# Mode Shape-Based Damage Detection Method (MSDI): Experimental Validation
## 3 Results and Discussion
### Effect of Multiple Damages  
The remaining damage cases were analyzed to primarily investigate the effect of multiple damages on the MSDI method. In damage cases DC5 (DC4 + element C4) and DC6 (DCS + element C3), the effect of multiple damages and the effect of the damage zone size were considered by adding another damage location on the plate. When we compared the results for both damage cases in Figure 9, we found that the MSDI method was able to register both damages, regardless of the damage zone size. The peak MSDI values at the two locations coincided with the reduction of stiffness. Moreover, the damage severity was smaller at the single damaged element C4 (see Figure 9, DC5) than the damaged zone C4-C3 (see Figure 9, DC6).  
Figure 8: Damage localization for damage cases DC3 and DC4: (a) 2D; (b) peak values in 3D.  
Figure 9: Damage localization for damage cases DC5 and DC6: (a) 2D; (b) peak values in 3D.  
The following two multiple damage cases DC7 and DC8 included damaged elements at the free edges of the plate. The results shown in Figure 10 indicate that the method effectively identified multiple damages regardless of the location of the damaged zone. Nevertheless, as previously concluded in the finite element analysis [30], the damage severity was influenced by the damage location. Therefore, the severity of multiple damages cannot be determined by using this method.  
The last two damage cases DC9 and DC10 considered two additional random single damage locations in elements H13 and H4. The results of simulated damages are shown in Figure 11, and it can be found that all simulated damages were accurately localized by the proposed algorithm regardless of the damaged zone size or the damage location.  
The diagonal elements of the MAC and \(\Delta\)MAC matrices are shown for the damage cases DC5 to DC10 in Figure 12. It is noted that the number of mode shapes that were participating in damage detection decreased with the introduction of new damages. The first reason was that the intensity (\(\alpha_{kl}\) value) decreased due to the low degree of consistency between estimated modal vectors in the undamaged and damaged states. The second reason was that some mode shapes entirely disappeared due to a significant change of consistency between estimated modal vectors. Even though a smaller number of mode shapes were used for damage detection based on the MSDI method, they were still able to provide useful information about the location of structural damage.  
The accuracy of the MSDI method for damage localization depends on the number of measurement points (degrees of freedom) for some element or structure. In order to apply this method in practice within the structural health monitoring system (e.g., bridges, tall buildings), one must optimize the number of measuring points.  
To obtain better reliability of the damage detection by using the presented method, we recommend as many experimentally obtained mode shapes as possible. In the paper, all experimentally observed mode shapes are presented and were used in the MSDI method, although a large number of mode shapes (for instance, Figure 12, DC 9) did not participate at all in damage detection or participate with significantly reduced impact.  
The environmental (e.g., temperature) and serviceability effects were not considered in this research. It is necessary to consider the effects of temperature changes depending  
Figure 10: Damage localization for damage cases DC7 and DC8: (**a**) 2D; (**b**) peak values in 3D.  
on the boundary conditions of the structure. Under the influence of different temperatures, the mode shapes can be changed significantly, and this can affect the MSDI analysis.  
Figure 11: Damage localization for damage cases DC9 and DC10: (**a**) 2D; (**b**) peak values in 3D.  
Figure 12: Cont.