Events

Floods, tsunamis and earthquakes and violent vibrations of dynamical systems are commonly described by extremes of random functions of time and/or space. Generally, these functions satisfy stochastic equations, i.e., equations with random entries. Analytical solutions of these types of equations, referred to as target solutions, are available in special cases. Most stochastic equations encountered in applications have to be solved by numerical methods. Their implementation requires us to represent the input random functions by finite dimensional (FD) models, i.e., deterministic functions of time/space and finite sets of random variables. The resulting solutions, referred to as FD solutions, are FD models depending on the set of random variables of the input FD models. Our objective is to establish conditions under which FD solutions can be used as surrogates for target solutions. Under these conditions, the distributions of extremes of target solutions can be estimated from samples of FD solutions, which can be generated by standard algorithms. The talk will present theoretical arguments related to representation of target solutions by FD solutions and illustrate them by numerous examples dealing with dynamical systems and microstructures.

Professor Mircea Grigoriu received degrees in Civil Engineering and Mathematics from the Bucharest Institute of Civil Engineering and the University of Bucharest, Romania, respectively. He received his PhD in Civil Engineering from MIT. His research interests are in random vibration, stochastic calculus, numerical methods for solving stochastic problems, probabilistic models for microstructures, wind/earthquake engineering, climate models, and Monte Carlo simulation. He is the author of over 200 journal papers, a co-author of a book on random vibration, and the author of three books on non-Gaussian processes, Stochastic Calculus, and Stochastic Systems. His research and education efforts have been recognized by the 1993 IASSAR Research Prize, the 1998 SAE Distinguished Probabilistic Methods Education Award, the election to the Romanian Academy of Technical Sciences (2004), the 2002 Alfred Freudenthal Medal, Daniel M. Lazar '29 Excellence in Teaching Award (2003), Doctor Honoris Causa from the Technical University of Civil Engineering, Bucharest, Romania (2004), and the 2005 Norman Medal of ASCE. Prof. Grigoriu is on the editorial board of the Probabilistic Engineering Mechanics, Structural Safety journals, International Journal of Reliability and Safety, and Structure and Infrastructure Engineering Journal, and he is a past Editor in Chief for the Journal of Engineering Mechanics.