Copula‐based joint probability function for PGA and CAV: a case study from Taiwan

Abstract

Summary This study aims to develop a joint probability function of peak ground acceleration (PGA) and cumulative absolute velocity (CAV) for the strong ground motion data from Taiwan. First, a total of 40,385 earthquake time histories are collected from the Taiwan Strong Motion Instrumentation Program. Then, the copula approach is introduced and applied to model the joint probability distribution of PGA and CAV. Finally, the correlation results using the PGA‐CAV empirical data and the normalized residuals are compared. The results indicate that there exists a strong positive correlation between PGA and CAV. For both the PGA and CAV empirical data and the normalized residuals, the multivariate lognormal distribution composed of two lognormal marginal distributions and the Gaussian copula provides adequate characterization of the PGA‐CAV joint distribution observed in Taiwan. This finding demonstrates the validity of the conventional two‐step approach for developing empirical ground motion prediction equations (GMPEs) of multiple ground motion parameters from the copula viewpoint. Copyright © 2016 John Wiley & Sons, Ltd.

Ground Motion Models for the Horizontal Components of Arias Intensity (AI) and Cumulative Absolute Velocity (CAV) Using the NGA-West2 Database

“…In addition, several investigators have found that AI, CAV, or both sometimes in combination with other GMIMs are optimally correlated with EDPs proposed for buildings and bridges (e.g., Padget et al 2008, Fontara et al 2011, Katona 2012, Elenas 2013, Mollaioli et al 2013, Katona and Tóth 2013a, 2013b, Ebrahimian et al 2015, Hancilar and Çakti 2015, Perrault and Guéguen 2015, Tarbali and Bradley 2015, Massumi and Gholami 2016, Kiani and Pezeshk 2017, Muin and Mosalam 2017, Fiore et al 2018, Jahangiri et al 2018, Kiani et al 2018, Liang et al 2018, Mashayekhi et al 2018, Wang et al 2018). Other investigators have developed relationships correlating these GMIMs with amplitude- and spectrum-based GMIMs (e.g., Wang and Du 2012, Bradley 2012, Du and Wang 2013a, Liu et al 2016, Xu et al 2016) and ground motion duration measures (Bradley 2011). Tothong and Luco (2007), Roy et al (2014), Tarbali and Bradley (2015), Armstrong (2016), Kiani and Pezeshk (2017), Du and Wang (2018), and Yeow et al (2018) recommend that AI, CAV, or both should be included in the selection and scaling of scenario earthquake time series to capture important characteristics provided by these cumulative-based GMIMs that are not inherent in the use of amplitude- and spectrum-based GMIMs alone.…”

Copula‐based joint distribution analysis of wind speed and wind direction: Wind energy development for Hong Kong

“…Their detailed information and mathematical expressions are summarized in Table 1. The parameter ε in the copula functions can be adjusted by the inversion of the Kendall correlation coefficient τ 31,41 . It is noteworthy that the copula parameter ε is solely dependent on the correlation of two variables and has no association with the underlying marginal distributions.…”

Improved seismic risk evaluation for high‐voltage switchgear equipment: A copula‐based framework considering joint failure modes

“…Among numerous established Copula function models, it becomes possible to construct and select an optimized Copula function that accurately describes the joint distributions of multivariate variables. [40][41][42][43] A comprehensive introduction to Copula theory will be provided in Section 2.…”