## 2 Framework of Vibration-Based Damage Identification  
Generally speaking, damage is defined as changes introduced into a system, which adversely affects the current or future performance [4]. The definition implies that it is only meaningful when two different states of the system are compared. In addition, the damage in structural and mechanical systems is referred to changes to the material and/or geometric properties of these systems and changes to the boundary conditions and system connectivity [11]. Damage identification is always carried out in conjunction with five closely related disciplines including structural health monitoring (SHM), condition monitoring, non-destructive evaluation (NDE), statistical process control (SPC), and damage prognosis [11]. SHM is a process of implementing a damage identification strategy in structures, focusing on the online global damage identification. Similar to SHM, condition monitoring mainly addresses damage identification in rotating and reciprocating machinery. NDE is primarily used for damage characterization and as a severity check in an offline local manner after the damage location is determined. SPC is a process using a variety of sensors to monitor changes due to structural damage. Once the damage has been identified, damage prognosis is adopted to predict the remaining useful life of a system. The main objective of damage identification is to identify structural damage at a very early stage and predict the remaining service life of structures for the decision making. Based on the amount of information provided regarding the damage state, the structure damage identification can be classified into four levels [12]: determination of damage occurrence (Level 1), determination of damage geometric location (Level 2), quantification of damage severity (Level 3), and prediction of the remaining service life and decision making (Level 4). The vibration-based methods can be classified as response-based and model-based methods. As for the response-based method, by directly or indirectly interpreting the structural dynamic response, the changes of modal parameters between the intact and damaged states of the structure are used to identify damage in structures. Model-based methods assume that the structure responds in some predetermined manner that can be simulated by an analytical or numerical model such as the usually used finite element model. By comparing the updated model correlated with the measured data of the damaged structure to the original model, the damage location and severity can be identified. In terms of identification levels, the response-based detection methods are mostly able to detect damage in Level 1 and in some cases in Level 2, which is sufficient for many practical applications. Challenges on this level include how to select sensitive features, detect damage in a rather early stage without getting false alarms, eliminate the environmental and operational effects, and quantify the probability of detection [13]. In order to identify damage in Level 2 and Level 3, the model-based methods are usually adopted. In most cases, the location and extent of damage are determined simultaneously. The most sophisticated level is Level 4, i.e., predicting the structural remaining lifetime and making decisions based on damage diagnosis results. Level 4 is generally associated with the fields of fracture mechanics, fatigue-life analysis, and structural assessment, which requires the combination of global structural models with local damage models to predict the evolution of damage, or the probabilistic failure models based on previously failed or damaged components [14], etc. Figure 1 demonstrates the procedure of damage identification for the four levels. The first step is to take measurements from the structure and apply the response-based methods to determine the occurrence of structure damage. After the structure damage is confirmed, a structure model is created using the finite element or other methods.