Uncertainty Quantification of Structures with Unknown Probabilistic Dependency

It is common practice in the analysis of structural safety to assume that random variables are independent.   Assuming independence can result in significant underestimation of risk (Ferson et al. 2004).   In this talk, I will investigate methods for probabilistic analysis when the dependency between components of random variables is unknown.  The treatment of unknown dependency will be discussed in the context of finite element structural analysis.  To the authors knowledge, analysis of unknown dependency was first posed by Kolmogorov (Frank, Nelsen, Schweizer, 1987) “what are the optimal bounds for the probability distribution of a sum of two random variables X and Y whose individual distribution Fx and Fy are given?”   I will first review the treatment of dependency in terms of statistical moments and copulas.  The general problem of any-dependency will be addressed by using the bounding Fréchet–Hoeffding copulas.  The concept of probability bounds will then be discussed.   A finite element method for implementing probability bounds calculations will be presented.   Results of application of probability bounds on exemplar structures will be presented.   The impact of unknown dependency on the prediction of the safety of a structure will be discussed. 

Speaker Bio: Robert L. Mullen is Professor and Chair of the Department of Civil and Environmental Engineering at the University of South Carolina.  Prior to joining the faculty at South Carolina in 2010, he was the Frank Neff Professor and Chair of the Civil Engineering Department at Case Western Reserve University. Dr. Mullen received his PhD in Applied Mechanics from Northwestern University, under Ted Belytschko.  Prof. Mullen’s research is focused on computational mechanics and reliability.   He has modeled various MEMS based sensors for their intrinsic uncertainty in their measurements, developed a computer based vision system for condition monitoring of highway pavement for the Ohio Department of Transportation, as well as introducing methods to propagate independently epistemic and aleortory uncertainties through a finite element analysis.    He is the Co-Director of the Centre for Reliable Engineering Computing at Georgia Institute of Technology. He is a Fellow of the American Society of Civil Engineers, member of the American Society of Mechanical Engineers and the American Society for Engineering Education.

Presentation Slides: PPT

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