吸附动力学模型拟合优度的统计评估及模型比较研究  

Statistical Evaluation of Adsorption Kinetic Models:Goodness of Fit and Model Comparison

作　　者：胡启立 何智浩 张帅 杨杰 王权峰 HU Qili;HE Zhihao;ZHANG Shuai;YANG Jie;WANG Quanfeng(School of Chemical and Environmental Engineering,Sichuan University of Science&Engineering,Zigong 643000,China;School of Emergency Management,Xihua University,Chengdu 610039,China;No.4 Engineering Corporation Limited of CR20G,Qingdao 266075,China;College of Mathematics and Physics,Chengdu University of Technology,Chengdu 610059,China)

机构地区：[1]四川轻化工大学化学与环境工程学院,四川自贡643000 [2]西华大学应急管理学院,四川成都610039 [3]中铁二十局集团第四工程有限公司,山东青岛266075 [4]成都理工大学数理学院,四川成都610059

出　　处：《水处理技术》2025年第3期23-30,共8页Technology of Water Treatment

基　　金：四川省自然科学基金(2024NSFSC0888);东达山隧道高渗透压力水预防预排综合施工技术研究(YF2299SD01A,AH 2014-0156);四川轻化工大学第二批人才引进项目(2024RC060)。

摘　　要：对动力学数据进行建模有助于了解吸附质的动态吸附行为和预测特定条件下的平衡吸附量。由于模型复杂度的增加会提升拟合优度,仅基于误差统计量选择最佳模型并不充分。因此,误差统计量需结合其他评估方法来进行综合判断。本研究选取了吸附研究中常用的15个动力学模型,采用残差平方和(RSS)、决定系数(R^(2))、校正决定系数(Adj.R^(2))、减少卡方(χ_(v)^(2))和均方根误差(RMSE)来评估模型的拟合优度,并通过赤池信息准则(AIC)和贝叶斯信息准则(BIC)及其权重来比较模型。结果表明,较复杂的模型可以提供更好的拟合优度,但易导致过拟合,AIC和BIC可以平衡模型的复杂度和拟合优度。分形伪二级动力学模型具有最低的AIC和BIC值,并且相应的权重值也最大,表明磷酸盐吸附符合分形伪二级动力学模型。本研究为最佳吸附动力学模型的选择提供了一套较为完善的评估方法,也适用于最佳吸附等温线模型和穿透模型的选择。The modeling of kinetic data helped to understand the dynamic adsorption behaviors and predict the equilibrium loading under specific conditions.Since the increase in the complexity of a model could promoted the goodness of fit,it was not sufficient to select the optimal model based solely on error statistics.Thus,error statistics needed to be combined with other evaluation methods for a comprehensive judgment.This study selected fifteen commonly-used kinetic models in adsorption studies and evaluated their goodness of fit using the residual sum of squares(RSS),coefficient of determination(R^(2)),adjusted coefficient of determination(Adj.R^(2)),reduced chi-square(χ_(v)^(2))and root of mean squared error(RMSE).The models were compared by Akaike information criterion(AIC)and Bayesian information criterion(BIC)and their weights.The results indicated that the complex model could provide higher fitting quality,but easily led to overfitting.AIC and BIC could balance the complexity and goodness of fit of the model.The fractal-like pseudo-second-order kinetic model had the lowest values of AIC and BIC,and the corresponding weight values were also the largest,indicating that phosphate adsorption followed the fractal-like pseudo-second-order kinetic model.This study provided a relatively perfect evaluation method for the selection of the optimal adsorption kinetic model,which was also applicable to the selection of the optimal adsorption isotherm model and breakthrough model.

关 键 词：动力学模型 吸附 模型选择 误差统计量 信息准则 

分 类 号：TQ424[化学工程]