Double control law multi-hazard AMD design through particle swarm optimization under LCC constraints

Abstract

An innovative double control law strategy is proposed for active mass dampers (AMDs) considered for tall buildings under multi-hazard conditions. In this strategy, the AMDs operate with one control law for wind loads and a different control law for earthquakes. Both laws are designed using an LQR optimal control formulation, defined through an optimization problem with probabilistic constraints. While the damper mass is the primary cost component, the multi-hazard life-cycle cost (LCC) - that is, the long-term hazard-induced restoration cost - is the primary design constraint. The weighting matrices Q and R serve as indirect design variables, defining the balance between performance improvement and cost reduction. The optimization is performed with the particle swarm optimization (PSO) algorithm, embedded in two solution strategies: a direct approach and a 3-step approach. The computational demand is reduced by an efficient model-reduction technique. Results show that double control laws outperform the single-law strategy for identical LCC reductions, with savings of 13.4 - 27.7% when using the double-law solutions from the 3-step approach. This improvement is mainly due to the enhanced seismic control achieved by adopting the double-law strategy. Additional analyses indicate that the adopted model reduction does not degrade control performance and does not introduce stability issues.