Calorimetry under non-ideal conditions using system identification

We report a model-based method for quantifying heat flow and storage in thermal systems using data from multiple thermal sensors. This approach avoids stringent requirements on the system geometry and sensor positions and enables calorimetry to be performed under a broader range of circumstances than is accessible with existing calorimeters, such as when nonlinear heat transfer occurs, when spatially separated heat sources are active or when multiple thermal masses participate. Using experimental data from a model thermal system, this paper provides a tutorial on the construction of nonlinear lumped-element heat transfer models and the use of system identification to estimate the parameters of these models from calibration data. The calibrated models are then used to estimate unknown energy inputs to the thermal system from sensor data. Our best model enabled the measurement of the total input energy with 0.02{%} accuracy; the instantaneous input power could be measured with a root-mean-square error of 10{%} of the average input power.