I am working on a data science project on an industrial machine. This machine has two heating infrastructures. (fuel and electricity). It uses these two heatings at the same time, and I am trying to estimate the temperature value that occurs in the thermocouple as a result of this heating. However, this heating process takes place with some delay/lag. In other words, the one-unit change I have made in fuel and electrical heating is reflected in the thermocouple hours later. I want to find these hours, i.e. I'm trying to calculate the temperature change delay time on the thermocouple for the change in fuel and electricity. These three data are non-stationary time series data. I have data in frequency per second. I thought of using cross correlation but having two different heat sources confuses me. Which method do you think is better to use? Also, should I keep them in units like kwh/m3 or convert them to heat calorie units?
Time series in an industrial environment might be difficult, as there could be several external features (such as the ambient temperature that might change with seasons), in addition to the heat sources you've mentionned. Consequently I would suggest to modelize the heat conduction with a thermal physics library (ex: https://github.com/ElsevierSoftwareX/SOFTX_2018_105) in order to have an accurate understanding of the influence of each heat source, and not doing mistakes mixing impacts on the system.
Then, it should be much easier to evaluate the impact of each source and make reliable time series predictions, as you can accurately estimate the heat impact later on the system.
This conduction heat modelling doesn't need to be very detailled: as long as the conductive components can be represented in a simple way and be able to make accurate results, it is good enough.
However, in order to modelize the impact of the heat source, it would be better to know the influence of each heat source separatelly, and then evaluate the impact using both sources at the same time: the physical behavior is generally not linear when there are 2 different sources in parallel.