A fundamental study on introducing time-delay embedding to enhance the applicability of dynamic mode decomposition for seismic response analysis

Abstract

Mechanics-based seismic response analysis methods have significantly improved structural design and risk assessment. However, these methods require detailed geotechnical investigations and have computational limitations in large-scale applications. This study aims to develop an accurate, data-driven approach for geotechnical-seismic response analysis, particularly in expansive urban areas where the demand for resilience-focused risk control is increasing. Our foundational research emphasizes a data-driven methodology that utilizes simultaneous observations from both the ground surface and engineering bedrock, paving the way for broader regional applications. Various complex data-driven models based on neural networks have been developed and proven effective. However, interpretable linear system models remain highly valuable in practical engineering applications. By leveraging dynamic mode decomposition (DMD), we explored a modeling approach that preserves the interpretability of linear models while capturing the seismic behavior complexity as effectively as possible. The primary objective of this study is to evaluate a learning model employing DMD using seismic data from a critical port facility in Japan, while identifying practical implementation challenges. Our analysis demonstrates that applying a time-delay embedding with carefully calibrated delays effectively reconstructs the dynamic characteristics of earthquake motion amplitude and soil material nonlinearity. However, we also identified a tendency of the model to produce biased predictions when exposed to unfamiliar and untrained earthquake motions. This limitation primarily stems from the challenges of accurately capturing nonlinear soil behavior. The study demonstrates both the strengths and limitations of linear machine-learning models enhanced by time-delay embedding, while suggesting possible directions for integrating nonlinear machine-learning approaches.