A stochastic gradient approach for the reliability maximization of passively controlled structures

This paper addresses the reduction of the computational burden of structural reliability maximization of passively controlled buildings subject to transient loading. Such a reduction is accomplished by means of Stochastic Gradient Descent (SGD) algorithms, which replace expensive multi-dimensional Monte Carlo integration by a singleton multi-iteration integration. In order to be able to apply SGD methods, the time-dependent structural reliability evaluation was constructed based on the out-crossing rate approach. Design of single and multi Friction Tuned Mass Dampers (FTMDs) are considered as design examples. The proposed SGD algorithm, the accelerated stochastic gradient descent (ASGD) algorithm, efficiently combines Nesterov acceleration, Polyak-Ruppert averaging and restart techniques. The main result drew from the numerical analysis is that SGD algorithms were able to maximize the structural reliability by providing more accurate results and requiring lower computational cost than well-known optimization methods. Finally, the limitation of the proposed optimization procedure is linked to the validity of the out-crossing rate to approximate the time-dependent structural reliability.