Fuzzy systems methods in structural engineering

The simulation of dynamic physical systems requires using simplified linear models built upon idealized assumptions. Earthquake engineering and structural dynamics are two fields of study in structural engineering that use such models. These models are used because the traditional simulation paradigm does not allow for the simulation of ill-defined real world systems with complex nonlinear behavior.; Rigid blocks are idealized rigid structures used to formulate the governing equations of motion to simulate the response of rigid structures such as pre-cast concrete buildings, electric power transformers, historic monuments, and wine barrel stacks subject to ground motion. These types of systems have associated with them much uncertainty in both the defined parameters as well as the governing equations of motion. The goal of this dissertation is to assimilate uncertainty into a robust dynamic simulation model that accounts for nonlinear complexity.; Sources of uncertainty in dynamic physical system simulations abound. Ambiguous states, ignorance in the governing physical laws, imprecise geometrical measurements and ill-defined system parameters are just a few examples. Uncertainty theory is a recent concept that encompasses various theories such as probability theory, possibility theory, evidence theory and fuzzy systems theory in an attempt to quantify uncertainty depending on its source.; We are researching fuzzy systems theory as a new paradigm to physical system simulation that extracts linguistic fuzzy sets and rules from observations to form simulation results. We illustrate the usefulness of fuzzy systems theory on the simulation of the nonlinear and conditionally stable problem, rocking rigid blocks. Furthermore, we are researching how to optimize these fuzzy systems by using two rule-reduction methods: Singular Value Decomposition and Combs Method for Rapid Inference.