改进的灰色模型在光催化数据预测中的应用

doi:10.15541/jim20200661

无机材料学报 ›› 2021, Vol. 36 ›› Issue (8): 871-876.DOI: 10.15541/jim20200661

改进的灰色模型在光催化数据预测中的应用

王路平¹(), 卢占会¹(), 魏鑫², 方明³, 王祥科³()

1. 数理学院, 华北电力大学, 资源环境系统优化教育部重点实验室, 北京 102206
2.控制与计算机工程学院, 华北电力大学, 资源环境系统优化教育部重点实验室, 北京 102206
3.环境科学与工程学院, 华北电力大学, 资源环境系统优化教育部重点实验室, 北京 102206

收稿日期:2020-11-19 修回日期:2021-02-04 出版日期:2021-08-20 网络出版日期:2021-03-01
通讯作者: 卢占会, 教授. E-mail: luzhanhui@ncepu.edu.cn; 王祥科, 教授. E-mail: xkwang@ncepu.edu.cn
作者简介:王路平(1996-), 女, 硕士研究生. E-mail: lupingwang@ncepu.edu.cn
基金资助:
科技部重大研发计划(2018YFC1900105,);科技部重大研发计划(2017YFA0207002);中央高校基本科研业务费专项资金(2019MS040)

Application of Improved Grey Model in Photocatalytic Data Prediction

WANG Luping¹(), LU Zhanhui¹(), WEI Xin², FANG Ming³, WANG Xiangke³()

1. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
2. College of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China
3. MOE Key Laboratory of Resources and Environmental System Optimization, College of Environmental Science and Engineering, North China Electric Power University, Beijing 102206, China

Received:2020-11-19 Revised:2021-02-04 Published:2021-08-20 Online:2021-03-01
Contact: LU Zhanhui, professor. E-mail: luzhanhui@ncepu.edu.cn; WANG Xiangke, professor. E-mail: xkwang@ncepu.edu.cn
About author:WANG Luping (1996-), female, Master candidate. E-mail: lupingwang@ncepu.edu.cn
Supported by:
National Key Research and Development Program of China(2018YFC1900105,);National Key Research and Development Program of China(2017YFA0207002);Fundamental Research Funds for Central Universities(2019MS040)

摘要/Abstract

摘要：

光催化去除水中污染物的研究通常得到的是小样本的离散数据, 利用拟一级动力学模型对实验结果进行模拟和分析, 有时拟合效果较差, 且无法用于数据预测。本研究在离散灰色预测模型(DGM(1, 1))的基础上, 考虑数据的非线性特征并结合等维信息替代思想建立了非线性动态离散灰色模型(EDGM(1, 1,α)), 利用该模型对三元复合材料Bi/BiOCl/Au光催化去除四环素实验所得数据进行了预测, 其平均相对误差和拟合度数据显示: 相比于DGM(1, 1)等3种模型, EDGM(1, 1, α)模型对光催化实验数据具有良好的预测水平, 与实验结果吻合。该预测方法可以用于指导下一步实验, 有望减少实验次数, 降低成本和能耗。

关键词: 光催化, 预测, 灰色模型, 等维信息替代

Abstract:

Discrete and small samples data are usually obtained from the studies on photocatalytic removal of pollutants in water. The first-order kinetic model used to simulate and analyze the experimental data sometimes has poor fitting effect and cannot be used for data prediction. In this study, based on the discrete grey model (DGM(1, 1)), the nonlinear dynamic discrete gray model (EDGM(1, 1, α)) are established by considering the nonlinear characteristics of the data and equal dimensional information substitution method. The model is used to predict the experimental data of photocatalytic degradation of tetracycline by Bi/BiOCl/Au. As compared with DGM(1, 1) and other three models, the EDGM(1, 1, α) model has a better prediction level for the experimental data of photocatalysis. The results are in good agreement with the experimental results. This model can be used to guide the next step of experiments, which is expected to reduce the number of experiments and realize the rapid development of experimental research with low cost and energy consumption.

Key words: photocatalysis, predict, grey model, equivalent substitution method

中图分类号:

TQ174

王路平, 卢占会, 魏鑫, 方明, 王祥科. 改进的灰色模型在光催化数据预测中的应用[J]. 无机材料学报, 2021, 36(8): 871-876.

WANG Luping, LU Zhanhui, WEI Xin, FANG Ming, WANG Xiangke. Application of Improved Grey Model in Photocatalytic Data Prediction[J]. Journal of Inorganic Materials, 2021, 36(8): 871-876.

图/表 8

图1 EDGM(1, 1, α)的建模步骤

Fig. 1 Modelling steps of EDGM(1, 1, α)

图2 Bi/BiOCl/Au的XRD谱图

Fig. 2 XRD pattern of Bi/BiOCl/Au

表1 时间-四环素浓度实验数据

Table 1 Experimental data of tetracycline concentration

Time/min	0	15	30	45	60	75	90	105	120	135
Con./(mg·L^-1)	38.66	34.52	31.39	29.10	27.00	25.15	23.16	21.24	19.40	18.29

表2 不同数据规模预测比较

Table 2 Different data size forecast comparison

Date size	Experimental data/(mg·L^-1)		Forecast data /(mg·L^-1)		MRE
4	27.00	25.15	26.93	24.89	0.005
5	25.15	23.16	25.13	23.42	0.006
6	23.16	21.24	23.50	21.98	0.025
7	21.24	19.40	21.46	19.84	0.017
8	19.40	18.29	19.56	17.97	0.025

表3 DGM(1, 1)、DGM(1, 1, α)、EDGM(1, 1)和EDGM(1, 1,α)模型预测值

Table 3 Predicted values of DGM(1, 1), DGM(1, 1, α), EDGM(1, 1), and EDGM(1, 1, α) models

Time /min	Con. /(mg·L^-1)	DGM (1, 1)	DGM (1, 1, α)	EDGM (1, 1)	EDGM (1, 1, α)
60	27.00	26.60	26.93	26.60	26.93
75	25.15	24.41	25.07	24.57	24.89
90	23.16	22.40	23.41	22.52	22.98
105	21.24	20.55	21.92	20.75	21.20
120	19.40	18.86	20.56	19.05	19.56
135	18.29	17.31	19.32	17.54	18.03

表4 DGM(1, 1)、DGM(1, 1, α)、EDGM(1, 1)和EDGM(1, 1, α)模型的MRE和FD

Table 4 The MRE and FD of DGM(1, 1), DGM(1, 1, α), EDGM(1, 1), and EDGM(1, 1, α) models

Model	MRE	FD
DGM(1, 1)	0.032	0.984
DGM(1, 1, α)	0.028	0.985
EDGM(1, 1)	0.025	0.988
EDGM(1, 1, α)	0.008	0.995

图3 (a)DGM(1, 1), (b)DGM(1, 1, α), (c)EDGM(1, 1), (d)EDGM(1, 1, α)模型对四环素浓度的预测结果

Fig. 3 Simulating results of tetracycline concentration from (a) DGM(1, 1), (b) DGM(1, 1, α), (c) EDGM(1, 1), and (d) EDGM(1, 1, α) models

图4 DGM(1, 1), DGM(1, 1, α), EDGM(1, 1), EDGM(1, 1, α)模型对四环素浓度的预测误差

Fig. 4 Simulated epsilon of tetracycline concentration from DGM(1, 1), DGM(1, 1, α), EDGM(1, 1), and EDGM(1, 1, α) models

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改进的灰色模型在光催化数据预测中的应用

Application of Improved Grey Model in Photocatalytic Data Prediction

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