Optimal Sensor Placement via a POD-QR Framework for High-Fidelity 3D Temperature Field Reconstruction in Large-Scale...

Reliable temperature distribution measurement in ultra-low temperature (ULT) chest freezers is crucial for preserving biospecimen integrity in cryopreservation, but dense sensor arrays required for accuracy are often impractical due to space constraints and cost limitations. To address this critical challenge, this work presents a systematic data-driven framework for optimal sensor placement in large-scale (3 m³) ULT chest freezers under stable operating conditions. To our knowledge, it is the first realization of high-fidelity cryogenic temperature field reconstruction coupled with sparse sensor layout optimization tailored to large-volume ULT chest freezers. First, high-resolution reference temperature fields were constructed via universal kriging interpolation, validated with leave-one-out cross-validation (LOOCV) to achieve mean absolute error (MAE) ≤0.67 °C and coefficient of determination R2>0.92. Principal component analysis (PCA) was then applied to training data to extract a tailored proper orthogonal decomposition (POD) basis. The first three principal components captured 99.8% of cumulative energy. Optimal sensor locations were determined via QR-column pivoting on the rank-3 POD basis, converging to a minimal configuration of 3 sensors (a 94% reduction from the 48-sensor full-scale setup). This sparse sensor network achieved exceptional reconstruction performance: grid-level MAE ≤0.079 °C and root mean squared error (RMSE) ≤0.093 °C against reference fields (R2≥0.999), while point-level validation against experimental measurements yielded MAE ≤0.502 °C and RMSE ≤0.842 °C (R2≥0.971). The results demonstrate that, for large-scale ULT chest freezers, the proposed data-driven approach is capable of automatically determining an optimal sparse sensor subset and enabling reliable 3D cryogenic temperature field reconstruction for efficient thermal monitoring. By resolving the trade-off between monitoring accuracy, space efficiency, and cost-effectiveness, this framework provides a scientifically rigorous alternative to empirical sensor deployment standards, offering practical scalability for cryogenic biobanking applications.