Automatic optimal design of passive vibration control devices for buildings using two-level evolutionary algorithm

Unlike most studies on passive vibration control devices wherein mechanical topologies are fixed and only parameters need to be optimized, this study proposes a generic automatic design approach for both topology and parameters to explore control devices built up from different topological permutations of inerters, dampers, springs, rigid links, empty links, and auxiliary masses. The design problem is first transformed into a constrained multi-objective optimization problem (CMOP), whose objectives and constraints can be customized according to requirements and practical considerations. To prevent missing optimal control devices during solution processes, the CMOP is further divided into two coupled CMOPs addressing topology- and parameter-related variables separately. Correspondingly, a two-level (outer and inner) evolutionary algorithm is proposed to solve the coupled CMOPs. The effectiveness of the proposed design approach is numerically verified under two cases, i.e., a 3-story building under ground-motion excitation and a 64-story tall building under wind loading. Two representative automatically-designed control devices are compared with tuned mass damper-inerter (TMDI) and tuned viscous mass damper (TVMD) in terms of response reduction and robustness evaluated by exerting perturbations on the mass, damping, and stiffness matrices of the uncontrolled structure. The obtained control devices outperform TMDI and TVMD in both cases on at least one objective. Especially in the second case, 13.5% and 17.3% more reduction on responses with only 52.9% and 36.0% sensitivity to perturbations in comparison to TMDI and TVMD are achieved, respectively.