Comparison of traditional and bayesian calibration techniques for gray-box modeling

Bayesian and nonlinear least-squares methods of calibration were evaluated and compared for gray-box modeling of a retail building. Gray-box model calibration is one form of system identification and is examined here with perturbations to the simple yet popular European Committee for Standardization (CEN)-ISO thermal network model. The primary objective was to understand whether the computational expense of probabilistic Bayesian techniques is required to provide robustness to signal noise, specifically with regard to lower dimensional problems (physical or semiphysical), where model calibration is preferred over uncertainty quantification. The Bayesian approach allows parameter interactions and trade-offs to be revealed, one form of sensitivity analysis, but its full power for uncertainty quantification cannot be harnessed with gray-box or other simplified models. Surrogate data from a detailed building energy simulation program were used to ensure command over latent variables, whereas a range of signal-to-noise and noise colors were considered in the experimental study. The fidelity to the building zone temperature and thermal load was the basis for comparing results. Utilization of uniform priors showed that both methods performed similarly well. Bayesian calibration outperformed traditional methods on noisy data sets; however, traditional methods were adequate up to an approximately 25% noise level. The thermal gray-box model calibration has the intended application of embedded model predictive control, where speed, accuracy, and robustness are crucial. Traditional methods required approximately 100 times less CPU time and are recommended given the model simplicity, application, and expected system noise levels.