Application of GA-BP Neural Network in Accurately Characterizing the Diffusion Range of Groundwater Pollutants in the Site
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摘要:
自2021年最新生态环境损害鉴定评估指南发布实施以来，对地下水中污染物如(铬、铅、铁、锰等污染物)的扩散范围刻画的精度要求越来越高。受研究区场地条件限制，采样点无法完全分布均匀，现有插值方法难以解决采样点分布不均而导致扩散范围刻画不准确的问题。本文通过ArcGIS空间插值图展示某化工园区地下水溶质的空间分布，发现Mn2+离子分布与其形成机制规律相差较大，且尝试使用GIS多种插值方法(比如克里金法，反距离权重法，样条函数等插值方法)效果均不理想，其扩散方向与研究区地下水流向及形成机理不符，可能是由于其监测点位分布不均，因此以重金属Mn2+为例，使用GA-BP神经网络与标准BP神经网络对园区各点位Mn2+浓度进行回归预测，建立其浓度与空间分布的神经网络模型，选取拟合程度较好的神经网络模型对监测点位缺失区域进行浓度预测，并结合空间插值圈定化工园区中心Mn2+的扩散范围，同时用Mn2+的产生机制对扩散范围进行验证。结果表明：GA-BP神经网络的Mn2+浓度预测效果最好，使用其补充监测点缺失位置的Mn2+浓度并重新绘制Mn2+浓度分布图，新Mn2+分布图显示化工园区中心Mn2+扩散范围为1.16×106m2，超出化工园区面积为1.70×105m2。与优化前的扩散范围相比，校正后的扩散范围符合Mn2+产生和运移规律。GA-BP神经网络对场地地下水污染物扩散范围的精确圈定有较好的辅助效果，可为环境污染评估提供更加科学有效的方法支持。
要点(1)研究区地下水Mn2+浓度分布不符合其Mn2+产生及运移规律，需要进行校正。
(2) GA-BP神经网络预测补全采样点分布较少区域的Mn2+浓度，校正Mn2+分布。
(3)经验证，校正后Mn2+浓度分布符合场地Mn2+产生机制及地下水动力学条件。
HIGHLIGHTS(1) The distribution of groundwater Mn2+ concentration in the study area does not conform to the law of Mn2+ production and migration, and needs to be corrected.
(2) The GA-BP neural network was used to predict the concentration of Mn2+ in the area with less distribution of sampling points and correct the distribution of Mn2+.
(3) It is verified that the corrected Mn2+ concentration distribution conforms to the site Mn2+ production mechanism and groundwater dynamics conditions.
Abstract:This study addresses the issue of unevenly distributed sampling points, which leads to inaccurate characterization of pollutant diffusion ranges. Using ArcGIS spatial interpolation, the distribution of Mn2+ ions in a chemical park was analyzed, revealing discrepancies due to uneven sampling. To overcome this, two neural network models—GA-BP and standard BP—were applied to predict Mn2+ concentrations at unsampled locations. The GA-BP neural network, optimized with a Genetic Algorithm, showed the best performance, filling gaps in data and allowing for a more accurate concentration distribution map. This revised map was used to delineate the Mn2+ diffusion range, which was further validated with the known production and migration mechanisms of Mn2+. The results demonstrate that the GA-BP model significantly improves the accuracy of pollutant diffusion mapping and offers a more reliable method for environmental pollution assessment, especially in areas with limited sampling data.
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Keywords:
- groundwater /
- chemical industrial park /
- GA-BP neural network /
- influence range
BRIEF REPORTSignificance: Groundwater pollution is a common environmental issue in industrial areas，in which heavy metal pollution (e.g.，Mn2+，chromium，lead，iron，etc.) poses a serious threat to ecosystems and human health. The Technical Guidelines for Identification and Assessment of Ecological Environmental Damage Environmental Elements Part 1: Soil and Groundwater (GB/T 39792.1—2020) released in 2021 sets more stringent standards for the accuracy of characterizing groundwater pollutant diffusion. However，due to site constraints limiting groundwater monitoring points and the uneven distribution of sampling locations，traditional spatial interpolation methods (such as the Kriging method，inverse distance weighting，and spline functions) introduce significant errors in predicting pollutant diffusion，making it difficult to accurately capture their migration patterns.
Methods: Using Mn2+ pollution in a chemical industry park as a case study，this research utilizes ArcGIS spatial interpolation analysis to reveal that there is a large deviation in the distribution trend of Mn2+ concentration and its formation mechanism，and explores multiple interpolation methods for correction，yet the results still do not meet the required accuracy. In view of this，in this paper，the back propagation neural network (GA-BP) optimized by genetic algorithm is compared with the standard back propagation neural network (BP) to optimize the prediction of pollutant concentration and improve the characterization accuracy of the diffusion range.
First，a spatial interpolation of Mn2+ concentrations using GIS interpolation methods (Kriging method，inverse distance weighting，spline functions，etc.) shows that the predictions of these methods do not correspond to the direction of groundwater in the study area and to the mechanism of Mn2+ formation，indicating the low applicability of traditional interpolation methods when monitoring points are unevenly distributed. Therefore，this paper further uses GA-BP neural network for concentration prediction，chooses the model with the best fit for Mn2+ concentration prediction at unmonitored points. In combination with ArcGIS spatial interpolation，we delimit the diffusion range of Mn2+ and verify it in accordance with the mechanism of Mn2+ production.
In this study，twelve groundwater monitoring sites were deployed in the chemical industry park，and the data were divided into training sets and test sets. The training set includes points upstream，contamination plume and downstream of pollution sources to ensure that the model can learn pollution migration characteristics under different hydrodynamic conditions. In the test set，three monitoring points were selected，located in the contamination plume and downstream，to test the prediction ability of the model.
Data and Results: This study first models the relationship between Mn2+ concentration and spatial distribution using a standard BP neural network，then applies a genetic algorithm (GA) to optimize its weights and thresholds for improved prediction accuracy. After training，an optimized GA-BP neural network is used to predict the concentration of Mn2+ in an unmonitored area and to optimize the delineation of the extent of pollutant dispersion. Finally，model reliability is validated through comparison with measured data，considering Mn2+ migration mechanisms and groundwater dynamics. GA-BP neural networks perform best in the prediction of Mn2+ concentration，with a prediction error close to 0 and a higher fitting accuracy than standard BP neural networks. Using a GA-BP neural network to supplement the Mn2+ concentration data for the missing regions of the monitoring points and to replot the Mn2+ concentration distribution，the result shows that: the dispersion of Mn2+ in the centre of the chemical park is 1.16×106 m2，of which 2.13×105 m2 goes beyond the chemical park. A comparison of the extent of pollutant dispersion before and after optimization demonstrates that the revised Mn2+ extent aligns more closely with its generation mechanism and migration dynamics. That is，the direction of Mn2+ migration is influenced jointly by the degradation of organic matter and the flow of groundwater rather than by the distribution of monitoring points alone. After a review of the literature，it was found that the electron acceptor response in microbial degradation is in the order of O2＞NO3-＞Mn4+，only when the nitrate degradation reaction has been substantially completed does petroleum degradation lead to the release of Mn2+.
It was found that the concentration of Mn2+ is highest when the concentration of nitrate is lowest and that all monitoring points have concentrations below 1 mg/L in the dispersion of Mn2+，which is consistent with the theoretical mechanism. Among them，the highest concentration of Mn2+ at the M03 point indicates that the degradation of nitrate in the region is largely complete，leading to a large release of Mn2+. This finding further confirms that Mn2+ migration is influenced by the degradation of petroleum and that the removal of nitrate is a key premise for Mn2+ release.
In summary，this study verifies the mechanism of microbial degradation and Mn2+ release described in the literature by means of data. It shows that in petroleum-contaminated areas the dispersion of Mn2+ is influenced not only by the degree of degradation of petroleum but also by the direction of groundwater. This finding helps to explain the migration patterns of pollutants in groundwater system more accurately，and provides scientific basis for groundwater pollution control.
This study shows that the GA-BP neural network has obvious advantages in the characterization of pollutant diffusion range，its prediction error is low，the fitting effect is good，and even in the case of limited sampling points and uneven distribution，it can still maintain a high prediction accuracy. Compared with traditional GIS spatial interpolation methods (Kriging method，inverse distance weighting method，spline function，etc.)，the GA-BP neural network is more accurate in pollutant concentration prediction and diffusion range delineation，and the results are more consistent with the migration mechanism and hydrodynamic conditions of pollutants.
Furthermore，this study found that the migration of Mn2+ is mainly influenced by the combination of the degradation of petroleum pollutants and the flow of groundwater. In areas where the nitrate concentration is near zero and the concentration of petroleum pollutants is moderate，the concentration of Mn2+ is highest and migrates along groundwater flows，forming three Mn2+ rich areas in the center of the industrial park，the north-west corner and the south-east corner. The revised Mn2+ diffusion range is more consistent with known migration laws and further validates the accuracy of the GA-BP neural network predictions.
Nevertheless，this study has limitations. The limited number and uneven distribution of sampling points may introduce certain errors in model predictions. In the future，more field monitoring data can be combined to further optimize the parameters of the GA-BP neural network model and improve the accuracy and applicability of prediction.
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清洁安全的地下水是社会和人类可持续发展的基本保障。世界上大多数城市都面临着地下水枯竭和水质恶化导致的双重水资源压力［1］。随着中国城市化和工业化的不断推进，工业场地地下水污染问题较为严重［2-3］。且随着我国化工企业的发展，有机物及其降解产生的Mn2+二次污染物对人体的危害也逐渐受到重视［4］。为保护人体健康和环境的安全，需要精细刻画出地下水污染物(如铬、铅、铁、锰等污染物)扩散范围［5］，并将二次污染纳入损害评估体系［6］，这对控制地下水污染十分重要［7］。
《生态环境损害鉴定评估技术指南 环境要素 第1部分：土壤和地下水》(GB/T 39792.1-2020)指出，损害鉴定需要明确地下水的当前损害范围和评估时间范围内的可能损害范围［8］，计算可能受损的地下水面积［9］，以便更好地评估环境损害。但研究者采样时，受研究区条件限制，采样点常常无法均匀分布。时而发生现有ArcGIS插值方法的插值结果与真实情况有较大差别的情况。王兴等［10］分析了不同插值方法对海水盐度插值适用性，并指出无论采用哪种空间插值方法，都会引入较大的误差，适度加密监测站位是必要的，尤其是在插值误差较大的区域。Mohammed等［11］指出适当使用机器学习方法对插值精度有一定提升，BP神经网络用于拟合时间较早，是深度学习的一个关键分支，它能拟合变量之间的非线性关系。多名研究者在水文地质方面将其用于浓度预测，方法较为成熟［12］。
近年来，优化BP神经网络的算法不断迭代［13］，经过验证，遗传算法优化的BP神经网络优化效果较好。且由于研究区监测点位分布不均，Mn2+离子浓度分布与其产生规律及水动力条件不符，研究区地下水Mn2+浓度受多因素影响，采样点Mn2+浓度和极角和极径有较强的非线性关系，因此本文采用遗传算法优化的BP神经网络(GA-BP)来生成缺失点位的Mn2+浓度数据，从而对其扩散范围进行校正，减少采样点分布不均对扩散范围圈定的影响。同时，通过Mn2+成因机制结合其分布特征，验证校正后的Mn2+扩散范围［14］。校正后的Mn2+浓度符合场地水动力条件及Mn2+产生规律，校正效果较好，相较优化前刻画的扩散范围更为准确。
1. 研究区概况
研究区为河北省某工业园区，场地面积约5.25km2，主要生产化学原料、化学制品、医药、橡胶和纸制品。该园区周边皆为农田与果园，以旱地农作物为主，主要种植小麦、玉米、鸭梨、葡萄和山楂等。地貌单元为滹沱河冲洪积扇水文地质亚区。第四系发育较为齐全，地层由新至老分为全新统(Q4)、上更新统(Q3)、中更新统(Q2)和下更新统(Q1)。岩性由黄土状粉质黏土和冲积粉土组成，并夹有砂层，厚度约130m左右。研究区年平均降水量456mm，主要集中在夏季。浅层地下水位埋深总趋势是自西向东、由北往南由浅变深，埋深由北部30～35m变至南部50～60m，地下水位年内变幅一般为2m左右。场地地下水排泄途径主要为人工开采，其次是侧向流出和潜水蒸发，其主要补给来源为大气降水与河渠渗漏。场地内企业产生的污染物均经过污水处理厂等设施处理后排放。
2. 研究方法
2.1 数据收集
为了研究该化工园区地下水系统有机物对锰元素迁移规律的影响，本研究结合场地水化学指标分布特征，针对地下水中有机污染区域进行地下水采集，共采集12组地下水水样。水样主要取自监测井，依据园区地下水水动力条件以及前期获取的地下水污染源分布情况确定地下水取样深度，本研究采集深度为地下水水位线0.5m以下。地下水水样的采样、密封、保存以及检测均按照《地下水环境监测技术规范》要求进行。本次地下水检测指标包括锰、硝酸盐(以N计)、亚硝酸盐(以N计)、苯酚、丙酮、硝基苯、4-硝基苯胺、石油烃(C10～C40)、石油类、甲苯、乙苯、间二甲苯+对二甲苯、邻二甲苯。参照“35+N”的原则确定化工园区地下水检测指标，“35”为《地下水质量标准》(GB/T 14848—2017)扣除微生物指标和放射性指标后的35项常规指标，“N”为场地特征污染物指标。具体测试方法列于表1，每个平行样品采样点位采集的3份平行样品，其中2份地下水测试样品送河北省地质实验测试中心，另1份地下水质控测试样品送华测检测认证集团股份有限公司。所得数据均经过了准确度检验。
表 1 地下水样品分析测试方法Table 1. Analysis methods for groundwater sample检测项目
Aanalytical items分析测试方法
Analysis methods方法检出限
Method detection limit硝酸盐
Nitrate离子色谱法
Ion chromatography0.004mg/L 锰
Manganese电感耦合等离子体质谱法
Inductively coupled plasma mass spectrometer0.00012mg/L 石油类
Oil红外分光光度法
Infrared spectrophotometry0.06mg/L 石油烃(C10～C40)
Petroleum hydrocarbons ( C10-C40 )气相色谱法
Gas chromatography0.004mg/L 丙酮
Acetone气相色谱法
Gas chromatography0.2mg/L 4-硝基苯胺
4-Nitroaniline气相色谱-质谱法
Gas chromatography-mass spectrometry4.6μg/L 苯酚
Phenol气相色谱-质谱法
Gas chromatography-mass spectrometry0.1μg/L 甲苯
Toluene气相色谱-质谱法
Gas chromatography-mass spectrometry0.3μg/L 乙苯
Ethylbenzene气相色谱-质谱法
Gas chromatography-mass spectrometry1.2μg/L 间二甲苯+对二甲苯
m-xylene+p-xylene气相色谱-质谱法
Gas chromatography-mass spectrometry1.2μg/L 邻二甲苯
o-Xylene气相色谱-质谱法
Gas chromatography-mass spectrometry1.2μg/L 2.2 BP神经网络模型构建
BP神经网络是一类多层的前馈神经网络，最早由Rumelhart等在1986年提出，结构精简，可调参数多，训练算法众多，操作性优良，因此，BP神经网络应用范围广泛，接近90%的神经网络模型均为BP神经网络或其改进版本。BP网络是前向网络的核心部分，是神经网络的精华部分［15］。然而，它也存在网络结构难以确定、学习收敛速度慢、不能够保证收敛至全局最小点等缺点。除此之外，网络训练在很大程度上受网络结构、初始连接权值和阈值选择影响，因此本研究使用遗传算法对神经网络进行优化［16］。BP神经网络的遗传算法流程图如图1所示。
2.2.1 模型构建及主要参数设置
以污染源中心点作为极坐标的原点，以东方向为极轴。将极角和极径为输入值，Mn2+浓度设置为输出值。设置输入层的节点数为i，隐含层节点数为j，输出层节点数为k，输入层到隐含层的权值为wij，隐含层到输出层的权值为wjk，输入层到隐含层的阈值为bj［17］，隐含层到输出层的阈值为ck，学习速率为η。其中q为0-10之间的任意数，其中k为期望输出值。
隐含层节点数：
$$ \begin{array}{c}j=\sqrt{i+k}+q\end{array} $$ (1) 隐含层输出：
$$ \begin{array}{c}{\mathit{a}}_{\mathit{j}}=f\left({\displaystyle\sum }_{i=1}^{l}{w}_{\text{ij}}{\mathit{x}}_{\mathit{i}}+{\mathit{b}}_{\mathit{j}}\right)\end{array} $$ (2) 输出层输出：
$$ \begin{array}{c}\begin{array}{c}{\mathit{y}}_{\mathit{k}}=f\left({\displaystyle\sum }_{j=1}^{l}{w}_{\text{jk}}{a}_{j}+{c}_{k}\right)\end{array}\end{array} $$ (3) 误差计算：
$$ \begin{array}{c}E=\dfrac{1}{2}{\displaystyle\sum }_{k=1}^{m}{\left({Y}_{k}-{y}_{k}\right)}^{2}\end{array} $$ (4) 2.2.2 遗传算法优化BP神经网络
遗传算法存在共享机制，整个种群具有一致的向最优值移动速度，GA-BP神经网络的算法流程如下［18］。
步骤一：对数据进行预处理，确定BP神经网络输入层、隐含层以及输出层的节点数，初始化权值及阈值。
步骤二：设置初始种群规模为200，最大进化代数为100，交叉概率为0.8，变异概率为0.2。遗传算法通过计算适应度函数，执行选择、交叉、变异运算优化权值及阈值［19］，当父代个体的适应度满足终止条件或进化代数大于设定代数得到最优解时输出结果；
步骤三：使用遗传算法得到的最佳权值和阈值，训练BP神经网络，并输出最终结果。
2.2.3 选择点位预测并进行插值
第一步：选取与监测点距离相近点位，对其Mn2+浓度进行预测：对于与训练与测试数据相近的点，预测数值精度更高。
第二步：选取能与实测点位一起均匀分布在园区及其附近的点位，对其Mn2+浓度进行预测：点位分布均匀，扩散范围刻画的越为准确。
第三步：将这些点位与实测点位Mn2+数据一起进行插值，对扩散范围进行刻画。
3. 结果与讨论
3.1 实测点位Mn2+污染晕及研究区流场
采用反距离权重插值法绘制场地各监测点Mn2+浓度空间分布，如图2所示。该化工园区地下水中Mn2+主要呈现局部性点状富集特征，化工园区中部偏西区域的Mn2+浓度最高，为0.74mg/L，整体上Mn2+浓度自西向东呈降低趋势。但由于采样点分布不均，扩散范围刻画的精确度较低，M07与M12点之间扩散范围向西北方向延伸，而水流方向为西北向东南，与Mn2+扩散机制不符。其扩散方向与地下水流向相反，且Mn2+的产生与地下水中的有机物有关，在还原条件下，NO3−、Fe3+和Mn4+先后与有机物反应，生成Mn2+。地下水中有机物越多，离子被还原的越多。研究区监测数据表见表2。
表 2 研究区监测数据Table 2. Monitoring data of the study area点位
Point positions锰
Manganese
(mg/L)苯酚
Phenol
(µg/L)丙酮
Acetone
(µg/L)硝基苯
Nitrobenzene
(µg/L)4-硝基苯胺
4-Nitroaniline
(µg/L)石油烃(C10～C40)
Petroleum hydrocarbons (C10-C40)
(mg/L)M01 0.184 0.3 — — — 0.24 M02 0.18 0.2 — — — 2.37 M03 0.768 0.1 — — — 5.46 M04 0.031 1.1 — 0.00864 39.7 34.8 M05 0.0658 — — 0.00552 6.3 0.62 M06 0.0452 — — — — 0.14 M07 0.0752 — — — — 2.78 M08 0.182 0.4 — — — 23.5 M09 0.0024 — — — — 0.55 M10 0.18 0.5 — — — 27.6 M11 0.194 — 58 — — 8.95 M12 0.0018 — — — — — 点位
Point positions石油类
Oil
(mg/L)甲苯
Toluene
(µg/L)乙苯
Ethylbenzene
(µg/L)间-二甲苯+对-二甲苯
m-Xylene+p-Xylene
(µg/L)邻-二甲苯
o-Xylene
(µg/L)石油烃(C10～C40)
Petroleum hydrocarbons (C10-C40)
(mg/L)M01 0.45 — — — — 0.24 M02 0.29 2.4 — — — 2.37 M03 0.98 — 0.4 1.3 0.6 5.46 M04 1.64 18.2 0.4 1.2 0.4 34.8 M05 0.11 2.3 — — — 0.62 M06 0.11 — — — — 0.14 M07 0.17 1 — — — 2.78 M08 2.52 — — — — 23.5 M09 0.17 — — — — 0.55 M10 2.95 — — — — 27.6 M11 8.98 — — — — 8.95 M12 0.03 — — — — 0.02 注：“—”表示未检出。 3.2 有机物污染物的空间分布特征
根据不同监测井检出的10种有机污染物的浓度，绘制出极坐标热力图(图3)，可以看出，研究区丙酮、4-硝基苯胺、石油烃(C10～C40)、石油类在地下水中浓度相对较大，分布点位相对较多，而硝基苯仅在M11监测井含量显著，甲苯、乙苯仅在监测井M04含量较高，其余点位含量较少，苯酚、间二甲苯+对二甲苯、邻二甲苯在各检测点位含量均较少。对4种典型有机指标(丙酮、4-硝基苯胺、石油烃(C10～C40)、石油类)进行空间插值(图4)。
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图 3 各监测井有机指标极坐标热力图Figure 3. Polar heatmap of organic indicators in each monitoring well![]()
图 4 四种典型有机指标空间分布Figure 4. Spatial distribution maps of four typical organic indicators丙酮、石油类浓度总体空间分布相似，4-硝基苯胺、石油烃(C10～C40)浓度空间分布相似(图4)。丙酮、石油类空间分布不均匀，高值区主要分布在场地中下部位置的M11监测井，最高浓度分别为57.98mg/L、9mg/L，在横向上呈现点源污染特性，随着与污染源距离增加，丙酮与石油类浓度均降低，但丙酮浓度降低速率比石油类浓度大得多。4-硝基苯胺、石油烃(C10～C40)在厂区范围内分布不均，浓度呈现由东南部向西北部逐渐减少的特征，浓度最高的监测井为M04，最高浓度分别为30.58mg/L、25.82mg/L。
3.3 Mn2+扩散范围圈定
3.3.1 神经网络训练结果
为确定标准BP神经网络最佳隐含层节点数，利用经验公式确定标准BP神经网络隐含层节点的数量范围［20］，通过均方根误差确定最佳隐含层节点数量为6，相应的均方根误差为0.031883(表3)。
表 3 隐含层节点的确定过程Table 3. Determination process of hidden layer nodes隐藏层节点
Hidden layer node训练集的均方误差
Mean square error of training set隐藏层节点
Hidden layer node训练集的均方误差
Mean square error of training set2 0.12601 8 0.67715 3 0.27314 9 0.32133 4 0.11288 10 0.2487 5 0.20273 11 0.06521 6 0.031883 12 2.0155 7 0.069991 同时训练遗传算法优化的BP神经网络，其拟合效果见图5。训练集R为0.9921，R2=0.99747大于0.9，测试集R为0.9987，R2=0.9974证明训练集拟合良好，具有较强的可信度。GA-BP、BP神经网络预测结果与误差见表4。
表 4 GA-BP、BP神经网络预测结果与误差Table 4. Prediction results and errors of GA-BP and BP neural network样本序号
Sample serial numberMn2+实测值
Mn2+ measured value
(mg/L)BP
预测值
(mg/L)GA-BP
预测值
(mg/L)BP误差
(mg/L)GA-BP误差
(mg/L)1 0.1800 −0.1366 0.1849 −0.3166 0.0049 2 0.1940 −0.1669 0.1876 −0.3609 −0.0064 3 0.0018 −0.1581 0.0057 −0.1599 0.0039 根据表5可看出，优化后的BP神经网络误差比没有优化的BP神经网络mae、mse、rmse、mape更小，拟合效果更好。训练集与测试集拟合效果均较好，且最近隐含点层数按照均方根误差获得，训练集与测试集样本点种类分布均匀，设计合理，没有发生过拟合［21］。
表 5 BP神经网络误差Table 5. Error of BP neural networkBP神经网络种类的误差
Error in types of BP neural networkmae mse rmse mape 标准的BP神经网络模型
Standard BP neural network model0.279 0.085 0.292 3082.097% 遗传算法优化的BP神经网络模型
Genetic algorithm optimized BP neural network0.005 2.694×106 0.005 75.066% 实测值与预测值对比见图6，GA-BP实测值与预测值相较于标准BP神经网络更为拟合，且GA-BP神经网络误差均接近于0，GA-BP神经网络预测效果明显优于BP神经网络。研究区数据点不多，因此数据分成了训练集与测试集两个集。三个测试集点分布在污染源中心的污染羽及下游位置，且训练集具有污染源上游，污染羽以及污染源下游三种类型的点位，训练的模型结果拟合较好。测试集结果验证通过后，模型可靠［22］。
选取与监测点距离相近或能够较为均匀地将园区Mn2+源中心紧密围绕的点位，对Mn2+浓度进行预测。结合实测数据以精确地将化工园区中心Mn2+扩散范围精确刻画出来。预测点、监测点以及校正后Mn2+扩散范围图见图7。
按照国家水质标准，Mn2+浓度低于0.05mg/L即为一类水，因此本研究将地下水Mn2+浓度在0.05mg/L以下的区域视为没有受到Mn2+污染。由图7可知，园区Mn2+沿着水流方向从中心向东南方向迁移，距离中心924m处浓度降至0.05mg/L，园区中心Mn2+影响消失。将园区中心Mn2+扩散范围进行大致圈定，扩散范围约为1.7×106m2，园区内扩散范围约为1.59×106m2，园区外扩散范围约为2.13×105m2。扩散范围延伸方向与水流方向一致。
3.3.2 现象机理验证
将精细刻画后的化工园区中心Mn2+污染范围与有机物指标分布进行对比，研究表明有机物自然生物降解过程中铁锰还原过程比硫酸盐过程发生更早［23］，有机物的降解过程中会增加土壤中锰的迁移性［24］，将原有的锰的氧化物转化成Mn2+，使原有系统中土里的Mn2+减少，水中Mn2+增加［25］。化工园区中心Mn2+扩散范围与石油类分布特征相一致，即化工园区中心Mn2+与石油类扩散范围均分别向东北与东南方向延伸。石油类污染物从园区中心向东北方向延伸M07点位石油类浓度较低，仅为0.17mg/L，M03、M04、M08、M10、M11等点均大于1mg/L或接近1mg/L，M11点浓度最大为8.98mg/L。丙酮仅在M11处检出，且此处也为有机物浓度最高点。丙酮分子量与大部分石油类污染物相比，分子量很小，自然降解速度较快，同时微生物降解能力受石油烃的物理状态影响显著［26］，溶解态、乳化态以及分散态是石油类在水中的主要存在形态，其生物降解速率比大分子量的石油烃与4-硝基苯胺大得多［27］。同时，硝基具有的亲电子性、苯环结构具有对称性［28］，这决定了4-硝基苯胺的低生物降解能力［29］。因此，4-硝基苯胺生物降解对地下水中锰元素的影响可以忽略不计。锰在自然条件下一般浓度较低，厂区浓度较高可能为石油类有机物自然降解将岩层中的高价锰元素还原为低价态的Mn2+迁移至地下水中［29］，使得化工园区中心Mn2+扩散范围向东北方向延伸。石油类扩散范围与园区中心Mn2+扩散范围向东南方向延伸则是因为此区域地下水水流方向为自西北向东南［30］。Mn2+扩散范围受石油类浓度分布与水流方向控制［31］。
选取已圈定扩散范围内的采样点，绘制Mn2+浓度与石油类和硝酸根浓度关系图，石油类与硝酸根的范围是通过现测打井数据插值，并通过地表检测的泄漏点分布验证过的，且符合水动力条件流向。当硝酸根浓度(mg/L)最低时，Mn2+浓度最高。圈画的园区中心Mn2+扩散范围内，监测点硝酸根浓度均小于1mg/L，园区中心的Mn2+浓度在M03点附近浓度最高。原因是为微生物降解过程中电子受体的反应顺序是O2＞NO3−＞Mn4+，只有当硝酸根反应基本完全［32］，石油类降解才会产生Mn2+[33］，因此M03点Mn2+浓度最高，园区中心Mn2+扩散范围内硝酸根浓度均低于1mg/L［34］。
本文分析了各点位硝酸根浓度与Mn2+和石油类浓度关系，由NO3−、Mn2+和石油类浓度分布图8可知，石油类的范围主要受M07与M09处硝酸根点源污染的扩散范围控制，在研究区中心呈条状分布，西北方向低浓度石油类小区域呈面状分布。Mn2+基本产生于硝酸根等于零且具有一定石油类浓度的区域，硝酸根浓度为0区域共有三个区域，化工园区中心条区域、化工园区西北角以及化工园区东南角。将此三个区域内具有一定石油类浓度的位置视为Mn2+产出区域，将区域沿着水流方向拉伸(西北向东南)，即与Mn2+浓度分布基本一致。西北方向石油类降解的Mn2+沿水流方向扩散与园区中心Mn2+扩散范围相接。校正后的扩散范围符合Mn2+产生和运移规律。
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图 8 石油类、硝酸根、Mn2+浓度分布图Figure 8. Concentration distribution of petroleum，nitrate and Mn2+4. 结论
采用GA-BP神经网络对化工园区地下水中Mn2+浓度与其空间位置的关系进行了拟合分析，取得了较好的拟合效果，并对Mn2+的扩散范围进行了修正。结果表明，修正后的Mn2+扩散范围从园区中心向东南方向延伸，最远可达924m，扩散面积达到1.16×106m2，且超出园区范围2.13×105m2。修正后，扩散方向与地下水流向与一致，且扩散范围符合Mn2+产生机制。GA-BP神经网络对场地地下水污染物扩散范围的精确圈定有较好的辅助效果。
该方法为污染范围刻画不准确的问题提供了一种有效的解决方式，也为地下水污染治理提供了新的技术手段。但实际应用中仍存在一定局限性，如模型参数敏感性和输入数据的精确性等问题。未来研究中，可以结合更多现场监测数据和不同区域的环境特征，进一步优化模型参数，提升预测的准确性和适用性。
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图 3 各监测井有机指标极坐标热力图
Figure 3. Polar heatmap of organic indicators in each monitoring well
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图 4 四种典型有机指标空间分布
Figure 4. Spatial distribution maps of four typical organic indicators
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图 8 石油类、硝酸根、Mn2+浓度分布图
Figure 8. Concentration distribution of petroleum，nitrate and Mn2+
表 1 地下水样品分析测试方法
Table 1 Analysis methods for groundwater sample
检测项目
Aanalytical items分析测试方法
Analysis methods方法检出限
Method detection limit硝酸盐
Nitrate离子色谱法
Ion chromatography0.004mg/L 锰
Manganese电感耦合等离子体质谱法
Inductively coupled plasma mass spectrometer0.00012mg/L 石油类
Oil红外分光光度法
Infrared spectrophotometry0.06mg/L 石油烃(C10～C40)
Petroleum hydrocarbons ( C10-C40 )气相色谱法
Gas chromatography0.004mg/L 丙酮
Acetone气相色谱法
Gas chromatography0.2mg/L 4-硝基苯胺
4-Nitroaniline气相色谱-质谱法
Gas chromatography-mass spectrometry4.6μg/L 苯酚
Phenol气相色谱-质谱法
Gas chromatography-mass spectrometry0.1μg/L 甲苯
Toluene气相色谱-质谱法
Gas chromatography-mass spectrometry0.3μg/L 乙苯
Ethylbenzene气相色谱-质谱法
Gas chromatography-mass spectrometry1.2μg/L 间二甲苯+对二甲苯
m-xylene+p-xylene气相色谱-质谱法
Gas chromatography-mass spectrometry1.2μg/L 邻二甲苯
o-Xylene气相色谱-质谱法
Gas chromatography-mass spectrometry1.2μg/L 
下载: 导出CSV
表 2 研究区监测数据
Table 2 Monitoring data of the study area
点位
Point positions锰
Manganese
(mg/L)苯酚
Phenol
(µg/L)丙酮
Acetone
(µg/L)硝基苯
Nitrobenzene
(µg/L)4-硝基苯胺
4-Nitroaniline
(µg/L)石油烃(C10～C40)
Petroleum hydrocarbons (C10-C40)
(mg/L)M01 0.184 0.3 — — — 0.24 M02 0.18 0.2 — — — 2.37 M03 0.768 0.1 — — — 5.46 M04 0.031 1.1 — 0.00864 39.7 34.8 M05 0.0658 — — 0.00552 6.3 0.62 M06 0.0452 — — — — 0.14 M07 0.0752 — — — — 2.78 M08 0.182 0.4 — — — 23.5 M09 0.0024 — — — — 0.55 M10 0.18 0.5 — — — 27.6 M11 0.194 — 58 — — 8.95 M12 0.0018 — — — — — 点位
Point positions石油类
Oil
(mg/L)甲苯
Toluene
(µg/L)乙苯
Ethylbenzene
(µg/L)间-二甲苯+对-二甲苯
m-Xylene+p-Xylene
(µg/L)邻-二甲苯
o-Xylene
(µg/L)石油烃(C10～C40)
Petroleum hydrocarbons (C10-C40)
(mg/L)M01 0.45 — — — — 0.24 M02 0.29 2.4 — — — 2.37 M03 0.98 — 0.4 1.3 0.6 5.46 M04 1.64 18.2 0.4 1.2 0.4 34.8 M05 0.11 2.3 — — — 0.62 M06 0.11 — — — — 0.14 M07 0.17 1 — — — 2.78 M08 2.52 — — — — 23.5 M09 0.17 — — — — 0.55 M10 2.95 — — — — 27.6 M11 8.98 — — — — 8.95 M12 0.03 — — — — 0.02 注：“—”表示未检出。
下载: 导出CSV
表 3 隐含层节点的确定过程
Table 3 Determination process of hidden layer nodes
隐藏层节点
Hidden layer node训练集的均方误差
Mean square error of training set隐藏层节点
Hidden layer node训练集的均方误差
Mean square error of training set2 0.12601 8 0.67715 3 0.27314 9 0.32133 4 0.11288 10 0.2487 5 0.20273 11 0.06521 6 0.031883 12 2.0155 7 0.069991
下载: 导出CSV
表 4 GA-BP、BP神经网络预测结果与误差
Table 4 Prediction results and errors of GA-BP and BP neural network
样本序号
Sample serial numberMn2+实测值
Mn2+ measured value
(mg/L)BP
预测值
(mg/L)GA-BP
预测值
(mg/L)BP误差
(mg/L)GA-BP误差
(mg/L)1 0.1800 −0.1366 0.1849 −0.3166 0.0049 2 0.1940 −0.1669 0.1876 −0.3609 −0.0064 3 0.0018 −0.1581 0.0057 −0.1599 0.0039
下载: 导出CSV
表 5 BP神经网络误差
Table 5 Error of BP neural network
BP神经网络种类的误差
Error in types of BP neural networkmae mse rmse mape 标准的BP神经网络模型
Standard BP neural network model0.279 0.085 0.292 3082.097% 遗传算法优化的BP神经网络模型
Genetic algorithm optimized BP neural network0.005 2.694×106 0.005 75.066%
下载: 导出CSV
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