Robust reliability-based design of liquid column mass dampers under earthquake excitation using an analytical reliability approximation

The robust reliability-based design of Tuned Liquid Column Dampers (TLCD) and Liquid Column Vibration Absorbers (LCVA) under earthquake excitation is studied. The design objective is the minimization of the probability of failure, where failure is defined as the first-passage of the dynamical system trajectory out of a hypercubic safe region in the space of the performance variables. These variables correspond to response characteristics of the system that are considered important. Versions of the approach are described for the case of a nominal model and the case considering model uncertainty. In the latter case the concept of robust probability of failure is employed which considers a set of possible models for the dynamic system. The nonlinear characteristics of the damper response are addressed by including the excitation intensity as an uncertain parameter in the system description. An analytical approximation is used for the reliability estimation that allows for computationally efficient, gradient-based design optimization. Numerical issues are discussed. The validity of the reliability approximation is checked by comparing the results to those derived through direct Monte Carlo simulation of the nonlinear model. Applications to dynamical systems with single and multiple degrees of freedom are presented. For the latter case, other standard control synthesis methods are also considered and significant differences are illustrated between them and robust reliability-based design. Although this study focuses on optimization of TLCDs and LCVAs, it shows the efficiency of the proposed methodology for other systems that also involve model uncertainty.