Inverse method for detection and sizing of cracks in thin sections using a hybrid genetic algorithm based signal parametrisation L. Satyanarayan, K. Bharath Kumaran, C.V. Krishnamurthy, Krishnan Balasubramaniam * Center for Non-Destructive Evaluation and Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600 036, India Available online 8 December 2007 Abstract A hybrid-GA method, based on signal parameterization, has been reported here for the improved detection and sizing of surface cracks of small sizes/depths in thin sections. The method relies on parameterizing the composite reference from the defect into its indi- vidual components i.e., the crack tip diffracted echo and the corner trap echo and subsequently use the relative arrival time technique (RATT). The phased array ultrasonic technique was employed in the investigation. Both experimental and simulated signals were used in the study. It is shown through both simulations and experiments that the hybrid-GA is successful in parameterizing both non-over- lapping and overlapping echoes encountered in thin sections. It is additionally shown that the hybrid-GA improves the signal to noise ratio and correct for under-sampling of data. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Ultrasound; Signal parameterization; FDTD; Genetic algorithms; Small crack; Sizing; NDE; NDT; Phased array 1. Introduction Ultrasonic diagnostic methods find applications in the non-destructive evaluation (NDE) of engineering materials as well as in the field of medical imaging. Back-scattered echoes generated by the reflection/diffraction of ultrasonic waves contain information pertaining to the location, size and characteristics of defects, along with the material and the geometry of the object under evaluation [1]. The accu- rate detection, location and sizing of the defects are limited by the ability to precisely estimate the information con- tained in the ultrasonic signals obtained during an inspection. Phased array ultrasound has emerged as a rapid non- destructive evaluation technique for detection and imaging of crack like defects in structural components due to the flexibility it offers in varying the angle of inspection and/ or focusing of the beam to a point of interest. The principle of phased array ultrasonic beam generation is based on the use of individual transducer elements that can each be independently driven with controlled phase delays of exci- tation. Using this phase delay, the parameters of the ultra- sonic beam, such as the depth of focus and/or the beam angle can be varied while the testing is being carried out [2–5]. Relative arrival time technique (RATT) involves the measurement of the corner trap and the tip diffracted ech- oes (by the same angle) from a single A-scan signal for the estimation of the size of the crack [6–9]. Hence, the accu- racy in estimating the time of arrival of the echoes assumes importance. A minimum mean square error (MMSE) based estimator is described for the estimation of the time of arrival of an ultrasonic signal [10]. Fig. 1a shows the schematic representation of the ultrasound ray path between crack tip and corner trap signal for an internal surface breaking crack. Fig. 1b shows an A-scan signal showing the tip diffracted and the corner trap echoes. If the relative ultrasound path between the corner trap and the top tip diffracted echo is ‘‘UT path ”, then size (height) of the crack (H) is given by 0167-8442/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.tafmec.2007.11.004 * Corresponding author. E-mail address: balas@iitm.ac.in (K. Balasubramaniam). www.elsevier.com/locate/tafmec Available online at www.sciencedirect.com Theoretical and Applied Fracture Mechanics 49 (2008) 185–198