Copula-based approach coupling information diffusion distribution for slope reliability analysis

Copula‐based importance sampling method for efficient slope reliability analysis

“…According to our previous studies, 42 different copulas describe different dependence structures. Therefore, the estimation accuracy of the joint distribution is significantly affected by the copulas.…”

“…From Equations (8) and (10), it can be found that different copulas describe different dependence structures. Therefore, the optimal copula function is commonly selected by the Akaike information criterion (AIC) and Bayesian information criterion (BIC), which are defined as follows 42 : $$$$\begin{equation}AIC = 2k - 2\sum_{j = 1}^m {\ln {\bf{D}}({u}_1,{u}_2, \ldots {u}_m)} ,\end{equation}$$$$ $$$$\begin{equation}BIC = k \cdot \ln n - 2\sum_{j = 1}^m {\ln {\bf{D}}({u}_1,{u}_2, \ldots {u}_m)} ,\end{equation}$$$$where k is the number of parameters in the estimation model. The model associated with the minimum AIC and BIC scores is considered to be the preferable candidate.…”

“…To this end, arbitrary margins can be dependently integrated together. Recently, copulas have been introduced to slope reliability analysis 39–45 . For instance, Fang et al 40 .…”

“…constructed cross‐correlated random fields of soil profiles based on copulas and carried out a probabilistic assessment of the soil slope. Zhou et al 42 . investigated the effects of correlations between variables on the slope reliability using copulas.…”

“…Recently, copulas have been introduced to slope reliability analysis. [39][40][41][42][43][44][45] For instance, Fang et al 40 modeled bivariate stochastic processes and their dependencies using copulas. Wang et al 41 constructed cross-correlated random fields of soil profiles based on copulas and carried out a probabilistic assessment of the soil slope.…”