suitable for the detection of surface defects with arbitrary shapes.Meanwhile, effects of the depth and width of surface defects on the accuracy of defect reconstruction have been investigated. It is noted that the reconstructive error is less than 10%, providing the defect depth is no more than half of the pipe thickness.
Defect inspection in pipes at the early stage is of crucial importance to maintain the ongoing safety and suitability of the equipment before it presents an unacceptable risk. Due to the nature of detection methods being costly or complex, the efficiency and accuracy of results obtained hardly meet the requirements from industries. To explore a rapid and accurate technique for surface defects detection, a novel approach QDFT (Quantitative Detection of Fourier Transform) has been recently proposed by authors to efficiently reconstruct defects. However, the accuracy of this approach needs to be further improved. In this paper, a modified QDFT method with integration of an integral coefficient updating strategy, called QDFTU (quantitative detection of Fourier transform of updating), is developed to reconstruct the defect profile with a high level of accuracy throughout iterative calculations of integral coefficients from the reference model updated by a termination criteria (RMSE, root mean square error). Moreover, dispersion equations of circumferential guided waves in pipes are derived in the helical coordinate to accommodate the stress and displacement calculations in the scattered field using hybrid FEM. To demonstrate the superiority of the developed QDFTU in terms of accuracy and efficiency, four types of defect profiles, i.e., a rectangular flaw, a multi-step flaw, a double-rectangular flaw, and a triple-rectangular flaw, are examined. Results show the fast convergence of QDFTU can be identified by no more than three updates for each case and its high accuracy is observed by a smallest difference between the predicted defect profile and the real one in terms of mean absolute percentage error (MSPE) value, which is 6.69% in the rectangular-flaw detection example. INDEX TERMSCircumferential guided wave, Hybrid FEM, reconstruction, reference model, updating strategy. YIHUI DA received the B.S. degree in theoretical and applied mechanics from Henan Polytechnic University, Henan, China, in 2009, and the M.S. degree in general and fundamental mechanics and the Ph.D. degree in engineering mechanics from the Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2014 and 2018, respectively.Since 2019, he has been working as a Postdoctoral Researcher with the Nanjing University of Aeronautics and Astronautics. His research interests include the numerical modeling of ultrasonic guided waves, ultrasonic nondestructive evaluation, and signal processing.
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