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Optimization of Sparse Sensor Layouts and Data-Driven Reconstruction Methods for Steady-State and Transient Thermal
Qingyang Yuan1,2, 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.
This study validates the Gappy Clustering-based Proper Orthogonal Decomposition (Gappy C-POD) method for inverse temperature field reconstruction. Gappy C-POD, combined with optimal sensor placement, offers robust and stable temperature field recovery in complex thermal systems.
Area of Science:
- * Thermal Science and Engineering
- * Computational Heat Transfer
- * Data-Driven Modeling
Background:
- * Inverse problems in heat conduction are crucial for understanding thermal behavior.
- * Existing methods often lack robust frameworks for sensor optimization and data-driven reconstruction.
- * Proper Orthogonal Decomposition (POD) and its variants are powerful tools for dimensionality reduction.
Purpose of the Study:
- * To develop and validate the Gappy Clustering-based Proper Orthogonal Decomposition (Gappy C-POD) method for inverse temperature field reconstruction.
- * To integrate sparse sensor layout optimization with data-driven field reconstruction techniques.
- * To systematically evaluate reconstruction performance across various sensor placement strategies and algorithms.
Main Methods:
- * Finite difference method for solving numerical models with internal heat sources and heterogeneous boundary conditions.
- * Development of a comprehensive framework integrating sensor layout optimization (random, S-OPT, CCFM, uniform) and database generation (Latin Hypercube, Sobol, maximum-minimum distance sampling).
- * Implementation and validation of Gappy POD and Gappy C-POD for inverse reconstruction.
Main Results:
- * Gappy POD and Gappy C-POD demonstrate strong robustness in low-modal scenarios (1-5 modes).
- * Gappy C-POD, coupled with Correlation Coefficient Filtering Method (CCFM) and maximum distance sampling, achieves superior reconstruction stability.
- * POD-MLP and POD-RBF show good performance at higher modal numbers (>10) but are sensitive to sensor configuration and sample size.
Conclusions:
- * The study presents the first complete implementation and validation of the Gappy C-POD methodology.
- * Optimal sensor network design significantly impacts the accuracy and stability of inverse temperature field reconstruction.
- * The findings provide valuable insights for integrating data-driven modeling and sensor design in complex thermal environments.
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