Multi-Fidelity Surrogate Modeling for Reliability Optimization with Implicit Functions

Reliability-based design optimization techniques are widely used for complex, coupled systems to coordinate solving the different subsystem optimization problems for engineering systems design. However, practically, not all constraints are clearly defined for complex systems. Some implicit constraints could cause difficulty when mathematically representing systems and could hinder the application of reliability optimization methods, since they could lead to difficulty decomposing the problem. Although surrogate modeling methods can be used to provide a functional representation for the implicit constraints, they require abundant data to accurately predict the functional form. This study utilizes MFNets to reduce data requirements and allow for an accurate representation of implicit functions through incorporating multi-fidelity data and exploiting the relationship between the data sources. The study also integrates the approximated implicit function with reliability optimization methods to allow large-scale composite systems to be decomposed and coordinates their solution strategies. Results show that by leveraging the embedded Gaussian Process Regression (GPR) model in MFNets with the conditional independence Bayesian properties of Bayesian Networks, an accurate representation of the functional form facilitates system decomposition.