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In the service period, some engineering structures may have cracks or other nonlinear damages. The nonlinear damages are the major influence to the safety of engineering structures, which should be detected as early as possible. Currently, the effective nonlinear damage detection method is still lacking. Therefore, a penalty conversion index based on generalized autoregressive conditional heteroskedasticity (GARCH) model is presented to identify the nonlinear damage. First, an exact expression of GARCH model is described, the bilinear stiffness characteristic of nonlinear damage is given, and acceleration responses are used to establish the GARCH model. Then, through the GARCH model analysis of nonlinear damages responses, it can be found that the variance of conditional variance are sensitive to the nonlinear damage information of acceleration responses, so a basic conversion index based on the variance of conditional variance is proposed. Finally, a penalty conversion index based on GARCH model is presented, which can reduce the interference induced by the adjacent unrelated factors. Numerical and experimental examples show that the identification results of the proposed penalty conversion index based on GARCH model are superior to those of the basic conversion index and the cepstral metric (CM) index.

In order to solve a structural multi-damage identification problem, a two-stage damage identification method based on evidence fusion and improved particle swarm optimization (IPSO) is presented. First, structural modal strain energy and frequency are considered as two kinds of information sources. Then, evidence fusion theory is utilized to integrate the two information sources and preliminarily identify structural damage locations. After the damaged locations are determined, particle swarm optimization (PSO) is used to identify the extent of structural damage. Considering that the search efficiency of a basic PSO is still not very good, some improved strategies are presented, such as mutation position iteration formula, micro-search of an elitist, two convergence conditions, etc. The simulation results demonstrate that the proposed two-stage method can estimate the damage locations and extent with good accuracy.

In order to solve structural multi-damage identification problem, a two-stage damage detection method based on Bayesian theory and immune genetic algorithm (IGA) is presented. First, structural modal strain energy and frequency are considered as two kinds of information sources, and Bayesian theory is utilized to integrate the two information sources and preliminarily identify structural damage locations. After the damaged locations are determined, immune genetic algorithm is used to identify structural damage extent. Considering the search efficiency of the simple IGA is still not very good, some improved strategies are presented, such as culture vaccine, concentration control of the best antibody, and two termination conditions etc. Simulation results show that the two-stage method can precisely identify structural damage locations and extent, and the calculated results of the proposed improved IGA are obviously better than those of both the simple IGA and the genetic algorithm with elitist strategy.

In order to solve structural damage identification problem, a damage identification method based on improved Particle Swarm Optimization (IPSO) is presented. First, structural frequency and modal strain energy are utilized to obtain damage information. Then, evidence fusion theory is utilized to integrate the information and preliminarily identify structural damage locations. After the damaged locations are determined, Particle Swarm Optimization (PSO) is used to identify structural damage extent. Some improved strategies are presented to enhance the search efficiency. The simulation results demonstrate that the proposed method can estimate the damage locations and extent with good accuracy.

In order to solve structural multi-damage identification problem, a two-stage damage detection method based on energy balance equation and evidence fusion is presented. First, a Frequency Change Identification (FCI) method and Modal Strain Energy Dissipation Ratio (MSEDR) method are utilized to preliminarily identify structural damage locations, and then a Fusion Damage Localization (FDL) method based on evidence theory is proposed to precisely detect damage locations. The FDL method mainly utilizes evidence theory to combine both the FCI localization information and the MSEDR localization information. Thus, more precise damage localization information can be acquired. After the damaged locations are determined, an Energy Balance Equation (EBE) index is presented to identify structural damage extent. Considering that strain energy dissipation should be equal to the change of modal strain energy, a quartic EBE equation is deduced, and structural damage extent can be obtained through the solution of the equation. An average quantification index is also proposed to improve identification precision. The simulation results demonstrate that the FDL method can perfectly detect structural damage locations, and the EBE index and average index can identify structural damage extent.