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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.

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Summary
This summary is machine-generated.

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.

Keywords:
data-driven reconstructiongappy C-PODinverse temperature field reconstructionsparse sensor layout optimizationsteady-state and transient heat conduction

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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.