Structural Damage Identification Based on AR Model with Additive Noises Using an Improved TLS Solution

Structural damage is inevitable due to the structural aging and disastrous external excitation. The auto-regressive (AR) based method is one of the most widely used methods for structural damage identification. In this regard, the classical least-squares algorithm is often utilized to solve the AR model. However, this algorithm generally could not take all the observed noises into account. In this study, a partial errors-in-variables (EIV) model is used so that both the current and prior observation errors are considered. Accordingly, a total least-squares (TLS(E)) solution is introduced to solve the partial EIV model. The solution estimates and accounts for the correlations between the current observed data and the design matrix. An effective damage indicator is chosen to count for damage levels of the structures. Both mathematical and finite element simulation results show that the proposed TLS(E) method yields better accuracy than the classical LS method and the AR model. Finally, the response data of a high-rise building shaking table test is used for demonstrating the effectiveness of the proposed method in identifying the location and damage degree of a model structure.