## 3 Numerical Experimental Analysis
### Test Platform Based on DIC Method  
An experimental platform for fatigue detection of hole-edge crack damage based on fiber Bragg grating sensors was constructed; this involved a fatigue crack measurement system, an optical sensing system, a DIC measurement system, and a fatigue load cycle system, as shown in Figure 3a. The specimens for the target system were made of 2024-T3 aluminum alloy, which is the alloy most widely used in aircraft structures. The Poisson's ratio of the materials was 0.33, the elastic modulus was 0.0731 Gpa, and the ultimate tensile strength and yield were 0.483 and 0.345 Gpa, respectively. A specimen with dimensions of 300 \(\times\) 100 \(\times\) 2 mm and a 10 mm hole was placed in the plate center, into which a penetrating crack of 2 mm width had previously been introduced by electric discharge machining to promote the initiation of a fatigue crack. In the experiment, a uniform tensile load was applied to the bottom of the sub-specimen, and the top was bounded so that freedom was exhibited only in the z-axis direction. The frequency of the cyclic load was set to 10 Hz, the maximum load was 0.05 GPa, and the stress ratio was a sine wave signal of 0.1. In order to avoid the problem of delay caused by high stress, the load was set to 0.04 GPa during signal acquisition, as shown in Figure 3a. In order to avoid abnormal experimental phenomena caused by operational errors, two parallel experimental procedures were used in this study. In the upper part of the test piece, two FBG sensors (FBG1 and FBG2) were bonded perpendicular to the crack propagation direction with epoxy resin glue of 1 mm thickness, with a fixed gluing length more than twice the length of the grating area, so that the best strain transfer efficiency could be obtained. FBG1 and FBG2 were also used as local sensors to detect the axial strain distribution of the patched area during crack growth, as shown in Figure 3b, and they were also used comparatively to determine the grating length's influence on the monitoring level. In order to eliminate the temperature influence on the wavelength shift of the FBG reflection spectrum, the FBG3 was bonded in a free-strain condition onto the back of the specimen that served as the control experiment with the FBG1. The central air conditioner of the experimental system was adjusted, and the temperature was set to 18.5 \({}^{\circ}\)C. The parameters of the FBG sensors are shown in Table 1.  
Because the reference area in the DIC experiment was initially in a state of uniform strain, it was necessary to place FBG1 at a sufficient distance from the crack tip. In light of previous research findings, we set a distance of 6 mm between the center hole and FBG1, so that the radial distance between the two sensors was 3 mm. The 2 sensors (model FSSR5025) were used to monitor crack lengths of 1-12 mm, as shown in Figure 3c. For every 1 mm of crack extension, a low-light spectral demodulator device for FBG signal acquisition was used to obtain the reflection spectrum deformation. The wavelength test step size was 0.01 nm, which was the same as the optical fiber grating reflected spectra accuracy obtained by the TMM simulation. On the back side of the specimen, a plate was used to design the DIC experiment (specimen 1), as shown in Figure 3d. To investigate strain distribution and gradient close to a growing fatigue crack tip, experimental DIC measurements were used to obtain strain fields over whole-plate areas, as well as high-resolution strain fields for differing crack lengths under differing fatigue loading cycles. To identify alterations in different observation areas, the marks were labeled to determine the strain field within a region of interest (ROI) for the specimen undergoing deformation by crack propagation. In DIC, image processing techniques are employed to obtain a one-to-one correspondence between subsets in the initial uniformed picture and in the subsequent deformed images. In this study, strain information for the reference