Wavelet-based approach of time series model for modal identification of a bridge with incomplete input

Identification of modal parameters of a bridge from its earthquake responses is crucial for performing damage assessment of the structure. However, all the input base excitations of the bridge may not be measured because of economic concerns and sensor malfunctions. Consequently, evaluating the modal parameters of a bridge under the consideration of incomplete input measurements is a challenging and important task. An approach that combines the continuous Cauchy wavelet transform with an autoregressive time-varying moving average with exogenous input (AR-TVMA-X) model is proposed in this study to identify the modal parameters of a multispan bridge under multiple support earthquake excitations with incomplete measurements. The efficiency and efficacy of the proposed approach are first validated using numerically simulated responses of a three-span continuous beam subjected to multiple support nonstationary excitations. A standard procedure of using the proposed approach to identify the modal parameters is established according to comprehensive studies on the effects of noise in the data, the number of supports whose excitations are used in the AR-TVMA-X model, and the orders of the AR-TVMA-X model on the accuracy of identifying the modal parameters. This procedure is further applied to process the earthquake responses of a two-span cable-stayed 510-m-long bridge to demonstrate the engineering applicability of the proposed approach.