Stochastic Optimization with Multiple Failure Modes of Systems Subjected to Random Vibrations

It has been demonstrated that the effect of inherent uncertainties can be substantial for systems subjected to random vibrations. In the context of optimization, these uncertainties, in addition to the randomness of the load, are accounted for in a reliability-based design optimization (RBDO) problem. The probabilistic constraints of the RBDO problems require the computation of a total probability which accounts for the effect of both the stochastic parameters and random excitation. In this work, the focus is on RBDO problems with multiple failure modes such as first-passage and fatigue. In order to reduce the computational burden, surrogates are used to approximate the root mean square (RMS) of both the response and its time derivative. This provides an easy way to modify the threshold in the case of the first-passage failure, and it also allows a direct computation of the expected frequency. Additionally, this study uses a Gaussian process-based sampling scheme that utilizes its predictive variance to minimize the number of function calls, particularly in scenarios involving multiple failure modes. This sampling scheme considers the joint distribution of random parameters and prioritizes regions of the space with high probabilistic density. The methodology is applied to two problems: a cantilever beam with a tip mass and a launcher payload adapter, both modeled with finite elements.