2.2.1. Accelerations

FE updating methods can be applied to accelerations for SHM [97], similar to frequencies and mode shapes. Tikhonov regularization [98,99], adaptive Tikhonov regularization [100], and L1 regularization [101] were successfully used to identify local damages based on accelerations. However, the dataset of time history of accelerations is much larger than the dataset of frequencies and mode shapes, hence the convergency is difficult to achieve. Moreover, there is no proven procedures on how to select the certain time history of accelerations, which is now generally dependent on experience.

Machine learning methods can also be applied to accelerations and variances for SHM [102–108], including both supervised and unsupervised methods. Although research showed that the machine learning methods can locate and evaluate local damages successfully in lad-scale experiments and numerical benchmark studies, no evidence have been provided that they can also be applied to real structure in practice. On the other hand, unlike frequencies and mode shapes which are only dependent on the structure itself, the accelerations are highly dependent on environmental excitations. The environmental excitations are always varying with respect to time, therefore it is quite difficult for the training algorithms in machine learning methods to differentiate the change of accelerations due to local damage and that due to environmental excitations.

Bayesian methods are also applicable when accelerations are used [109,110], and they show grea<sup>t</sup> potential in application to real structures. Research work has been conducted through experimental and numerical study. It should be noted that since the prior information is important to the Bayesian methods, hence the change of operational conditions should be considered carefully. For example, the traffic load of a bridge may increase with the economy development, therefore the prior information constructed previously may change with respect to time.

Statistical time series methods [111,112] are proposed especially for time history of dynamic responses, which usually fit time series models such as autoregressive model, autoregressive with exogenous model, and Mahalanobis squared distance, etc. All of them show their distinguishing advantages, but they still have their own limitations. For autoregressive model and autoregressive with exogenous model, it is difficult to determine the model order, which is currently highly dependent on experience. For Mahalanobis squared distance method, the data from the undamaged structures under various conditions is required, which is almost impossible for old building and structures. Statistical moment of accelerations can also be used to identify local damages of structure, Yang et al. [113,114] proposed a fusion of statistical moments by combining the fourthorder statistical moment of displacement with the eighth-order statistical moment of acceleration for the damage identification of structures. However, the order of moment to be selected is highly dependent on experience since different structures may have various statistical moments sensitive to damages, which limits the widely application of statistical moment. Temperature also plays an important role in SHM approach in time domain. Hios et al. [115] proposed a new stochastic global model method based on statistical hypothesis testing, and determined a functional hybrid model that can describe temperature-dependent dynamics. OBrien et al. [116] used temperature data to validate damage indicators based on measured data collected under uncontrolled traffic conditions, and showed that temperature can be used as a proxy for damage since stiffness of concrete structure is dependent on temperature.
