Probabilistic Active Control of Structures Using a Probabilistic Fuzzy Logic Controller

Because uncertainty is inherent in engineering structures, it is essential to improve the procedures of structural control. The present study focuses on applying a probabilistic fuzzy logic system (PFLS) in active tendons for the covariance response control of buildings. In contrast to an ordinary fuzzy logic system, PFLS integrates the probabilistic theory into a fuzzy logic system that can handle the linguistic and stochastic uncertainties existing in the process. To investigate the proficiency of the proposed controller, a single degree of freedom (SDOF) system and a three-story multiple degree of freedom (MDOF) system with different arrangements of tendons on the floors are considered. The structures are subjected to a random dynamic load modeled using Gaussian white noise, and the modeling parameters such as damping, stiffness, and mass are considered to be random Gaussian samples with a dispersion coefficient of 10%. The results of the proposed intelligent control scheme are compared with those of an uncontrolled structural model and a linear quadratic regulator (LQR) controller model. The numerical results reveal that the probabilistic fuzzy logic controller (PFLC) is more efficient than the LQR controller in decreasing the structural covariance responses. Moreover, the maximum and minimum reductions in displacement responses for the MDOF structures are, respectively, about 36% and 12.5%compared to the LQR controller. It is also showed that the PFLC is more accurate because it includes stochastic uncertainty.