## 4 Results and Discussion
So, it is not easy to judge the existence or absence of narrow cracks from the signal's behavior. This is probably due to the uneven and banding shape surface of the carbon steel, the variation of the lift-off of a probe, and the presence of structures on the pipe surface. In the simulation, it is probably due to the change in physical properties. From the same Figures 10-12, the signal is small and because of that the noise appears to be high. To overcome this limitation and the lack of precision of the conventional probe given in Figure 8b, detecting and finding defects in weld joints while reducing the signal noise usually involves obtaining information through proper inspection, for which greater accuracy is required. To achieve this, a horizontal probe design (with an exciting coil used as an emitter and a GMR as receiver, both for simulation and experiment) may potentially lead to better detection and avoid such noises as proposed. In order to fully assess the behavior of the probe's output signals as it scans the pipe's different zones, and to propose a suitable configuration of the probe, the use of the finite element analysis offers significant advantages in addressing this issue. The frequency is a critical factor in eddy current testing. It relates to the skin depth and the amplitude of the probe signal. This parameter must be selected appropriately by the experimenter. Figure 16: Impedance variation in (%) at 80 kHz with (**a**) depth = 0.3 mm, (**b**) depth = 0.5 mm, and (**c**) depth = 1 mm. Figure 15: Impedance variation in (%) at 40 kHz with (**a**) depth = 0.3 mm, (**b**) depth = 0.5 mm, and (**c**) depth = 1 mm. The experimental distribution of the SA106 specimen properties is reproduced by means of the Monte Carlo method based on PRNG in order to conceive a numerical model that reflects the real model of the studied problem, which is important to evaluate the impact of the heat treatment on these properties in the presence of cracks as it allows a proper evaluation and comparison of the response derived with the experimental ones. The distribution of electrical conductivity and magnetic permeability are almost symmetrical with respect to the symmetry position of the device (x = 20). The carbon steel was massive, and the impedance was calculated from the magnetic vector potential, and it also remains symmetric regarding the symmetry position of the device. The behavior of the impedance signal increases gradually to attain a maximum amplitude and afterwards decreases until the last displacement of the probe. Fluctuations at the peak of the Delta impedance amplitude appear, indicating a change in the physical milieu, i.e., a change in physical properties (the crack and weld). This is explainable, as it indicates the existence of narrow cracks in the weld area. In Figures 10-12, which correspond to the vertical probe configuration, the ECT signals are significantly affected by the relative permeability and electrical conductivity changing gradiently randomly in the HAZ due to the heat treatment. This change then impacts the coupling of the probe to the carbon steel specimen, leading to the occurrence of noises; therefore, the results are not easy to work with. The results presented in Figures 13-16 clearly show the superiority of the horizontal probe over the vertical probe configuration regarding the apparition of the noises. These noises generated can lead to the misinterpretation of the signals as flaws. The horizontal probe configuration was very efficient with regard to the detection performance of these types of cracks, as it does not generate such noises.