# The Current Development of Structural Health Monitoring for Bridges: A Review
## 5 Damage Identification Methods
### Optimization Algorithm-Based Methods
#### 5.3.1 Meta-Heuristic Optimization Algorithm  
The meta-heuristic optimization algorithm is a kind of method to solve the optimal solution by simulating nature. Starting from the genetic algorithm (GA) [150], the developed meta-heuristic algorithms have been widely used in the optimization of various practical problems. [PERSON] et al. [151] improved the three basic operators in the classical GA and introduced an objective function based on the dynamic response of the bridge under train load to solve the problem of damage identification when the model element division is different from the actual damage location. [PERSON] et al. [152] proposed a hybrid optimization algorithm based on PSO and cuckoo search (CS). The temperature was parameterized in the study. The numerical model and real bridge test results showed that the hybrid algorithm can distinguish the deviation caused by the temperature effect from the actual damage and achieve Level 3 SDI. [PERSON] et al. [153] studied the local minimum problem of ANN and used CS to improve the training parameters to solve this problem. [PERSON] et al. [154] proposed a double jump strategy in bare bones particle swarm optimization (BBPSO) algorithm, and the results showed that this method can effectively improve the efficiency and robustness of BBPSO in SDI. [PERSON] et al. [155] introduced a clustering strategy into the original Java algorithm and optimized the update equation for the best solution. The objective function of the proposed I-Jaya algorithm was obtained by sparse regularization and Bayesian inference. Considering significant noise and modeling errors, the reliability of the algorithm was proved by numerical and laboratory studies.  
[PERSON] and [PERSON] [156] developed a hybrid moth-flame optimization algorithm based on a variety of optimization methods. In numerical and experimental tests, the hybrid algorithm showed a better global search ability and was feasible in practice. [PERSON] et al. [157] introduced a strategy for eliminating low-adaptive individuals in the directional bat algorithm (DBA). When elimination is complete, a new random individual will be created, which induces an increase in population diversity. The experimental examples showed that this improved DBA algorithm can accurately identify damage and has good robustness. [PERSON] et al. [158] used a modal flexibility curvature overlay to accurately locate the damage, and then determined the damage degree by an enhanced whale optimization algorithm (WOA). The experimental results showed that the proposed method was effective without noise, but it was slightly sensitive to noise when quantifying the damage degree. Later, [PERSON] et al. [159] proposed a new objective function based on fractal dimension (FD) for WOA. In the simulation test, WOA could effectively identify the damage degree under noise conditions. Table 5 shows the optimization algorithms reviewed in this section.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Authors** & **Method** & **Feature and/or Advantage** & **SDI Level** \\ \hline [PERSON] et al. [151] & Improved GA & Enhanced local optimization capability & 1–3 \\ \hline [PERSON] et al. [152] & PSO–CS & \
\begin{tabular}{c} Consider temperature variations and better \\ optimization performance \\ \end{tabular} & 1–3 \\ \hline [PERSON] et al. [153] & ANN–CS & Avoid local minimum & 1–3 \\ \hline [PERSON] et al. [154] & Improved BBPSO & Avoid local minimum & 1–3 \\ \hline [PERSON] et al. [155] & Improved Java algorithm &
\begin{tabular}{c} Improved objective function based on sparse \\ regularization and Bayesian inference \\ \end{tabular} & 1–3 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Optimization Algorithms.