## 1 Introduction  
Deterioration and degradation of structures are of great concerns worldwide. The deficient structures can potentially endanger the safety and economical use of the infrastructure system, and even develop into structure failures if the damage is not detected in the early stage. The research need on detecting damage at the earliest possible stage is universal throughout the fields of civil, mechanical, and aerospace engineering. Most non-destructive damage detection methods can be categorized as either local or global techniques. The non-destructive testing (NDT) methods, such as the ultrasound, X-ray, dye penetrates, magnetic particle, and acoustic emission [1, 2], are local techniques that can complement visual inspections as objective methods leading to quantifiable results. However, all these experimental methods require that the vicinity of the damage is known a priori and that the portion of the structure being inspected is readily accessible. Subjected to these limitations, the local NDT methods can only detect damage on or near the surface of the structure. The need for global damage detection methods that can be applied to complex structures has led to the development of vibration-based methods.  
The research on the vibration-based damage identification was initiated in the late 1970s, particularly in the aerospace and offshore oil industries, and has been rapidly expanding to civil engineering industries over recent decades [3]. The basic idea behind this technology is that modal parameters (e.g., natural frequencies, modal shapes, modal damping, etc.) are functions of the physical properties of the structure (e.g., mass, damping, and stiffness) [4]. Therefore, changes or damages in the physical properties will cause detectable changes in the modal properties. There have been a few review publications on this topic. [PERSON] et al. [4] presented an extensive review of vibration-based damage identification methods up to 1997. [PERSON] et al. [5] then presented an updated version containing new technical developments up to 2001. [PERSON] and [PERSON] [3] presented a review with particular emphasis on structural engineering applications. [PERSON] et al. [6] introduced the development of modern-type vibration-based methods using modern signal-processing techniques and artificial intelligence. [PERSON] and [PERSON] [7] reviewed the recent development in statistical damage detection and condition assessment techniques for bridge structures. [PERSON] and [PERSON] [8] comprehensively reviewed the modal parameter-based damage identification methods for beam- or plate-type structures and conducted a comparative study of five algorithms. [PERSON] and [PERSON] [9] reviewed the developments with particular focus on the utilization of advanced computational methods. [PERSON] et al. [10] presented a review through a comparative study among different vibration-based damage detection methods. All the above literature reviews concentrate primarily on the damage identification Levels 1 to 3, i.e., determination of damage occurrence, location, and severity. However, they did not cover research topics such as the prediction of the remaining service life of structures and the decision making for maintenance, which is the ultimate objective of damage detection.  
Therefore, this study is aimed to more systematically review the state-of-the-art on the framework of vibration-based damage identification in different levels, that is, the damage occurrence, damage location, damage severity, remaining life prediction, and decision making, to give a general guideline for researchers and engineers. Several major parts of the framework are to be discussed: (1) detecting damage occurrences using response-based methods; (2) building reasonable structural models; (3) damage characterization, objective functions, and optimization algorithms; (4) remaining life prediction; and (5) decision making.