## 2 Materials and Methods  
Experimental work was performed to verify the simulation findings, and the configuration of the experiment is illustrated in Figure 1. The same experiment was carried out with two coil configurations (positions), the first using a vertical probe and the second a horizontal probe. In the first case, ECT equipment was utilized. It is an Olympus Nortek 500 eddy current fault detector, which monitors the power supply and frequency. The signal obtained from this system is passed to a laptop through an analog-to-digital converter. Moreover, in the second experiment, a power supply was used to generate the input power and frequency. The SA106 pipe was placed on a rotating stage platform and the ECT probe and coil were fixed parallel to the pipe to scan the different regions of the pipe, from x = 0 to x = 40 mm with a constant scanning step of 1 mm. The position of the probe can be adjusted to minimize the lift-off difference that may be caused by the banding surface of the pipe and provide the same test conditions for each scan. The heat-affected zone length is deemed to be 12.7 mm (1/2 inch), in conformity with the KEPIC MI technical standard [18]. The experimental investigations were conducted by an ASNT Level II qualified examiner by complying to the ISO 7912 instructions [37]. Prefabricated cracks were made by the electrical discharge machining (EDM) process and introduced into the weld area. Their length and width are 5 mm and 0.2 mm with different depths (0.3 mm, 0.5 mm, and 1.0 mm), designated as (C0.3, C0.5, and C1.0),  
Figure 1: Experimental setup. (**a**) Bloc diagram of ECT equipment and (**b**) inspection setup. respectively, as shown in Figure 2. The inner diameter, outer diameter, and height of the conventional vertical probe are 3 mm, 4 mm, and 7.5 mm. The sensor probe shown in Figure 3 has a LIGiS placed under an air core exciting coil [38], as illustrated in Figure 4. The exciting coil is made of 0.2 mm diameter copper wire. The LIGiS has 32 GMR sensor elements arrayed at 0.6 mm intervals to form a sensing length of 19.2 mm. The GMR sensors are oriented at 45\({}^{\circ}\) to the array length to prevent their saturation by the magnetic field of the exciting coil. The sizes of the horizontal probe are listed in the same figure. Figure 4: Scan configuration. Figure 3: (a) Sensor array and (b) exciting coil (unit: mm). Figure 2: Specim with artificial narrow cracks. According to the Faraday-Lenz law, the electromagnetic force \(V_{emf}\) is defined by the following equation:  
\[V_{emf}=-N\frac{d\varnothing}{dt}=-N\int\limits_{s}\frac{\partial\overset{ \rightarrow}{B}}{dt}\overset{\rightarrow}{ds} \tag{2}\]  
where \(N\), \(\overset{\rightarrow}{\partial\overset{\rightarrow}{B}}\), and \(s\) are the numbers of turns of the coil, frequency of excitation, and area of the coil probe, respectively. To achieve a good S/N ratio, a large, high frequency probe with many turns is required. A high excitation frequency is limited in ferromagnetic materials such as carbon steel due to the skin depth given in Equation (1). In addition, the large probe is limited by the spatial resolution of the sensor array. Furthermore, the electromagnetic interference of each sensor and the coverage performance are affected in the vertical probe array. To reduce the electromagnetic interference and improve the coverage performance, a single large excitation coil is used. As well, to improve the spatial resolution, the density of the induced magnetic flux density around the crack is detected using semiconductor based on GMR sensors. Finally, the longitudinal direction of the induced current on the specimen must be parallel to the weld wave (marks) in order to reduce noise due to weld marks and weld beads.