Heterogeneous uncertainty quantification using Bayesian inference for simulation-based design optimization

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Heterogeneous uncertainties due to model imperfection, lack of training data, and input variations coexist in simulation-based design optimization. In this work, a Bayesian-enhanced meta-model is developed to handle heterogeneous uncertainties concurrently in reliability-based design optimization. To account for model form uncertainty, a Bayesian model inference approach is first employed to calibrate unknown parameters of simulation models. Then a hybrid GP model is constructed based on a set of simulation data and experimental observations to predict the response of the actual physical system. By using Monte Carlo simulation (MCS), the resultant hybrid GP model predictions are utilized to form a Gaussian mixture model (GMM) for propagating heterogeneous uncertainties in system reliability analysis. An aggregative reliability index (ARI) is then defined based on GMM to approximate the probability of failure under heterogeneous uncertainties. The proposed approach is further integrated with the RBDO framework to search for optimal system designs. The effectiveness of the proposed approach is demonstrated through three case studies.