Modal Parameter Identification Using Eigensystem Realization Algorithm (ERA)

This documentation presents the source code implementation of the Eigensystem Realization Algorithm (ERA) for modal parameter identification, which enables structural modal analysis under ambient excitation conditions. To facilitate deeper understanding of the methodology, we first examine the background and fundamental principles of ERA, along with its applications in structural dynamics. The ERA method represents a modal parameter identification technique based on signal processing and system identification theory, capable of extracting modal parameters - including natural frequencies, damping ratios, and mode shapes - directly from structural response data. The implementation typically involves constructing Hankel matrices from response measurements, performing singular value decomposition for system order determination, and solving state-space models to obtain modal characteristics. In practical applications, ERA has been extensively utilized in structural health monitoring, damage diagnosis, and optimization design. Therefore, mastering modal parameter identification techniques is crucial for structural engineering applications. The provided code includes key functions for data preprocessing, system realization, and modal validation, implementing the core algorithm through matrix operations and eigenvalue solutions.