Efficient optimal design and design‐under‐uncertainty of passive control devices with application to a cable‐stayed bridge

Abstract

Structures today may be equipped with passive structural control devices to achieve some performance criteria. The optimal design of these passive control devices, whether via a formal optimization algorithm or a response surface parameter study, requires multiple solutions of the dynamic response of that structure, incurring a significant computational cost for complex structures. These passive control elements are typically point-located, introducing a local change (possibly nonlinear, possibly uncertain) that affects the global behavior of the rest of the structure. When the structure, other than these localized devices, is linear and deterministic, conventional solvers (e.g., Runge-Kutta, MATLAB's ode45, etc.) ignore the localized nature of the passive control elements. The methodology applied in this paper exploits the locality of the uncertain and/or nonlinear passive control element(s) by exactly converting the form of the dynamics of the high-order structural model to a low-dimensional Volterra integral equation. Design optimization for parameters and placement of linear and nonlinear passive dampers, tuned mass dampers, and their combination, as well as their design-under-uncertainty for a benchmark cablestayed bridge, is performed using this approach. For the examples considered herein, the proposed method achieves a two-orders-of-magnitude gain in computational efficiency compared with a conventional method of comparable accuracy.

Reliability-based Topology Optimization using Stochastic Gradients

“…To achieve a robust design, i.e., a design whose performance does not depend much on stochastic variations, these uncertainties must be incorporated in the optimization process. For example, in design under uncertainty the mean of the cost function is minimized subjected to constraints that are satisfied in expectation (Nikolaidis et al, 2004;Beyer and Sendhoff, 2007;De et al, 2017;Diwekar, 2020). To reduce variability in the design's performance a standard deviation or variance term can also be added to the objective (Beyer and Sendhoff, 2007;Dunning and Kim, 2013;De et al, 2020a).…”

Uncertainty Quantification of Locally Nonlinear Dynamical Systems Using Neural Networks

“…In structural engineering, an otherwise linear structure often contains spatially local nonlinearities. For example, a building superstructure or a bridge, which behaves linearly under most earthquake or wind excitation, may have a nonlinear base isolation layer [14,15,16] or nonlinear tuned-mass damper attached to it [17]. Similarly, spacecrafts often have nonlinear joints [18,19,20].…”

Development and validation of a nonlinear dynamic model for tuned liquid multiple columns dampers

“…Advances in construction methods and materials have led to more flexible structures, thereby raising the demand on reducing vibrations caused by natural hazards. Such vibrations can be mitigated through the incorporation of supplemental damping devices, including passive [1,2], semi-active [3,4,5] and active [6,7] systems. Of interest to this paper are passive systems, which have been widely accepted by the field due to their mechanical robustness and mitigation performance without necessitating external power [8].…”