Enhancement of Time Resolution in Ultrasonic Time-of-Flight Diffraction Technique With Frequency-Domain Sparsity-Decomposability Inversion (FDSDI) Method

The lack of time resolution restricts the quantitative detection of shallow subsurface defects with ultrasonic time-of-flight diffraction (TOFD) technique due to the superposition between lateral wave and diffracted waves from upper and lower tips. In this article, the frequency-domain sparsity-decomposability inversion (FDSDI) method was proposed to enhance the time resolution in TOFD based on the sparsity and decomposability of the ultrasonic reflection sequence. An optimization problem was formulated in the frequency domain by combining ${l}_{{1}}$ - and ${l}_{{2}}$ -norm constraints. The simulation was performed with a carbon steel model containing a series of shallow subsurface cracks at the depths of 2.0, 2.5, 3.0, 3.5, and 4.0 mm. The relative measurement errors of defect depths and heights were no more than 6.57%, and the depth of the dead zone was reduced by 70%. Subsequently, the feasibility of the FDSDI method was experimentally verified on a carbon steel specimen with an artificial defect. The defect depth and height were calculated with relative errors within 6.0%. Finally, the detection capacity of the FDSDI method was discussed, and the effects of frequency bandwidth, regularization parameter, and noise on inversion results were analyzed by experiments. It is concluded that the FDSDI method decouples the multiple overlapped signals and significantly improves the time resolution to quantify the small defects in the dead zone.

I. Introduction

Ultrasonic time-of-flight diffraction (TOFD) is one of the nondestructive testing (NDT) techniques widely used in industry [1]–[3], having got much attention for the high inspection speed and accurate size measurement [4]–[6]. However, the dead zone is unavoidable in the actual applications of the TOFD technique [4]. The lack of time resolution induces the superposition between lateral wave and tip-diffracted waves, restricting the quantitative detection of near-surface defects [7]. Especially, the defect depths and heights are difficult to quantify for the small defects in the dead zone, i.e., shallow subsurface defects, due to multiple overlapped signals.