Quantification of margins and uncertainties of complex systems in the presence of aleatoric and epistemic uncertainty

A fuzzy-based approach for characterization of uncertainties in emergy synthesis: an example of paved road system

“…Moreover, sometimes particular data are deliberately hidden. Recently, numerous efforts have been made to gain better knowledge of systems, processes, or mechanisms in order to evaluate epistemic uncertainty (Urbina et al, 2011), and methods such as fuzzy logic and evidence theory are suggested to handle the epistemic type of uncertainty (e.g. Curcurù et al, 2012;Hanss and Turrin, 2010).…”

Quantification of margins and mixed uncertainties using evidence theory and stochastic expansions

“…Oberkampf et al [12] have described various methods for estimating total uncertainty by identifying all possible sources of variability, uncertainty and error in computational simulations. Urbina et al [13] proposed a methodology to quantify the margins and uncertainty in presence of mixed uncertainties through a framework based on Bayes networks and further developed a QMU metric in terms of probability of failure. A new formalism based on Bayesian inference, known as probabilistic QMU or pQMU, was introduced by Wallstrom [14], which was fully probabilistic and showed how QMU may be interpreted within the framework of system reliability theory.…”

An extended probabilistic method for reliability analysis under mixed aleatory and epistemic uncertainties with flexible intervals

“…Due to the necessity and importance of treating the aleatory and epistemic uncertainties properly with corresponding mathematical methods rather than simply using the traditional probabilistic methods to treat all the uncertainties as random ones under strong assumptions (Der Kiureghian and Ditlevsen 2009), there emerges increasing literature in recent years to address the reliability analysis problems under both aleatory and epistemic uncertainties, e.g. Fuzzy set theory (Zhang and Huang 2010;Li et al 2014;He et al 2015), random set theory (Oberguggenberger 2015) and probabilistic bounding analysis (Sentz and Ferson 2011), combined probabilistic and interval analysis method (Jiang et al 2013), combined probabilistic and evidence theory method (Du 2008;Eldred et al 2011;Yao et al 2013b), and other numerical approaches such as doubleloop Monte-Carlo Simulation (MCS) (Du et al 2009), perturbation based method (Gao et al 2010(Gao et al , 2011, encapsulation based method (Jakeman et al 2010;Chen et al 2013), families of Johnson distributions based probabilistic method (Urbina et al 2011;Zaman et al 2011), etc. Among these researches, one of the widely used methods is to model the epistemic uncertainties with intervals and generally the interval bounds are fixed.…”