A Gibbs sampling algorithm for structural modal identification under seismic excitation

• Published in: Earthquake engineering & structural dynamics Vol. 47; no. 14; pp. 2735 - 2755
• Main Authors: Li, Binbin, Der Kiureghian, Armen, Au, Siu‐Kui
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.11.2018
• Subjects: Algorithms; Bayesian analysis; Computer simulation; Data; Earthquakes; Gibbs sampling; Identification; Mathematical models; Modal analysis; Modal identification; operational modal analysis; Parameter identification; Parameter uncertainty; Parameters; Probability theory; Robustness (mathematics); Sampling; Seismic activity; Seismic engineering; seismic excitation; Seismic response; State space models; state‐space model; Statistical analysis; Statistical methods; uncertainty quantification; White noise
• ISSN: 0098-8847; 1096-9845
• DOI: 10.1002/eqe.3094

Summary Identification of structural modal parameters under seismic excitation using operational modal analysis (OMA) is a challenging task because it violates the basic assumptions of OMA: linear time‐invariant model, stationary white noise input, and adequately long data. The consequence is significant uncertainties associated with the identified modal parameters. This study aims at developing an algorithm to quantify these uncertainties from a Bayesian perspective. Representing the structure and the seismic excitation by a state‐space model, a probabilistic OMA scheme is formulated. The analytical solution for the posterior statistics is not achievable, and a Gibbs sampling algorithm is developed to provide an efficient and robust numerical solution appropriate for practical applications. The performance of the proposed method is validated by identifying a shear‐type building using simulated response data under 4 recorded earthquake motions, and a supertall building—the One Rincon Hill in San Francisco—using field‐recorded data under seismic and ambient excitations. The computed posterior distributions of modal parameters represent the knowledge extracted from the measured data; they can be reliably used for model validation and health monitoring.