CN108469507B - 一种基于自组织rbf神经网络的出水bod软测量方法 - Google Patents
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Abstract
一种基于自组织RBF神经网络的出水BOD软测量方法涉及人工智能领域,直接应用于污水处理领域。针对当前污水处理过程出水BOD无法实时获取、仪器设备造价高、测量结果准确性低等问题,本发明提出了一种基于自组织RBF神经网络的出水BOD软测量方法,该方法包括:使用基于互信息的方法提取出水BOD特征参量作为软测量模型的输入变量;设计一种基于误差校正‑敏感度分析的自组织RBF神经网络,使用改进的Levenberg–Marquardt(LM)算法对网络进行训练以提高训练速度;结果表明该软测量模型结构紧凑,能够快速、准确地预测污水处理出水BOD浓度,为污水处理过程安全、平稳运行提供理论支撑与技术保障。
Description
技术领域:
本发明涉及人工智能领域,直接应用于污水处理领域,尤其涉及一种基于自组织RBF神经网络的出水BOD软测量方法。
背景技术:
生化需氧量(Biochemical Oxygen Demand,BOD)是反映水体被有机物污染程度的重要参数,是评价污水水质的重要指标及污水处理过程的重要控制参数,能否对BOD进行快速、准确测量是有效控制水体污染的关键所在。目前BOD测量的标准方法是稀释与接种法,但是该方法程序较为繁琐,测定周期较长,存在严重的滞后性,并不能及时反映水体中BOD的变化。近年来,多种BOD微生物传感器相继问世,然而如何适应强酸碱、毒害、高盐度等特殊水质环境成为微生物传感器面临的主要问题,同时其具有造价高、寿命短、稳定性差等缺点,降低了微生物传感器的普适性。因此,如何低成本、高效率地对出水BOD浓度进行检测是污水处理过程面临的难题。
软测量方法采用间接测量的思路,利用易测变量,通过构建模型对难测变量或不可测变量进行实时预测,是解决污水处理过程关键水质参数测量的关键技术。本发明设计了一种基于自组织RBF神经网络的污水处理出水BOD软测量方法,实现出水BOD浓度的在线预测。
发明内容
1、本发明需要且能够解决的技术问题。
本发明提出了一种基于自组织RBF神经网络的污水处理出水BOD软测量方法。使用基于互信息的特征提取方法提取出水BOD辅助变量作为软测量模型的输入变量,并设计一种基于误差校正-敏感度分析的自组织RBF神经网络,对污水处理出水BOD进行预测,旨在提高预测精度及实时性。
2、本发明具体的技术方案:
本发明提供了一种基于自组织RBF神经网络的污水处理出水生化需氧量(BOD)软测量方法。该算法包括:
步骤1:确定出水BOD辅助变量;
采集污水处理厂实际水质参数数据,记O={op|k=1,2,...,P}为出水BOD浓度,为初步选择的可能与出水BOD相关的第j个水质变量,其中J为水质变量个数,P为水质变量的样本个数,为第j个水质变量的第p个样本值;
步骤1.1:计算各变量Fj与输出变量O之间的归一化互信息NI(Fj;O),计算公式为:
其中,H(Fj)与H(O)分别为变量Fj与输出变量O的熵,I(Fj;O)为变量Fj与输出变量O的互信息;
步骤1.2:设置阈值δ∈[0,1],选取满足NI(Fj;O)>δ的特征变量,个数记为I,所形成的相关特征集合记为SR;
步骤1.3:初始化参数i1=1,i2=i1+1;
步骤1.7:令i1=i1+1,返回步骤1.4;
步骤1.8:令S=SR,S为选取的辅助变量集合,结束;
经步骤1,得到出水BOD的辅助变量,个数记为M;
步骤2:设计出水BOD的RBF神经网络预测模型结构;
步骤2.1:将由步骤1获取的M个辅助变量按照公式(3)归一化至[-1,1],输出变量出水BOD按照公式(4)归一化至[0,1]:
其中,Fm表示第m个辅助变量,O表示输出变量,xm和y分别表示归一化后的第m个辅助变量和输出变量;
步骤2.2:设计出水BOD软测量模型结构包括三层:输入层、隐含层和输出层,确定其拓扑结构为M-H-1,即输入层包含M个神经元,分别对应步骤2.1中归一化后的M个辅助变量,隐含层包含H个神经元,输出层包含1个神经元,对应出水BOD变量;
步骤2.3:设共有P个训练样本,对第p个样本(p=1,2,…,P),神经网络输入为xp=[xp,1,xp,2,...,xp,M],其中xp,m(m=1,2,…,M)表示第m个辅助变量的第p个样本;此时,神经网络的输出层神经元的输出为:
其中,wh为第h个(h=1,2,…,H)隐含层神经元与输出层神经元的连接权值,φh(xp)为RBF神经网络第h个隐含层神经元的激活函数,定义如公式(6)所示:
其中,ch、σh分别为第h个隐含层神经元的中心和宽度;
步骤2.4:选取均方误差函数为性能指标,由下式定义:
其中,dp为第p个样本的期望输出,yp为第p个样本的网络输出,P为训练样本数;
步骤3:出水BOD软测量模型结构自组织设计
步骤3.1:神经网络隐含层神经元个数H初始化为0,神经元变化次数n初始化为0;
步骤3.2:计算当前第p个样本的网络输出误差:
ep=dp-yp (8)
其中p=1,2,…,P;对所有训练样本,寻找误差最大的训练样本,如公式(9):
其中e=[e1,e2,...,eP]T;新增加一个RBF神经元,神经元个数H=H+1,按照公式(10)-(12)设置神经元初始参数;
cH=xpmax (10)
σH=1 (11)
wH=1 (12)
其中,cH=[cH,1,cH,2,...,cH,10]、σH分别为第H个隐含层神经元的中心和宽度,wH为第H个隐含层神经元与输出层神经元的连接权值,xpmax为第pmax个输入样本;设置参数n=n+1;
步骤3.3:在当前网络结构下,令向量Δ包含所有需要更新的参数,即:
更新规则如下:
Δ(k+1)=Δ(k)-(Q(k)+μ(k)I)-1g(k) (14)
其中,k表示迭代步数,Q为类海森矩阵,g为梯度向量,I为单位矩阵,μ为学习率参数。类海森矩阵及梯度向量分别根据公式(15)和(16)计算得到:
其中,ep为第p个样本的网络输出误差,根据式(8)计算,jp为对应样本的雅可比矩阵行向量,定义如下:
根据公式(5)-(8),求得:
通过公式(18)-(20),可得到雅可比矩阵的行向量jp,当将所有训练样本遍历一遍后,则可得到类海森矩阵Q和梯度向量g,进而根据参数更新公式(14)对各参数进行更新;
在训练过程中,当E(k+1)≤E(k)时,μ(k+1)=μ(k)/10,神经网络当前参数保留;反之,μ(k+1)=μ(k)×10,神经网络参数恢复至参数调整前,基于当前μ对网络参数进行更新;设最大迭代步数为Tmax,Tmax∈[100,500],期望误差值为Ed,Ed∈(0,0.01];神经网络参数学习过程经过不断迭代,当迭代步数T=Tmax或当前训练误差E≤Ed时,对当前网络训练停止;若训练停止时训练误差E>Ed,当时,返回步骤3.2,当时,执行步骤3.4,这里为求余操作,N为[3,10]范围内的整数;否则,跳至步骤3.5;
步骤3.4:在当前网络结构下,计算第h个隐含层神经元的敏感度:
定义隐含层神经元的删减规则为:当NSIh<γNSImean时,神经元个数H=H-R,将隐含层对应神经元删除,这里NSImean为当前所有隐含层神经元的归一化敏感度均值,R为满足删减条件的隐含层神经元个数,γ在[0,0.5]范围内取值;
选择与所删除神经元欧式距离最近的神经元,其中心和宽度不变,对其与输出神经元的连接权值进行更新,更新规则如下:
其中,ws为所删除神经元s与输出神经元之间的连接权值,wt和w't分别为在删除神经元s前后与神经元s欧式距离最近的神经元t与输出神经元之间的连接权值;
令n=n+1,返回步骤3.3;
步骤3.5:设最大总迭代次数为Ttmax,Ttmax∈[1000,2000];当训练误差E≤Ed或总迭代次数Ttotal=Ttmax时,训练停止,得到训练后的神经网络结构及对应参数;
步骤4:将测试样本数据作为训练后的自组织RBF神经网络的输入,得到自组织RBF神经网络的输出,将其进行反归一化得到出水BOD浓度的预测值。
3、本发明与现有技术相比,具有以下明显的优势和有益效果:
本发明针对当前污水处理过程出水BOD测量存在的不足,采用基于互信息的方法提取出与出水BOD相关的辅助变量,提出了一种基于自组织RBF神经网络的出水BOD软测量方法,实现了出水BOD浓度的实时测量,在一定程度上提高了出水BOD的预测精度,具有实时性好、稳定性好、精度高等特点。
附图说明:
图1为本发明的出水BOD软测量模型的结构示意图;
图2为本实施例出水BOD软测量模型的训练均方根误差(RMSE)变化图;
图3为本实施例训练过程中隐含层节点变化图;
图4为本实施例出水BOD软测量模型的预测结果图;
图5为本实施例出水BOD测试误差图。
具体实施方式:
本发明提供了一种基于自组织RBF神经网络的出水BOD软测量方法,实现了出水BOD的实时测量,解决了污水处理过程出水BOD浓度难以实时测量的问题,提高了城市污水处理厂出水BOD实时监控水平,保障污水处理过程正常运行;
本发明实例采用某污水厂2011年水质分析数据,共包含360组数据,23个水质变量,包括(1)进水PH;(2)出水PH;(3)进水固体悬浮物浓度(Suspended Solid,SS);(4)出水SS;(5)进水BOD浓度;(6)进水化学需氧量(Chemical Oxygen Demand,COD)浓度;(7)出水COD浓度;(8)生化池污泥沉降比(Settling Velocity,SV);(9)生化池混合液悬浮固体浓度(Mixed Liquid Suspended Solids,MLSS);(10)生化池溶解氧浓度(Dissolved Oxygen,DO);(11)进水油类;(12)出水油类;(13)进水氨氮浓度;(14)出水氨氮浓度;(15)进水色度;(16)出水色度;(17)进水总氮浓度;(18)出水总氮浓度;(19)进水磷酸盐浓度;(20)出水磷酸盐浓度;(21)进水水温;(22)出水水温;(23)出水BOD浓度;随机选取260组数据作为训练样本,剩余100组数据作为测试样本;
一种基于自组织RBF神经网络的出水BOD软测量方法包括以下步骤:
步骤1:确定出水BOD辅助变量;
采集污水处理厂实际水质参数数据,记O={op|k=1,2,...,P}为出水BOD浓度,为初步选择的可能与出水BOD相关的第j个水质变量,其中J为水质变量个数,P为水质变量的样本个数,为第j个水质变量的第p个样本值;
步骤1.1:计算各变量Fj与输出变量O之间的归一化互信息NI(Fj;O),计算公式为:
其中,H(Fj)与H(O)分别为变量Fj与输出变量O的熵,I(Fj;O)为变量Fj与输出变量O的互信息;
步骤1.2:设置阈值δ∈[0,1],选取满足NI(Fj;O)>δ的特征变量,个数记为I,所形成的相关特征集合记为SR;
步骤1.3:初始化参数i1=1,i2=i1+1;
步骤1.7:令i1=i1+1,返回步骤1.4;
步骤1.8:令S=SR,S为选取的辅助变量集合,结束;
本实施例中,设定阈值δ=0.8,经此步骤,共得到M=10个出水BOD的辅助变量,包括:(1)出水总氮浓度;(2)出水氨氮浓度;(3)进水总氮浓度;(4)进水BOD浓度;(5)进水氨氮浓度;(6)出水磷酸盐浓度;(7)生化MLSS浓度;(8)生化池DO浓度;(9)进水磷酸盐浓度;(10)进水COD浓度;
步骤2:设计出水BOD的RBF神经网络预测模型结构;
步骤2.1:将由步骤1获取的M个辅助变量按照公式(26)归一化至[-1,1],输出变量出水BOD按照公式(27)归一化至[0,1]:
其中,Fm表示第m个辅助变量,O表示输出变量,xm和y分别表示归一化后的第m个辅助变量和输出变量;
步骤2.2:设计出水BOD软测量模型结构包括三层:输入层、隐含层和输出层,确定其拓扑结构为M-H-1,即输入层包含M个神经元,分别对应步骤2.1中归一化后的M个辅助变量,隐含层包含H个神经元,输出层包含1个神经元,对应出水BOD变量;模型结构如图1所示;
步骤2.3:设共有P个训练样本,对第p个样本(p=1,2,…,P),神经网络输入为xp=[xp,1,xp,2,...,xp,M],其中xp,m(m=1,2,…,M)表示第m个辅助变量的第p个样本;此时,神经网络的输出层神经元的输出为:
其中,wh为第h个(h=1,2,…,H)隐含层神经元与输出层神经元的连接权值,φh(xp)为RBF神经网络第h个隐含层神经元的激活函数,定义如公式(29)所示:
其中,ch、σh分别为第h个隐含层神经元的中心和宽度;
步骤2.4:选取均方误差函数为性能指标,由下式定义:
其中,dp为第p个样本的期望输出,yp为第p个样本的网络输出,P为训练样本数;
步骤3:出水BOD软测量模型结构自组织设计
步骤3.1:神经网络隐含层神经元个数H初始化为0,神经元变化次数n初始化为0;
步骤3.2:计算当前第p个样本的网络输出误差:
ep=dp-yp (31)
其中p=1,2,…,P;对所有训练样本,寻找误差最大的训练样本,如公式(32):
其中e=[e1,e2,...,eP]T;新增加一个RBF神经元,神经元个数H=H+1,按照公式(33)-(35)设置神经元初始参数;
cH=xpmax (33)
σH=1 (34)
wH=1 (35)
其中,cH=[cH,1,cH,2,...,cH,10]、σH分别为第H个隐含层神经元的中心和宽度,wH为第H个隐含层神经元与输出层神经元的连接权值;xpmax为第pmax个输入样本;设置参数n=n+1;
步骤3.3:在当前网络结构下,令向量Δ包含所有需要更新的参数,即:
更新规则如下:
Δ(k+1)=Δ(k)-(Q(k)+μ(k)I)-1g(k) (37)
其中,k表示迭代步数,Q为类海森矩阵,g为梯度向量,I为单位矩阵,μ为学习率参数。类海森矩阵及梯度向量分别根据公式(38)和(39)计算得到:
其中,ep为第p个样本的网络输出误差,根据式(31)计算,jp为对应样本的雅可比矩阵行向量,定义如下:
根据公式(28)-(31),求得:
通过公式(41)-(43),可得到雅可比矩阵的行向量jp,当将所有训练样本遍历一遍后,则可得到类海森矩阵Q和梯度向量g,进而根据参数更新公式(37)对各参数进行更新;
在训练过程中,当E(k+1)≤E(k)时,μ(k+1)=μ(k)/10,神经网络当前参数保留;反之,μ(k+1)=μ(k)×10,神经网络参数恢复至参数调整前,基于当前μ对网络参数进行更新;设最大迭代步数为Tmax=100,期望误差值为Ed=0.01;神经网络参数学习过程经过不断迭代,当迭代步数T=Tmax或当前训练误差E≤Ed时,对当前网络训练停止;若训练停止时训练误差E>Ed,当mod(n,N)=0时,执行步骤3.4,这里为求余操作,设置N=5;否则,跳至步骤3.5;
步骤3.4:在当前网络结构下,计算第h个隐含层神经元的敏感度:
定义隐含层神经元的删减规则为:当NSIh<γNSImean时,神经元个数H=H-R,将隐含层对应神经元删除,这里NSImean为当前所有隐含层神经元的归一化敏感度均值,R为满足删减条件的隐含层神经元个数,本实施例中设置γ=0.3;
选择与所删除神经元欧式距离最近的神经元,其中心和宽度不变,对其与输出神经元的连接权值进行更新,更新规则如下:
其中,ws为所删除神经元s与输出神经元之间的连接权值,wt和w't分别为在删除神经元s前后与神经元s欧式距离最近的神经元t与输出神经元之间的连接权值;
令n=n+1,返回步骤3.3;
步骤3.5:设最大总迭代次数为Ttmax=1000,当训练误差E≤Ed或总迭代次数Ttotal=Ttmax时,训练停止,得到训练后的神经网络结构及对应参数;
在本实施例中,出水BOD软测量模型的训练均方根误差(RMSE)变化图如图2所示,X轴:训练总迭代次数,Y轴:训练RMSE,单位是mg/L;训练过程中隐含层节点变化如图3所示,X轴:训练总迭代次数,Y轴:训练过程隐含层神经元个数,单位是个;
步骤4:将测试样本数据作为训练后的自组织RBF神经网络的输入,得到自组织RBF神经网络的输出,将其进行反归一化得到出水BOD浓度的预测值;
在本实施例中,出水BOD软测量模型的预测结果如图4所示,X轴:测试样本个数,单位是个,Y轴:预测出水BOD浓度值,单位是mg/L,实线为出水BOD浓度预测输出值,虚线为出水BOD浓度期望输出值;测试误差如图5所示,X轴:测试样本个数,单位是个,Y轴:出水BOD预测误差,单位是mg/L;结果表明基于自组织RBF神经网络的出水BOD软测量方法的有效性。
表1-23是本发明实验数据,其中表1-11为训练样本:出水总氮、出水氨氮、进水总氮、进水BOD、进水氨氮、出水磷酸盐、生化MLSS、生化池DO、进水磷酸盐、进水COD和实测出水BOD浓度,表12-22为测试样本:出水总氮、出水氨氮、进水总氮、进水BOD、进水氨氮、出水磷酸盐、生化MLSS、生化池DO、进水磷酸盐、进水COD和实测出水BOD浓度,表23为本发明出水BOD浓度预测值。
训练样本:
表1.辅助变量出水总氮(mg/L)
表2.辅助变量出水氨氮(mg/L)
表3.辅助变量进水总氮(mg/L)
10.7400 | 13.8277 | 14.3774 | 9.0199 | 10.6588 | 10.9643 | 13.9733 | 8.6603 | 12.6598 | 9.9619 |
8.6030 | 7.6164 | 10.0112 | 10.3533 | 13.4553 | 11.4942 | 13.3670 | 10.2889 | 7.8591 | 14.6686 |
9.8040 | 10.6461 | 12.7043 | 10.7066 | 10.6198 | 7.9824 | 12.3534 | 8.8194 | 12.3733 | 10.8482 |
10.8275 | 12.4235 | 8.7772 | 16.8016 | 14.9821 | 12.0973 | 14.5032 | 12.8945 | 8.4009 | 10.7654 |
7.7724 | 13.6757 | 9.0422 | 9.0438 | 9.9900 | 10.8466 | 10.2691 | 12.5587 | 9.6691 | 10.7081 |
14.6137 | 10.6095 | 8.3182 | 8.7454 | 12.9048 | 12.1331 | 12.6136 | 9.9881 | 17.3387 | 10.1544 |
10.5124 | 8.4964 | 12.0662 | 14.9574 | 10.9341 | 12.5698 | 9.6953 | 8.6523 | 10.3541 | 13.2023 |
15.7872 | 11.4075 | 13.4386 | 12.9740 | 10.6063 | 15.0036 | 9.5250 | 12.4577 | 9.1002 | 10.7225 |
10.6652 | 13.0758 | 14.6997 | 8.3007 | 8.1145 | 11.1139 | 9.9762 | 14.6541 | 13.0416 | 9.2434 |
9.5768 | 14.1046 | 8.8297 | 10.9802 | 10.7097 | 12.2532 | 18.5005 | 8.9897 | 10.2562 | 9.3262 |
11.9127 | 10.7750 | 13.3145 | 10.8370 | 9.7399 | 10.9134 | 6.7540 | 10.4846 | 12.8356 | 7.5639 |
13.9446 | 13.1650 | 6.7270 | 9.0644 | 10.1640 | 10.5188 | 10.2276 | 10.6763 | 13.6121 | 9.7248 |
10.6700 | 17.5137 | 14.9805 | 8.7470 | 9.0867 | 11.1473 | 10.7798 | 10.9787 | 10.4456 | 11.8697 |
8.4343 | 10.6509 | 10.2037 | 10.1760 | 11.4369 | 10.8895 | 14.1722 | 8.6428 | 10.1019 | 9.2697 |
8.9531 | 11.1775 | 10.9182 | 8.3444 | 15.2035 | 17.4015 | 10.6938 | 16.8520 | 11.0948 | 13.5389 |
10.9301 | 14.9081 | 13.4347 | 13.7282 | 13.2262 | 10.1560 | 9.7200 | 8.4821 | 12.5738 | 10.7416 |
12.8817 | 8.5942 | 10.5904 | 11.0200 | 10.6135 | 11.1059 | 8.7955 | 7.1455 | 12.2556 | 14.9328 |
14.0067 | 12.0710 | 7.9546 | 12.3272 | 11.7822 | 12.2293 | 8.2163 | 10.3621 | 11.3208 | 10.5649 |
10.3867 | 14.0528 | 12.8539 | 14.2207 | 10.3215 | 10.8800 | 12.5921 | 9.2761 | 13.6200 | 10.3008 |
11.0479 | 12.9629 | 5.8900 | 12.6804 | 7.9586 | 11.6676 | 10.5936 | 8.3404 | 10.0112 | 7.7947 |
13.7712 | 9.4320 | 9.1599 | 12.3566 | 9.1042 | 11.3072 | 10.4790 | 9.4320 | 9.0724 | 15.9026 |
12.5460 | 14.8834 | 10.4520 | 12.9279 | 10.8052 | 12.7337 | 8.0501 | 12.8125 | 8.8822 | 11.4982 |
13.8364 | 9.1726 | 10.3438 | 9.5991 | 10.8689 | 10.7622 | 8.9411 | 11.2340 | 14.2692 | 17.6012 |
11.5085 | 12.4163 | 14.8588 | 13.8412 | 9.1201 | 12.6486 | 7.1860 | 10.7885 | 12.7767 | 9.4917 |
11.0757 | 8.9873 | 12.9533 | 12.8587 | 17.9624 | 17.6887 | 14.3377 | 15.0068 | 11.0471 | 10.4313 |
12.6144 | 12.8618 | 10.7813 | 10.0830 | 12.4967 | 8.9308 | 10.6779 | 11.0391 | 11.4282 | 9.2363 |
表4.辅助变量进水BOD(mg/L)
表5.辅助变量进水氨氮(mg/L)
表6.辅助变量出水磷酸盐(mg/L)
17.0525 | 11.3244 | 13.7038 | 13.1456 | 12.5288 | 16.5238 | 12.9400 | 15.3781 | 9.4444 | 16.1419 |
16.8175 | 16.1713 | 17.4050 | 15.6131 | 14.1738 | 13.1456 | 11.7944 | 15.3488 | 16.3475 | 13.6744 |
16.9938 | 16.1419 | 14.5556 | 16.8469 | 17.4344 | 16.6706 | 7.2706 | 16.7881 | 7.5938 | 17.6694 |
17.0819 | 14.0269 | 16.7294 | 17.7575 | 14.2031 | 17.2875 | 13.8506 | 14.1738 | 16.7294 | 16.7294 |
15.9656 | 15.5544 | 13.0575 | 13.9094 | 17.1994 | 16.7588 | 17.5078 | 8.9156 | 17.2288 | 16.4944 |
13.3219 | 16.6119 | 16.5825 | 16.9350 | 11.5006 | 5.8900 | 9.2975 | 14.2325 | 17.9925 | 17.1700 |
16.3769 | 17.1113 | 8.7981 | 14.0856 | 17.7575 | 14.2619 | 17.0231 | 17.2288 | 14.9375 | 18.8444 |
13.4688 | 13.0281 | 14.4381 | 11.8531 | 16.8469 | 17.5225 | 16.6853 | 8.3869 | 14.1150 | 16.8469 |
17.2288 | 14.2619 | 12.7050 | 16.5238 | 16.7588 | 16.1713 | 15.7894 | 17.2222 | 9.3269 | 14.4088 |
17.6106 | 17.4050 | 17.0525 | 16.4650 | 17.3756 | 6.7419 | 15.9428 | 13.3513 | 15.5544 | 14.9375 |
13.6744 | 16.9644 | 15.1431 | 17.7281 | 14.2913 | 16.6119 | 16.6119 | 14.1150 | 11.1481 | 16.6119 |
14.1738 | 11.4125 | 16.4944 | 12.9694 | 17.3463 | 16.5238 | 15.6719 | 17.4931 | 11.9413 | 15.9069 |
16.7294 | 18.3450 | 18.1688 | 14.5263 | 12.8813 | 12.6756 | 16.9056 | 13.1456 | 16.3769 | 13.4981 |
16.9350 | 16.2594 | 16.2594 | 17.4050 | 10.4138 | 16.7000 | 14.2031 | 16.7000 | 15.7306 | 14.7319 |
13.4100 | 11.1188 | 11.8238 | 16.7000 | 17.0394 | 16.3083 | 17.1700 | 16.4911 | 17.7869 | 17.7281 |
14.6731 | 13.8506 | 10.3256 | 14.4088 | 14.4675 | 16.7881 | 16.0244 | 17.0819 | 8.6513 | 17.4638 |
11.3831 | 17.0231 | 17.4050 | 17.8456 | 17.3169 | 17.9338 | 14.2913 | 16.5531 | 7.3294 | 13.9681 |
14.3794 | 13.8506 | 16.6706 | 13.9388 | 10.2669 | 14.0269 | 15.6719 | 17.6106 | 12.9106 | 16.4944 |
14.7319 | 14.0563 | 11.0013 | 12.3231 | 15.1431 | 17.1994 | 14.3206 | 17.6988 | 14.5263 | 16.5825 |
11.4713 | 11.0306 | 16.3769 | 9.9731 | 16.3475 | 13.3806 | 16.0244 | 16.9938 | 16.9938 | 16.5825 |
12.5581 | 17.8163 | 16.9644 | 7.8581 | 15.0844 | 10.7663 | 15.5544 | 16.5825 | 17.2288 | 17.6400 |
14.3794 | 13.7331 | 14.3206 | 11.6181 | 17.6400 | 10.1494 | 16.9644 | 11.0306 | 15.2313 | 11.7356 |
14.2913 | 17.2875 | 15.8775 | 15.9656 | 17.8163 | 17.5813 | 13.5863 | 12.7931 | 13.8213 | 18.5213 |
13.0869 | 7.8581 | 13.6156 | 14.5556 | 17.5813 | 8.3281 | 16.7294 | 12.1763 | 14.2031 | 14.3500 |
17.5225 | 13.7038 | 14.7319 | 11.2656 | 14.9963 | 18.6975 | 14.0269 | 14.3206 | 16.3181 | 16.2006 |
9.4444 | 10.5019 | 17.4931 | 17.3022 | 14.1444 | 13.4981 | 17.2875 | 16.3475 | 13.4100 | 16.8763 |
表7.辅助变量生化MLSS(mg/L)
表8.辅助变量生化池DO(mg/L)
16.7213 | 9.1935 | 11.0349 | 14.4467 | 11.2515 | 13.0116 | 9.5726 | 13.2011 | 7.6772 | 13.0928 |
12.6054 | 13.1470 | 10.3308 | 12.2805 | 10.4933 | 10.1684 | 10.0600 | 16.3963 | 16.1797 | 10.3850 |
11.0349 | 10.0059 | 11.7389 | 14.9883 | 16.3422 | 14.5009 | 9.2477 | 15.9089 | 10.2225 | 14.1759 |
15.0966 | 11.3056 | 14.2301 | 16.0172 | 10.6016 | 15.5840 | 9.0311 | 11.0890 | 14.9883 | 15.9089 |
14.7716 | 9.9517 | 16.3963 | 16.4505 | 10.1142 | 13.9051 | 9.4643 | 9.0311 | 15.8548 | 15.9631 |
8.9769 | 16.1797 | 12.6595 | 12.8220 | 11.1432 | 10.2767 | 9.8434 | 14.2842 | 14.2842 | 12.6595 |
11.8472 | 12.8762 | 10.0600 | 11.5764 | 15.9631 | 9.4643 | 12.3888 | 13.2011 | 13.3094 | 16.6130 |
9.4102 | 9.2477 | 11.0349 | 11.0349 | 16.1797 | 16.1256 | 10.6558 | 10.7641 | 14.2842 | 12.9303 |
16.1256 | 10.1142 | 10.7641 | 15.9089 | 14.7716 | 15.3132 | 10.7641 | 12.5512 | 10.1142 | 16.1797 |
16.2339 | 11.4681 | 17.9127 | 16.0172 | 16.2880 | 11.0890 | 11.4140 | 13.8510 | 15.9089 | 16.1256 |
9.9517 | 13.9051 | 9.9517 | 16.8837 | 15.9631 | 11.7389 | 13.9051 | 17.1004 | 9.7893 | 10.3308 |
8.1646 | 11.3598 | 14.5550 | 14.8258 | 16.9379 | 15.9089 | 15.3674 | 16.9921 | 11.2515 | 14.9883 |
15.9089 | 13.5802 | 16.2339 | 16.9379 | 14.1218 | 8.9769 | 16.1797 | 10.8182 | 13.3636 | 10.8724 |
15.3674 | 12.6054 | 14.0135 | 10.1142 | 10.6558 | 12.4971 | 9.0311 | 12.6595 | 15.7465 | 14.8258 |
11.9014 | 8.3812 | 10.6016 | 12.9303 | 10.6016 | 11.2515 | 16.3422 | 10.3308 | 14.0676 | 16.0172 |
9.3560 | 9.9517 | 10.8724 | 9.4102 | 11.1432 | 14.4467 | 13.7968 | 13.8510 | 9.5185 | 16.7213 |
10.1142 | 19.0500 | 16.2339 | 16.0172 | 14.2842 | 16.4505 | 15.0424 | 16.9921 | 5.8900 | 10.8724 |
10.7099 | 11.8472 | 15.2049 | 10.5474 | 8.8686 | 7.1356 | 15.8548 | 8.9769 | 10.7641 | 13.4719 |
16.3422 | 10.0600 | 11.3598 | 10.4933 | 16.0172 | 14.0135 | 9.7351 | 15.1507 | 10.0600 | 13.7968 |
11.3598 | 10.0600 | 14.9341 | 10.2225 | 11.6847 | 10.2225 | 15.6381 | 15.4215 | 15.8006 | 16.0714 |
10.5474 | 15.8006 | 13.5802 | 10.1684 | 15.3674 | 10.9807 | 16.0172 | 11.1432 | 12.6595 | 14.2842 |
11.3598 | 9.4643 | 15.5840 | 9.6809 | 16.5047 | 11.0349 | 16.5047 | 10.0600 | 16.0172 | 10.0059 |
10.0600 | 16.2339 | 16.5588 | 12.7137 | 14.6092 | 13.5260 | 16.1256 | 8.1646 | 10.2225 | 16.6130 |
8.9228 | 10.2225 | 12.6595 | 9.3560 | 8.2729 | 8.9769 | 17.5878 | 10.4933 | 10.8724 | 14.8258 |
11.7930 | 13.0928 | 14.1218 | 9.6809 | 11.4140 | 14.4467 | 10.6558 | 9.6268 | 15.0966 | 16.1797 |
11.1973 | 7.7313 | 15.3674 | 10.9265 | 10.9807 | 15.9089 | 17.2628 | 16.5047 | 10.2767 | 12.4971 |
表9.辅助变量进水磷酸盐(mg/L)
7.2501 | 11.6090 | 12.0624 | 7.0671 | 10.8229 | 7.0629 | 11.6881 | 7.0588 | 12.1248 | 6.4806 |
6.5472 | 5.8900 | 6.9964 | 6.6179 | 8.7058 | 8.3731 | 11.1265 | 7.1045 | 6.0314 | 9.7831 |
15.8182 | 17.5485 | 8.9596 | 7.3458 | 7.4248 | 6.4515 | 7.2085 | 6.6761 | 7.2834 | 7.4248 |
7.2376 | 9.6042 | 6.6012 | 7.8365 | 9.7997 | 7.2750 | 10.0659 | 10.0160 | 6.5638 | 7.0712 |
6.6761 | 9.0053 | 7.1212 | 6.9922 | 16.8955 | 7.0213 | 18.5114 | 12.5823 | 6.8383 | 6.9922 |
10.4361 | 7.3166 | 6.4141 | 6.6137 | 8.2941 | 6.9090 | 7.6577 | 7.0047 | 7.8989 | 7.1627 |
7.2875 | 6.7510 | 10.0410 | 9.7498 | 7.4414 | 9.4046 | 6.9756 | 6.8258 | 7.1461 | 8.0736 |
11.3304 | 8.2691 | 10.3280 | 8.2192 | 7.3000 | 7.7035 | 14.2023 | 13.0398 | 7.0629 | 7.2542 |
7.3125 | 10.1200 | 11.7463 | 6.2061 | 7.3166 | 6.9381 | 6.4432 | 7.9086 | 12.7819 | 6.6678 |
7.1378 | 7.6369 | 6.5971 | 6.9797 | 7.1919 | 7.0962 | 9.8108 | 7.0047 | 7.0837 | 7.3458 |
8.7308 | 7.2459 | 8.8556 | 7.4081 | 6.8924 | 7.0005 | 6.3392 | 7.2293 | 8.3689 | 6.3392 |
11.1307 | 10.9394 | 6.1146 | 7.1752 | 7.2750 | 7.2459 | 6.5596 | 7.3915 | 12.1622 | 6.3267 |
7.2626 | 7.9572 | 7.6743 | 6.4432 | 7.2293 | 7.9572 | 7.0421 | 10.6066 | 6.7635 | 8.2566 |
7.3749 | 6.9132 | 6.6220 | 17.9727 | 12.9941 | 7.1253 | 10.6316 | 6.3642 | 6.5014 | 7.2750 |
6.9049 | 12.2704 | 11.5466 | 6.3142 | 8.1804 | 9.2673 | 7.3541 | 8.9956 | 7.4622 | 7.4747 |
16.0470 | 9.6500 | 12.1955 | 10.6649 | 11.3345 | 6.8882 | 6.3392 | 7.2376 | 7.5080 | 7.2459 |
8.3190 | 7.4040 | 7.3749 | 7.4581 | 7.3499 | 7.4747 | 6.5555 | 6.2269 | 13.9549 | 9.6999 |
10.9144 | 8.7765 | 7.2875 | 11.0434 | 11.5425 | 8.8223 | 6.8674 | 19.0500 | 8.1651 | 7.2792 |
7.1669 | 11.3636 | 8.0320 | 11.0226 | 7.1253 | 7.2293 | 8.5561 | 7.1253 | 10.4319 | 6.8258 |
11.9085 | 10.7522 | 5.8900 | 8.4355 | 6.0481 | 8.5811 | 6.8342 | 6.6761 | 6.9506 | 7.2584 |
11.5009 | 7.2002 | 6.7676 | 13.4973 | 7.2501 | 12.6322 | 6.6761 | 13.6637 | 6.7385 | 7.7700 |
8.9138 | 9.6001 | 7.2085 | 8.2691 | 7.3541 | 7.8449 | 7.0130 | 8.3939 | 7.1544 | 13.0440 |
10.8978 | 6.8134 | 7.1378 | 6.2685 | 7.4622 | 7.4081 | 6.8924 | 8.0612 | 11.8295 | 7.9863 |
8.1069 | 8.5187 | 9.5502 | 11.1973 | 7.0504 | 13.3684 | 6.5638 | 11.1848 | 11.1889 | 6.7801 |
7.5745 | 6.9215 | 8.7058 | 8.3440 | 10.4985 | 8.0154 | 10.3488 | 9.8496 | 6.9589 | 7.1919 |
8.4563 | 11.2097 | 7.4081 | 17.4341 | 9.5044 | 6.8508 | 7.1378 | 7.0005 | 10.7522 | 6.7884 |
表10.辅助变量进水COD(mg/L)
表11.实测出水BOD浓度(mg/L)
11.2000 | 14.2000 | 14.8000 | 11.8571 | 11.6714 | 10.9000 | 14.5142 | 11.5285 | 14.3142 | 10.7285 |
11.0285 | 10.1000 | 10.3000 | 11.1571 | 13.1428 | 12.4285 | 14.0857 | 11.4285 | 10.1714 | 13.0714 |
12.5200 | 12.1714 | 12.6428 | 10.5142 | 10.4142 | 11.0857 | 12.8571 | 11.0000 | 12.7142 | 11.3571 |
10.7142 | 13.6285 | 11.1000 | 13.4714 | 13.5285 | 11.8714 | 13.0428 | 13.8428 | 11.0428 | 10.9142 |
11.7000 | 13.2000 | 12.2714 | 10.5428 | 12.3800 | 10.9857 | 12.1700 | 14.4857 | 10.2714 | 10.9714 |
13.8000 | 10.3571 | 11.2000 | 10.9428 | 12.6714 | 12.8000 | 12.6285 | 11.6857 | 12.9571 | 10.8000 |
10.2000 | 10.4000 | 12.5285 | 13.4571 | 11.3428 | 13.2857 | 10.9000 | 10.6000 | 11.4857 | 11.9000 |
13.1285 | 12.2714 | 13.8857 | 12.5000 | 11.6285 | 14.9571 | 12.7300 | 14.6571 | 10.7142 | 10.5428 |
11.3000 | 13.8571 | 12.8714 | 10.1571 | 12.2428 | 10.7000 | 11.0285 | 15.5000 | 14.6000 | 11.8142 |
11.4428 | 15.7000 | 10.4571 | 10.8428 | 11.3714 | 12.7571 | 14.1000 | 12.7571 | 11.4000 | 11.4000 |
12.8571 | 10.6285 | 13.0000 | 11.7142 | 11.7285 | 10.9142 | 11.6714 | 11.6000 | 12.8428 | 11.1285 |
14.2857 | 13.9428 | 11.2142 | 12.6857 | 10.3714 | 11.5714 | 11.1142 | 11.3857 | 12.6142 | 10.9428 |
10.4571 | 12.6714 | 11.9857 | 11.9000 | 13.1000 | 11.8000 | 11.0571 | 11.7857 | 10.5000 | 12.2000 |
12.3857 | 11.0285 | 10.6142 | 12.2400 | 12.1000 | 11.0000 | 12.9857 | 10.1857 | 11.0714 | 11.2285 |
10.6142 | 11.9571 | 11.8142 | 10.3142 | 15.3000 | 14.5000 | 11.6857 | 14.7000 | 11.1428 | 11.9285 |
12.2428 | 13.3142 | 14.4000 | 14.0285 | 12.7142 | 10.8142 | 10.8428 | 12.4142 | 12.9142 | 11.4571 |
12.7285 | 12.4571 | 11.4000 | 11.3285 | 10.7000 | 11.3142 | 12.0714 | 11.1714 | 15.0000 | 13.3857 |
12.9571 | 12.8142 | 12.1714 | 12.3428 | 12.4571 | 12.7714 | 11.6142 | 12.1000 | 12.1142 | 10.2857 |
11.5142 | 14.4142 | 12.5428 | 14.0000 | 11.4571 | 10.8000 | 12.6000 | 11.4000 | 13.9000 | 10.6571 |
11.8857 | 13.8000 | 11.3000 | 12.8142 | 10.1285 | 12.7428 | 11.0857 | 10.2000 | 10.9714 | 12.1000 |
14.3714 | 11.6000 | 10.8000 | 14.8285 | 11.4428 | 12.0285 | 11.2000 | 12.8000 | 10.5285 | 14.2142 |
12.6857 | 13.2428 | 11.5714 | 12.6142 | 11.6285 | 12.5857 | 12.2285 | 12.9000 | 11.4857 | 12.3857 |
14.1571 | 10.6857 | 11.4571 | 10.9000 | 11.8000 | 11.3714 | 12.5857 | 11.9571 | 14.6714 | 12.5285 |
12.0000 | 12.6428 | 13.1714 | 12.9285 | 11.2000 | 14.8000 | 11.8571 | 11.7428 | 12.5285 | 11.7714 |
10.4571 | 10.3714 | 12.8000 | 12.7857 | 13.6428 | 12.3857 | 13.0142 | 13.6000 | 10.7714 | 11.5142 |
12.7714 | 13.9714 | 11.7428 | 12.3100 | 13.4571 | 10.2000 | 11.2857 | 10.8000 | 11.9714 | 11.0000 |
测试样本:
表12.辅助变量出水总氮(mg/L)
9.9242 | 10.3871 | 16.6500 | 6.3685 | 15.9342 | 8.8142 | 11.4314 | 15.6500 | 14.2200 | 9.3600 |
7.2500 | 10.5414 | 11.3822 | 7.0557 | 14.9885 | 9.7466 | 14.7428 | 16.2850 | 16.2071 | 7.4600 |
16.2914 | 15.3800 | 15.6871 | 15.9800 | 11.8285 | 7.3800 | 15.9510 | 6.8357 | 16.3314 | 5.9857 |
10.9085 | 16.0857 | 14.9742 | 6.6671 | 15.4428 | 10.1555 | 8.9614 | 7.7200 | 8.8914 | 13.5642 |
8.1285 | 11.2014 | 15.2614 | 15.7928 | 16.1885 | 12.2000 | 15.7840 | 8.9200 | 12.2914 | 15.0057 |
5.8900 | 11.0342 | 15.5400 | 15.6214 | 7.8042 | 15.4200 | 8.8800 | 6.0814 | 7.6442 | 14.2714 |
15.3700 | 8.0314 | 15.4314 | 6.5785 | 9.1771 | 15.6171 | 14.8828 | 15.4857 | 9.2957 | 7.2871 |
15.3157 | 15.8257 | 15.8000 | 7.8971 | 14.2914 | 15.9642 | 15.9828 | 8.7714 | 13.8942 | 16.0957 |
6.8685 | 9.3800 | 16.5071 | 13.7571 | 15.1228 | 7.5257 | 15.2771 | 9.1200 | 8.0871 | 8.1700 |
15.0400 | 15.2885 | 11.0714 | 14.1771 | 15.9571 | 14.4600 | 8.6400 | 15.5657 | 15.5185 | 16.4971 |
表13.辅助变量出水氨氮(mg/L)
9.4897 | 8.7420 | 16.2193 | 6.9261 | 15.3113 | 7.1718 | 9.9490 | 14.6918 | 10.5472 | 9.0090 |
7.6418 | 9.3295 | 6.1463 | 7.4068 | 14.3179 | 8.2827 | 16.3581 | 13.0361 | 15.3327 | 6.2745 |
15.3968 | 15.2793 | 14.3713 | 10.8570 | 8.4429 | 6.3600 | 12.4059 | 8.1331 | 15.0656 | 7.2572 |
8.8168 | 17.1913 | 14.8840 | 6.7659 | 14.1470 | 8.5604 | 8.4536 | 6.6056 | 7.6952 | 10.4190 |
6.7231 | 8.5177 | 13.9868 | 14.3286 | 16.3154 | 7.7806 | 11.9465 | 7.4602 | 9.3936 | 14.8627 |
7.3747 | 9.4363 | 14.2325 | 15.2900 | 7.4602 | 16.8495 | 8.3361 | 7.5990 | 7.2786 | 11.2736 |
14.2004 | 8.3254 | 14.2325 | 7.6845 | 7.6845 | 15.8240 | 15.2259 | 17.7681 | 8.8275 | 9.5218 |
14.4888 | 13.5381 | 16.6893 | 6.2852 | 15.1190 | 14.6704 | 16.3581 | 6.3386 | 10.9745 | 14.6170 |
7.7272 | 8.7420 | 15.6104 | 15.0763 | 9.8102 | 6.6056 | 14.2218 | 9.1693 | 7.6204 | 7.9943 |
15.7172 | 14.2645 | 6.7659 | 10.6006 | 14.7345 | 12.0320 | 8.4322 | 15.0656 | 16.4329 | 13.7090 |
表14.辅助变量进水总氮(mg/L)
9.0382 | 8.8926 | 11.5316 | 13.2572 | 8.8083 | 12.5245 | 13.0146 | 10.7129 | 12.9509 | 17.2512 |
12.8626 | 8.8441 | 17.9510 | 12.7894 | 9.8409 | 15.7530 | 8.5871 | 9.8970 | 9.8664 | 14.1610 |
9.3302 | 8.9141 | 10.8148 | 11.2141 | 12.7942 | 10.5291 | 9.7110 | 8.4383 | 9.7216 | 12.5317 |
8.9952 | 9.6707 | 8.7542 | 12.6430 | 10.5363 | 16.3025 | 16.4221 | 13.6757 | 12.2309 | 12.4935 |
13.5691 | 10.2364 | 10.8036 | 9.2522 | 9.5004 | 19.0500 | 9.6180 | 14.8341 | 10.4193 | 8.9849 |
12.3503 | 13.2350 | 10.6461 | 8.7963 | 9.2132 | 9.3151 | 15.4531 | 12.7131 | 12.3877 | 12.4823 |
11.1919 | 9.1567 | 10.6174 | 7.9944 | 8.9753 | 8.4606 | 9.8505 | 9.0302 | 8.9976 | 10.6556 |
10.9977 | 10.7734 | 10.5013 | 14.1754 | 8.1018 | 9.7081 | 9.8409 | 12.7608 | 12.7465 | 8.9642 |
9.2140 | 17.8638 | 11.0725 | 8.2744 | 7.6180 | 11.8777 | 10.0828 | 16.3521 | 11.5809 | 11.7544 |
6.3085 | 10.9007 | 16.8748 | 12.5484 | 10.8227 | 12.3503 | 14.5541 | 10.3247 | 8.8878 | 8.9897 |
表15.辅助变量进水BOD(mg/L)
表16.辅助变量进水氨氮(mg/L)
10.0260 | 10.1931 | 12.9922 | 15.1124 | 9.5664 | 16.8201 | 13.9531 | 10.0469 | 12.4021 | 17.2483 |
13.1854 | 10.4647 | 11.5300 | 12.7729 | 9.3680 | 14.7260 | 10.8407 | 13.0340 | 11.1853 | 13.2794 |
11.5822 | 10.7623 | 9.3262 | 13.0967 | 13.0236 | 11.6762 | 10.4856 | 9.5247 | 10.9138 | 11.8642 |
10.5117 | 11.7807 | 10.3811 | 12.1880 | 8.6264 | 15.5250 | 17.4416 | 13.8904 | 13.1698 | 13.6816 |
14.4544 | 9.8432 | 10.0991 | 10.1304 | 12.8460 | 17.1178 | 11.8642 | 15.3161 | 9.7231 | 11.0078 |
12.7990 | 14.8043 | 9.8693 | 10.3393 | 10.7519 | 10.0991 | 14.7469 | 12.7572 | 13.5614 | 12.2298 |
10.3602 | 9.7701 | 10.1722 | 10.1304 | 10.2767 | 10.7728 | 10.0521 | 9.6239 | 8.6317 | 17.0917 |
10.3498 | 9.7388 | 9.6604 | 13.6972 | 9.5351 | 8.2922 | 10.3811 | 16.7418 | 12.8982 | 9.9007 |
18.3084 | 17.7967 | 11.1644 | 9.5560 | 16.9193 | 12.1149 | 9.8902 | 13.6711 | 12.4700 | 13.2951 |
13.1228 | 9.5612 | 13.8173 | 13.1384 | 9.7179 | 13.0862 | 15.2743 | 9.8798 | 11.3629 | 6.5167 |
表17.辅助变量出水磷酸盐(mg/L)
13.1163 | 13.8213 | 17.6106 | 14.3500 | 17.3463 | 11.1775 | 11.4125 | 17.0525 | 11.7356 | 17.8163 |
14.7319 | 14.0563 | 16.1256 | 14.6144 | 16.0831 | 16.8567 | 16.8763 | 17.0966 | 17.1994 | 13.9388 |
17.0525 | 17.1994 | 16.8763 | 13.2044 | 10.0319 | 12.8813 | 16.8909 | 15.5250 | 17.4050 | 13.9975 |
14.4675 | 17.2288 | 17.1113 | 14.3794 | 15.7894 | 16.6739 | 18.6094 | 14.7319 | 13.9094 | 8.4456 |
12.1763 | 14.1738 | 17.0819 | 17.1700 | 17.1406 | 15.7600 | 16.7881 | 13.4981 | 14.5263 | 16.8763 |
13.9094 | 12.7931 | 17.1994 | 17.0819 | 14.5263 | 17.4050 | 17.5813 | 14.0856 | 14.2031 | 8.3869 |
18.0219 | 14.3206 | 16.6119 | 15.8188 | 13.3219 | 16.7000 | 15.8481 | 17.1700 | 13.2338 | 16.8469 |
17.5519 | 17.5519 | 17.8163 | 13.3219 | 16.5238 | 17.2581 | 17.3169 | 9.9731 | 10.5019 | 17.4638 |
16.4063 | 19.0500 | 17.4638 | 16.8469 | 16.8469 | 13.6744 | 16.2006 | 17.6988 | 13.2631 | 13.4981 |
16.4356 | 17.3169 | 14.2325 | 8.9156 | 16.9644 | 7.3294 | 17.4638 | 16.3181 | 17.0525 | 16.8763 |
表18.辅助变量生化MLSS(mg/L)
14.8134 | 14.1204 | 18.3070 | 13.4559 | 17.1710 | 15.4849 | 13.9417 | 14.2704 | 14.2204 | 7.1903 |
13.8846 | 13.7917 | 16.0279 | 13.7703 | 17.3496 | 15.4064 | 16.9281 | 13.7774 | 17.6926 | 13.8774 |
17.3496 | 18.1855 | 12.9773 | 15.6064 | 13.8846 | 14.7062 | 13.1702 | 15.0706 | 17.4711 | 14.1204 |
13.0844 | 17.7069 | 18.3713 | 14.6062 | 17.6068 | 16.0851 | 15.5278 | 14.5419 | 14.1204 | 13.5202 |
13.9632 | 11.7913 | 14.0632 | 17.6997 | 17.5711 | 15.8850 | 13.9489 | 11.8699 | 12.2700 | 17.5568 |
14.3490 | 14.3561 | 13.9918 | 17.4639 | 15.4206 | 16.9924 | 7.2260 | 13.9346 | 14.2275 | 14.8134 |
13.0987 | 15.6921 | 16.2137 | 15.5993 | 15.2706 | 17.7783 | 17.8926 | 17.1567 | 15.6921 | 15.4135 |
13.6345 | 15.1634 | 16.8352 | 14.0561 | 17.5140 | 18.0355 | 18.2498 | 14.0346 | 15.6135 | 17.3139 |
15.1277 | 15.2920 | 18.2284 | 18.5285 | 18.1427 | 14.5847 | 17.4854 | 7.2260 | 14.9563 | 15.6207 |
17.8712 | 13.8632 | 15.7779 | 14.9420 | 17.5282 | 15.5278 | 7.5118 | 17.4854 | 17.3496 | 17.3496 |
表19.辅助变量生化池DO(mg/L)
15.8548 | 15.8548 | 16.5047 | 11.9014 | 15.2591 | 12.3346 | 10.5474 | 16.5588 | 11.1432 | 13.5802 |
11.2515 | 14.7716 | 12.3346 | 11.3056 | 14.2842 | 11.3056 | 13.4719 | 10.6016 | 14.0135 | 11.0349 |
14.1759 | 14.7716 | 11.1973 | 8.1646 | 8.1646 | 11.7930 | 9.0852 | 14.7716 | 13.7427 | 9.5726 |
17.1545 | 14.8258 | 13.8510 | 10.0600 | 16.1256 | 11.3598 | 14.8258 | 10.7641 | 9.9517 | 9.7893 |
8.9228 | 16.1797 | 15.8548 | 14.7175 | 12.7137 | 11.6306 | 11.1432 | 8.5437 | 16.9379 | 15.8548 |
11.1432 | 9.4643 | 14.5009 | 12.5512 | 14.2301 | 13.0386 | 13.1470 | 8.8686 | 11.3056 | 10.6016 |
14.3384 | 16.0172 | 14.4467 | 15.6381 | 15.0424 | 13.7427 | 16.5588 | 12.9303 | 15.8548 | 14.3926 |
11.6847 | 16.2880 | 16.1256 | 10.0600 | 16.3963 | 14.3384 | 16.0172 | 8.3812 | 10.6558 | 16.1797 |
12.4971 | 16.6671 | 17.3712 | 15.9631 | 16.4505 | 11.0890 | 14.3926 | 16.4505 | 10.7641 | 9.7893 |
14.1759 | 16.1797 | 10.2767 | 10.1142 | 13.3636 | 9.5185 | 13.5260 | 13.0928 | 14.9341 | 15.2591 |
表20.辅助变量进水磷酸盐(mg/L)
7.1170 | 6.7801 | 7.7242 | 10.2240 | 6.9007 | 12.5781 | 8.1069 | 7.0629 | 8.2442 | 7.8698 |
9.0053 | 6.6678 | 9.5391 | 9.1051 | 6.4099 | 8.4521 | 6.4557 | 16.3569 | 7.0130 | 11.5965 |
6.8134 | 7.4622 | 7.1877 | 14.5455 | 7.8074 | 10.4611 | 15.2796 | 6.9631 | 7.0754 | 9.8081 |
6.5555 | 6.9049 | 7.4331 | 9.3048 | 6.7551 | 8.7239 | 7.8740 | 11.4801 | 8.4064 | 7.4705 |
11.3137 | 7.1170 | 7.3749 | 6.9756 | 6.8591 | 10.0826 | 14.7410 | 9.5003 | 7.1877 | 6.5222 |
9.7041 | 8.4064 | 7.0837 | 6.8258 | 7.2043 | 6.8799 | 7.7367 | 9.9120 | 8.8681 | 8.4979 |
7.4913 | 7.1336 | 7.2709 | 6.7718 | 6.9589 | 6.4806 | 6.3850 | 6.7468 | 7.0130 | 7.0754 |
7.4331 | 7.3000 | 7.6660 | 11.8752 | 6.1728 | 7.1253 | 6.9506 | 11.6673 | 8.4147 | 6.9756 |
6.8758 | 8.0736 | 7.5371 | 7.3458 | 6.7884 | 10.8978 | 6.5513 | 7.8033 | 8.4771 | 8.6850 |
6.0023 | 7.4040 | 10.9144 | 8.4771 | 7.1503 | 8.5395 | 7.6702 | 6.6927 | 6.6803 | 6.7219 |
表21.辅助变量进水COD(mg/L)
9.5898 | 12.2124 | 16.6615 | 13.0554 | 10.7138 | 14.6477 | 12.7276 | 10.9948 | 11.5099 | 12.7744 |
11.6036 | 12.9149 | 11.3226 | 12.7276 | 9.6366 | 11.5099 | 14.8351 | 12.3998 | 12.6807 | 11.4631 |
11.2758 | 12.1188 | 11.6973 | 13.3364 | 11.3694 | 11.0416 | 17.2704 | 10.6201 | 13.5237 | 11.3694 |
10.6669 | 13.0086 | 11.6973 | 9.1215 | 10.9948 | 12.7744 | 14.0389 | 10.9948 | 11.9783 | 12.4466 |
12.6339 | 10.9011 | 12.2593 | 12.6807 | 15.1629 | 19.0500 | 14.3199 | 13.3832 | 9.9644 | 13.1959 |
12.4466 | 14.5541 | 9.7303 | 12.1656 | 12.7744 | 14.2731 | 10.9948 | 12.5402 | 14.1794 | 12.9149 |
12.3998 | 11.0416 | 10.5264 | 9.0746 | 12.1188 | 13.7579 | 10.9011 | 8.5595 | 9.1215 | 14.8351 |
10.3391 | 11.6036 | 9.3556 | 13.0086 | 10.4328 | 13.6174 | 13.5706 | 14.2262 | 13.8516 | 9.4025 |
11.7441 | 16.2400 | 12.9617 | 12.4466 | 8.5595 | 10.5733 | 10.1986 | 16.0059 | 9.8708 | 15.6312 |
11.5568 | 9.7303 | 11.4631 | 11.3694 | 7.7633 | 14.3667 | 14.5541 | 11.9783 | 10.6669 | 8.5595 |
表22.实测出水BOD浓度(mg/L)
表23.本发明软测量方法预测出水BOD浓度(mg/L)
12.3012 | 12.4063 | 10.0738 | 13.5495 | 11.1561 | 11.8998 | 13.0365 | 10.9740 | 12.4393 | 13.0020 |
13.0202 | 11.9871 | 14.4076 | 12.9695 | 10.6744 | 15.1676 | 10.7208 | 12.1363 | 10.7420 | 14.0322 |
10.5762 | 11.7449 | 10.9842 | 11.7074 | 12.9429 | 11.6178 | 11.9279 | 11.5582 | 11.0198 | 13.7503 |
12.0108 | 10.1506 | 11.5980 | 13.6717 | 11.2448 | 15.2082 | 12.8048 | 12.9067 | 12.2390 | 12.7064 |
14.9625 | 11.7361 | 11.3409 | 11.0117 | 10.6975 | 13.1275 | 12.2201 | 13.6888 | 11.6820 | 10.4145 |
13.7645 | 13.2533 | 10.9305 | 10.7398 | 10.9274 | 11.2147 | 14.3724 | 13.7712 | 12.8628 | 12.7559 |
11.6087 | 10.8911 | 10.5529 | 11.3161 | 11.0784 | 11.2001 | 11.2575 | 10.5034 | 11.6298 | 11.9925 |
10.9896 | 11.6701 | 10.8099 | 14.5843 | 10.0582 | 10.7411 | 10.3779 | 13.5264 | 12.5899 | 11.0596 |
11.7661 | 12.6594 | 10.3705 | 12.3322 | 11.9743 | 12.3991 | 10.7649 | 14.2594 | 12.5445 | 13.8940 |
11.6297 | 11.0983 | 12.9800 | 12.9553 | 10.7406 | 12.5919 | 15.7655 | 10.6892 | 9.9580 | 11.3962 |
Claims (1)
1.一种基于自组织RBF神经网络的出水BOD软测量方法,其特征在于,包括:
步骤1:确定出水BOD辅助变量;
采集污水处理厂实际水质变量数据,记O={op|k=1,2,...,P}为出水BOD浓度,为初步选择的可能与出水BOD相关的第j个水质变量,包括(1)进水pH;(2)出水pH;(3)进水固体悬浮物浓度;(4)出水固体悬浮物浓度;(5)进水BOD浓度;(6)进水化学需氧量浓度;(7)出水化学需氧量浓度;(8)生化池污泥沉降比;(9)生化池混合液悬浮固体浓度;(10)生化池溶解氧浓度;(11)进水油类;(12)出水油类;(13)进水氨氮浓度;(14)出水氨氮浓度;(15)进水色度;(16)出水色度;(17)进水总氮浓度;(18)出水总氮浓度;(19)进水磷酸盐浓度;(20)出水磷酸盐浓度;(21)进水水温;(22)出水水温;其中J为水质变量个数,P为水质变量的样本个数,为第j个水质变量的第p个样本值;
步骤1.1:计算各变量Fj与输出变量O之间的归一化互信息NI(Fj;O),计算公式为:
其中,H(Fj)与H(O)分别为变量Fj与输出变量O的熵,I(Fj;O)为变量Fj与输出变量O的互信息;
步骤1.2:设置阈值δ∈[0,1],选取满足NI(Fj;O)>δ的特征变量,个数记为I,所形成的相关特征集合记为SR;
步骤1.3:初始化参数i1=1,i2=i1+1;
步骤1.7:令i1=i1+1,返回步骤1.4;
步骤1.8:令S=SR,S为选取的辅助变量集合,结束;
经步骤1,得到出水BOD的辅助变量,个数记为M;
步骤2:设计出水BOD的RBF神经网络预测模型结构;
步骤2.1:将由步骤1获取的M个辅助变量按照公式(3)归一化至[-1,1],输出变量出水BOD按照公式(4)归一化至[0,1]:
其中,Fm表示第m个辅助变量,O表示输出变量,xm和y分别表示归一化后的第m个辅助变量和输出变量;
步骤2.2:设计出水BOD软测量模型结构包括三层:输入层、隐含层和输出层,确定其拓扑结构为M-H-1,即输入层包含M个神经元,分别对应步骤2.1中归一化后的M个辅助变量,隐含层包含H个神经元,输出层包含1个神经元,对应出水BOD变量;
步骤2.3:设共有P个训练样本,对第p个样本,p=1,2,…,P,神经网络输入为xp=[xp,1,xp,2,...,xp,M],其中xp,m,m=1,2,…,M,表示第m个辅助变量的第p个样本;此时,神经网络的输出层神经元的输出为:
其中,wh为第h个(h=1,2,…,H)隐含层神经元与输出层神经元的连接权值,φh(xp)为RBF神经网络第h个隐含层神经元的激活函数,定义如公式(6)所示:
其中,ch、σh分别为第h个隐含层神经元的中心和宽度;
步骤2.4:选取均方误差函数为性能指标,由下式定义:
其中,dp为第p个样本的期望输出,yp为第p个样本的神经网络输出,P为训练样本数;
步骤3:出水BOD软测量模型结构自组织设计
步骤3.1:神经网络隐含层神经元个数H初始化为0,神经元变化次数n初始化为0;
步骤3.2:计算当前第p个样本的神经网络输出误差:
ep=dp-yp (8)
其中p=1,2,…,P;对所有训练样本,寻找误差最大的训练样本,如公式(9):
其中e=[e1,e2,...,eP]T;新增加一个RBF神经元,神经元个数H=H+1,按照公式(10)-(12)设置神经元初始参数cH、σH、wH;
σH=1 (11)
wH=1 (12)
步骤3.3:在当前神经网络结构下,令向量Δ包含所有需要更新的参数,包括隐含层神经元与输出层神经元连接权值、隐含层神经元的中心值及宽度值,即:
更新规则如下:
Δ(k+1)=Δ(k)-(Q(k)+μ(k)I)-1g(k) (14)
其中,k表示迭代步数,Q为类海森矩阵,g为梯度向量,I为单位矩阵,μ为学习率参数;类海森矩阵及梯度向量分别根据公式(15)和(16)计算得到:
其中,ep为第p个样本的神经网络输出误差,根据式(8)计算,jp为对应样本的雅可比矩阵行向量,定义如下:
根据公式(5)-(8),求得:
通过公式(18)-(20),可得到雅可比矩阵的行向量jp,当将所有训练样本遍历一遍后,则可得到类海森矩阵Q和梯度向量g,进而根据参数更新公式(14)对各参数进行更新,包括神经网络隐含层神经元与输出层神经元的连接权值、隐含层神经元中心值以及宽度值;
在训练过程中,当E(k+1)≤E(k)时,μ(k+1)=μ(k)/10,神经网络当前参数保留,包括神经网络隐含层神经元与输出层神经元的连接权值、隐含层神经元中心值以及宽度值;反之,μ(k+1)=μ(k)×10,神经网络参数恢复至参数调整前,基于当前μ对神经网络参数进行更新;设最大迭代步数为Tmax,Tmax∈[100,500],期望误差值为Ed,Ed∈(0,0.01];神经网络参数学习过程经过不断迭代,当迭代步数T=Tmax或当前训练误差E≤Ed时,对当前神经网络训练停止;若训练停止时训练误差E>Ed,当mod(n,N)≠0时,返回步骤3.2,当mod(n,N)=0时,执行步骤3.4,这里为求余操作,N为[3,10]范围内的整数;否则,跳至步骤3.5;
步骤3.4:在当前神经网络结构下,计算第h个隐含层神经元的敏感度:
定义隐含层神经元的删减规则为:当NSIh<γNSImean时,神经元个数H=H-R,将隐含层对应神经元删除,这里NSImean为当前所有隐含层神经元的归一化敏感度均值,R为满足删减条件的隐含层神经元个数,γ在[0,0.5]范围内取值;
选择与所删除神经元欧式距离最近的神经元,其中心和宽度不变,对其与输出神经元的连接权值进行更新,更新规则如下:
其中,ws为所删除神经元s与输出神经元之间的连接权值,wt和w′t分别为在删除神经元s前后与神经元s欧式距离最近的神经元t与输出神经元之间的连接权值;
令n=n+1,返回步骤3.3;
步骤3.5:设最大总迭代次数为Ttmax,Ttmax∈[1000,2000];当训练误差E≤Ed或总迭代次数Ttotal=Ttmax时,训练停止,得到训练后的神经网络结构及对应参数,包括神经网络隐含层神经元与输出层神经元的连接权值、隐含层神经元中心值以及宽度值;
步骤4:将测试样本数据作为训练后的自组织RBF神经网络的输入,得到自组织RBF神经网络的输出,将其进行反归一化得到出水BOD浓度的预测值。
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