## 4 Experimental Results  
Training, testing, and analysis processes were performed using MATLAB R2021a software on a Dell ALIENWARE PC with an Intel(r)Core(tm) i9-9900 HQ 3.6 GHz of CPU and 32 GB of RAM. Several positive results were achieved in this study and a theoretical model of magnetic metal memory was proposed to estimate the depth direction of a fatigue crack (see Figures 7-9). To provide a comparison, an experiment was conducted using a 3-axis TMR sensor on CT scan specimens with fatigue cracks on three variations of depth angle: 0\({}^{\circ}\), 30\({}^{\circ}\), and 60\({}^{\circ}\). In addition, to maintain the validity of the measurement, the experiment was conducted on a wide demagnetized aluminum plate to reduce the probability of an external magnetic field disturbing the recorded dataset. Figure 15 shows the raw output signal of the 3-axis TMR sensor in the x- (V\({}_{\rm raw,\chi}\)), y- (V\({}_{\rm raw,Y}\)), and z- (V\({}_{\rm raw,Z}\)) directions. To map the distribution of the magnetic fields, the contour lines are added to all of the variations. In addition, the coordination of the specimen boundaries and the centerline line of the fatigue cracks are represented by the brown box and thick pink line on the vertical axis. The upper part of the rectangle is the surface side of the CT specimen, and the lower part is the center surface which is cut by EDM processes. To provide clear data for supporting the analysis, signal processing was conducted. The idea is to delete the background distribution of SMFD data by subtracting the raw data (\(\overset{\rightarrow}{\rm V}_{\rm raw}(\rm x,y)\)) from the background distribution (\(\overset{\rightarrow}{\rm V}_{\rm back}(\rm x,y)\)). The \(\overset{\rightarrow}{\rm V}_{\rm back}(\rm x,y)\) was gathered  
Figure 14: Experimental setup. (**a**) experimental set-up on the optical board; (**b**) 3-axis TMR sensor scanning on a specimen. by measuring the distribution of SMFD in the air by removing the specimen from the setup. The signal processing processes can be described mathematically as follow:  
\[\Delta\overset{\rightarrow}{\mathrm{V}}_{1}(\mathrm{x},\mathrm{y})=\overset{ \rightarrow}{\mathrm{V}}_{\mathrm{raw}}(\mathrm{x},\mathrm{y})-\overset{ \rightarrow}{\mathrm{V}}_{\mathrm{back}}(\mathrm{x},\mathrm{y}) \tag{46}\]  
\[\overset{\rightarrow}{\mathrm{V}}_{\mathrm{raw}}(\mathrm{x},\mathrm{y})= \mathrm{V}_{\mathrm{raw},\mathrm{X}}(\mathrm{x},\mathrm{y})\overset{ \rightarrow}{\mathrm{a}}_{\mathrm{x}}+\mathrm{V}_{\mathrm{raw},\mathrm{Y}}( \mathrm{x},\mathrm{y})\overset{\rightarrow}{\mathrm{a}}_{\mathrm{y}}+\mathrm{V }_{\mathrm{raw},\mathrm{Z}}(\mathrm{x},\mathrm{y})\overset{\rightarrow}{ \mathrm{a}}_{\mathrm{Z}} \tag{47}\]  
\[\overset{\rightarrow}{\mathrm{V}}_{\mathrm{back}}(\mathrm{x},\mathrm{y})= \mathrm{V}_{\mathrm{back},\mathrm{X}}(\mathrm{x},\mathrm{y})\overset{ \rightarrow}{\mathrm{a}}_{\mathrm{x}}+\mathrm{V}_{\mathrm{back},\mathrm{Y}}( \mathrm{x},\mathrm{y})\overset{\rightarrow}{\mathrm{a}}_{\mathrm{y}}+\mathrm{V }_{\mathrm{back},\mathrm{Z}}(\mathrm{x},\mathrm{y})\overset{\rightarrow}{ \mathrm{a}}_{\mathrm{Z}} \tag{48}\]  
where, Figure 16 shows the distribution of Equation (46) and corresponds to the background signal in the x- (V\({}_{\mathrm{back},\mathrm{x}}\)), y- (V\({}_{\mathrm{back},\mathrm{Y}}\)), and z- (V\({}_{\mathrm{back},\mathrm{Z}}\)) directions. Interestingly, the overall trends in each case in Figures 15 and 16 are very similar, indicating that the external magnetic field has negligible effect on the experimental values. As shown in Figure 16a,d,g, the X-component, \(\Delta\)V\({}_{1,\mathrm{X}}\), has a maximum value near the center of the crack, regardless of the depth angle of the crack, and has a symmetrical shape. As shown in Figure 16c,f,i, the Z-component, \(\Delta\)V\({}_{1,\mathrm{Z}}\), represents the distribution of the different signs on the left and right sides around the crack. This phenomenon can be explained by the VDM in Figures 9 and 10.