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In order to precisely identify the location and extent of structural damage, a two-stage damage detection method using frequency responses and statistical theory is presented in this paper. First, a damage index, which comes from the product of the stiffness changes and measured responses, is proposed. We can utilize degree-of-freedom (d.f.) damage index to localize the damage locations. Then, in order to calculate the extent of damage, a damage quantification formula is deduced from a reduced degree-of-freedom system. Finally, the effect of measurement noise is taken into account in the identification process and the measurement noise sensitivity formula based on statistical theory is presented. The numerical example and analysis demonstrate the excellent performance of the proposed two-stage method to identify damage locations and extent compared with other methods, such as the directness generalized inverse method.

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 problems, a damage detection method based on modal strain energy equivalence index (MSEEI) is presented. First, an accurate expression of modal strain energy (MSE) before and after damage occurs is given. Then, according to the energy equivalence theory that the change in MSE caused by the damage should be equivalent to the energy dissipation caused by the same damage, an energy equivalence equation is deduced. Finally, four roots of the energy equivalence equation are found and a MSEEI is obtained from the four roots. Simulation results demonstrate that the proposed MSEEI method can identify structural damage locations and extent with good accuracy. Identification precision of the proposed method is clearly better than that of the modal strain energy dissipation ratio index (MSEDRI) method.

In order to solve the damage detection problem, a damage detection method based on strain energy and evidence theory is presented in this paper. First, an evidence theory method is proposed to identify structural damage locations. Then, structural modal strain energy is utilized to quantify structural damage extents. In general, structural strain energy dissipation should be equal to the change of modal strain energy, according to this theory, a new energy equation is deduced, and structural damage extent can be obtained through the solution of the equation. The simulation results show that the method can perfectly identify damage locations and extents. Therefore, the proposed method is effective for the structural damage identification.