Temperature Sensor Position Planning

Abstract

One of the challenges in large volume metrology is that it is often difficult or impossible to control the ambient conditions in which the object is to be measured. Dimensional measurement results vary with those conditions and it becomes necessary to apply some form of compensation. Thermal compensation of dimensional measurement is primarily reliant on the ability to properly measure temperature across the volume, which can differ by several degrees, but conventionally a uniform scaling has been applied. This paper focuses upon temperature sensor network planning improvement to facilitate thermal compensation. Beyond assembly environments, data from sensor networks are increasingly used to make decisions, but appropriate design and testing of such networks can be limited. As the demand for production digital twins increase, appropriate methods to quantify and optimise uncertainty to improve confidence will be invaluable. A virtual test bed has been created for the design, test, and optimisation of temperature sensor networks supported by physical simulation. Sensor networks have been used to take virtual measurements from a known temperature distribution and used to reconstruct the temperature distribution. Random search optimisation on a subset of the sensor network was carried out to determine some initial rules for sensor network design. The positioning of the sensors within the measurement volume and the method of reconstructing the temperature field was found to be more important than the capability of the individual sensors. Two means of interpolating the ambient field have been investigated: polynomial fitting and kriging. Temperature sensor networks appeared more sensitive to changes at the spatial boundary and these positions seem to be most critical for accurate reconstruction. In the case of the barrel section assembly it was found that asymmetric sensor heights produced better results, for example. A polynomial interpolation model using a 16-sensor network with 0.1 °C (confidence interval, k = 2) uncertainty sensors could produce a consistent temperature reconstruction error of ~0.04 °C RMS, corresponding to a thermal expansion error of ~1.5 μm in aluminium over a 1.6 m-tall structure.