Multi-objective parameter and topology optimization of structures equipped with tuned viscous mass dampers using automatic differentiation

Abstract

Traditional earthquake-resistant design often prioritizes low upfront costs by relying on structural ductility, which inherently leads to severe inelastic damage, high repair expenses, and extensive operational downtime following major seismic events. On the other hand, passive control technologies like tuned viscous mass dampers (TVMDs) offer supplemental damping without external power requirements, and allow to keep the structure essentially in the elastic range during extreme seismic events. However, optimizing both damper parameters and spatial topology within multiple-degree-of-freedom (MDOF) systems remains computationally prohibitive due to non-classical damping, modal interactions, and the non-smooth nature of real-world time-domain design objectives. To overcome these limitations, this study introduces an original formulation for the simultaneous multi-objective parameter and topology optimization of TVMDs. Furthermore, we propose a novel, high-performance computing framework that leverages hardware-accelerated automatic differentiation (AD) implemented via the PyTorch library that backs the latest developments in machine learning (ML) and artificial intelligence (AI). By treating the dynamic structural analysis program as a differentiable computation tree, exact, down to machine precision, sensitivities are systematically propagated through time-domain analyses and then used by the optimization algorithm. The proposed AD-powered framework bypasses the computational bottlenecks, truncation errors, and step-size sensitivities associated with conventional finite-difference gradient approximations. The efficiency and numerical robustness of the approach are validated using a ten-story benchmark shear building subjected to strong ground motions. The results demonstrate that the proposed method significantly accelerates the optimization convergence, lowers computational overhead, and provides structural engineers with a highly scalable tool to rapidly deliver safe, economic, and high-performance seismic designs.