Performance-based bi-objective design optimization of wind-excited building systems

This paper proposes a framework for the bi-objective optimization of uncertain and dynamic wind-excited systems whose susceptibility to system-level damage is modeled through probabilistic fragility-based loss measures. In particular, the proposed framework is based on first reformulating the bi-objective stochastic optimization problem into a suite of single-objective optimization problems through the e-constraint approach. Secondly, a new optimization sub-problem is introduced for efficiently solving the single-objective problems, whose formulation is based on combining the auxiliary variable vector approach with a new kriging-enhanced approximation scheme. Because the sub-problem can be fully calibrated and subsequently solved from the results of a single performance assessment carried out in a fixed point of the design space, efficiency and scalability to high-dimensional problems is achieved. Through solving a sequence of sub-problems, solutions to the epsilon-constraint problems are obtained leading to the identification of the Pareto-optimal solutions of the original bi-objective optimization problem. To illustrate the applicability, efficiency and scalability of the proposed framework, an example of application to a large-scale structure is presented, where structural material volume and a system-level loss measure defined in terms of expectation and standard deviation of the total repair cost are simultaneously minimized.