Identification of the Gordon- Ng Chiller Model: Linear or Nonlinear Least Squares?

Abstract

In this paper, the calibration of the parameters of the Gordon-Ng Universal (GNU) chiller model is investigated. In its standard formulation, the GNU model is written as a linear-in-parameter model that can be calibrated by Ordinary Least Squares. It has been already observed elsewhere that, since the regressors are subject to measurement inaccuracies, the OLS approach is prone to yield biased estimates of the parameters. As a remedy, Andersen and Reddy proposed the adoption of an Errors in Variable (EIV) framework, showing that bias could be reduced or even eliminated by means of a corrected least squares algorithm. However, some questions remained open. Given that the EIV approach achieves bias reduction at the cost of increasing the variance, is it really preferable to OLS? If the final goal is not parameter estimation, but the prediction of the Coefficient of Performance (COP), how does OLS compare with EIV? And what is the most appropriate calibration method, under a statistical viewpoint? Finally, is the added complexity of a statistically rigorous approach employing Nonlinear Least Squares (NLS) really worth the potential improvements in COP prediction? In order to answer these questions, three estimation methods, OLS, EIV and NLS, are tested on two benchmarks: a public precise chiller performance dataset and an ASHRAE dataset. The results suggest, that OLS estimation, in spite of its suboptimality, may prove largely satisfactory both for parameter estimation and COP prediction, although it may be worth analyzing other more challenging COP prediction problem before the final word is said.