## 4 Structural Models
### Mapping Model and Meta-Model  
For a large structure with enormous elements, a simplified model is always necessary in the inverse problem. One type of models is the mapping model that is used to build a mapping relationship between the structural parameters and the structure responses. The representative method is the neural network (NN) method that is inspired by the architecture of the neurons and the human brain function [117] and has been widely applied in structural analysis due to its strong nonlinear mapping ability. The NN method is found capable of replacing conventional finite element updating methods in solving the inverse problems without utilizing the sensitivity matrix. However, the training process could be very time-consuming, and the accuracy of the predictions of this trained NN model is very dependent on the training data. Meanwhile, the other type of models is the meta-model (surrogate model) that replaces the structure model with an approximation model. This model is traditionally a polynomial function describing the relation between the structural responses and the model parameters. Meta-models have been extensively used in the design and optimization of computationally expensive problems. Different meta-models have been shown to perform well in different conditions, such as the response surface method (RSM) [118; 119; 120; 121; 122; 123; 124; 125], Kriging method [126; 127], radial basis function method (RBF) [128], and feed-forward neural network [129]. [PERSON] and [PERSON] [130] and [PERSON] et al. [131] recently reviewed different surrogate models used in the aerospace industry, and [PERSON] et al. [132] summarized the characteristics of different meta-model types and the experiment designs for fitting them. It is recommended to use RBF for high-order nonlinear problems, Kriging for low-order nonlinear problems in high dimension spaces, and polynomial RSM for low-order nonlinear problems [133]. Although there are many methods available for structural models, the construction of those models usually results in model errors from simplified assumptions. In order to detect damage rather than the artificial errors from the model construction, a good quality model that could accurately predict the behavior of the structure is required, but is usually a quite challenge. As for damage detection in different levels, the complexity of the structure model and corresponding damage parameters depends on the structure type and required detection level. In the preliminary stage, a simplified FE model might be sufficient. If the damage is already localized in a limited range, a mapping/meta model or a detailed model could be built for the vicinity of the damage while other part of the structure could be simplified. The substructure method is a good alternative to build a fine model for the vicinity of the damage [134]. The compromise between the accuracy and simplicity of the model specifically depends on the problem. The above conventional model-based methods always require a baseline data of vibration response from a healthy structure. However, in many cases the baseline model cannot be obtained for structures such as those with preexisting damage. Therefore, many studies have been devoted on the baseline-free method with no information about the original undamaged structure. [PERSON] [101] introduced a modified Laplacian operator for non-baseline damage detection from the mode shape data. [PERSON] et al. [135] suggested a method to extract localized changes (damage peaks) from strain energy modal shapes based on Fourier analysis of the strain energy distribution. [PERSON] et al. [136] developed an instantaneous damage detection scheme based on time reversal acoustics and consecutive outlier analysis. [PERSON] and [PERSON] [137] developed a guided-wave-based nondestructive testing to detect crack damage in a thin metal structure without using prior baseline data.