Optimal Performance-Based Control of Structures against Earthquakes Considering Excitation Stochasticity and System Nonlinearity

摘要

Natural disasters are one of the constant challenges for designing new and strengthening existing infrastructures. Such hazards in the past have incurred significant loss of life and economic damage; therefore, further research is warranted in this area to enhance the health and minimize the cost of maintaining and upgrading infrastructures, improve residents’ comfort, and enable achieving higher levels of life safety. To this end, the field of hazard mitigation and control focuses on performance improvement, safety, and cost effectiveness of structures mostly through minimizing large deformations of seismic-excited structures and suppressing the damage and collapse in dynamic systems due to excessive vibrations.;Past developments in active and semi-active control designs, such as the commonly used state space controllers (e.g. linear quadratic regulator for fully observed systems and linear quadratic Gaussian for partially observed systems), consider linear feedback strategies. Meanwhile, such control strategies require linearization, and the system is usually linearized based on linear elastic properties. The control force is proportional to the state space vector and the dynamics and constraints of control devices are mainly ignored. The objective functions have restrictive forms, and are solely dependent on a second order convex function of the response variables. To overcome the aforementioned shortcomings, this dissertation develops new stochastic control algorithms for active and semi-active control strategies. This research concentrates on the development of frameworks that incorporate nonlinearity of the system, uncertainty of the excitation, and constraints and dynamics of the control device. Control designs are developed based on different objective functions such as higher order polynomials of response variables, reliability of the structure, and life cycle cost of the system considering hazard risks in seismic prone areas.;In particular, a nonlinear sliding mode control algorithm based on stochastic linearization is developed; this method supports higher order objective functions and therefore enhances the ability of designers to achieve design objectives. The proposed control algorithm is designed, optimized, and tested on a seismically excited multi-span bridge equipped with semi-active magnetorheological dampers. Next, a stochastic control algorithm is presented based on a proposed stochastic averaging method called enhanced stochastic averaging. This method conserves the nonlinear behavior of the system and the stochastic nature of the excitation in optimal control design. In order to directly minimize the probability of failures, the stochastic control algorithm is extended to a reliability-based control algorithm. These control algorithms are implemented in a system with nonlinear soil-structure interactions. Furthermore, a risk-based control methodology is developed to minimize life cycle cost of a nonlinear multi-story building subjected to seismic excitations. The findings of these proposed control methodologies are found to be superior to conventional control techniques. This doctoral research aims at filling a major gap in smart control technology in terms of conserving nonlinearity and stochasticity in control design. Moreover, they provide explicit optimization processes based on reliability and risk. Future investigations include advancing the proposed methods and applying them to different structural systems subjected to various hazard types.