Statistics Seminars: Efficient Monte Carlo strategies for dealing with aleatory and epistemic uncertainty
30 November 2015 14:00 in CM221
In many real world situations, engineers are not able to perfectly model or predict the performance of systems or components due to the quality and amount of information available and the presence of unavoidable uncertainty. The unavoidable uncertainties must be appropriately accounted to guarantee that the components or systems will continue to perform satisfactory despite fluctuations. Despite the different levels of uncertainty and imprecision, it is still necessary to be able to propagate the uncertainty through the model and quantify the risk. In particular, decision makers need to know the confidence associated with the methodology adopted to model the uncertainty and avoid wrong decisions due to artificial restrictions introduced by the modelling.
Hence, a generalized uncertainty quantification methodology for dealing with different representation of the uncertainty is needed as shown by the NASA Langley Uncertainty Quantification Challenge problem . The challenge problem has been the catalyst for the further development of uncertainty quantification strategies and tools for extreme case analysis [2,5,7].
This talk presents a generally applicable and efficient simulation approach for dealing with aleatory and epistemic representation of the uncertainty . The theoretical framework of random set is used to represent in a unified framework different representation of the uncertainty such as random variables, probability boxes, intervals and fuzzy variables . Efficient advanced Monte Carlo sampling techniques based on Line Sampling and "forced" Monte Carlo methods are proposed. The approach can be applied to estimate efficiently e.g . the bounds of the failure probability  and the reliability of a complex systems using survival signature .
Finally, an application for the robust design of inspection schedules of a fatigue-prone weld in a bridge girder is presented .
 Crespo, L. G. & S. P. Kenny (2015). Special edition on uncertainty quantification of the AIAA journal of aerospace computing, information, and communication. Journal of Aerospace Information Systems 12(1), 1–9.
 Patelli, E., D. A. Alvarez, M. Broggi, & M. de Angelis (2015). Uncertainty management in multidisciplinary design of critical safety systems. Journal of Aerospace Information Systems 12, 140–169.
 Patelli, E., M. Broggi, M. Angelis, & M. Beer (2014). Opencossan: An efficient open tool for dealing with epistemic and aleatory uncertainties. In Vulnerability, Uncertainty, and Risk, pp. 2564–2573. American Society of Civil Engineers.
 Klir, G. J. (2006). Uncertainty and Information : Foundations of Generalized Information Theory. New Jersey: John Wiley and Sons.
 Patelli, E. & de Angelis, (2015) M. Line Sampling approach for Extreme Case Analysis in presence of Aleatory and Epistemic Uncertainties Safety and Reliability of Complex Engineered Systems: ESREL 2015 7-10 September, CRC Press / Balkema.
F. P. Coolen, T. Coolen-Maturi, (2012) Generalizing the signature to systems with multiple types of components, in: Complex Systems and Dependability, Springer, pp. 115–130.
 Angelis, M.; Patelli, E. & Beer (2015), M. Robust design of inspection schedules by means of probability boxes for structural systems prone to damage accumulation Safety and Reliability of Complex Engineered Systems: ESREL 2015 7-10 September, CRC Press / Balkema.
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