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稀疏传感器布局的优化和数据驱动的重建方法用于稳定状态和短暂的热场反向问题

Qingyang Yuan^1,2, Peijun Yao³, Wenjun Zhao¹

¹Key Laboratory of Complex Energy Conversion and Efficient Utilization of Liaoning Province, School of Energy and Power Engineering, Dalian University of Technology, Dalian 116081, China.

Sensors (Basel, Switzerland)

|August 28, 2025

概括

这项研究验证了基于Gappy集群的正确直角分解 (Gappy C-POD) 方法用于反向温度场的重建. Gappy C-POD与最佳传感器放置相结合,可在复杂的热系统中提供强大而稳定的温度场恢复.

科学领域:

* 热科学与工程
* 计算式热传输
* 数据驱动模型

背景情况:

*热传导的反向问题对于理解热行为至关重要.
现有的方法往往缺乏用于传感器优化和数据驱动的重建的强大框架.
*正确的直角分解 (POD) 和它的变体是大小缩小的强大工具.

研究的目的:

* 开发和验证基于Gappy集群的正确直角分解 (Gappy C-POD) 方法用于反向温度场的重建.
* 将稀疏的传感器布局优化与数据驱动的现场重建技术相结合.
在各种传感器放置策略和算法中系统评估重建性能.

主要方法:

* 有限差异方法用于解决内部热源和异质边界条件的数值模型.
* 开发一个全面的框架,集成传感器布局优化 (随机,S-OPT,CCFM,统一) 和数据库生成 (拉丁式超立方体,Sobol,最大-最小距离采样).
* 实施和验证Gappy POD和Gappy C-POD用于反向重建.

主要成果:

*Gappy POD和Gappy C-POD在低模式场景 (1-5模式) 中表现出强大的稳定性.
* Gappy C-POD与相关系数过方法 (CCFM) 和最大距离采样相结合,可以实现卓越的重建稳定性.
* POD-MLP和POD-RBF在较高的模式数 (> 10) 时表现良好,但对传感器配置和样本大小敏感.

结论:

这项研究是Gappy C-POD方法的首次全面实施和验证.
*最佳的传感器网络设计显著影响逆温度场重建的准确性和稳定性.
这些发现为在复杂的热环境中集成数据驱动的建模和传感器设计提供了宝贵的见解.

关键词:

数据驱动的重建皮的 C-POD 逆温度场的重建稀疏的传感器布局优化恒定和短暂的热传导

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