Assessment of Uncertainty Propagation in the Dynamic Response of Single-Degree-of-Freedom Structures Using Reachability Analysis

A novel method to compute the bounds of the response of structures to dynamic loads, including earthquakes, is presented. This method, based on reachability analysis, deterministically predicts the sets of states an elastic structural system can reach under uncertain dynamic excitation starting from uncertain initial conditions, where deterministic uncertainty ranges describe uncertainties. Ellipsoidal approximations of these reachable sets for three canonical dynamic problems are presented to demonstrate the applicability of this method to single-degree-of-freedom (SDOF) systems. The principle of superposition is formulated as a concatenation of ellipsoidal reachable sets using their semigroup properties. Using this extension, computation of the external (worst-case) ellipsoidal approximation of reachable sets for a SDOF system under earthquake excitation is presented. Possible applications of this method for software validation and hybrid simulation are discussed.