Identification and Interpretation of Nonstationary Dynamics Using Extended-Kalman-Filter-based DMD

Ground seismic response is strongly affected by nonlinearity and observation noise, which motivates a robust and interpretable framework for identifying nonstationary dynamics from limited observations. This study analyzes 30 earthquake records at the Sendai Port site, where observations consist solely of acceleration recordings at two points: bedrock (input) and ground surface (response). We examine three input-aware formulations: Dynamic Mode Decomposition with control (DMDc), its sliding-window variant (DMDswc), and Extended-Kalman-filter-based DMD with control (EKFDMDc). DMDc cannot explicitly track event-internal temporal evolution because it identifies a single operator per event, whereas DMDswc can recover temporal changes through moving windows but is more sensitive to noise. To address this trade-off, we extend EKFDMD by Nonomura et al. (2019), originally formulated for no-input systems, by incorporating the input operator into the augmented state and estimating two operators online. Real-data results show that EKFDMDc preserves temporal transitions of modal frequency and damping while suppressing estimate dispersion, providing more stable tracking than DMDc and less noise-sensitive behavior than DMDswc.