## 3 Numerical Studies
### iFEM Studies Involving Uniaxial Strain Data
#### 3.2.1 Results for Damage Case-1  
The iFEM results for Damage Case-1, using strain data corresponding to Unitcells-1 and 2 are shown in Figure 12.  
Results for Unitcell-2 are similar to the benchmark results, while Unitcell-1 results are deficient. Both plots showed a \(I_{D}\) concentration at the center of the plate; however, the results of Unitcell-1 are asymmetric. A greater \(I_{D}\) concentration is observed in the vicinity of those elements along which actual strain measurements are made using the optical fiber (see Figure 12a). This asymmetry is not observed in the results of Unitcell-2. A comparison with the benchmark results revealed differences in the strain field distribution around the damage site. Compared to the benchmark results, the results of Unitcell-2 showed a greater dispersion of the damaged strain field to far-field locations. As the benchmark model used a greater number of strain-sensors along with a symmetric sensor grid, the results are symmetric with a well-defined strain peak at the center (see Figure 5b). Despite these shortcomings, the plots of Figure 12 offered sufficient information for successful damage detection. Next, the effect of measurement noise on the results is investigated. The strain data is contaminated using random noise, added as a percentage of the strain magnitude. The noise distribution is based on a Gaussian curve with zero mean and the value of three standard deviations equal to 5%. The use of random noise in the measured strain data allowed for the introduction of various external factors that affected the method's practical implementation. One key issue is the sensor bonding to the host structure [37]. As the strain is transmitted from the host structure through the bonding surface (typically an epoxy adhesive) to the sensor, a strong and complete bond must be ensured for ideal strain transfer to the sensor and avoid any measurement errors. A similar issue is faced when  
Figure 12: iFEM reconstructed \(I_{D}\) distribution for Damage Case-1 using: (**a**) Unitcell-1, and (**b**) Unitcell-2. fiber optic sensors are embedded within structures. Incorrect inclusion could lead to stress concentration between the structure and the sensor leading to erroneous measurements and potential damages to the host structure. Strain transfer analysis between the fiber cable, protective layer, bonding material, and the host structure [38; 39] offers a way of identifying the parameters influencing the actual and measured strains and could be used for improving the strain measurements using fiber optic sensors. The current study adopted a more simplistic approach by using random noise to introduce these experimental effects in the numerical examples. The contour plots of \(I_{D}\) using contaminated strain data are shown in Figure 13.  
Figure 13 shows that the introduction of noise lead to further diffusion of the strain field, with a prominent \(I_{D}\) peak at the center and smaller \(I_{D}\) peaks at far-field locations. This could be better illustrated using a \(I_{D}\) threshold of 0.5, i.e., the lower limit of the \(I_{D}\) plot is restricted to 0.5. The contour plots with this threshold level are shown in Figure 14.  
The use of a threshold helped to discriminate between regions with and without damage. Figure 14 shows that the damage is located at the center of the plate. As discussed previously, asymmetry in Figure 14a may lead to a false conclusion that the damage is not at the center but slightly off centric. Similarly, the dual peaks observed in Figure 14b may also lead to a false interpretation of multiple damages present. Instead, these \(I_{D}\) distributions could be considered a feature of the method. These results are compared with benchmark iFEM results for Damage Case-1 using strain data contaminated with 5% noise and enforcing a threshold of 0.5 for isolating the damage location.