544 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 62, NO. 3, MARCH 2013 Crack Depth Estimation by Using a Multi-Frequency ECT Method Andrea Bernieri, Giovanni Betta, Senior Member, IEEE, Luigi Ferrigno, Member, IEEE, and Marco Laracca, Member, IEEE Abstract—In many industrial application fields as manufactur- ing, quality control, and so on, it is very important to highlight, to locate, and to characterize the presence of thin defects (cracks) in conductive materials. The characterization phase tries to deter- mine the geometrical characteristics of the thin defect namely the length, the width, the height, and the depth. The analysis of these characteristics allows the user in accepting or discarding realized components and in tuning and improving the production chain. The authors have engaged this line of research with particular reference to non-destructive testing applied to the conductive ma- terial through the use of eddy currents. They realized methods and instruments able to detect, locate, and characterize thin defects. In this paper, a novel measurement method able to improve the characterization of the crack depth is proposed. It is based on the use of a suitable multi-frequency excitation signals and of digital signal processing algorithms. Tests carried out in an emulation environment have shown the applicability of the method and have allowed the tuning of the measurement algorithm. Tests carried out in a real environment confirm the goodness of the proposal. Index Terms—Defect depth estimation, GMR sensor, multi- frequency eddy current testing. I. I NTRODUCTION S EVERAL techniques are today adopted to perform non- destructive testings (NDTs). The use of eddy current testing (ECT) is probably one of the most widespread electro- magnetic techniques for the inspection of conductive materials [1]. By adopting this technique some measurement stages con- cerning with the detection, the location, and the characterization of the geometrical characteristics of defects are possible with relatively low cost and simple hardware setup. Hence, the physical principle that lies upstream of the tech- nique of ECT is very simple; the eddy currents measurement and their processing to retrieve defect information is a key issue of ECT. Many digital processing methods are today adopted to carry out this task. In recent years, techniques based on image segmentations, ECT camera, and frequency domain-based anal- ysis are widespread. In addition, with the aim of improving the accuracy in the estimation of dimensional characteristics of thin Manuscript received April 6, 2012; revised August 2, 2012; accepted November 1, 2012. Date of publication January 9, 2013; date of current version February 5, 2013. The Associate Editor coordinating the review process for this paper was Dr. Jiong Tang. The authors are with the Department of Electrical and Information Engi- neering, “Maurizio Scarano,” University of Cassino, 03043 Cassino (FR), Italy (e-mail: bernieri@unicas.it; betta@unicas.it; ferrigno@unicas.it; m.laracca@ unicas.it). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2012.2232471 defects, digital signal processing techniques based on artificial intelligence algorithms as artificial neural networks or support vector machine (SVM) [2]–[7] are proposed in the scientific literature. In the earliest versions of the ECT technique, the excitation was always sinusoidal, due to the simplicity of implementation. Nowadays, thanks to the presence of arbitrary power sources and the diffusion of low-cost digital signal processing devices, alternative techniques of excitation have been experienced. To this aim, the multi-frequency ECT (MFECT) and the pulsed eddy current (PEC) are emerging techniques proposed as alter- natives to traditional ECT in order to improve the sensitivity of defect detection in some particular application field, and in par- ticular for small cracks embedded deep in layered components [8], [9]. These excitation methods use wideband signals and consequently give rise to so some design problems: the depth of eddy current is determined by the exciting frequency since the exciting signals with lower frequencies penetrate deeper in the material than the exciting signals with higher ones, but the lower the exciting signal frequency, the lower the amplitude of the reaction signal to be measured. Suitable excitation sig- nals are therefore required in order to achieve a compromise between the need to discover and characterize sub-superficial defect and to obtain good values of the signals to be measured. In recent years, also PEC and MFECT have been applied to found suitable solutions to these issues [10]–[15]. In particular, He et al. have proposed feature extraction techniques for PEC defect classification with a reduction of the lift off effect [15], while Gao et al. have proposed a new MFECT technology for the defect classification, named as spectrum barycenter excursion [14]. However, the main attention of the these researches was focused on the classification of the defect superficiality or sub- superficiality, whereas the determination of the defect depth with a numeric value and its measurement uncertainty seems to be still a challenge to be faced. The authors have engaged this field [16], [17] proposing an innovative low-cost NDT measurement instrument composed by suitable probes and signal processing to perform crack char- acterizations by means of a model-free method. The realized measurement instrument shows very good performance in the estimation of the length and the width of the detected thin crack. The greatest difficulties in the crack characterization are related to the estimation of both the crack depth and height since they have similar effect on the magnetic field response in EC test. The aim of this paper is to overcome this problem introducing a method able to identify the crack depth with a negligible 0018-9456/$31.00 © 2013 IEEE