面向数字孪生应用中导数信息高斯过程代理的流式稀疏Cholesky方法
A Streaming Sparse Cholesky Method for Derivative-Informed Gaussian Process Surrogates Within Digital Twin Applications
AI总结：
提出一种流式稀疏Cholesky方法，通过动态更新和导数信息增强高斯过程代理，降低协方差矩阵维度，实现数字孪生中飞机结构性能的实时预测。
摘要：
数字孪生被开发用于模拟特定物理资产（或孪生体）的行为，它们可以由高保真基于物理的模型或代理组成。高精度代理通常优于多物理场模型，因为它们能够实时预测物理孪生体的未来状态。为了适应特定的物理孪生体，必须使用来自该物理孪生体的在役数据更新数字孪生模型。在本文中，我们结合并扩展了几项先前与代理相关的进展，旨在展示一个端到端的数字孪生（DT）解决方案，用于预测飞机结构（物理资产）的性能。为此，我们将高斯过程（GP）模型扩展到包含导数数据，以提高精度，并通过动态更新来吸收在役期间的物理孪生体数据。然而，包含导数数据会带来协方差矩阵维度增加的过高成本。我们通过改进的动态稀疏Cholesky线性系统求解器规避了这个问题。数值实验表明，导数增强的稀疏Cholesky GP方法在动态数据添加时产生了改进的模型预测精度。最后，我们在一个数字孪生框架内演示了所开发的算法，用于模拟航空航天飞行器中的疲劳裂纹扩展，从而通过我们组装的工程系统展示了数字孪生技术如何在实践中结合。
英文摘要：
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. In this paper, we combine and extend several previous surrogate-related advancements with the goal of demonstrating an end-to-end digital twin (DT) solution for predicting performance of an aircraft structure (the physical asset). To this end, 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 through our modified dynamic sparse Cholesky linear system solver. Numerical experiments demonstrate that the prediction accuracy of the derivative-enhanced sparse Cholesky GP method produces improved models upon dynamic data additions. Lastly, we demonstrate the developed algorithm within a DT framework to model fatigue crack growth in an aerospace vehicle, thereby exhibiting through our assembled engineered system how digital twin technologies can be combined in practice.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
