Model Falsification for Predicting Dynamical Responses of Uncertain Structural Systems

Abstract Accurate prediction of the dynamical response of a structural system depends on appropriate modeling of that system. However, modeling becomes increasingly challenging when numerous candidate models are available to describe the system behavior. Although different model classes can be used to represent the behavior of individual components of a dynamical system, uncertainties may still exist in the parameters of these model classes. The plausibility of each input-output model class for structures with uncertain components can be assessed within a Bayesian framework using measured dynamic responses to one or more input records, after which predictions of the structural response to alternative input records can be made. However, this approach may require a large number of model simulations, even though most candidate model classes are ultimately implausible. An approach is proposed herein to falsify models that fail to reproduce the measured data with sufficient accuracy. This is achieved by imposing a lower bound, derived from the false discovery rate (FDR), on the likelihood that each model would predict the observed data. Response prediction is then performed using the unfalsified models in an approximate Bayesian sense by assigning likelihood-based weights only to these models. When predicting responses to one or more new input scenarios, the proposed approach requires only a fraction of the computational cost of a standard Bayesian analysis since response simulations are not performed for models that have been falsified. The proposed response prediction framework is illustrated using three structural examples: a 4-degree-of-freedom (4-DOF) base-isolated building with a hysteretic isolation layer subjected to earthquake excitation; a 1,623-DOF three-dimensional building equipped with roof-mounted, tuned mass dampers (TMDs) and subjected to wind loading; and a full-scale, four-story building tested on the world’s largest shake table at Japan’s E-Defense laboratory. The results demonstrate highly accurate response predictions and significant computational savings, highlighting the potential of the proposed method.