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A Moment-based Correction for Non-stationarity in Random Vibration Theory

Random vibration theory (RVT) is a robust probabilistic tool for the bidirectional conversion between Fourier amplitude spectra (FAS) and expected pseudo-spectral acceleration (PSA) without explicit time domain information. In practice, RVT allows for the development of ground-motion models in the FAS domain and the computation of associated time domain peak values (e.g., PSA) for engineering analyses. This approach offers several advantages over traditional methods due to the inherent limitations of PSA, such as oscillator frequency interdependence, which presents challenges in ground motion development, limits adaptability, and restricts the utilization of small-magnitude motion data. However, earthquake ground motions do not meet the assumption of stationarity (i.e., time-invariant statistics), a fundamental assumption of RVT. Various authors have proposed adjustments to RVT to address this deficiency. These adjustments, which are typically developed using simulated time series, rely on additional parameters and often fail to capture the effects of spectral shape due to site response or regional differences. We present a new correction for RVT based on the moments of the FAS of the oscillator response. This approach is based on the theory of transient random vibrations and is calibrated to recorded earthquake ground motions. By using the moments of the FAS in the calculation of the correction factor, the factor changes as the shape of the FAS changes. The calibration is performed using records from the NGA-West2 database at multiple damping levels (0.5 to 30 %), and then tested against the NGA-East and a preliminary NGA-West3 databases. The results show that the proposed correction is robust.

Session: Data-driven and Computational Characterization of Non-earthquake Seismoacoustic Sources [Poster]

Type: Poster

Room: Exhibit Hall

Date: 4/16/2025

Presentation Time: 08:00 AM (local time)

Presenting Author: Albert Kottke

Student Presenter: No

Invited Presentation: 

Poster Number: 77

Additional Authors