Reliability-Based Design Optimization of Uncertain Linear Systems Subjected to Random Vibrations

A reliability-based design optimization (RBDO) approach for uncertain linear systems subjected to random vibrations is presented. The computation of the first-passage failure probability with uncertain system parameters is computed as the total probability, which accounts for both the stochastic excitation and the randomness of the parameters. This quantity, which is dependent on the failure rate, is in general difficult to compute for complex problems involving finite element simulations. This difficulty becomes even more pronounced in the case of RBDO. To mitigate this problem, this work uses surrogate models and a dedicated adaptive sampling scheme to significantly reduce the number of simulations. Gaussian processes (GPs) are used as surrogates to approximate the failure rate over the extended space that includes design variables and random parameters. The adaptive sampling scheme leverages the availability of the prediction variance while accounting for the joint distribution of the system's random parameters, enabling the scheme to focus on regions of the space with high probabilistic content. The RBDO algorithm is applied to two test problems modeled with finite elements: a cantilever beam with tip mass and a payload adapter.