It is well known that design optimization techniques are hampered by computationally intensive function evaluations and non-smooth system responses. These difficulties are amplified when uncertainties are included in the optimization formulation. This represents a serious limitation since problems exhibiting discontinuities are, by definition, highly sensitive to uncertainties.

In order to tackle these difficulties, the CODES laboratory had developed algorithms for reliability-based design optimization (RBDO), which are based on a support vector machine classifier (SVM), insensitive to discontinuities, and adaptive sampling schemes, which considerably limit the number of function calls. After providing the necessary background, this seminar will introduce a series of new developments related to SVM-based failure domain approximation, and probability of failure estimation.

As an application, the presentation will focus on the optimization under uncertainty of Nonlinear Energy Sinks (NES), which represent a promising avenue for vibration mitigation. NES are characterized by an acute sensitivity to uncertainty with marked discontinuities in efficiency and, therefore, require dedicated optimization approaches. Several examples of NES optimization for the maximization of the expected value of the efficiency will be presented. The problems will include both random design variables (e.g., stiffness) and aleatory variables (e.g., loading).