# Research on Damage Localization of Steel Truss-Concrete Composite Beam Based on Digital Orthoimage
## 2 Structural Damage Identification Method Based on Digital Image Processing  
### Damage Recognition Principle  
The structure consists of several spatial units, and the characteristics of each unit can be reflected by the spatial stiffness matrix. Structural damage is essentially a change in the local stiffness of the structure: i.e., a change in the substructure stiffness matrix, and a change in the substructure position of the stiffness matrix, which can be interpreted as the appearance of bridge damage. The rod end force vector of an element can be expressed as  
\[F^{(e)}=\left\{\begin{array}{cccccccccccc}F_{Ni}&F_{Qij}&F_{Qiz}&M_{ix}&M_{ ij}&M_{iz}&F_{Nj}&F_{Qij}&F_{Qiz}&M_{jx}&M_{jy}&M_{jz}\end{array}\right\}^{T} \tag{1}\]  
The rod end displacement vector of an element can be expressed as  
\[\delta^{(e)}=\left\{\begin{array}{cccccccccccc}u_{i}&v_{i}&w_{i}&\theta_{ix}& \theta_{iy}&\theta_{i}&u_{j}&v_{j}&w_{j}&\theta_{jx}&\theta_{iy}&\theta_{jz} \end{array}\right\}^{T} \tag{2}\]  
The stiffness equation of an element can be expressed as  
\[F^{(e)}=K^{(e)}\delta^{(e)} \tag{3}\]  
Several elements can be superimposed together to form a bridge stiffness matrix equation, as shown in Equation (4).  
\[\left[\begin{array}{cccccccc}k_{11}&k_{12}&k_{13}&\cdots&k_{1,n-2}&k_{1,n-1} &k_{1,n}\\ k_{21}&k_{22}&k_{23}&\cdots&k_{2,n-2}&k_{2,n-1}&k_{2,n}\\ k_{31}&k_{32}&k_{33}&\cdots&k_{2,n-2}&k_{3,n-1}&k_{3,n}\\ \vdots&\vdots&\vdots&\vdots&\ddots&\vdots&\vdots&\vdots\\ k_{n-2,1}&k_{n-2,2}&k_{n-2,3}&\cdots&k_{n-2,n-2}&k_{n-2,n-1}&k_{n-2,n}\\ k_{n-1,1}&k_{n-1,2}&k_{n-1,3}&\cdots&k_{n-1,n-2}&k_{n-1,n-1}&k_{n-1,n}\\ k_{n,1}&k_{n,2}&k_{n,3}&\cdots&k_{n,n-2}&k_{n,n-1}&k_{n,n}\\ \end{array}\right]\left\{\begin{array}{c}u_{1}\\ v_{1}\\ w_{1}\\ \vdots\\ u_{n}\\ v_{n}\\ w_{n}\end{array}\right\}=\left\{\begin{array}{c}X_{1}\\ Y_{1}\\ Z_{1}\\ \vdots\\ X_{n}\\ Y_{n}\\ Z_{n}\end{array}\right\} \tag{4}\]  
The bridge structural system necessarily follows the mechanical matrix equation as  
\[\{d\}=[K]^{-1}\{F\} \tag{5}\]  
Equation (5) shows that there is an inevitable intrinsic connection between the displacement state \(\{d\}\), which reflects the deformation characteristics of the bridge, and the stiffness matrix \([K]\), which characterizes the safety state of the bridge structure, and the various load effects \(\{F\}\) acting on the bridge structure. If essential damage occurs in a part of the bridge structure, the stiffness of the corresponding member or linkage in the stiffness matrix \([K]\) is degraded, and there is a change in the displacement state \(\{d\}\) of the bridge corresponding to it, meaning that the structural morphology will be different from the previous state. In summary, the changes in the morphology of a structure are bound to have a gradual development and evolution process due to the accumulation of internal damage and external loading effects, which is the landing point of various technologies in the field of structural health monitoring: trying to detect and capture the abnormal deformation of the structure as early as possible and then invert the safety state of the structure based on the monitoring data.