Multivariate Joint Probability Function of Earthquake Ground Motion Prediction Equations Based on Vine Copula Approach

Jun Du,Yin Cheng,Hao Ji

doi:10.1155/2020/1697352

Abstract

In the structural earthquake engineering, a single parameter is often not sufficient enough to depict the severity of ground motions, and it is thus necessary to use multiple ones. In this sense, the correlation among multiple parameters is generally considered as an importance issue. The conventional approach for developing the correlation is based on regression analysis, along with simple pair copula approaches proposed in recent years. In this study, an innovative mathematical technique—vine copula—is firstly introduced to develop the empirical model for the multivariate dependence of pseudospectral accelerations (PSAs), which are the most commonly used earthquake ground motion parameters. This advancement not only offers a more flexible way of describing nonlinear dependence among multivariate PSAs from the marginal distribution functions but also highlights the extreme dependence. The results can be conventionally acquired in the ground motion selection and seismic risk and loss assessment based on multivariate parameters.

Highlights

In the structural earthquake engineering, a single ground motion parameter (GMP) is often not sufficient enough to characterize the severity of earthquake ground motions, and it is necessary to use multiple ones
We investigate the multivariate dependence of pseudospectral accelerations (PSAs) using vine copula technique. e residuals of PSAs calibrated with equation (21) are used to model the multivariate dependence structure based on vine copula: rPSA ln PSAobs􏼁 − f(M, R, θ), (21)
In this study a multivariate joint probability function of PSAs at di erent vibration periods is calibrated using the vine copula technique. e dependence structure is developed based on a large set of ground motion data consisting of 1550 ground motion records

Summary

Introduction

In the structural earthquake engineering, a single ground motion parameter (GMP) is often not sufficient enough to characterize the severity of earthquake ground motions, and it is necessary to use multiple ones. The correlation model of earthquake parameters (such as PSAs at various vibration periods) is developed using regression analysis (such as [6,7,8]) on Pearson product-moment correlation coefficients which are derived from the residuals of the GMPEs. In recent years, copula techniques have been more and more widely applied in engineering [14,15,16,17,18] due to the advantages in the probabilistic analysis [19, 20]. It validates that the conventional twostep approach is appropriate to develop the correlation model These techniques can only describe a linear correlation and take a bivariate interperiod dependence of parameters into account. Since there are two orthogonal horizontal components for each ground motion record, we use the geometric mean of two components at different periods to calculate the interperiod dependence

Vine Copula Dependence

Multivariate Dependence Structure of Ground Motion Parameters

Vine Copula-Based Multivariate Dependence Structure

Conclusion