Surrogate modeling is an essential data-driven technique for quantifying relationships between input variables and system responses in manufacturing and engineering systems. Two major challenges limit its effectiveness: (1) large data requirements for learning complex nonlinear relationships, and (2) heterogeneous data collected from sources with varying fidelity levels. Multi-task learning (MTL) addresses the first challenge by enabling information sharing across related processes, while multi-fidelity modeling addresses the second by accounting for fidelity-dependent uncertainty. However, existing approaches typically address these challenges separately, and no unified framework simultaneously leverages inter-task similarity and fidelity-dependent data characteristics. This paper develops a novel hierarchical multi-task multi-fidelity (H-MT-MF) framework for Gaussian process-based surrogate modeling. The proposed framework decomposes each task's response into a task-specific global trend and a residual local variability component that is jointly learned across tasks using a hierarchical Bayesian formulation. The framework accommodates an arbitrary number of tasks, design points, and fidelity levels while providing predictive uncertainty quantification. We demonstrate the effectiveness of the proposed method using a 1D synthetic example and a real-world engine surface shape prediction case study. Compared to (1) a state-of-the-art MTL model that does not account for fidelity information and (2) a stochastic kriging model that learns tasks independently, the proposed approach improves prediction accuracy by up to 19% and 23%, respectively. The H-MT-MF framework provides a general and extensible solution for surrogate modeling in manufacturing systems characterized by heterogeneous data sources.

翻译：代理建模是制造与工程系统中量化输入变量与系统响应间关系的重要数据驱动技术。其有效性受两大挑战制约：(1) 学习复杂非线性关系需要大量数据；(2) 从不同保真度来源收集的异构数据。多任务学习通过跨相关过程的信息共享应对第一项挑战，而多保真度建模则通过考虑保真度相关不确定性应对第二项挑战。然而，现有方法通常单独处理这些挑战，缺乏能同时利用任务间相似性与保真度相关数据特征的统一框架。本文提出一种基于高斯过程的新型分层多任务多保真度框架用于代理建模。该框架将每个任务的响应分解为任务特定的全局趋势分量和通过分层贝叶斯公式跨任务联合学习的残差局部变异分量。该框架可容纳任意数量的任务、设计点和保真度级别，同时提供预测不确定性量化。我们通过一维合成示例和真实世界发动机表面形状预测案例研究验证了所提方法的有效性。相较于(1)未考虑保真度信息的先进多任务学习模型，以及(2)独立学习任务的随机克里金模型，所提方法分别将预测精度最高提升19%和23%。该分层多任务多保真度框架为具有异构数据源特征的制造系统代理建模提供了通用且可扩展的解决方案。