M5 model tree and Monte Carlo simulation for efficient structural reliability analysis

Offshore riser systems are subjected to wind, wave and current loadings, which are random in nature. Nevertheless, the current deterministic based design and analysis practice could not quantitatively evaluate the safety of structures taking random environmental loadings into consideration, due to high computational costs. Structural reliability method, as an analysis tool to quantify probability of failure of components or systems, can account for uncertainties in environmental conditions and system parameters. It is particularly useful in cases where limited experience exists or a risk-based evaluation of design is required. Monte Carlo Simulation (MCS) method is the most widely accepted method and usually used to benchmark other proposed reliability methods. However, MCS is computationally demanding for predicting low failure probabilities, especially for offshore dynamic problems involving many types of uncertainties. Innovative structural reliability methods are desired to perform reliability analysis, so as to predict the low failure probabilities associated with extreme values. Variety of structural reliability methods are proposed in the literature to reduce the computational burden of MCS. The post processing methods, which recover PDF or tail distribution of random variable from sample data to perform structural reliability analysis, have great advantages over the methods from other categories on solving engineering problems. Thus the main focus of our study is on post processing structural reliability methods. In this paper, four post processing reliability methods are compared on the prediction of low failure probabilities with applications to a drilling riser system and a steel catenary riser (SCR) system: Enhanced Monte Carlo Simulation (EMCS) assumes the failure probability follows the asymptotic behavior and uses high failure probabilities to predict low failure probabilities; Multi-Gaussian Maximum Entropy Method (MGMEM) assumes the probability density function (PDF) is a summation of Gaussian density functions and adopts maximum entropy methods to obtain the model parameters; Shifted Generalized Lognormal Distribution (SGLD) method proposes a distribution that specializes to the normal distribution for zero skewness and is able to assume any finite value of skewness for versatility; and Generalized Extreme-Value Distribution method (GEV) comprises three distribution families: the Gumbel-type, Frechet-type and Weibull-type distribution. The study compares the bias errors (the difference between the predicted values and the exact values) and variance errors (the variability of the predicted values) of these methods on the prediction of low failure probabilities with applications to two riser systems. This study could provide offshore engineers and researchers feasible options for marine riser system structural reliability analysis.

Download Full-text