## 3 Detection of Damage Occurrence
### Modal Domain Methods  
Modal information can be extracted from input-output measurements by means of the classical modal analysis methods or from output-only data measured under the ambient excitation from wind, traffic loads, etc. without the artificial forces. The modal domain methods evolve along with the rapid development of experimental modal analysis technique and gain the popularity because the modal properties (i.e., natural frequencies, modal damping, modal shapes, etc.) have physical meanings. Thus, they are easier to be interpreted or interrogated than those abstract mathematical features extracted from the time or frequency domain. Response-based damage detection methods using modal information are relatively straightforward. That is, the changes between modal parameters of the intact structure and those of the damaged structure are directly used, or correlated with other relevant information, to develop the damage indicators for locating damage in the structure. The modal domain provides a large set of damage sensitive features, such as the shifts of natural frequencies [84], changes in the Modal Assurance Criteria (MAC) that correlates modal shapes of the damaged and undamaged structures [85], changes in the Coordinate Modal Assurance Criteria (COMAC) [86], changes in the Multiple Damage Location Assurance Criterion (MDLAC) [87], changes in modal strain energy [88; 89], changes in modal shape curvature [90], strain modal shapes [91], dynamic flexibility matrix [92], and dynamic flexibility curvature [93]. [PERSON] [94] presented a comprehensive review on the direct use of modal parameters for damage detection in linear systems. Since the effect of small damage on modal properties, such as natural frequency shifts and local changes in the mode shapes, are likely to be masked by experimental uncertainties and data reduction [95], the response-based methods that directly use modal parameters are not efficient to detect small damage. In order to enhance the sensitivity and accuracy of damage detection in modal domain, a simple and effective approach is to use the higher-order derivatives of modal shapes, such as rotations (first derivative), curvatures (second derivative) and third and four derivatives. The behavior of higher-order derivatives has been numerically studied and experimentally validated in damaged beam-like structures [96; 97]. Especially, the mode shape derivatives have been widely used to localize damage in laminated composite structures. For example, [PERSON] et al. [98] explored the synergy between a wavelet transform and a Teager energy operator (TEO) to ameliorate the curvature mode shape, and also used two-dimensional curvature mode shape method to detect damage in plates [99]. [PERSON] [100] proposed a Ritz based method to improve the computation of mode shape derivatives. In addition, the incorporation of advanced signal processing procedures has been widely studied. [PERSON] [101] applied a modified Laplacian operator solely on modal shapes of damaged structure and successfully identifies the damage location. [PERSON] and [PERSON] [102] used Gaussian fuzzy sets to fuzzify changes in the modal curvatures due to damage and used a fuzzy logic system to accurately locate the damage. [PERSON] and [PERSON] [103] presented an analysis to determine the optimal sampling interval of strain energy mode shapes. [PERSON] et al. [104] used a gapped smoothing method to extract local features in vibration curvature shapes. [PERSON] et al. [105] proposed a fractal dimension based method from the measured displacement mode shape in beam structures. In recent years, the wavelet transform (WT) technique was used as an effective signal analysis tool to filter out noise and to enhance robustness of damage detection. This approach involves the application of wavelet analysis to modal data and shows high sensitivity to non-continuities and singularities in the measurement signals. [PERSON] et al.