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AKOIS: An adaptive Kriging oriented importance sampling method for structural system reliability analysis

Abstract A major issue in the structural reliability analysis is to determine an accurate estimation result of the failure probability ideally based on a small number of model evaluations. In this regard, the active-learning Kriging based importance sampling method has been received considerable attentions. However, the utility of the most probable failure point (MPP) as the unique sampling center has limited its potential applications for multi-MPP problems. To this end, the paper presents an a...

Polymorphic uncertainty modeling for the simulation of geometric imperfections in probabilistic design of cylindrical shells

Abstract Geometric imperfections are part of the disagreement between theoretically and experimentally determined buckling loads of cylindrical shells. Due to the random nature of the initial deviations, a probabilistic approach is used to predict the buckling loads, where spatial varying imperfections are modeled as Gaussian random fields. The shape of the fields depends, among others, on the autocorrelation structure, which depends on the manufacturing process. Underlying uncertainties like a ...

AK-ARBIS: An improved AK-MCS based on the adaptive radial-based importance sampling for small failure probability

Abstract The pivotal problem in reliability analysis is how to use a smaller number of model evaluations to get more accurate failure probabilities. To achieve this aim, an iterative method based on the Monte Carlo simulation and the adaptive Kriging (AK) model (abbreviated as AK-MCS) has been proposed in 2011 by Echard et al. But for small failure probability, the number of the candidate points is extremely large for convergent solution. These points need to be evaluated by the current Kriging ...

A combined Importance Sampling and active learning Kriging reliability method for small failure probability with random and correlated interval variables

Abstract The existing hybrid reliability analysis (HRA) method (Yang et al., 2015; Zhang et al., 2015; Yang et al., 2015) is found not suitable for estimating small failure probabilities. Meanwhile, the previous ALK-HRA algorithm (ALK-HRA: an active learning HRA method combining Kriging and Monte Carlo simulation) reduces its numerical efficiency when number of uncertain variables increases. Furthermore, the ALK-HRA approach with both random and interval/ellipsoid variables cannot deal with comp...

Abstract This paper proposes numerical strategies to robustly and efficiently propagate probability boxes through expensive black box models. An interval is obtained for the system failure probability, with a confidence level. The three proposed algorithms are sampling based, and so can be easily parallelised, and make no assumptions about the functional form of the model. In the first two algorithms, the performance function is modelled as a function with unknown noise structure in the aleatory...

Abstract Eurocode 7 recommends that when statistical methods are used, the characteristic value of a geotechnical parameter can be selected as the 0.05 quantile. However, Eurocode 7 does not state how to select characteristic values when there are multiple correlated input geotechnical parameters, e.g., cohesion and friction angle. One possible interpretation is that the 0.05 quantile has to be applied to each geotechnical parameter. Another possible interpretation is that the 0.05 quantile shou...

Abstract Recent developments in theory and solution algorithms have facilitated the application of Bayesian Probabilistic Networks (BPNs) to probabilistic engineering problems. BPNs’ ability to easily perform backward analysis and parameter updating offers advantage over existing methods. This paper attempts to propose a BPN for reliability assessment of structural systems based on their cut-set representation. A five-layer Bayesian network is proposed which includes random variables, component ...

Normalization of correlated random variables in structural reliability analysis using fourth-moment transformation

Abstract In this paper, a fourth-moment transformation technique is proposed to transform correlated nonnormal random variables into independent standard normal ones. The procedure mainly includes two steps: First, the correlated nonnormal random variables are transformed into correlated standard normal ones using the fourth-moment transformation, where the complete mathematical formula of the correlation coefficient in standard normal space, i.e., equivalent correlation coefficient, is proposed...

An efficient new PDEM-COM based approach for time-variant reliability assessment of structures with monotonically deteriorating materials

Abstract Life-cycle time-variant reliability of engineering structures with material deterioration is of paramount importance but still a great challenge. Generally, the computational costs due to embedded structural analyses tracing the life-cycle performance process with monotonically deteriorating material, are prohibitively large. In the present paper, a new method by synthesizing the probability density evolution method (PDEM) and the change of probability measure (COM) is proposed for this...

Abstract Reliability analysis of deteriorating structural systems requires the solution of time-variant reliability problems. In the general case, both the capacity of and the loads on the structure vary with time. This analysis can be approached by approximation through a series of time-invariant reliability problems, which is a potentially effective strategy for cases where direct solutions of the time-variant reliability problem are challenging, e.g. for structural systems with many elements ...

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