This research introduces an innovative framework to engineering design to tackle the challenges of robustness against manufacturing deviations and holistic optimization simultaneously in a multi-disciplinary, multi-subsystems context. The methodology is based on an application of ensemble artificial neural networks, which significantly accelerates computational processes. Coupled with the Non-dominated Sorting Genetic Algorithm III, this approach facilitates efficient multi-objective optimization, yielding a comprehensive Pareto front and high-quality design solutions. Here, the framework is applied to the design of gas-bearing-supported turbocompressors. These systems are challenging due to their sensitivity to manufacturing variations, particularly in the gas-bearing geometry, which can lead to rotordynamic instability. Additionally, the interdependencies between the subsystems, such as axial and journal bearings, rotor, compressor impellers, and magnets, necessitate a multidisciplinary approach that spans aerodynamics, structural dynamics, rotordynamics, mechanics, loss analyses, and more. A clear tradeoff between system efficiency, mass-flow range, and robustness has been identified for the compressor design. Higher nominal compressor mass-flows, i.e. increased nominal power, is suggested to decrease the hypervolume of feasible manufacturing deviations. Hence, there is a sweet power spot for gas-bearing supported turbomachinery. Further, the framework's computational efficiency is on par with that of a university cluster, while only employing a desktop computer equipped with a consumer-grade graphics card. This work demonstrates a significant advancement in the design of complex engineering systems and sets a new standard for speed and efficiency in computational engineering design.

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