Robust identification of volumetric heat capacity and analysis of thermal response tests by Bayesian inference with correlated residuals

Bayesian inference has tremendous potential for thermal response test analysis, as it provides uncertainty metrics that are useful for the design of ground-coupled heat pump systems. The inference process is computationally heavy and has so far been limited to a few thermal parameters and under the unrealistic assumption of residuals' independence. In this work, a new closed-form expression of the likelihood and an improved artificial neural network are used to speed up Bayesian inference and consider the strong temporal correlation of the residuals. This efficient strategy allowed the robust inference of the joint distribution of five parameters. Using data measured during a real test of 168 h, this work shows that it is possible to robustly identify the volumetric heat capacity of the ground and grout with an uncertainty of 16.3 and 13.8%, a significant improvement. For the specific data used, it is shown that with independence assumption, some parameters are clearly unrealistic, a problem not encountered when the correlation of the residuals is considered. The impact of the interpretation model, of the test duration and of the sampling frequency was also assessed and illustrated by the sizing of a ground heat exchanger. Results reveal that joint identification of some thermal parameters cannot be achieved reliably by the finite line source model, that duration of thermal response tests should be at least 72 h to avoid large uncertainties on the parameters, and that recording temperature every 2 min degrades the identification of the volumetric heat capacity.