Rocking rigid blocks simulations using fuzzy systems theory with rule reduction

Abstract

In an attempt to understand the nonlinear and poorly conditioned phenomena of the response of rigid structures subject to ground motion or vibrating (rocking) freely, these structures are idealized as rigid blocks. Despite this idealization, the problem of simulating the response of rigid blocks is still a very difficult problem in solid mechanics. This work represents a new paradigm to simulate this complex problem, by using linguistic descriptions of the system behavior within a fuzzy systems environment. This work also addresses computational efficiencies using rule-base reduction. Two methods for rule-base reduction are implemented, Singular Value Decomposition and Combs Method for Rapid Inference. These methods have been previously shown to be effective for reducing rule-base size. The two methods are compared on the same physical system. This comparison elucidates their accuracy and limitations.