Prof. Ioannis Kougioumtzoglou,Ioannis Kougioumtzoglou photo
Assistant Professor, Dept. of Civil Engineering & Engineering Mechanics, Columbia University, USA
Compressive Sensing and Path Integral Techniques for Uncertainty Modeling and Propagation in Complex Dynamic Systems

Thursday, Dec 3, 2015, 3:00pm to 4:00pm | Room 3-350

Abstract

"...The ubiquity of uncertainty in computational estimates of reality and the necessity for its quantification..." has been recently recognized by the National Academies / Research Council. In this regard, a large portion of the engineering mechanics/dynamics community has focused on multi-scale/physics problems with stochastic media properties, random excitations and uncertain initial/boundary conditions. Two main challenges associated with uncertainty treatment relate to the (A) modeling, and the (B) propagation of the uncertainties.

- Addressing challenge (A) relates to the development of methodologies for the interpretation/analysis of measured/available data, as well as for the estimation of pertinent stochastic models, i.e. quantification of the underlying stochastic process/field statistics. Nevertheless, in real-life situations, (A.1): measured/available data most often exhibit a time/space-varying behavior, and (A.2): most often there are limited, incomplete and/or missing data. Currently, there exist very few (if any) methodologies that can address both cases (A.1) and (A.2) simultaneously in a consistent, efficient manner. In this regard, in the first part of the seminar talk some preliminary results for spectral analysis and stochastic process/field statistics quantification subject to vastly sparse/limited/incomplete data will be presented based on the emerging concept of Compressive Sensing (CS). Preliminary work indicates satisfactory accuracy for up to 80% missing data.

- Addressing challenge (B) relates to the development of methodologies for determining the complex system response/reliability statistics, i.e. development of analytical/numerical methodologies for solving nonlinear high-dimensional stochastic (partial) differential equations efficiently. Monte Carlo Simulation (MCS) has been the most versatile approach for addressing this challenge. However, it can be computationally prohibitive for relatively large-scale complex systems, or when the quantity of interest has a small probability of occurrence (e.g. failure probability). In this regard, in the second part of the talk some preliminary results for efficient response determination and reliability assessment of complex stochastic systems will be presented based on the potent concept of the Wiener Path Integral (WPI). Preliminary work indicates gaining orders of magnitude in terms of computational efficiency as compared to standard MCS based schemes.

Short Bio:

Dr. Ioannis A. Kougioumtzoglou received his five-year Diploma in Civil Engineering from the National Technical University of Athens in Greece (2007), and his M.Sc. (2009) and Ph.D. (2011) degrees from the Department of Civil and Environmental Engineering at Rice University, USA. In 2011 he started his academic career as a Lecturer in Uncertainty & Engineering at the School of Engineering, and as a member of the Institute for Risk and Uncertainty at the University of Liverpool, UK. In September 2014, Dr. Kougioumtzoglou joined Columbia University, USA, as an Assistant Professor at the Department of Civil Engineering & Engineering Mechanics.