# Vision-Based Structural FE Model Updating Using Genetic Algorithm
## 3 System Development
### Structural FE Model Updating Using Genetic Algorithm  
An FE analysis has been considered a powerful tool for decades, and is capable of simulating the behavior of the structures. However, creating accurate FE models is not an easy task. Various modeling techniques and guidelines are used to make the appropriate selection of the element type (beam, plate, or solid), degrees of freedom, and analysis methods. These modeling techniques depend on the skills and experience of the engineer, and the purpose of the model (e.g., a static FE analysis and a dynamic FE analysis require different FE models for the same accuracy). The initial FE model, created on the basis of the techniques described above, can accurately predict the initial (undamaged) state of the structure. However, as the structure ages, the FE model created in the design stage does not reflect the characteristics of the as-is structure. Therefore, the FE model updating technique is used to reflect the as-is (damaged) state of the structure. The FE model updating procedure involves three steps: (1) measuring the response as the reference data, (2) selecting the parameters to update, and (3) tuning the model. Prior experience has shown that measuring the accurate response and selecting the model parameters are the key components for successfully updating the FE model [28]. The genetic algorithm is an optimization algorithm rooted in the principles of biological evolution, applying the natural law that individuals with superior traits produce superior offspring. The genetic algorithm is quite different from classical optimization algorithms. Traditional optimization methods use derivatives and search for the objective function of all points in a limited space one at a time, or select an arbitrary point to start the search. However, the genetic algorithm conducts a directional search and a probability search without using the concept of derivatives. This leads to an advantage of solving optimization problems, including continuous-discontinuous mixing, discontinuity, and non-convex regions. The genetic algorithm optimizes the problem by taking a population of individuals consisting of a combination of binary numbers and performing three processes: selection, crossover, and mutation as shown in Figure 3[29]. In this study, the natural frequency of the structure was used as the objective function, which can best describe the dynamic characteristics of the structure. Decision variables were considered as the cross-sectional area and the thickness of the structure members, and the objective function, decision variables, and constraint set for the discrete optimization problem are shown in Equations (1)-(3). Figure 2: Overview of the vision-based displacement technique [14]. \[Minimize\ :W=\sqrt{\sum_{i=1}^{n}\frac{\left(\overline{\omega_{i}}-\omega_{i} \right)^{2}}{n}} \tag{1}\] \[Subject\ to\ :0<\ A_{obj}\ \leq\ A_{0}\] (2) \[0<\ t_{obj}\ \leq\ t_{0} \tag{3}\]  
In Equations (1)-(3), \(\overline{\omega}_{i}\) is the \(i\)th natural frequency of the structure of the FE model, and \(\omega_{i}\) is the \(i\)th natural frequency of the structure obtained from the experiment. In addition, \(A_{0}\) is the cross-sectional area of the undamaged column, \(A_{obj}\) is the cross-sectional area of the damaged column, \(t_{obj}\) is the thickness of the damaged column, and \(t_{0}\) is the thickness of the undamaged column. Crossover and mutation are as important items as the objective function in the genetic algorithm (GA). Crossover specifies how the genetic algorithm combines two parents to form a crossover son for the next generation and mutation specifies how the genetic algorithm randomly alters individuals in a population to create a mutant son. Mutation provides genetic diversity and enables the genetic algorithm to search a broader space. In this study, because the wall stiffness was set as an input parameter, individuals of each generation were set for six.