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Article(id=1234106388436284174, tenantId=1146029695717560320, journalId=1234093305789726721, issueId=1234106384963400440, articleNumber=null, orderNo=null, doi=null, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1730822400000, receivedDateStr=2024-11-06, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1772163491590, onlineDateStr=2026-02-27, pubDate=1750348800000, pubDateStr=2025-06-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1772163491590, onlineIssueDateStr=2026-02-27, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1772163491590, creator=13701087609, updateTime=1772163491590, updator=13701087609, issue=Issue{id=1234106384963400440, tenantId=1146029695717560320, journalId=1234093305789726721, year='2025', volume='45', issue='6', pageStart='2961', pageEnd='3552', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1772163490763, creator=13701087609, updateTime=1772163969484, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1234108392948682946, tenantId=1146029695717560320, journalId=1234093305789726721, issueId=1234106384963400440, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1234108392948682947, tenantId=1146029695717560320, journalId=1234093305789726721, issueId=1234106384963400440, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=3151, endPage=3160, ext={EN=ArticleExt(id=1234106389958816571, articleId=1234106388436284174, tenantId=1146029695717560320, journalId=1234093305789726721, language=EN, title=Optimization of total phosphorus removal process in artificial percolation system based on BP-ANN, columnId=1234106386360103680, journalTitle=China Environmental Science, columnName=Water Pollution Control, runingTitle=null, highlight=null, articleAbstract=

Box-Behnken response surface methodology (BBD-RSM) and back propagation artificial neural network (BP-ANN) algorithms were used to model and predict the process parameters (contact time, initial concentration, temperature, pH) of activated carbon adsorption of total phosphorus (TP), and the reaction conditions in the BP-ANN model were optimized in combination with genetic algorithms (GA). The results showed that in the BBD-RSM model, the P<0.0001, which could better predict the TP removal process, and contact time was the most significant parameter for TP removal, with the relative influence order of the factors in the TP adsorption process being: contact time > pH > temperature > initial concentration. The BP-ANN model was used for optimization, and the optimal network structure was 4-8-1. Sensitivity analysis showed that the factors affecting the TP removal rate were ranked as contact time (34.05%) > pH (28.67%) > temperature (19.56%) > initial concentration (17.72%). Based on the BP-ANN model, the GA was used to optimize the operating conditions of the artificial percolation system, and the optimization results for the TP removal process were: contact time of 720.53min, initial concentration of 2.75mg/L, temperature of 30.62℃, and pH value of 5, achieving the optimal removal rate (99.63%). Experimental validation analysis showed that BP-ANN-GA had a higher R2 (0.9939) and lower RMSE (1.2851) compared with BBD-RSM when predicting against the experimental values, indicating that this model had better predictive ability and could better describe the TP removal process in the constructed rapid infiltration (CRI) system.

, correspAuthors=Yuan-kun LIU, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, authorCompany=null, fund=null, authors=null, authorsList=Yuan-kun LIU, Yuan-qi CAO, Ai-xin YU, Xing LI, Xiao-tian GUO), CN=ArticleExt(id=1234106398347424104, articleId=1234106388436284174, tenantId=1146029695717560320, journalId=1234093305789726721, language=CN, title=基于BP-ANN的人工渗滤系统去除总磷过程优化, columnId=1234106386565624579, journalTitle=中国环境科学, columnName=水污染与控制, runingTitle=null, highlight=null, articleAbstract=

本文利用BBD响应面法(BBD-RSM)和反向传播人工神经网络(BP-ANN)算法对活性炭吸附总磷(TP)的过程参数(接触时间、初始浓度、温度、pH值)进行了建模和预测，并结合遗传算法(GA)对BP-ANN模型中的反应条件进行优化.结果表明，在BBD-RSM模型中，P<0.0001，可较好的对TP的去除过程进行预测，接触时间为TP去除率最显著的参数，TP吸附过程中各因素的相对影响顺序为：接触时间>pH值>温度>初始浓度.采用BP-ANN模型进行优化，最佳网络结构为4-8-1.敏感性分析表明，影响TP去除率的因素依次为接触时间(34.05%)>pH值(28.67%)>温度(19.56%)>初始浓度(17.72%).基于BP-ANN模型，采用GA优化人工渗滤系统运行条件，对TP去除过程的优化结果为：接触时间为720.53min、初始浓度为2.75mg/L、温度为30.62℃、pH为5，达到最佳去除率(99.63%).试验验证分析表明，BP-ANN-GA较BBD-RSM的预测值与实验值相比拥有较高的R2(0.9939)和较低的RSME(1.2851)，说明该模型具有更好的预测能力，能更好的描述人工快速渗滤系统对TP的去除过程.

, correspAuthors=刘元坤, authorNote=null, correspAuthorsNote=
* 责任作者，副教授，
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刘元坤(1985-)，女，河北石家庄人，副教授，博士，主要从事水污染控制研究.发表论文20余篇..

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刘元坤(1985-)，女，河北石家庄人，副教授，博士，主要从事水污染控制研究.发表论文20余篇..

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刘元坤(1985-)，女，河北石家庄人，副教授，博士，主要从事水污染控制研究.发表论文20余篇..

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Journal of Cleaner Production，2019，232:1418-1429., articleTitle=Development of NOx reduction system utilizing artificial neural network (ANN) and genetic algorithm (GA), refAbstract=null)], funds=[Fund(id=1234106411907608871, tenantId=1146029695717560320, journalId=1234093305789726721, articleId=1234106388436284174, awardId=2018YFC0406203, language=CN, fundingSource=国家重点研发计划项目(2018YFC0406203), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1234106398771048852, tenantId=1146029695717560320, journalId=1234093305789726721, articleId=1234106388436284174, xref=null, ext=[AuthorCompanyExt(id=1234106398779437461, tenantId=1146029695717560320, journalId=1234093305789726721, articleId=1234106388436284174, companyId=1234106398771048852, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China), 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journalId=1234093305789726721, articleId=1234106388436284174, language=EN, label=Fig.2, caption=The correlation between the predicted BBD-RSM value and the experimental value, figureFileSmall=fA2K8dn6PtuC8Jtv8vElGQ==, figureFileBig=wpANeC8WUXUXTTgPiyw2QA==, tableContent=null), ArticleFig(id=1234106406090109872, tenantId=1146029695717560320, journalId=1234093305789726721, articleId=1234106388436284174, language=CN, label=图2, caption=BBD-RSM预测值与试验值的相关性, figureFileSmall=fA2K8dn6PtuC8Jtv8vElGQ==, figureFileBig=wpANeC8WUXUXTTgPiyw2QA==, tableContent=null), ArticleFig(id=1234106406249493436, tenantId=1146029695717560320, journalId=1234093305789726721, articleId=1234106388436284174, language=EN, label=Fig.3, caption=Effect of contact time and pH on TP removal under BBD-RSM model optimization, figureFileSmall=6UW7Yd462S2qz2B9cZeOgw==, figureFileBig=5/HZVEWL58yZqo0v5gXlzQ==, tableContent=null), ArticleFig(id=1234106406408877003, tenantId=1146029695717560320, journalId=1234093305789726721, 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values of neural networks under different hidden layer neurons of BP-ANN model, figureFileSmall=J1EZclz0WC6eGrb//XUWGQ==, figureFileBig=ArF/O5wfkNNZiLfgJrtxgQ==, tableContent=null), ArticleFig(id=1234106407168045058, tenantId=1146029695717560320, journalId=1234093305789726721, articleId=1234106388436284174, language=CN, label=图5, caption=BP-ANN模型不同隐藏层神经元下神经网络的MSE值, figureFileSmall=J1EZclz0WC6eGrb//XUWGQ==, figureFileBig=ArF/O5wfkNNZiLfgJrtxgQ==, tableContent=null), ArticleFig(id=1234106407344205840, tenantId=1146029695717560320, journalId=1234093305789726721, articleId=1234106388436284174, language=EN, label=Fig.6, caption=Correlation of TP removal test data with BP-ANN model simulation values, figureFileSmall=zenv5oqJMnRZq2W8fS99rA==, figureFileBig=pRKyNjoPhgh4uwmdm/yOgA==, tableContent=null), ArticleFig(id=1234106407486812186, tenantId=1146029695717560320, journalId=1234093305789726721, articleId=1234106388436284174, language=CN, label=图6, caption=TP去除试验数据与BP-ANN模型模拟值的相关性, 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ArticleFig(id=1234106408594108523, tenantId=1146029695717560320, journalId=1234093305789726721, articleId=1234106388436284174, language=EN, label=Table 1, caption=

Test variable horizontal range

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编号变量单位水平
低(-1)中(0)高(+1)
A接触时间min300600900
B初试浓度-总磷mg/L123
C温度℃152535
DpH值579
), ArticleFig(id=1234106408677994613, tenantId=1146029695717560320, journalId=1234093305789726721, articleId=1234106388436284174, language=CN, label=表1, caption=

试验变量水平范围

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编号变量单位水平
低(-1)中(0)高(+1)
A接触时间min300600900
B初试浓度-总磷mg/L123
C温度℃152535
DpH值579
), ArticleFig(id=1234106408778657915, tenantId=1146029695717560320, journalId=1234093305789726721, articleId=1234106388436284174, language=EN, label=Table 2, caption=

Predicted values and errors of TP removal rate under different conditions of different models

, figureFileSmall=null, figureFileBig=null, tableContent=
编号变量TP去除率(%)
ABCD试验值BBD-RSM预测误差BP-ANN预测误差
1300235779.6778.860.010279.78-0.0014
2600225789.7890.26-0.005389.450.0037
3900225987.6488.41-0.008887.66-0.0002
4900235791.3489.670.018391.35-0.0001
5600115785.385.84-0.006385.67-0.0043
6900325790.6190.82-0.002390.560.0006
7300325779.3879.190.002477.680.0214
8600125591.4191.040.004091.340.0008
9600225791.3790.260.012191.370.0000
10300215774.6375.02-0.005275.34-0.0095
11300125778.4277.80.007977.650.0098
12600315786.3786.66-0.003486.74-0.0043
13900125789.3889.160.002589.320.0007
14600235592.6492.110.005791.990.0070
15600225790.1390.26-0.001490.52-0.0043
16900215787.6887.210.005487.200.0055
17600135786.8888.28-0.016186.880.0000
18600215588.6387.770.009788.350.0032
19600225789.6490.26-0.006989.330.0035
20300225974.3974.69-0.004074.48-0.0012
21600125986.3485.610.008586.39-0.0006
22600335789.3690.51-0.012989.350.0001
23900225589.6191-0.015589.560.0006
24600225790.3890.260.001390.76-0.0042
25600235985.6686.11-0.005385.430.0027
26600325988.6687.750.010389.04-0.0043
27300225580.881.72-0.011481.01-0.0026
28600215984.0361.320.270384.020.0001
29600325592.4956.020.394392.400.0010
), ArticleFig(id=1234106408912875661, tenantId=1146029695717560320, journalId=1234093305789726721, articleId=1234106388436284174, language=CN, label=表2, caption=

不同模型不同条件下对TP去除率预测值和误差

, figureFileSmall=null, figureFileBig=null, tableContent=
编号变量TP去除率(%)
ABCD试验值BBD-RSM预测误差BP-ANN预测误差
1300235779.6778.860.010279.78-0.0014
2600225789.7890.26-0.005389.450.0037
3900225987.6488.41-0.008887.66-0.0002
4900235791.3489.670.018391.35-0.0001
5600115785.385.84-0.006385.67-0.0043
6900325790.6190.82-0.002390.560.0006
7300325779.3879.190.002477.680.0214
8600125591.4191.040.004091.340.0008
9600225791.3790.260.012191.370.0000
10300215774.6375.02-0.005275.34-0.0095
11300125778.4277.80.007977.650.0098
12600315786.3786.66-0.003486.74-0.0043
13900125789.3889.160.002589.320.0007
14600235592.6492.110.005791.990.0070
15600225790.1390.26-0.001490.52-0.0043
16900215787.6887.210.005487.200.0055
17600135786.8888.28-0.016186.880.0000
18600215588.6387.770.009788.350.0032
19600225789.6490.26-0.006989.330.0035
20300225974.3974.69-0.004074.48-0.0012
21600125986.3485.610.008586.39-0.0006
22600335789.3690.51-0.012989.350.0001
23900225589.6191-0.015589.560.0006
24600225790.3890.260.001390.76-0.0042
25600235985.6686.11-0.005385.430.0027
26600325988.6687.750.010389.04-0.0043
27300225580.881.72-0.011481.01-0.0026
28600215984.0361.320.270384.020.0001
29600325592.4956.020.394392.400.0010
), ArticleFig(id=1234106409042899096, tenantId=1146029695717560320, journalId=1234093305789726721, articleId=1234106388436284174, language=EN, label=Table 3, caption=

BBD-RSM Analysis of variance

, figureFileSmall=null, figureFileBig=null, tableContent=
项平方和自由度均方差FP
模型722.761451.6344.17< 0.0001显著
A-接触时间396.411396.41339.13< 0.0001显著
B-初始浓度6.9616.965.960.0286显著
C-温度29.8129.825.490.0002显著
D-pH值69.41169.4159.38< 0.0001显著
AB0.018210.01820.01560.9024不显著
AC0.476110.47610.40730.5336不显著
AD4.9314.934.220.0592不显著
BC0.49710.4970.42520.5249不显著
BD0.384410.38440.32890.5754不显著
CD1.4211.421.210.2896不显著
A2201.571201.57172.45< 0.0001显著
B21.2711.271.090.314不显著
C225.81125.8122.080.0003显著
D23.4613.462.960.1072不显著
残差16.36141.17
失拟项14.49101.453.090.1445不显著
纯误差1.8840.4696
总和739.1328
), ArticleFig(id=1234106410527682724, tenantId=1146029695717560320, journalId=1234093305789726721, articleId=1234106388436284174, language=CN, label=表3, caption=

BBD-RSM方差分析

, figureFileSmall=null, figureFileBig=null, tableContent=
项平方和自由度均方差FP
模型722.761451.6344.17< 0.0001显著
A-接触时间396.411396.41339.13< 0.0001显著
B-初始浓度6.9616.965.960.0286显著
C-温度29.8129.825.490.0002显著
D-pH值69.41169.4159.38< 0.0001显著
AB0.018210.01820.01560.9024不显著
AC0.476110.47610.40730.5336不显著
AD4.9314.934.220.0592不显著
BC0.49710.4970.42520.5249不显著
BD0.384410.38440.32890.5754不显著
CD1.4211.421.210.2896不显著
A2201.571201.57172.45< 0.0001显著
B21.2711.271.090.314不显著
C225.81125.8122.080.0003显著
D23.4613.462.960.1072不显著
残差16.36141.17
失拟项14.49101.453.090.1445不显著
纯误差1.8840.4696
总和739.1328
), ArticleFig(id=1234106410766758074, tenantId=1146029695717560320, journalId=1234093305789726721, articleId=1234106388436284174, language=EN, label=Table 4, caption=

BBD-RSM ANOVA fits statistical parameters

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标准差平均值变异系数C.V(%)决定系数R2调整决定系数Radj2预测决定系数Rpred2信噪比
1.0886.641.250.97790.95570.883122.4012
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BBD-RSM ANOVA拟合统计量参数

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标准差平均值变异系数C.V(%)决定系数R2调整决定系数Radj2预测决定系数Rpred2信噪比
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Table of weights and thresholds for BP-ANN models

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神经元输入层权重wi输入层偏置bi输出层权重wj输出层偏置bj
接触时间初始浓度温度pH值
11.08390.40440.4657-1.3216-2.8592-0.1367-0.7658
2-1.0990.2140.7553-1.97981.6648-0.0295
31.0578-1.17521.53-0.1994-1.10530.1699
42.02940.23031.2785-0.05771.02490.3969
50.3863-1.09791.5579-0.30371.15150.472
61.3232-1.61550.5562-0.75891.5121-0.0238
7-0.73730.50622.4609-0.6022-1.6372-0.4231
81.02680.2175-1.9051-0.77062.34990.2478
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BP-ANN模型的权值和阈值

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神经元输入层权重wi输入层偏置bi输出层权重wj输出层偏置bj
接触时间初始浓度温度pH值
11.08390.40440.4657-1.3216-2.8592-0.1367-0.7658
2-1.0990.2140.7553-1.97981.6648-0.0295
31.0578-1.17521.53-0.1994-1.10530.1699
42.02940.23031.2785-0.05771.02490.3969
50.3863-1.09791.5579-0.30371.15150.472
61.3232-1.61550.5562-0.75891.5121-0.0238
7-0.73730.50622.4609-0.6022-1.6372-0.4231
81.02680.2175-1.9051-0.77062.34990.2478
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Experimental validation of BBD-RSM and BP-ANN-GA models

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变量BBD-RSMBP-ANN-GA
预测试验预测试验
接触时间(min)703.81704720.53720
初始浓度(mg/L)2.612.62.752.8
温度31.4631.530.6230.5
pH值3.974.055
去除率(%)99.8097.7399.6398.82
相对误差(%)2.070.81
R20.97790.9939
RMSE2.97621.2851
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BBD-RSM和BP-ANN-GA模型的试验验证

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变量BBD-RSMBP-ANN-GA
预测试验预测试验
接触时间(min)703.81704720.53720
初始浓度(mg/L)2.612.62.752.8
温度31.4631.530.6230.5
pH值3.974.055
去除率(%)99.8097.7399.6398.82
相对误差(%)2.070.81
R20.97790.9939
RMSE2.97621.2851
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基于BP-ANN的人工渗滤系统去除总磷过程优化
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刘元坤 * , 曹塬琪 , 于艾鑫 , 李星 , 郭晓天
中国环境科学 | 水污染与控制 2025,45(6): 3151-3160
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中国环境科学 | 水污染与控制 2025, 45(6): 3151-3160
基于BP-ANN的人工渗滤系统去除总磷过程优化
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刘元坤* , 曹塬琪, 于艾鑫, 李星, 郭晓天
作者信息
  • 北京工业大学建筑工程学院，北京 100124

    • 刘元坤(1985-)，女，河北石家庄人，副教授，博士，主要从事水污染控制研究.发表论文20余篇..

通讯作者:

* 责任作者，副教授，
Optimization of total phosphorus removal process in artificial percolation system based on BP-ANN
Yuan-kun LIU* , Yuan-qi CAO, Ai-xin YU, Xing LI, Xiao-tian GUO
Affiliations
  • College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China
出版时间: 2025-06-20
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摘要
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本文利用BBD响应面法(BBD-RSM)和反向传播人工神经网络(BP-ANN)算法对活性炭吸附总磷(TP)的过程参数(接触时间、初始浓度、温度、pH值)进行了建模和预测，并结合遗传算法(GA)对BP-ANN模型中的反应条件进行优化.结果表明，在BBD-RSM模型中，P<0.0001，可较好的对TP的去除过程进行预测，接触时间为TP去除率最显著的参数，TP吸附过程中各因素的相对影响顺序为：接触时间>pH值>温度>初始浓度.采用BP-ANN模型进行优化，最佳网络结构为4-8-1.敏感性分析表明，影响TP去除率的因素依次为接触时间(34.05%)>pH值(28.67%)>温度(19.56%)>初始浓度(17.72%).基于BP-ANN模型，采用GA优化人工渗滤系统运行条件，对TP去除过程的优化结果为：接触时间为720.53min、初始浓度为2.75mg/L、温度为30.62℃、pH为5，达到最佳去除率(99.63%).试验验证分析表明，BP-ANN-GA较BBD-RSM的预测值与实验值相比拥有较高的R2(0.9939)和较低的RSME(1.2851)，说明该模型具有更好的预测能力，能更好的描述人工快速渗滤系统对TP的去除过程.

BBD响应面法  /  反向传播人工神经网络  /  遗传算法  /  总磷  /  人工快速渗滤系统

Box-Behnken response surface methodology (BBD-RSM) and back propagation artificial neural network (BP-ANN) algorithms were used to model and predict the process parameters (contact time, initial concentration, temperature, pH) of activated carbon adsorption of total phosphorus (TP), and the reaction conditions in the BP-ANN model were optimized in combination with genetic algorithms (GA). The results showed that in the BBD-RSM model, the P<0.0001, which could better predict the TP removal process, and contact time was the most significant parameter for TP removal, with the relative influence order of the factors in the TP adsorption process being: contact time > pH > temperature > initial concentration. The BP-ANN model was used for optimization, and the optimal network structure was 4-8-1. Sensitivity analysis showed that the factors affecting the TP removal rate were ranked as contact time (34.05%) > pH (28.67%) > temperature (19.56%) > initial concentration (17.72%). Based on the BP-ANN model, the GA was used to optimize the operating conditions of the artificial percolation system, and the optimization results for the TP removal process were: contact time of 720.53min, initial concentration of 2.75mg/L, temperature of 30.62℃, and pH value of 5, achieving the optimal removal rate (99.63%). Experimental validation analysis showed that BP-ANN-GA had a higher R2 (0.9939) and lower RMSE (1.2851) compared with BBD-RSM when predicting against the experimental values, indicating that this model had better predictive ability and could better describe the TP removal process in the constructed rapid infiltration (CRI) system.

box-behnken design response surface methodology (BBD-RSM)  /  back propagation artificial neural network (BP-ANN)  /  genetic algorithm (GA)  /  total phosphorus (TP)  /  constructed rapid infiltration (CRI) system
刘元坤, 曹塬琪, 于艾鑫, 李星, 郭晓天. 基于BP-ANN的人工渗滤系统去除总磷过程优化. 中国环境科学, 2025 , 45 (6) : 3151 -3160 .
Yuan-kun LIU, Yuan-qi CAO, Ai-xin YU, Xing LI, Xiao-tian GUO. Optimization of total phosphorus removal process in artificial percolation system based on BP-ANN[J]. China Environmental Science, 2025 , 45 (6) : 3151 -3160 .
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雨水被认为是水资源紧张城市的替代水资源之一[1]，雨水利用也是一种生态和可持续的水管理方法，可减少城市径流和洪水[2].但雨水径流中的磷污染物进入水体后会引起水体的富营养化，破坏水生生物的生存环境，携带的有毒有害物质会随生态循环最终进入人体，危害人类健康.
多年来，研究人员提出了多种技术用于去除水体中的总磷，包括生物滞留系统、吸附材料和人工快速渗滤技术等.已有研究表明，通过添加赤泥、粉煤灰、金属氧化物等改性材料可有效提升磷的去除效率，同时吸附剂的重复利用、使用寿命和实际应用条件下的稳定性也成为研究关注的重点[3-7].人工快速渗滤工艺(CRI)是在传统快速渗滤工艺基础上发展起来的一种新型污水处理技术，因其结构简单、运行成本低、适用性强且具有良好的去除颗粒态磷和部分溶解态磷的能力，因此在污水处理领域应用广泛.国内开展了大量人工快速渗滤系统的研究和示范工程[8].
除此以外，现有的滞留系统、吸附技术以及人工快速渗滤系统(CRI)等在实际应用中均需通过大量实验来优化填料、运行参数和操作条件，以实现最佳的除磷效果，这种实验设计不仅耗费大量时间和资源，还容易受实验条件的复杂性和不可控因素影响.以CRI为例，渗滤介质的吸附性能直接决定了处理效果和微生物生长状态.由于吸附过程复杂、变量间关系非线性，传统统计模型难以全面反映各因素对去除率的影响.考虑到试验成本高、数据有限，采用智能建模方法对吸附过程进行优化，这是获取最佳工艺条件、提升处理效率的有效途径[9-10].
响应面法(RSM)是一种集数学和统计于一体的方法，用于探究和建立一个或多个响应变量与多个因子之间的关系[11]，目前在废水处理等方面已有较多应用[12-17].人工神经网络(ANN)作为人工智能的主要工具之一，因其具有模拟非线性变化和处理不完全数据的能力而得到了广泛的应用[18-19].而在众多人工神经网络模型中，BP-ANN(反向传播人工神经网络)因其结构简单且功能强大，成为最经典且应用最广泛的一种.遗传算法(GA)是一种基于自然选择和遗传机制的全局优化方法，通过选择、交叉和变异等操作迭代搜索最优解，具有并行性强、鲁棒性高、适应性好等优势，特别适用于参数众多、搜索空间复杂或函数不可导的问题.相比其他优化算法，GA更能跳出局部最优，适合处理高维非线性优化任务.其在离散与连续变量混合优化方面表现优异，且参数设置相对简单，使其在优化BP-ANN模型时更具优势.因此，BP-ANN与GA的耦合(BP-ANN-GA)已成为预测和优化复杂过程参数的有效工具.当前，BP-ANN-GA方法已应用于各种废水处理过程，如膜过滤[20-21]，反渗透海水淡化装置[22]，催化剂高效分离[23]、废水厌氧消化[24].
本研究建立BBD-RSM和BP-ANN模型，分别对CRI处理雨水中TP的过程进行预测与优化.选取与TP去除密切相关的接触时间、TP初始浓度、温度、pH值为模型自变量，TP去除率为模型因变量.基于两类模型分别分析自变量与TP去除率响应的相互作用，同时寻找最优条件值确定TP最大去除率.采用均方根误差RMSE、决定系数R2评价两类模型预测精度及准确度，分析其适用性;对两种模型(BBD-RSM和BP-ANN-GA)的预测能力和建模效率进行了比较和评价.
1　材料与方法
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1.1　BBD-RSM
采用Design-Expert 12软件进行Box-Behnben试验设计，试验为4因素3水平，共29组试验，包括5个零点组，代表重复实验，用来估计试验误差，其中自变量分别为接触时间(A)、初始浓度(B)、温度(C)、pH值(D)，每个自变量包含高、中、低3个水平，分别被编码为-1,0,1，因变量为污染物(氨氮、TP)去除率，具体如表1所示.根据以上自变量和因变量建立二阶多项式模型，如公式(1)所示.
式中：Y表示污染物去除率;αi表示各项系数.
1.2　BP-ANN模型
采用Matlab 2019软件进行BP-ANN的设计，并对其进行训练.为了使输出值更加接近真实值，采用试差法确定隐含层神经元最优数量[25].将数据传入BP-ANN进行计算，基于相关文献和初步实验结果[26-27]学习速率设置为0.01，迭代次数设置为1000次，MSE目标设置为0.001时收敛速度和模型精度能够得到保证，且模型在不同隐藏层神经元数量下都能充分训练;输入层-隐藏层的函数选择具有良好的非线性建模能力、平滑性的Sigmoid函数，隐藏层-输出层函数选择适合处理回归任务的Linear函数.在选择反向传播算法时，Levenberge Marquardt(LM)算法作为二阶优化方法，能够提供更快速、更稳定的收敛性，能够有效处理小样本训练，也能通过精确的二阶信息加速收敛过程，尤其是在反向传播和权重更新的过程中，能够快速且准确地调节网络权重同时收敛更快速，拥有更强的全局搜索能力[28-29]，因此选用LM算法作为反向传播算法.本研究共采用29组实验数据作为神经网络的输入，这些数据集被分为四组，分别作为训练集(16组)、测试集(4组)、验证集(4组)和仿真测试集(5组).用仿真组数据来评估网络训练后的泛化能力.数据的标准化可以加快训练网络的收敛性并且减少不同数量级的影响，提高网络的训练速度[30].因此采用式(2)将所有的输入和输出变量都归一化到0~1之间.归一化后的数据作为输入集，用于训练和测试神经网络，最后输出数据再进行反归一化.
式中：Xi表示标准值;Xmin,Xmax分别为数据集中的最小值和数据集中的最大值.
1.3　模型精度评估
为了反应BBD-RSM及BP-ANN模型精度，选用均方误差MSE、均方根误差RMSE、决定系数R2 3个参数.MSE主要用于直观评判BP-ANN隐含层神经元个数的合适程度，R2、RMSE用于展示两个模型的耦合程度及结果预测的准确性，同时可据此判断模型是否出现过拟合.
1.4　敏感性分析
通过BP-ANN得到的权值，用Garson方程进行敏感性分析，Garson方程是一种用于分析人工神经网络中输入变量相对重要性的方法，主要用于确定哪些输入变量对输出结果有更大的影响[31].Garson方程如式(3)所示[32].
式中：N,L,M分别为输入层，隐藏层和输出层的神经元数量;w,v分别为输入层和隐藏层、隐藏层和输出层之间的权值.
1.5　遗传算法优化
为了快速寻找最优反应条件，采用遗传算法(GA)作为基于人工智能的随机非线性优化形式主义，将开发的ANN模型被用作适应度函数.算法开始时，随机生成一组解，通过计算每个解的适应度来评估解的优劣，再根据适应度值大小挑选出较优解进行繁殖，通过交叉和变异操作产生新的解，新产生的种群再次进行适应度评估，并重复选择、交叉和变异的过程[33].这个过程一直持续到收敛形成解，使总磷去除率达到最大，如式(4)所示：
条件值：
式中：Ai、Bi、Ci、Di分别为GA的第i次迭代中对应的4个条件的数值；Fitness函数为TP去除率；NeuralNetwork为经过训练的BP-ANN.GA与BP-ANN相结合对人工快速渗滤系统去除TP的优化流程如图1所示.
2　结果与讨论
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2.1　响应面模型建立与吸附过程优化
如表2所示，5个重复组(表2第2、9、15、19、24组)的试验值比较接近，说明数据具有较好的重现性.除28、29组外，其余相对误差均小于0.2，预测值与试验值吻合较好，表明模型具有较好的预测能力.用二次多项式模型来拟合因素之间的关系，模型结果如式(5)、式(6)所示.通过编码方程可知，接触时间(A)系数最高且为正，说明对TP去除率的影响最大，这与动力学模型结论一致.其次影响最大的变量是pH值(D)，系数为负，说明在试验范围内，TP吸附量随pH值的增大而降低，这与pH值影响因素试验中对TP的影响结果一致.
由表3、表4可以看出，F为44.17>0.1，P<0.0001，表明模型非常显著，在整个回归区域拟合良好.Radj2-Rpred2=0.0726<0.2，C.V.=1.15%<10%，表明实验具有较高的可靠性和准确性.Adeq精度是有效信噪比，模型的Adeq精度=22.8713>4，表明模型可靠，有足够的信号响应设计.如图2所示，R2=0.9779表明预测值与实际值有很强的相关性.因此，所得到的模型可以很好地估计研究范围内的预测响应.模型回归系数的显著性检验表明：只有A、B、C、D、A2、C2对TP去除率的影响是显著的.
如图3所示，随着pH的增加，TP去除率逐渐降低，且接触时间越长，其下降的幅度越小，说明当反应时间足够长时，pH对TP去除率的影响会逐渐减小.这主要是因为pH对TP的影响主要是改变雨水中磷酸根的形态，而随着反应时间的增加，雨水中的磷酸根不断被吸附到吸附剂表面，因此pH的影响也随之减弱.从接触时间来看，随着接触时间的增加，TP去除率也随之增加，达到一定值后趋势减缓，说明接触时间对TP去除率的贡献逐渐趋于饱和.这与动力学结果一致.
由图3(a)可以看出，接触时间与pH值的交互作用较显著[34].当pH值接近最优值时，随着接触时间的增加，TP去除率逐渐接近最优去除率.图3(b)接触时间与pH值的交互作用表明，存在一个最佳的TP去除率区域，即接触时间700~900min，pH5的一个半椭圆区域，该区域可以得到一个较高的TP去除率(90%以上).
如图4所示，随着温度的升高，TP的去除率逐渐升高，达到一定值后趋势放缓，说明在15~35℃范围内，温度的升高有利于TP去除.
Braun等[35]发现在pH=3时，载铁活性炭对磷的吸附容量随温度的升高而增加;而在pH=5.5时，磷的吸附容量随温度的升高先降低再增加;在pH=8.0时，磷的吸附容量随温度的升高先增加再降低.可能是铁的负载改变了活性炭的表面特性.图4(a)反映出，接触时间和温度之间的相互作用相对显著，即温度在接近最优值时，随着接触时间的增加，TP的去除率逐渐到达极限值，图4(b)接触时间为600~900min、温度为20~35℃的区域，TP去除率在90%以上.接触时间比温度对TP去除率的影响更大.
TP吸附的最优条件采用求偏微分法，计算试验范围内TP去除率的最大值及相应的试验条件.偏微分结果：
方程解为：A=703.81min，B=2.61mg/L，C=31.46℃，D=3.97.因此确定，在试验范围内，活性炭吸附去除TP的最佳条件为：接触时间703.81min，初始浓度2.61mg/L，温度31.46℃，pH =3.97，去除率为96.80%.
2.2　BP-ANN模型的建立
对BP-ANN进行训练，目的是确定隐含层神经元数量找到最佳网络结构.用试错法不断改变隐藏层神经元的数量，每种结构重复10次，对不同神经元对应的MSE取平均后进行比较，选择最小的MSE所对应的隐藏层神经元数量，以尽可能提高计算效率及模型准确率.如图5所示，在隐藏层神经元数量为8时MSE最低.因此，在后文研究中均采用4-8-1的神经网络结构，即输入层为4个神经元，隐藏层为8个神经元，输出层为1个神经元.
随后应用BP-ANN模型对TP去除率进行预测，如图6、7所示，预测值与试验值有非常强的线性关系，训练集、验证集、测试集以及仿真测试集的R2分别为0.98591、0.93628、0.96636和0.9939,4个数据集之间相差不大，且仿真测试集中模型的拟合较为准确，因此可以确定模型并没有出现过拟合的现象.表明该神经网络模型的试验结果与预测结果具有良好的一致性.
如图8所示，第一次迭代后，模型的MSE即达到最小值，说明此时模型的误差最小，可用来对试验进行预测.用试验数据对训练后的神经网络进行测试，预测结果与实际数据的R2为0.9939(表6)，说明BP-ANN模型对TP去除率具有较好的预测能力.
2.3　BP-ANN模型对人工渗滤系统运行参数的敏感性分析
对基于TP吸附数据训练的BP-ANN模型进行了敏感性分析，使用训练所得的权重和偏差值见表5.通过应用Garson方程，计算出各输入因素对TP去除率的贡献比例分别为：接触时间(34.05%)、初始浓度(17.72%)、温度(19.56%)、pH值(28.67%)，接触时间对TP去除率的影响最大，其次是pH值和温度，初始浓度的影响最小.这一排序与RSM的结果相符.
2.4　遗传算法优化人工渗滤系统运行条件
在完成BP-ANN模型构建后，将该模型的输出值作为适应度函数，以最大化吸附TP为目标，采用GA对网络的输入空间进行优化.设置初始种群数为500，交叉概率为0.9，变异概率选择0.001，模型迭代次数设置为500.通过在上下限之间搜索过程变量的最优点，确定优化目标.优化过程的收敛性如图9所示.经过大约35次迭代，适应值趋于稳定.在第294次迭代后，适应值基本没有进一步变化，表明遗传算法已找到最优解.优化结果表明，在接触时间为720.53min、初始浓度为2.75mg/L、温度为30.62℃、pH为5的条件下，TP的最大去除率可达99.63%.
2.5　BDD-RSM与BP-ANN-GA模型对比分析
由表6可以看出，相较于BDD-RSM, BP-ANN-GA拥有较高的R2(0.9939)和较低的RSME(1.2851)且相对误差也控制在1%以内，说明该模型具有更好的预测性能.这是因为BP-ANN-GA可以估计几乎所有的非线性问题，而响应面模型仅能对二阶多项式进行估计[36].经实验验证，BP-ANN-GA优化的结果更符合真实值，说明其优化性能优于BBD-RSM.
BBD-RSM模型优化结果显示了各因素相互作用对污染物去除率的影响，并提供了直观的图形解释自变量与响应值之间关系.该方法只需要少量的试验就可以获得更多的信息，减少了时间和成本.但它只能提供一阶或二阶多项式模型.而BP-ANN可以模拟任何形式的非线性问题，只需一定的数据量，不需要试验设计就可以确定其相互关系.GA可以在训练好的BP-ANN模型基础上对输入变量在规定的范围内寻找最优解，弥补BP-ANN在局部最优解、输入空间探索不足、输入参数选择依赖人工经验等方面的短板.因此，BP-ANN-GA模型具有更高的预测性能、鲁棒性和适用性，是一种应用更广泛的方法.然而BP-ANN-GA模型的训练数据来自特定实验条件下，环境因素(温度、pH值、初始污染物浓度等)的变化范围有限，数据量较小，如在实际应用中遇到极端条件等更复杂的变量之间的相互关系时，模型可能无法准确预测，需要进一步验证，但BP-ANN-GA模型的初步预测可为后续验证、优化起到一定指导作用.
2.6　BP-ANN-GA模型误差分析及改进
模型在预测时不可避免的会产生误差，产生的误差可能来源于：(1)实验中测量值可能存在一定误差，例如pH值、温度等变量的测量精度有限，可能会引入噪声，影响模型的训练效果和预测精度.(2)模型内部的初始权重是随机生成的，这可能导致后续训练中模型陷入局部最优，从而导致模型预测值与真实值之间存在一定偏差.在后续的改进中，可以通过：(1)增加数据点，覆盖更多变量范围和极端条件，提升模型的泛化能力.(2)对数据进行预处理，剔除数据中的异常值，减小数据中噪音的影响.(3)引入其他优化算法(如粒子群算法、模拟退火算法等)改进模型初始权重的选择，避免训练中权重陷入局部最优解.
BP-ANN-GA已经展现出了其强大的预测能力，在实际水处理应用中，可以将BP-ANN-GA模型嵌入在线监测系统，实时预测污染物去除率，同时寻求特定水质和处理目标下的最优运行条件，确保水处理工艺在不同负荷和环境条件下高效运行.辅助决策者快速调整工艺参数(如接触时间、pH值和温度).但同时，其在实际应用中可能面临以下挑战：(1)实际水处理系统中的数据可能包含更多噪声(如传感器误差和环境干扰)，对模型的预测精度构成威胁.(2)实际工艺条件可能与实验室环境差异较大，模型需要经过大量的校准和验证才能适应不同的实际场景.针对以上可能出现的问题，解决方案为：(1)开发自动化的数据清洗和异常检测方法，提高输入数据的质量和可靠性.(2)将BP-ANN-GA模型集成到水处理厂的智能控制系统中，针对不同类型的水处理工艺，通过现场数据重新训练或迁移学习技术增强模型的适用性.
3　结论
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3.1　采用BBD-RSM和BP-ANN-GA对活性炭吸附TP的过程参数(接触时间、初始浓度、温度、pH值)进行了建模和优化.经过试差法确定BP-ANN的模型结构为4-8-1.
3.2　通过Garson分析，影响TP去除率的因素及权重依次为：接触时间(34.05%)，pH值(28.67%)、温度(19.56%)和初始浓度(17.72%).
3.3　分别采用BBD-RSM和BP-ANN-GA模型对实验结果进行验证，结果发现BBD-RSM模型的R2为0.9779，RMSE为2.9762，而BP-ANN-GA模型的R2为0.9939，RMSE为1.2851，结果表明BP-ANN-GA模型的预测精度优于BBD-RSM模型，更符合真实情况.
3.4　BP-ANN-GA模型优化结果表明，在接触时间为720.53min、初始浓度为2.75mg/L、温度为30.62℃、pH值为5的条件下，TP的最大去除率可达99.63%.综合上述，BP-ANN-GA对活性炭吸附去除雨水TP的过程及参数优化具有更高的预测性能、鲁棒性和适用性.
基金
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2025年第45卷第6期
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  • 接收时间：2024-11-06
  • 首发时间：2026-02-27
  • 出版时间：2025-06-20
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  • 收稿日期：2024-11-06
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国家重点研发计划项目(2018YFC0406203)
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    北京工业大学建筑工程学院，北京 100124

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