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

F. Acerbi, G. Nicolao
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引用次数: 1

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.
Gordon- Ng制冷机模型的辨识:线性还是非线性最小二乘?
本文研究了Gordon-Ng通用型(GNU)制冷机模型参数的标定问题。在其标准公式中,GNU模型被写成一个参数线性模型,可以通过普通最小二乘进行校准。在其他地方已经观察到,由于回归量受到测量不准确性的影响,OLS方法容易产生有偏差的参数估计。作为补救措施,Andersen和Reddy提出采用变量误差(Errors in Variable, EIV)框架,表明通过修正的最小二乘算法可以减少甚至消除偏差。然而,一些问题仍然悬而未决。考虑到EIV方法以增加方差为代价实现了偏差减少,它真的比OLS更好吗?如果最终目标不是参数估计,而是性能系数(COP)的预测,OLS与EIV相比如何?从统计学的角度来看,什么是最合适的校准方法?最后,采用非线性最小二乘(NLS)的统计严谨方法所增加的复杂性是否真的值得COP预测的潜在改进?为了回答这些问题,三种估计方法,OLS, EIV和NLS,在两个基准上进行了测试:公共精确冷水机组性能数据集和ASHRAE数据集。结果表明,尽管OLS估计具有次优性,但在参数估计和COP预测方面可能在很大程度上令人满意,尽管在最后说之前可能值得分析其他更具挑战性的COP预测问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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