Multi-Task Multi-Fidelity Machine Learning for Reliability-Based Design With Partially Observed Information

Abstract In complex engineering systems, assessing system performance and underlying failure mechanisms with respect to uncertain variables requires repeated testing, which is often limited by test capacity and computational budget and fails to accurately capture the complex system’s high-dimensional nature. A method that can efficiently use information that is partially available from various sources is thus urgently needed for complex system design. This paper presents a multi-fidelity surrogate modeling strategy that efficiently utilizes partially observed information (POI) from various sources, including data with different fidelity and dimensionality. Additionally, in reliability analysis and design optimization tasks, multiple constraints must be evaluated concurrently for each design point. However, as the complexity of systems increases, the number of constraints grows, resulting in a rapid increase in computational effort. Therefore, a multi-fidelity multi-task surrogate modeling framework with POI was proposed to aid in the development of surrogate models, which increases the effectiveness of reliability analysis. The proposed multi-fidelity multi-task machine learning (MFMT-ML) model utilizes a Bayesian framework, which significantly improves the predictive model’s performance and provides uncertainty quantification of the prediction. It also offers premium features such as using multi-fidelity sources of data points and POI, allowing simultaneous evaluation of multiple constraints through a single test, and offering a highly accurate and efficient reliability-based design optimization framework through knowledge sharing. By incorporating partially observed information from various sources, our approach offers a promising avenue for improving system performance prediction accuracy and efficiency while reducing the cost and complexity of complex system design.