An Improved Objective Function for Modal-Based Damage Identification Using Substructural Virtual Distortion Method  
[PERSON]  
1 Department of Civil Engineering & State Key Laboratory of Coastal and Offshore Engineering,  
Dalian University of Technology, Dalian 116023, China; [EMAIL_ADDRESS]  
2 Key Laboratory of Structures Dynamic Behavior and Control of Ministry of Education,  
Harbin Institute of Technology, Harbin 150090, China  
3 Department of Civil Engineering, Dalian Minzu University, Dalian 116650, China; [EMAIL_ADDRESS]  
4 Institute of Fundamental Technological Research, Polish Academy of Sciences, 02-106 Warsaw, Poland; [EMAIL_ADDRESS]  
4 Correspondence: [EMAIL_ADDRESS]; Tel. : +86-411-847-064324  
of experimental modal analysis techniques, it is relatively easy to obtain accurate structural modal parameters, which further promotes the study of damage identification based on modal parameters. The structural modal parameters most often used for damage identification are: natural frequency [14; 15], mode shape [16], modal curvature [17], modal strain energy [18], etc. [PERSON] et al. [19] presented a methodology for nondestructive localization and estimation of the size of damage using few natural frequencies or mode shapes. [PERSON] et al. [20] performed a structural identification of a real caisson breakwater by using in situ vibration measurement and a simplified analytical model and investigated the feasibility of the wave force inference. [PERSON] et al. [21] identified structural damage in a FE model of Hong Kong Tsing Ma Bridge using modal sensitivity analysis. [PERSON] and [PERSON] [22] proposed an identification method based on the equivalent damage index of modal strain energy. The accurate expression of modal strain energy before and after damage was deduced, which allowed the location and extent of structural damage to be accurately identified. [PERSON] and [PERSON] [23] proposed a damage detection method based on Magnetic Charged System Search (MCSS) and Particle Swarm Optimization (PSO) using structural frequencies and mode shapes, and illustrated it by identifying the damage in a numerical five-story shear building. [PERSON] et al. [24] defined a novel damage detection method based on strain modes; the validity of the proposed method was verified under different damage cases. [PERSON] et al. [25] proposed a novel frequency-based co-integration technique for damage detection of bridges. The validity and robustness were illustrated and verified through a numerical simulation and experimentally using a real cable-stayed bridge under the influence of changing environmental temperature. Kriging surrogate models provide explicit functions to represent the relationships between the inputs and outputs of a linear or nonlinear system, which is a desirable advantage for response estimation and parameter identification in structural design and model updating problems. [PERSON] et al. [26] applied the kriging model and PSO algorithm for the dynamic model updating of bridge structures using the higher vibration modes under large-amplitude initial conditions. [PERSON] et al. [27] proposed a simple method for crack number identification based on a kriging surrogate model. [PERSON] et al. [28] proposed a new damage identification method by constructing the initial kriging surrogate model to represent the relationship between the dynamic response and the structural damage parameters, which can improve the efficiency of damage identification. [PERSON] et al. [29] proposed a damage identification method that used additional virtual masses to generate a large amount of structural modal information and applied Bayesian theory to localize and quantify the damage. Damage identification based on structural modal parameters has strong robustness to noise; thus, it requires less information about the initial state of structures and less accurate information about the excitation, which makes it more feasible in practical applications.