Structural reliability analysis via dimension reduction, adaptive sampling, and Monte Carlo simulation

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.

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Structural reliability analysis on the basis of small samples: An interval quasi-Monte Carlo method

Mechanical Systems and Signal Processing ◽

10.1016/j.ymssp.2012.03.001 ◽

2013 ◽

Vol 37 (1-2) ◽

pp. 137-151 ◽

Cited By ~ 81

Author(s):

Hao Zhang ◽

Hongzhe Dai ◽

Michael Beer ◽

Wei Wang

Keyword(s):

Monte Carlo ◽

Monte Carlo Method ◽

Reliability Analysis ◽

Structural Reliability ◽

Small Samples ◽

Quasi Monte Carlo ◽

Structural Reliability Analysis

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RCA-PCK: A new structural reliability analysis method based on PC-Kriging and radial centralized adaptive sampling strategy

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406220957711 ◽

2020 ◽

pp. 095440622095771

Author(s):

Zhenliang Yu ◽

Zhili Sun ◽

Runan Cao ◽

Jian Wang ◽

Yutao Yan

Keyword(s):

Reliability Analysis ◽

Failure Probability ◽

Adaptive Sampling ◽

Structural Reliability ◽

Sampling Strategy ◽

Kriging Model ◽

Strong Nonlinearity ◽

Analysis Method ◽

Structural Reliability Analysis ◽

Training Samples

To improve the efficiency and accuracy of reliability assessment for structures with small failure probability and time-consuming simulation, a new structural reliability analysis method (RCA-PCK) is proposed, which combines PC-Kriging model and radial centralized adaptive sampling strategy. Firstly, the PC-Kriging model is constructed by improving the basis function of Kriging model with sparse polynomials. Then, the sampling region which contributes a great impact on the failure probability is constructed by combining the radial concentration and important sampling technology. Subsequently, the k-means++ clustering technology and learning function LIF are adopted to select new training samples from each subdomains in each iteration. To avoid the sampling distance in one subdomain or the distance between the new training samples in two subdomains being too small, we construct a screening mechanism to ensure that the selected new training samples are evenly distributed in the limit state. In addition, a new convergence criterion is derived based on the relative error estimation of failure probability. Four benchmark examples are given to illustrate the convergence process, accuracy and stability of the proposed method. Finally, the transmission error reliability analysis of thermal-elastic coupled gears is carried out to prove the applicability of the proposed method RCA-PCK to the structures with strong nonlinearity and time-consuming simulation.

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