Estimating the calibration drift of thermocouples measuring temperature in high value manufacturing applications
In applications such as the heat treatment of high-value components in advanced manufacturing, it is important to be able to quantify in situ the calibration drift of the thermocouples used for measuring temperature. Doing so helps to avoid having to remove and re-calibrate the thermocouples, which would be done in the case of the more expensive noble metal thermocouples, or having to replace them, which would be done with the more common inexpensive base metal thermocouples.
Multi-wire thermocouples and sensor fusion
The use of a multi-wire thermocouple, considered as a network of co-located thermocouples comprising different pairs of wires and exposed to the same temperature gradient, offers the possibility to estimate the calibration drift of the individual thermocouples. Furthermore, the use of sensor fusion methods allows for the possibility to obtain an estimate of the common temperature measured by the thermocouples that is more accurate than the estimate provided by any individual thermocouple.
Sensor fusion methods for this purpose are under development within the FunSNM project with the aim to treat thermocouples with different calibration drift characteristics i.e., drifting at different rates depending on wire composition - as well as the handling of correlations and uncertainty in recorded sensor data.
Methods under consideration
Some of the methods under consideration are ‘data-driven’, in the sense that they make very few assumptions about the sensor network that generates the data, and they make no use of knowledge about the physical mechanism that leads to calibration drift.
Other methods use, to varying degrees, knowledge about the sensor network and those mechanisms. The figure below gives the results obtained from one relatively simple ‘data-driven’ method, showing the predicted temperature as a function of time for all possible pairs of thermocouples in a multi-wire thermocouple, and illustrates that the method appears to work quite well in this case.
Figure: Deviation of predictions from the true temperature for all possible pairs of thermocouples. Note the clustering of values around the true temperature.
Physical knowledge vs. data driven
A comparison has been made of the results obtained from some of the sensor fusion methods under development to understand whether there is benefit from including physics knowledge. The results suggest that, in terms of the accuracy of the estimate of the common temperature, there is generally a benefit in doing so. However, including physics knowledge does not necessarily translate into a smaller uncertainty associated with the estimate of the common temperature, although we might hope for a more realistic and reliable uncertainty in that case.
Future plans
Making use of physics knowledge is often challenging and although doing so can contribute to the trustworthiness of the results obtained, there is nevertheless a balance between the amount of physics knowledge included and the demands put on the data to then be consistent with that knowledge. Throughout, we are using data collected under controlled conditions, where the temperature is held constant or is varied in a pre-determined way, to test the methods. The consortium continues to liaise closely with stakeholders in the aerospace and other supply chains to access real-world data.