Digital twins are developed to model the behavior of a specific physical asset (or twin), and they can consist of high-fidelity physics-based models or surrogates. A highly accurate surrogate is often preferred over multi-physics models as they enable forecasting the physical twin future state in real-time. To adapt to a specific physical twin, the digital twin model must be updated using in-service data from that physical twin. Here, we extend Gaussian process (GP) models to include derivative data, for improved accuracy, with dynamic updating to ingest physical twin data during service. Including derivative data, however, comes at a prohibitive cost of increased covariance matrix dimension. We circumvent this issue by using a sparse GP approximation, for which we develop extensions to incorporate derivatives. Numerical experiments demonstrate that the prediction accuracy of the derivative-enhanced sparse GP method produces improved models upon dynamic data additions. Lastly, we apply the developed algorithm within a DT framework to model fatigue crack growth in an aerospace vehicle.

翻译：数字孪生旨在模拟特定物理资产（即孪生体）的行为，其可由高保真物理模型或代理模型构成。高精度代理模型常优于多物理场模型，因其能实时预测物理孪生体的未来状态。为适配特定物理孪生体，数字孪生模型需利用该物理孪生体的服役数据进行更新。本文扩展了高斯过程模型以纳入导数数据，从而提升精度，并通过动态更新机制在服役期间吸收物理孪生体数据。然而，引入导数数据会导致协方差矩阵维度急剧增加，带来难以承受的计算成本。我们通过采用稀疏高斯过程近似方法规避此问题，并发展了纳入导数的扩展形式。数值实验表明，导数增强的稀疏高斯过程方法在动态数据添加后能产生预测精度更高的模型。最后，我们将所提算法应用于数字孪生框架中，对航空航天器的疲劳裂纹扩展进行建模。