Uncertainty Analysis: A Dynamical Systems Approach

Igor Mezic, Mechanical Engineering, University of California Santa Barbara

Parametric and initial condition uncertainty is studied within a unified framework based on dynamical systems theory. A notion of uncertainty based on cumulative probability distribution of observables dynamically evolving on the >phase space is defined and its properties discussed using transfer operators (Peron-Frobenius and Koopman). Of particular interest are nonlinear processes for which parametric uncertainty encompasses bifurcation points - for which traditional methods such as sensitivity analysis fail. Uncertainty in systems having chaotic dynamics is discussed. The two-fold role of nonlinearities in uncertainty propagation - shrinking of uncertainty in the stable directions and expansion in unstable directions - is presented through simple examples.