A time series modeling approach for damage monitoring of concrete dam under seismic effects

Abstract

In order to improve the applicability of time series models for the diagnosis of concrete dam damage under seismic loading, this paper proposes a diagnostic method for structural damage by combining linear time series modeling and non-linear modeling of model residuals. Starting from the linear structural dynamic response transmissibility function, the expressions of the generalized Auto-Regressive with eXtra inputs (GARX) model for the dynamic response under stationary excitation conditions were derived. The GARX model with dynamic coefficients was extended to model the dynamic response under seismic loading and the generalized Auto-Regressive Conditional Heteroscedasticity (GARCH) model was used to nonlinearly model the model residuals. To track the coefficients of the GARX model, an adaptive least squares recursion method based on fuzzy forgetting factor was studied. The damage indicator of Minkowski distance based on the GARCH model coefficients was proposed. Finally, the effectiveness of the diagnostic methods of the GARX and GARCH models was verified by a numerical calculation of the non-linear damage to a dam. The results showed that GARX can effectively describe the input-output relationship of the dam in the absence of damage. After damage occurs, the GARCH model and the improved Minkowski distance index for the model residuals of GARX can effectively characterize the non-linear damage evolution of the dam.