Multi-Task Learning for Design Under Uncertainty With Multi-Fidelity Partially Observed Information

The assessment of system performance and identification of failure mechanisms in complex engineering systems often requires the use of computation-intensive finite element software or physical experiments, which are both costly and time-consuming. Moreover, when accounting for uncertainties in the manufacturing process, material properties, and loading conditions, the process of reliability-based design optimization (RBDO) for complex engineering systems necessitates the repeated execution of expensive tasks throughout the optimization process. To address this problem, this paper proposes a novel methodology for RBDO. First, a multi-fidelity surrogate modeling strategy is presented, leveraging partially observed information (POI) from diverse sources with varying fidelity and dimensionality to reduce computational cost associated with evaluating expensive high-dimensional complex systems. Second, a multi-task surrogate modeling framework is proposed to address the concurrent evaluation of multiple constraints for each design point. The multi-task framework aids in the development of surrogate models and enhances the effectiveness of reliability analysis and design optimization. The proposed multi-fidelity multi-task machine learning model utilizes a Bayesian framework, which significantly improves the performance of the predictive model and provides uncertainty quantification of the prediction. Additionally, the model provides a highly accurate and efficient framework for reliability-based design optimization through knowledge sharing. The proposed method was applied to two design case studies. By incorporating POI from various sources, the proposed approach improves the accuracy and efficiency of system performance prediction, while simultaneously addressing the cost and complexity associated with the design of complex systems.