The effect of copulas on time-variant reliability involving time-continuous stochastic processes: Fid-Bau Portal

The effect of copulas on time-variant reliability involving time-continuous stochastic processes

Rózsás, Árpád / Mogyorósi, Zsuzsa

Highlights•Gauss copula is almost exclusively used to model dependence.•Investigated the effect of Gauss copula assumption on time-variant reliability.•Demonstrated that Gauss copula can ten times overestimate failure probability.•Snow extreme observations do not support Gauss copula.•Copula function uncertainty should be considered.

AbstractIn structural reliability the dependence structure between random variables is almost exclusively modeled by Gauss (normal or Gaussian) copula; however, this implicit assumption is typically not corroborated. This paper is focusing on time-variant reliability problems with continuous stochastic processes, which are collection of dependent random variables and to our knowledge are not modeled by other than Gauss copula in structural reliability. Therefore, the aim of this contribution is to qualitatively and quantitatively analyze the impact of this copula assumption on failure probability. Three illustrative examples are studied considering bivariate Gauss, t, rotated Clayton, Gumbel, and rotated Gumbel copulas. Time-variant actions are modeled as stationary, ergodic, continuous stochastic processes, and the PHI2 method is adopted for the analyses. The calculations show that the copula function has significant effect on failure probability. In the studied examples, application of Gauss copula can four times underestimate or even 10 times overestimate failure probabilities obtained by other copulas. For normal structures agreement on copula type is recommended, while for safety critical ones inference of copula type from observations is advocated. If data are scare, multiple copula functions and model averaging could be used to explore this uncertainty.