# The Current Development of Structural Health Monitoring for Bridges: A Review
## 5 Damage Identification Methods
### Finite Element Model Updating Methods
#### 5.2.4 Other FEMU Methods  
[PERSON] et al. [145] proposed a hybrid technique that combines model-based and data-based SDI methods. In the proposed method, real monitoring data under normal conditions are fused with data obtained from FEM under extreme environmental conditions and input into machine learning algorithms for SDI. The reliability of this method was verified using monitoring data from the Z-24 Bridge. [PERSON] et al. [146] proposed a FEMU method that combined multiple meta-heuristic optimization algorithms for damage detection. They first used a genetic algorithm (GA), particle swarm optimization (PSO), and artificial bee colony (ABC) algorithms, respectively, for FEMU in numerical simulations. Then, the damage detection performance of each algorithm was compared, and the PSO and ABC methods were selected as a combination in this method due to their better performance. [PERSON] et al. [147] proposed a roaming damage method (RDM) in FEMU to identify local damage in large bridges. The reliability of the proposed method was verified in the case study of the I-40 bridge in New Mexico. [PERSON] et al. [148] introduced a mathematical statistical method, namely the response surface (RS) method. They reported that the optimal identification results between experimental and numerical analyses can be obtained by using this method in the updated FEM.  
It can be seen that the FEMU-based SDI methods have made new research progress in different directions in recent years, showing a bright application prospect. However, as mentioned above, these studies are limited in some ways. The FEMU method depends on the modified parameters of the model. Although some scholars have taken into account the uncertainty of these parameters [135; 137; 139; 149] and the nonlinearity of the structure [141; 142; 144], in the FEM analysis of complex structures, faced with a large number of correction parameters, a repeated calculation process will lead to a slow updating process or deviation. The substructure method can decompose the whole model correction process into several independent blocks to avoid the double calculation of local damage. It may serve as an auxiliary method to solve these problems. The FEMU methods mentioned in this section are summarized in Table 4.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Feature and/or Advantage** & **Application** \\ \hline \multirow{4}{*}{Gaussian Process} & First-order reliability method and modular Bayesian approach & Experimental box girder bridge [135] \\ \cline{2-3}  & Temperature consideration and longitudinal boundary stiffness & Jiangyin Suspension Bridge [136] \\ \cline{2-3}  & Boundary conditions consideration and influence lines & Large-span suspension bridge [137] \\ \hline \multirow{4}{*}{Bayesian Inference} & Transitional Markov chain Monte Carlo sampling and fast Bayesian FFT & Steel truss bridge [138] \\ \cline{2-3}  & Transfer learning is used to bridge the bias & Numerical and experimental models [139] \\ \cline{2-3}  & Radial basis function & Numerical and experimental models [140] \\ \hline \multirow{4}{*}{Nonlinear Model} & Transform to solve constrained optimization problems & Numerical model [141] \\ \cline{2-3}  & Evaluate strength and stiffness degradation in the time domain & Experimental RC bridge [142] \\ \cline{2-3}  & Considering bond-slip & A full-scale RC bridge column [143] \\ \cline{2-3}  & Time history analysis- and cluster computing-aided PSO algorithm & Numerical model [144] \\ \hline \multirow{4}{*}{Others} & Fusion of real data and simulation data & Z-24 Bridge [145] \\ \cline{2-3}  & Particle Swarm and Artificial Bee Colony Algorithms & Numerical model and a high-rise building [146] \\ \cline{2-3}  & Roaming damage method and perceptron regression neural network & I-40 bridge in New Mexico \\ \cline{1-1} \cline{2-3}  & Response surface & Numerical and experimental models [148] \\ \hline \hline \end{tabular}
\end{table}
Table 4: Finite element model updating methods.