Marković Dana D, Lekić Branislava M, Rajaković-Ognjanović Vladana N, Onjia Antonije E, Rajaković Ljubinka V
Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, 11000 Belgrade, Serbia.
Faculty of Civil Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia.
ScientificWorldJournal. 2014 Jan 30;2014:930879. doi: 10.1155/2014/930879. eCollection 2014.
Numerous regression approaches to isotherm parameters estimation appear in the literature. The real insight into the proper modeling pattern can be achieved only by testing methods on a very big number of cases. Experimentally, it cannot be done in a reasonable time, so the Monte Carlo simulation method was applied. The objective of this paper is to introduce and compare numerical approaches that involve different levels of knowledge about the noise structure of the analytical method used for initial and equilibrium concentration determination. Six levels of homoscedastic noise and five types of heteroscedastic noise precision models were considered. Performance of the methods was statistically evaluated based on median percentage error and mean absolute relative error in parameter estimates. The present study showed a clear distinction between two cases. When equilibrium experiments are performed only once, for the homoscedastic case, the winning error function is ordinary least squares, while for the case of heteroscedastic noise the use of orthogonal distance regression or Margart's percent standard deviation is suggested. It was found that in case when experiments are repeated three times the simple method of weighted least squares performed as well as more complicated orthogonal distance regression method.
文献中出现了许多用于等温线参数估计的回归方法。只有通过对大量案例进行测试方法，才能真正洞察合适的建模模式。在实验中，这无法在合理时间内完成，因此应用了蒙特卡罗模拟方法。本文的目的是介绍和比较数值方法，这些方法涉及对用于初始浓度和平衡浓度测定的分析方法的噪声结构的不同程度的了解。考虑了六种同方差噪声水平和五种异方差噪声精度模型。基于参数估计中的中位数百分比误差和平均绝对相对误差，对这些方法的性能进行了统计评估。本研究表明了两种情况之间的明显区别。当平衡实验仅进行一次时，对于同方差情况，最优误差函数是普通最小二乘法，而对于异方差噪声情况，建议使用正交距离回归或玛格特百分比标准偏差。研究发现，当实验重复三次时，简单的加权最小二乘法与更复杂的正交距离回归方法表现相当。
