Data-driven Detection of Structural Nonlinearity in the Time Domain Based on Output Measurements and Transmissibility Function

Detecting nonlinear behavior in structural systems can provide critical information on damage potentially occurred during an extreme event. However, traditional detection methods typically require knowledge of input forces and detailed finite element models, which are often unavailable in real-world scenarios. On the other hand, many output-only methods assume the dynamic properties before and after the damaging event to be different, potentially missing temporary nonlinear behavior due to, e.g., steel yielding. This paper presents a novel data-driven methodology for detecting nonlinearities using only output acceleration measurements. The proposed methodology leverages the transmissibility function (TF), which relates two structural response measurements and reflects how mechanical energy is transferred among different locations of the structure. The time domain representation of the TF, as an Autoregressive with eXogenous input model (TF-ARX), is used to locate the time instants when structural anomalies appear, which can be attributed to nonlinearities. Since the TF is independent of the time evolution of the loads, this methodology can be used in the case of non-stationary unknown loads such as earthquake-induced ground motions or extreme waves. The TF-ARX model is trained using measurements during operational conditions (linear regime) and subsequently applied to analyze potentially damaging events. Deviations from expected linear behavior are identified through statistical analysis of prediction residuals and their wavelet-based time-frequency decomposition. The methodology is validated through numerical simulations of a steel structure subjected to ground motion and responding in the nonlinear regime.