发表机构
Universidade Estadual Paulista — UNESP; Laboratório Nacional de Computação Científica — LNCC; Universidade do Estado do Rio de Janeiro — UERJ（圣保罗州立大学; 国家科学计算实验室; 里约热内卢州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对热监测受噪声与低分辨率测量制约的问题，研究经预处理和截断策略优化的动态模态分解（DMD），可从稀疏退化数据中恢复主导热行为，低秩模型稳定、高秩模型细节更丰富。
AI 中文摘要
实际应用中的热监测常受限于稀疏传感、测量噪声及有限空间分辨率，这阻碍了传热动力学的识别。在此类场景下，校准高保真物理模型的计算需求极高，因此催生了数据驱动方法。动态模态分解（DMD）提供了从测量数据中提取时空结构的框架，但其标准公式对噪声及退化观测敏感。本章研究了这些约束条件下DMD的应用，重点关注影响稳定性与可解释性的预处理及截断策略。考虑了两个案例：采用热电偶数据的强制对流，以及来自退化热图像的瞬态热传导。保留模态的数量被视为建模参数，决定了重构保真度与噪声敏感性之间的权衡。结果表明，当截断水平被适当选择时，DMD能从稀疏及退化数据集中恢复主导热行为。低秩模型提供稳定但简化的描述，而高秩模型以噪声敏感性提升为代价改善空间细节。
英文摘要
Thermal monitoring in practical applications is often constrained by sparse sensing, measurement noise, and limited spatial resolution, which hinder the identification of heat transfer dynamics. In such settings, calibrating high-fidelity physical models is computationally demanding, motivating data-driven approaches. Dynamic Mode Decomposition (DMD) provides a framework for extracting spatiotemporal structures from measurement data, but its standard formulation is sensitive to noise and degraded observations. This chapter examines the use of DMD under these constraints, focusing on preprocessing and truncation strategies that affect stability and interpretability. Two cases are considered: forced convection with thermocouple data and transient heat conduction from degraded thermal images. The number of retained modes is treated as a modeling parameter that governs the trade-off between reconstruction fidelity and noise sensitivity. The results indicate that DMD recovers dominant thermal behavior from both sparse and degraded datasets when the truncation level is appropriately selected. Low-rank models provide stable but simplified descriptions, while higher-rank models improve spatial detail at the cost of increased noise sensitivity.
