MAXIMIZATION OF THE RELIABILITY OF FRICTION TUNED MASS DAMPERS USING STOCHASTIC GRADIENT METHODS

Resumo

We use an efficient stochastic optimization framework to optimize the design of friction tuned
mass dampers (FTMD). To deal with the uncertainties in the model, we use a reliability analysis based
on the out-crossing rate approach. We formulate the unbiased gradient estimator of the reliability index
with respect to the design parameters, a condition for the use of stochastic gradient descent (SGD) and
its variations. We couple SGD with Nesterov’s acceleration, Polyak–Ruppert averaging, and a restart

technique to evaluate their improvement on SGD efficiency for design optimization. To assess the per-
formance of the proposed stochastic optimization framework, we optimize the parameters of an FTMD

in a steel frame building. Comparing the obtained results with the state-of-the-art in the literature, we
observe a reduction of up to an order of magnitude in cost to achieve a given accuracy. Given that an
unbiased estimator for the true gradient can be evaluated, stochastic gradient methods can efficiently
perform local search in design problems on the presence of uncertainties.