Abstract
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.
Highlights
Defects have a significant impact on the product quality and load-carrying capacity of structures and directly deteriorate effective material properties, which will lead to structural failure [1]–[3]
An iteration method was successful applied in guided wave tomography [17], [19], to the best of our knowledge, this is the first time to improve defect detection based on boundary integral equation (BIE)
QDFTU overcomes the problem that the iteration reconstruction method cannot be introduced to the traditional boundary integral equation
Summary
Defects have a significant impact on the product quality and load-carrying capacity of structures and directly deteriorate effective material properties, which will lead to structural failure [1]–[3]. DEFECT RECONSTRUCTION APPROACH WITH AN INTEGRAL COEFFICIENT UPDATING STRATEGY In following sections, the 1ˆst circumferential guided wave calculated in Section 2 is adopted as the incident wave to detect 2D flaws in a circular annulus. QDFT proposed by Da et al.[28] is suitable for the detection of 2D structures It demonstrates that the defect depth (η (α1)) depending on the propagation direction (α1) of guided waves can be written as the Fourier transform of the product of reflection coefficients (Cref (k)) of guided waves and integral coefficients (B0 (k)) obtained from the reference model. An iteration method was successful applied in guided wave tomography [17], [19], to the best of our knowledge, this is the first time to improve defect detection based on boundary integral equation (BIE). Flowchart of QDFTU method for surface defect reconstruction: (a) the simplified process of QDFTU; (b) the steps of QDFTU in detail
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