Assessment of ground motion amplitude scaling using interpretable Gaussian process regression: Application to steel moment frames

Jawad Fayaz, Pablo Torres-Rodas, Miguel Medalla, Farzad Naeim

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The process of ground motion selection and scaling is an integral part of hazard- and risk-consistent seismic demand analysis of structures. Due to the lack of ground motion records that naturally possess high amplitude and intensity, the research community generally relies on scaling the records to match a target hazard intensity level. The scaling factors used are frequently as high as 10. Due to the criticism received in previous research studies, the extent of amplitude scaling and its process has become a matter of debate, and various constraints on the scaling factors have been proposed. The primary argument against unrestricted amplitude scaling is the unrealistic nature of the scaled records and the possible biases caused in the engineering demand parameters (EDPs) of structures. This study presents a framework to utilize machine-learning and statistical techniques for the assessment of ground motion amplitude scaling for nonlinear time-history analysis (NTHA) of structures. The framework utilizes Bayesian non-parametric Gaussian process regressions (GPRs) as surrogate models to obtain statistical estimates of EDPs for scaled and unscaled ground motions. The GPR surrogate models are developed based on a large-scale analysis of five steel moment frames (SMFs) using 200 unscaled as-recorded ground motions for ten spectral acceleration levels, ((Formula presented.)) (ranging from 0 g to maximum considered earthquake, MCE) and 2500 scaled ground motions representing 50 scale factors ((Formula presented.)), and the 10 (Formula presented.) levels for each SMF. For each building, two types of EDPs are considered: i) peak inter-story drift ratio (PIDR) and ii) peak floor acceleration (PFA). To provide a better interpretation of the GPR surrogate models, the concept of explainable artificial intelligence (i.e., Shapley additive explanation, SHAP) is used to obtain insights into the decision-making process of the GPR models with respect to the (Formula presented.) and (Formula presented.). Then, for the 10 (Formula presented.) levels, the GPR-based EDP estimates under scaled ground motions corresponding to 50 different SFs are compared with the EDP estimates of unscaled ground motions. The comparison is conducted using Kolmogorov–Smirnov (KS) statistical hypothesis test. Results indicate that the range of allowable (Formula presented.) s depends on two factors: i) intensity level (characterized by (Formula presented.)), and ii) the dynamic properties of the building. In general, it is noticed that allowable (Formula presented.) s range between 0.5 and 3.0 for PIDRs, and from 0.6 to 2.0 for PFAs. Finally, the EDP between the unscaled and scaled ground motions are adhered to various discrepancies observed in different intensity measures representing amplitude-, duration-, energy-, and frequency- content of the two sets of ground motions.

Original languageEnglish
JournalEarthquake Engineering and Structural Dynamics
Early online date7 Jan 2023
Publication statusE-pub ahead of print - 7 Jan 2023

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© 2023 The Authors. Earthquake Engineering & Structural Dynamics published by John Wiley & Sons Ltd.


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