# The Current Development of Structural Health Monitoring for Bridges: A Review
## 5 Damage Identification Methods
### Bayesian Methods  
Damage identification in civil structures is confronted with the challenges of measurement noise and modeling errors, which may lead to inaccurate identification results. For example, the presence of measurement noise may mask small structural changes caused by damage. Therefore, deterministic methods may fail in practical applications. To overcome these challenges, many researchers have proposed probabilistic damage recognition methods. Among these methods, Bayesian inference has received much attention and has developed many practical methods in SDI today. [PERSON] et al. [172] proposed a probabilistic method to assess the state of bridge expansion joints and issue damage alarms. In their established Bayesian TDR model, model parameters are treated as random variables, which can eliminate uncertainty factors. They also reported that the method can quantify predicted uncertainty. The effectiveness of the method was validated by utilizing monitoring data from the Ting Kau Bridge in Hong Kong. [PERSON] et al. [173] developed a Dirichlet process (DP) Gaussian mixture model for training algorithms in the absence of SHM data. In laboratory and field tests, this DP hybrid model showed a strong Bayesian nonparametric clustering ability. [PERSON] et al. [174] introduced Bayes' rule into virtual sensor networks and proved that this method had better signal denoising performance than real sensors. [PERSON] et al. [175] considered both uncertainty and temperature change in sparse Bayesian learning (SBL). They established a functional relationship between vibration characteristics, temperature, and damage, and then took the temperature into account through a quantitative relationship. [PERSON] et al. [176] constructed the likelihood function and prior probability density function of the Bayesian model based on FFT data. The feasibility of this method for damage detection was verified in numerical and laboratory studies. [PERSON] and [PERSON] [177] proposed a two-step strategy based on Bayesian neural networks for the damage assessment of long-span suspension bridges. They first improved the neural network model based on the probability logic method, and then used the framework to detect and quantify bridge damage successively. [PERSON] and [PERSON] [178] developed a probabilistic fatigue damage model based on Bayesian learning for the wind-induced fatigue damage assessment of long-span bridges. By utilizing the wind information recorded by the SHM system, the Bayesian learning method was applied to determine the probability of fatigue damage in local components. The applicability of the proposed method is verified in the study of the Tsing Ma suspension Bridge in Hong Kong. [PERSON] et al. [179] studied a model simplification technique, through which damage detection based on SBL can be carried out under the condition that the measured degrees of freedom were limited. [PERSON] et al. [180] reported a combination of the Bayesian theory and perturbation methods to detect structural bearings. The posterior probability density function of the damage parameters was obtained by using the Bayesiandamage detection theory, and the calculation cost was saved by using the matrix perturbation method. [PERSON] et al. [181] proposed a new SBL-based approach, which was driven by probabilistic data. Firstly, damage-sensitive frequency bands were established based on monitoring data to construct the damage index. The predicted value of the SBL regression reference model was then used to judge the damage and the Bayes factor was used to quantify the damage degree. Finally, the feasibility of the proposed method was verified by using real bridge monitoring data. As a method of deriving sparse solutions in the context of regression and classification, SBL takes uncertainty into account by hyper-parameters with explicit physical meaning. The automatic updating of hyper-parameters solves the problem of regularization parameter selection in sparse recovery.