2.1.3. FRFs and Related Variants

FRFs are actually an extension of conventional modal parameters, because they contain the information over the entire frequency range. For different types of structure, the optimal frequency range may be various, which is highly dependent on experience and trial experiments. There is lack of theoretical analysis and numerical simulation investigations of how to select the sensitive frequency range to local damages for different structures. Operational deflection shapes [82–85] and their curvatures, power spectral density [86–88], frequency shift curve, and its curvature [89,90] are the most frequently used FRFs related variants.

FE updating methods can be applied to FRFs and related variants [91]. Conventional FE updating methods are effective in identifying local damages but have lower computational efficiency. Unfortunately, there are less investigations on applying substructure techniques, advanced regulation algorithms and optimization algorithms to FRFs and related variants, because it is difficult to select the sensitive frequency range for a given structure and it is also difficult to converge due to uncertainties in the measurement of FRFs.

Machine learning methods can also be applied to FRFs and related variants [92–94]. Conventional FRFs are curves which can be represented as one-column vectors, hence artificial neural network is suitable for identifying local damages by using FRFs. Usually, principal component analysis is applied to FRFs first to extract the most important components, which are then used as input to artificial neural network. Fourier amplitude spectra is a 2D surface FRFs related variant [95], therefore, convolutional neural network can be applied to it to construct the SHM system. In addition to neural networks, the Dirichlet process clustering [96] can be applied to SHM system to identify early-stage damages on bridges by using FRFs. However, these investigations have been conducted through numerical simulations and lab-scale experimental studies. Whether these machine learning methods based on FRFs and related variants are still effective should be further examined by field measurement. It should also be noted that since the quality of dataset for training is crucial for machine learning methods, therefore, the performance of these methods should be further examined when more FRFs data are available.

### *2.2. Time Domain Methods for Vibration-Based SHM*

Instead of extracting the frequency related properties from the time history of dynamic responses of a structure, the dynamic responses of a structure in time domain can be used for SHM directly. Among them, acceleration and displacement are the most frequently used. The time domain methods usually do not require much calculation resources and therefore are timesaving, but they are used for the structures subject to stabilize environmental excitations because different excitation may cause quite different dynamic response and may cause the methods to fail to identify damages.
