Active-learning Kriging-assisted robust design optimization of tuned mass dampers: Vibration mitigation of a steel-arch footbridge

Abstract

Many typical footbridges are designed as slender structures to highlight their aesthetic characteristic. As these bridges can be highly susceptible to pedestrian-induced excitations, tuned mass dampers have been adopted as energy absorbers in many applications to mitigate this issue. The design of tuned mass dampers can be formulated as a robust design optimization problem considering various sources of uncertainties related to the bridge state and environment. To alleviate the computational burden of analyzing the statistical moments, surrogate model-based approaches have been introduced to build cheaper-to-evaluate substitutes, and the analytical expression of the robustness has been discussed to facilitate the optimization procedure. Motivated by this, the present paper derives an analytical expression for the robustness index, considering both deterministic and uncertain variables as inputs of the ordinary Kriging surrogate model. An active-learning framework is proposed to streamline the design optimization of tuned mass dampers for the vibration mitigation of slender footbridges. Two numerical examples are firstly investigated to validate the performance of the proposed method; and then, a practical application of a steel-arch footbridge is carefully studied to demonstrate the engineering feasibility and superiority of the proposed method. The results exhibit that the proposed method can efficiently and accurately facilitate the robust design of vibration mitigation devices for practical engineering projects, and showcases the potential to be used in other engineering problems.