## 3 Advancements and Alternatives to Modal-Based Damage Identification
### Non-Modal Damage Sensitive Features
#### 3.3.1 Vibration Based Damage Sensitive Features  
Vibration-based DSFs are parameters extracted from raw accelerations that generally measure a variant of vibration energy or another vibration property. The premise of this lies in the fact that as the bridge is damaged, it needs to resist external loading using more kinetic energy as it attains less potential energy. [PERSON] [138] assessed the damage sensitivity of a number of vibration parameters extracted from a progressive damage test on the S101 Bridge in Austria subjected to ambient excitation [139]. The parameters assessed were: Max Peak-to-Peak Acceleration; Sustained Maximum Acceleration [140]; Mean Period [141]; Mean Frequency; Cumulative Absolute Velocity [142]; Arias Intensity [143]; Destructive Potential Factor [144]; and Vibration Intensity (in Vibirars) [145]. The authors employed the MSD outlier detection algorithm in conjunction with the MCD estimator to mitigate the uncertainties regarding sources of ambient vibration and to ensure that the training data were not corrupted by outliers. The results showed that vibration energy-based parameters exhibit considerable damage sensitivity, which can be further amplified through the incorporation of a frequency-based denominator, as in the case of Destructive Potential Factor and Vibration Intensity (in Vibirars). In the study by [PERSON] et al. [146], damage indicators were defined and tested based on the deck accelerations under action of operation forces designed as moving loads in a 2-PE model. A parametric study assessed a number of vibration parameters such as the maximum peak amplitude, minimum peak amplitude, standard deviation, and sum of squared differences between baseline acceleration and damaged acceleration. The results showed that many of the vibration-based DSFs possess strong damage sensitivity and the potential for damage localisation and quantification. [PERSON] & [PERSON] [147] assessed a number of pattern recognition-based damage identification algorithms using vibration data from the Yonghe Bridge. They determined that acceleration amplitude was quite responsive to damage and it was concluded that this method had the potential for online damage detection due to its ease of application. This conclusion echoed similar findings by [PERSON] & [PERSON] [148], who observed a correlation between peak acceleration amplitude and the existence of damage in a group of assessed bridges. [PERSON] et al. [149] implemented a baseline-free method of damage detection using symbolic data analysis (SDA) to reduce raw vibration data collected from the Samora Michel Bridge into smaller representative sets of statistical significant components such as interquartile intervals. The authors observed that the interquartile intervals attained enough damage sensitivity to accurately detect changes in the bridge condition over time. The dynamic cloud clustering algorithm was employed in the study, which is a more efficient adaptation of the popular k-means clustering algorithm; however, due to the methodology's tendency to converge to local minima, a cluster validation step was introduced to ensure robustness. It consists of computing a set of indices for each identified cluster that describes their density and location. Subsequent identified clusters are then compared to the indices obtained to determine the most likely number of clusters. [PERSON] [150,151] proposed a non-modal based damage detection technique, known as the Interpolation Damage Detection Method (IDDM). It operates by defining a damage index in terms of expected, or reference, deformed shapes calculated from Frequency Response Functions (FRFs) to monitor bridge condition. By using deformed shapes as a damage indicator, one can take advantage of concentrated vibration amplitude irregularities to detect and locate damage, as other authors have successfully achieved [152,153], while others focused on the variation of deformed shape curvatures to detect damage [154,155,156], the latter using a cubic polynomial to represent curvatures.