A physics-driven sensor placement optimization methodology for temperature field reconstruction

TL;DR

This paper introduces a physics-driven sensor placement optimization method for temperature field reconstruction that does not rely on large data sets, using a physics-based criterion and genetic algorithms to improve accuracy.

Contribution

The novel PSPO method derives error bounds based on physics principles and optimizes sensor locations without requiring extensive data, outperforming random and uniform methods.

Findings

Significantly improves reconstruction accuracy, nearly tenfold.

Outperforms random and uniform sensor placement strategies.

Achieves comparable results to data-driven methods without data dependency.

Abstract

Perceiving the global field from sparse sensors has been a grand challenge in the monitoring, analysis, and design of physical systems. In this context, sensor placement optimization is a crucial issue. Most existing works require large and sufficient data to construct data-based criteria, which are intractable in data-free scenarios without numerical and experimental data. To this end, we propose a novel physics-driven sensor placement optimization (PSPO) method for temperature field reconstruction using a physics-based criterion to optimize sensor locations. In our methodological framework, we firstly derive the theoretical upper and lower bounds of the reconstruction error under noise scenarios by analyzing the optimal solution, proving that error bounds correlate with the condition number determined by sensor locations. Furthermore, the condition number, as the physics-based criterion, is used to optimize sensor locations by the genetic algorithm. Finally, the best sensors are validated by reconstruction models, including non-invasive end-to-end models, non-invasive reduced-order models, and physics-informed models. Experimental results, both on a numerical and an application case, demonstrate that the PSPO method significantly outperforms random and uniform selection methods, improving the reconstruction accuracy by nearly an order of magnitude. Moreover, the PSPO method can achieve comparable reconstruction accuracy to the existing data-driven placement optimization methods.