# Research on Damage Localization of Steel Truss-Concrete Composite Beam Based on Digital Orthoimage
## 2 Structural Damage Identification Method Based on Digital Image Processing
### Numerical Validation of Image Matrix Similarity Damage Localization Method  
A numerical model of the simply supported beam is established to verify the above damage localization method. The model span is 500 mm, and the cross-section is a rectangular section of size 20 mm \(\times\) 6 mm. The beam is of uniform mass, the material is structural steel, the modulus of elasticity is 2 \(\times\) 10\({}^{5}\) MPa, and the concentrated force of 1 kN acts in the middle of the span, as shown in Figure 3.  
The mesh nodes on the \(X-Z\) surface of the numerical model are simulated as image matrices. The deflection diagram and the corresponding image matrix of the undamaged model under the action of 1 kN concentrated force are shown in Figure 4.  
Figure 3: Finite element model of simply supported beam. Figure 2: Image matrix similarity analysis process; (**a**) Image matrix of damage-free structure; (**b**) Image matrix of damaged structure; (**c**) Matching tie point; (**d**) Euclidean distance of the homologous points. (1) Single damage identification verification. A damage crack is set at 200 mm from the right support with a width of 1 mm and a depth of 3 mm. Figure 5 shows the deflection of the damage model. The Euclidean distances of the corresponding points of the structure with no damage and post-damage are calculated separately under the same load. Figure 6 shows the Euclidean distances of the upper and lower edges of the model. The image matrix similarity curves in Figure 6 have obvious peaks at the damage locations, indicating that the image matrix similarity analysis method can effectively identify the location of structural damage in the single damage condition. (2) Eccentric multi-damage identification verification. Set two cracks 100 mm and 200 mm from the right support, with a crack width of 1 mm and depth of 3 mm. The multi-damage model deformation is shown in Figure 7.  
Figure 4: Acquisition of finite element model image matrix; (**a**) the model nodes (red dots in the diagram) represent the non-zero elements of the image matrix; (**b**) image matrix for finite element models. Figure 5: Deflection diagram of \(X-Z\) section for a single crack in a simply supported beam. Calculate the Euclidean distances of the homologous point in the image matrix of undamaged and post-damaged structures. The results of the analysis of the upper and lower edges of the simply supported beam are shown in Figure 8.  
(3) Symmetric multi-damage identification verification. Similarly, set up two cracks 200 mm from each side of the support with a width of 1 mm and a depth of 3 mm. The symmetric multi-damage model is shown in Figure 9.  
Figure 8: Results of similarity analysis of two eccentric damage image matrices for simply supported beams; (**a**) Euclidean distance of the homologous point on the upper edge of the model; (**b**) Euclidean distance of the homologous point on the lower edge. Figure 4.0 Results of similarity analysis of single damage image matrix for simply supported beams; (**a**) Euclidean distance of the same name point on the upper edge of the model; (**b**) Euclidean distance of the same name point on the lower edge of the model. Figure 4.1 Location of the two cracks (eccentric situation). The Euclidean distances of the homologous points in the image matrix of the undamaged and post-damaged structures are calculated. The results of the upper and lower edge analysis are shown in Figure 4.2  
According to the above analysis, it is found that the extreme points of the similarity curve may not be the damage locations, and the discontinuity points are the damage locations, which is consistent with the deformation coordination of the structure. Therefore, the second-order derivative of the Euclidean distance curve is used to amplify this damage signal, so the similarity is calculated by Equation (7).