An efficient approach for taking into account uncertainties in structural parameters in Performance-Based Design Optimization

This paper introduces an efficient approach for taking into account the structural parameter uncertainties in Performance-Based Design Optimization (PBDO). The central concept of the proposed PBDO framework is the utilization of Stochastic Gradient (SG) algorithms. These algorithms streamline the solution process by circumventing the computation of the high-dimensional integral typically required in PBDO during the optimization process. Indeed, this circumvention negates the need for summation across the Intensity Measure (IM) and the random parameter space - a requisite for Monte Carlo Integration when assessing the expected cost of failure. To validate the effectiveness and robustness of the proposed method, two illustrative examples are examined. The first scrutinizes a multi-degree-of-freedom (MDOF) oscillator characterized by cubic nonlinearity in both damping and stiffness, exposed to stationary broadband excitation, while the second example optimizes a reinforced concrete building modeled as a nonlinear hysteretic MDOF oscillator endowed with fractional derivative terms and subject to non-stationary seismic excitation. The obtained results underscore the versatility and practical utility of the optimization strategy delineated in this paper, allowing the modeling of structural parameters as random variables and the efficient solution of PBDO problems.