Analysis of the sensor placement for optimal temperature distribution reconstruction

• Temperature distribution reconstructed from few measurement data is considered.
• Temperature distribution results from the process eigenfunctions.
• Reconstruction error is due to data uncertainty and limited resolution.
• Resolution errors and the data uncertainties are in opposition to one another.
• Sensor number and locations result from a trade off between the two error terms.

The temperature distribution as a function of time and space is reconstructed over a non-homogeneous media having an arbitrary three-dimensional geometry. This is done by applying an inverse problem to the collected data from optimally placed sensors on the boundary surface of the object under study. Sensor positioning and the choice of the number of sensors are optimized in terms of the resolution of the reconstructed temperature field and the error propagation of the method in case of uncertain measurements. The method can be performed in real time since the major computation burden is performed off-line.