Plenary Talk

Studies of Nonlinear Stochastic Dynamic Systems with Concepts and Methods from Data Science

November 23, 9:00-11:00 Am, Central Time 

Jian-Qiao Sun

Professor and Chair, ASME Fellow,
Department of Mechanical Engineering,
School of Engineering,
University of California, USA

Abstract: We are now in the age of data science when machine learning and artificial intelligence are beginning to reshape the traditional engineering research.  Examples of applications of machine learning, for example, are plenty already and are still coming out in large numbers.  While the research in fault detection and diagnosis has led the way to adopt the concepts of data science, other applications are fast growing including system identification, control design and response analysis of complex nonlinear systems. This talk reports recent applications of the concepts of data science to global analysis of nonlinear dynamic systems and to the solution of Fokker-Planck-Kolmogorov (FPK) equation of nonlinear stochastic dynamic systems. We outline the steps to conduct global analysis of nonlinear dynamical systems based on the observed responses of the system only without the knowledge of the system.  We use the generalized cell mapping method as a vehicle to achieve the objective of global analysis.  Some interesting examples are presented.  For stochastic systems, we introduce a highly efficient method for finding solutions of the FPK equation of high dimensional nonlinear stochastic dynamic systems.  Both the efficiency and accuracy of the solution have been substantially improved as compared to the studies reported about four years ago.