Uncertain identification method of structural damage for beam-like structures based on strain modes with noises

Strain modal parameters are more sensitive to the local structural damage than displacement modal parameters. Therefore, it will be more effective to locate damage based on the change of strain modes. In this paper, the sensitivity matrix between strain mode and elemental stiffness parameter is deduced. Further more, the relationship of strain modal information and damage parameter of beam-like structures is established. In order to quantify the influence of the uncertainty in the strain modal information on the identification results, this paper treats measurement noise as probabilistic and interval variable and deduces the corresponding formula of structural elemental stiffness parameters. Due to the definition of uncertainties, different damage indexes including deterministic index, uncertainty index and combination index are established or introduced to quantify the damage extent and damage possibility. The validity of the proposed method is verified by a numerical example and an experimental work. The effectiveness and robustness of the displacement modal information based method is compared with the proposed method. The characteristics of different damage indexes are discussed by statistical means in the numerical example. The results indicates that the combination index has more advantages in identifying the damage under uncertainties.