网络结构和样本集复杂性是影响BP网络泛化能力的两个最重要因素.对一个给定的训练样本集,为了构造一个与样本集复杂性相匹配的网络结构,使BP网络具有最佳泛化能力,在分析BP网络的泛化能力(用检测误差E2表示)与网络结构和样本集复杂性之间关系的基础上,建立了含参数的BP网络检测误差E2与网络隐节点数H、样本的因子数n、样本数N和样本集的复相关系数R之间的一般关系表达式,并提出了用于定量描述样本集复杂性的"广义"复相关系数Rn的新概念.借助于222个复杂函数的模拟仿真实验,应用免疫进化算法,对表达式中的参数进行优化,得到参数优化后的网络检测误差E2的定量解析表达式;依据误差理论和灵敏度概念,对优化得到的最小检测误差E20的表达式进行了可靠性论证.在此基础上导出了具有最佳泛化能力的BP网络隐节点数H0与"广义"复相关系数Rn之间满足的H0-Rn反比关系式.分别用满足H0-Rn反比关系式的隐节点数和6个经验公式的隐节点数构造的BP网络用于100个模拟检测函数进行仿真实验,发现前者构造的BP网络具有最佳泛化能力(即最小检测误差)的函数个数达到76个,远远多于后者构造的BP网络具有最佳泛化能力的函数个数;还将二者构造的BP网络用于环境预测的7个具体实例,进行预测效果比较,结果表明,前者预测的相对误差绝对值的平均值和最大值小于或远小于后者的相应值.从而验证了由H0-Rn反比关系式得出的BP网络隐节点数计算公式的可行性和实用性,为具有最佳泛化能力的BP网络的结构设计指出了新途径.

The water resources carrying capacity (WRCC) is fundamental in aiding sustainable socioeconomic regional development, and increasing attention is being paid to WRCC forecasting. The challenge of WRCC forecasting lies in the complex characteristics of nonlinear multiple indicator time series data. To address this problem, this study proposed a feedforward neural network (FNN) based on normalization and error correction for WRCC forecasting. Firstly, units and values of multiple indicators for use in the WRCC were normalized simultaneously to allow the data to be treated as a single equivalent indicator. Thus, the high-dimensional forecasting model was simplified to a low-dimensional model. To improve the effectiveness of the model, an error correction method was then adopted to correct forecasted WRCC values according to similar corresponding sample values. Two simple types of structured FNN were used to address the overfitting problem, and the bipolar sigmoid function was used as the activation function of hidden nodes. The final calibrated model was expressed as an equation rather than a programming language, thus making it easier to use. Yantai, a city in Shandong Province, was selected as a case study to validate this proposed method. Results showed that the mean relative absolute errors of these two simplified FNN models are 1.23% and 1.18%, respectively. Compared to other models, this model has been shown to be feasible and simple to use for WRCC forecasting.

为了建立适用于广义环境系统评价的普适指数公式,针对传统的环境评价指数公式不具有普适、规范和通用的局限,提出适用于广义环境系统任意指标的参照值和规范变换式的设计原则和方法;该变换要求变换后的任意指标的各分级标准规范值都能被限定在各自的较小区间内,从而用规范值表示的任意指标皆“等效”于同一个规范指标;再分别用不同限定区间内生成的随机数模拟任意指标的不同分级标准的规范值,不同区间内生成的所有随机数组成不同分级标准的全部训练(学习)样本,借助免疫进化算法优化不同评价指数公式中的参数,得到适用于广义环境系统评价的9个(广义)普适指数公式,并论证了公式的可靠性.分别将9个普适指数公式用于北京市朝阳区19个监测井的9项指标的地下水水质的综合评价,以及用于郑州、西安、上海三市2000年可持续发展评价.结果表明:9个普适指数公式用于同一监测井水质的评价结果几乎完全相同,也与传统评价方法的评价结果基本一致;用于郑州、西安、上海三市可持续发展评价的结果分别是3级、3级、2级,比传统评价法更符合实际情况.9个普适指数公式使广义环境系统的评价变得简洁、规范、统一和通用;基于指标规范变换的评价指数公式的建模思想和方法对建立广义环境系统的普适智能评价模型有借鉴作用.

传统的不同预测变量的预测模型之间不具有兼容性和等效性,而同型规范变换和误差修正相结合的不同变量的预测模型的预测相对误差与预测对象的维数、样本数及预测模型类型皆无关,仅与预测变量的数据特性、相似样本的模型输出值及其相对误差和相似度有关,因而同型规范变换的不同预测变量的预测模型之间具有兼容性和等效性.其重要意义在于:只要对任意一个预测变量建立了基于规范变换的某种预测模型,就可以将此预测模型直接用于具有同型规范变换的其他预测变量的预测;若再将其与误差修正法相结合,还可以极大地提高模型的预测精度,获得与实际值很接近的预测结果.依据受3个因子影响的灞河口CODMn指数数据、受4个因子影响的伊犁河雅马渡站年径流量数据和牡丹江市TSP年均值的时序数据,分别建立具有同型规范变换(nj=2)的3个不同预测变量的3种智能预测模型和一元线性回归预测模型,并验证了3个不同预测变量的预测模型之间的兼容性和等效性.对同一个预测样本,用同型规范变换和误差修正相结合的不同预测变量的预测模型的实际预测值及其预测相对误差绝对值不仅差异甚微,而且预测值与实际值非常接近,其预测的相对误差绝对值平均值几乎全都小于3％,最大相对误差绝对值均小于5％,小于或远小于20种传统预测模型和方法预测的相应误差.

为了建立适用于环境系统的结构简洁、形式统一、程序规范、应用普适的神经网络和投影寻踪回归预测模型,针对传统的神经网络和投影寻踪回归用于多因子、大样本预测建模,存在模型结构复杂、学习效率低的局限,提出设置环境系统预测量及其影响因子参照值和规范变换式的原则和方法,使规范变换后的影响因子皆“等效”于同一个规范影响因子,从而将多因子的的预测建模简化为等效规范因子的预测建模,使模型结构得到极大地简化,提高了学习效率;此外,为了提高预测模型的预测精度,还提出了对预测样本的模型输出值的误差修正公式.在对环境系统的预测量及其影响因子进行规范变换的基础上,将m个规范影响因子的每个建模样本组成m个“等效”训练样本,应用免疫进化算法优化模型参数,分别建立适用于环境系统的2个或3个规范影响因子的前向神经网络和投影寻踪回归两类预测模型;并依据误差理论,对误差修正公式修正后的模型预测精度的提高进行了严格的数学论证.将基于规范变换与相似样本误差修正相结合的两类预测模型,用于某市5个点位的SO2浓度预测,并与6种传统预测模型和方法的预测结果进行了比较.结果表明:对同一个预测样本,同类模型的两种不同结构的的预测值及其相对误差都几乎完全相同或彼此相差甚小;此外,两种不同结构的两类预测模型用于5个样本预测,其相对误差绝对值的平均值分别为2.59％、2.67％;2.18％、2.62％,均远小于传统BP神经网络模型的25.72％、传统PPR模型的14.20％、传统SVR模型的22.13％、模糊识别模型的21.57％、组合算子模型的18.36％和多元回归模型的25.31％;而两类模型预测的最大的相对误差绝对值分别为4.11％和3.57％,更加远远小于传统的6种预测模型的37.18％、56.07％、27.40％、32.14％、38.38％和60.26％.实例分析结果证实了误差修正公式对提高模型预测精度具有切实可行性.基于规范变换与误差修正相结合的前向神经网络和投影寻踪回归两类预测模型不仅避免了“维数灾难”,提高了学习效率和模型的预测精确度,而且具有简洁、普适、规范、统一和稳定的特点,对其他预测建模也有借鉴作用.

The purpose of this study was to establish prediction models of neural network and projection pursuit regression for environmental system, which have the charactertctics of simple structure, unified form, standardized procedures and universal application. The predictive models of traditional neural network and projection pursuit regression, which are used in multi⁃factor and large sample numbers, have limits of complex model structure, low learning efficiency. Therefore,the design principles and methods of reference values and the standard transformation formula used predicting variable and its influencing factors were proposed. The normalized influence factors were equivalent to the same normative influence factor. Thus, the predictive modeling of multiple factors is simplified as the predictive modeling of the " equivalent" norm factor, which greatly simplifies the model structure and improves the learning efficiency. In addition, in order to improve the prediction accuracy of the prediction model, the error correction formula for the model output value of the prediction sample was also proposed. On the basis of standard transformations for the predictive variable and its influencing factors of environment system, each modeling sample with m canonical influence factors were formed m " equivalent" training samples. Then, the immune evolutionary algorithm was used to optimize the model parameters, two different structures of prediction models of forward neural network and projection pursuit regression for environment system prediction were built: the case of 2⁃2⁃1 structure, which was used to any 2 normative impact factors and the case of 3⁃2⁃1 structure was, which was used to any 3 normative impact factors. Furthermore, based on the error theory, a rigorous mathematical demonstration was made for the 环 境 科 学 学 报 环 境 科 学 学 报 39 卷 improvement of the prediction accuracy of the model by the error correction formula. Two kinds of prediction models based on standard transformation and similar sample error correction were applied to predict the SO2 concentration of 5 spots in a city. Results were compared with the prediction results of six traditional prediction models and methods. The results show that for the same forecast sample, the predicted values and relative errors of two different structures of the same model ( forward neural networks or projection pursuit regression) were almost identical or very small. In addition, two kinds of prediction models with two different structures were used for the prediction of 5 samples, and the means of relative error absolute values were 2.59%, 2.67% and 2.18%, 2. 62%, respectively. They were far less than the results of 22. 13%, 25. 72%,14. 20%,21. 57%, 18. 36% and 25. 31% of the prediction models of traditional BP neural network(BP), traditional projection pursuit regression( PPR), traditional support vector machine( SVM), fuzzy recognition, combination operator and multiple regression respectively. The maximum relative error absolute values of samples of the two prediction models were 4.11% and 3.57%,respectively. They were smaller than the results of 56.07%, 27.40%, 37.18%, 32.14%, 38.38% and 60.26% of six traditional forecasting models. The example analysis results confirm that the error correction formula is feasible for improving the prediction accuracy of the model. Two prediction models of forward neural network and projection pursuit regression based on the combination of standard transformation and error correction can avoid the " dimension disaster" , improve the learning efficiency and model prediction accuracy. They have the characteristics of simplicity, universality, standardization, unity and stability. They can also be used for reference in other forecasting models.

针对高维、非线性环境系统的传统预测模型存在结构复杂、收敛速度慢、求解精度低的局限,提出对环境系统预测量及其影响因子进行幂函数与对数函数相结合的规范变换.此规范变换能使变换后的各影响因子皆等效于一个线性化的规范因子,从而将多因子、非线性的预测建模简化为简单的一个“等效”规范因子的一元线性回归建模;并对预测样本的模型输出进行误差修正,以提高样本的预测精度.在规范变换的基础上,由有m个规范因子的每个建模样本生成一个规范因子的m个“等效”训练样本,n个建模样本共生成N=m×n个训练样本.应用最小二乘法,建立基于规范变换的一元线性回归预测模型.将基于规范变换的一元线性回归预测模型与相似样本误差修正法相结合,分别用于菜市5个点位的SO2浓度预测和南昌市城市降水酸度pH值预测及某河段CODMn预测,并与多种传统预测模型和方法及基于规范变换与误差修正的3种智能预测模型的预测结果进行了比较.结果表明:该预测模型用于3个实例预测的相对误差绝对值的平均值分别为1.14％、0.49％和1.45％;最大相对误差绝对值分别为2.22％、0.87％和1.85％,与基于规范变换与误差修正的3种智能预测模型的相应误差几乎没有差异,甚至还要小;均远小于多种传统预测模型和方法的相应误差,其预测精度甚至提高了一个数量级以上.基于规范变换与误差修正的一元线性回归预测模型简单、预测精度高、稳定性好,不存在“维数灾难”,因而可广泛用于任意系统的预测建模.

Lake eutrophication is a serious environmental problem worldwide, caused by both natural processes and anthropogenic influences. For effective lake eutrophication management, a variety of models have been designed to investigate the complex interrelationship between physical, chemical and biological factors and processes in lakes. However, these models are inconvenient for predictions of lake eutrophication in practical application. To date, very few studies have focused on lake eutrophication in terms of anthropogenic influences (such as sewage emissions and agricultural practices), which are more readily regulated than natural processes. Effective lake eutrophication prediction models should base primarily on facile controlled or predictable indicators. Therefore, to meet this requirement, we designed simple predictive models to determine the interrelationship between the trophic states of lakes and nutrient inputs, which is a direct measurement to characterize anthropogenic influences. Lake Taihu (China) was used as a representative eutrophic water body to assess the accuracy of the proposed predictive models. Firstly, to comprehensively understand the role of nutrient input indicators (NIIs) during eutrophication, Pearson correlation coefficient analysis was conducted on 7 NIIs and 38 types of algae. Secondly, based on the NIIs identified with high correlation coefficients, we modified three commonly used growth models (Gompertz, logistic and Richards) to describe the lake's trophic state. A particle swarm optimization algorithm (PSOA) was used to optimize model variables. Results showed that the mean absolute percentage errors of the optimized Gompertz, logistic and the Richards models were 2.95%, 2.88% and 2.17%, respectively. Finally, these optimized models were used to predict lake eutrophication under several different nutrient input scenarios. Two adjustment scenarios revealed remarkably satisfied trophic states (including roughly oligotrophic and even ultra-oligotrophic) by the 2030s. Our results show that these established models are a simple way to support lake restoration projects by setting realistic and effective targets.

The purpose of this study was to build a universal,normative,simple and unified model of regression support vector machines,whieh can meet environment system predictions.The predictive model of traditional regression support vector machines has limits,which of the structure can not be universal,standardized and unified,the learning efficiency is low and the solution accuracy is poor for large sample and multi factor prediction.Therefore,the design principles and methods of reference values and the gauge transformation formula were proposed for predicting variable and its influencing factors of environment system,it makes all of the normalized influencing factors equivalent to the same normative influence factor.Furthermore,in order to improve the prediction accuracy of samples,an error correction method was also proposed for the model output of the predicted samples.On the basis of gauge transformations for the predictive variable and its influencing factors of environment system,each modeling sample with m canonical influence factors formed m training samples.Furthermore,from the modeling samples,the maximum values of the normative values of each influence factor was selected as the” reference sample” of the training sample set,and the norms of each training sample in a kernel function relative to the “ reference sample” were calculated.Then,the optimization algorithm was used to optimize the model parameters,two types of NV-SVR models for environment system prediction were built:the NV-SVR(2),which was suitable for the case involved any 2 support vectors and the NV-SVR (3),which was suitable for the case involved 3 support vectors.The regression support vector machine models of two simple structures based on normative canonical transformation,which were combined with the error correction method of similar samples,were used to predict the average monthly COD of 6 samples in Hejin bridge monitoring section,and were compared with a variety of traditional forecasting models and methods.The results show that for the same forecast sample,the predicted values of the two models are very close.In addition,two prediction models were used for the prediction of 6 samples,and the average values of relative error absolute values were 2.09％ and 2.79％ respectively,were far less than 41.63％,40.99％,25.94％ and 10.16％ of the prediction models of traditional projection pursuit regression,support vector machine,grey neural network and Markov respectively.The maximum relative error absolute values of the two prediction models for abnormal samples were 5.85％ and 5.13％ respectively,much smaller than 169.07％,180.45％,68.44％ and 41.96％ of the traditional 4 prediction models,respectively.Two types of NV-SVR,which avoid the difficulties of large sample size,improve learning efficiency and forecasting accuracy of models,are simple,universal,standard and unified.The two models are also useful for other prediction modeling and methods.

This paper aims to work out a few index formulae for assessing the environmental quality of the inside and outside the atmospheric conditions,which are characteristic of the features of being simple in form,easy in calculation and universal in application.Thus,it is on such a basis of the indoor air quality standards (GB/T 18883-2002) that we have proposed the essential formulae of the air quality so as to make the varied ranges of the normalized index systems consisting of 15 indexes in one single grade standard of the indoor air,which should be in conformity with those of the normalized index values of 7 ones for the same gradation standards of the open-air space,so that it can properly be set up as a reference to the normalized transformation form.In so doing,it would be easy and logic to make the formulae into a normalized transformation in accordance with the grade standards for each index of the indoor air.Thus,it is also possible to optimize the 6 universal index formulae by means of the monkey-king genetic algorithm with immune evolutionary (MKGAIEA),which are also suitable for environmental quality assessment of 7 normalized index values of the outdoor air.What is more,the formulae can also be made fit for the environmental quality assessment,consisting of 15 normalized indexes of the indoor air by means of the gauge symmetry principle.Based on the aforementioned study of the formulae,we have applied them to the air quality assessment practice of the indoor air for the two cases of the residential areas in Handan,Hebei,as well as for the public places of Guangzhou City,Guangdong,in hoping to test the practical effectiveness of the 6 index formulae.And,the assessment results of the aforementioned 6 universal index formulae for the 2 cases prove to be well in accord with the results assessed by using the traditional methods and consistent with each other.Thus,it can be concluded that the 6 index formulae can be taken as the up-to-date most convenient and regularized means for air quality assessment both for the indoor and outdoor air conditions at least at home.

针对现有的水资源可持续利用评价的回归支持向量机模型(LS-SVR)的不足,提出了水资源系统指标参照值和指标规范变换式的设置原则和方法,使不同的水资源指标经规范变换后皆“等效”于某一个规范指标,进而建立适用于任意m项指标规范值表示的回归支持向量机水资源可持续利用评价模型(NV-LS-SVR).将NV-LS-SVR模型应用于汉中盆地和淮河流域12个地区水资源可持续利用评价中,评价结果与BP神经网络的评价结果基本一致,验证了该模型的可行性和实用性,为水资源可持续利用评价提供了参考.

针对捕鱼策略优化算法未充分利用群体最优个体信息因而收敛速度较慢的缺陷,提出了将蜜蜂进化遗传算法与捕鱼策略相结合的混合优化算法.算法将蜂王具有最优遗传基因的特点引入到渔夫撒网捕鱼策略中,能较好利用群体当前最优个体的信息,提高搜索速率;并保留捕鱼策略中渔夫移动搜索策略的独立性,避免陷入不成熟收敛.通过对多个典型测试函数的测试表明:蜜蜂进化遗传算法与捕鱼策略相结合的优化算法,比简单的捕鱼策略的优化算法在寻优能力、稳定性和收敛速度等方面均有提高.

科学合理地评估气象灾害造成的损失,对减灾、防灾决策具有重要意义.为了建立不同气象灾害系统均能适用的投影寻踪回归(projection pursuit regression,PPR)矩阵表示灾情评估模型,在对气象灾情指标值进行规范变换基础上,规范变换后的各指标皆等效于同一个规范指标,因而只需构建对任意2个规范指标值适用的投影寻踪回归(projection pursuit regression based on normalized index value,NV-PPR) NV-PPR(2)模型和3个规范指标值适用的投影寻踪回归NV-PPR(3)模型;对3个以上指标的气象灾害系统NV-PPR建模,只需将其分解为若干个NV-PPR(2)模型和(或)NV-PPR(3)模型的组合即可.模型用于广东省台风和重庆市两起雷电灾情评估,并与其他方法的评估结果进行比较.结果表明:基于NV-PPR的气象灾情评估模型不受指标数量的限制,具有简单、实用的特点,该模型还可推广为适用于其他灾情评估.

This study aims to set up several index formulae for assessing the seawater quality ,which enjoy the prior-ity of being simple in form,easy in calculation and universal in applications.On the bases of the seawater quality standards(GB 3097-1997),the proposed formulae,which make the varied rage of the normalized index values of 27 indexes in each grade standards of seawater to be conformity with those of the normalized index values of 72 in-dexes in same grade standards of 3 classified water body ,have been established,if only it can be properly set a ref-erence value and normalized transformation form as well as make a normalized transformation in the grade standard value for each index of seawater .Therefore,the 6 optimized universal index formulae,which are suitable to the en-vironmental quality evaluation of 72 normalized index values of 3 classified water body,can also be suitable to the e-valuation of 27 normalized index values of seawater quality.Furthermore,in order to test the practical effectiveness of the 6 index formulae,it could be applied to the practical quality evaluations of seawater for 2 cases of the coastal waters in Xiamen City and in Yangtze River Estuary.The evaluation results of 6 universal index formulae proved to be basically in full conformity with those obtained from the commonly used evaluation methods.The results showed that not only the 6 universal index formulae to make the evaluations between land water body and seawater body universal,unified,normalized and simplified,but also the ideas and methods of normalized transformation can be reference for the studies of water resources and water security.

为了建立由水环境、空气环境、生态环境、水资源环境、灾害环境、遥感环境、社会经济环境等不同环境系统组成的广义环境系统评价都能普适、通用的神经网络模型,针对BP神经网络因收敛速度慢、易于陷入局部极值而使实用性受限的缺陷,提出以双极性sigmoid函数作为网络隐层节点(神经元)的激活函数,而网络输出为所有隐层节点输出的线性求和的前向神经网络的广义环境系统评价模型.在设置广义环境系统指标参照值和指标值规范变换式,并对指标值进行规范变换的基础上,分别构建了适用于广义环境系统评价的任意2个指标规范值的前向神经网模型(NV-FNN(2)结构)和任意3个指标规范值的前向神经网模型(NV-FNN(3)结构).而对于指标较多的广义环境系统评价,只要将多指标分解为以上2个指标和3个指标的两种简单结构的前向神经网络的广义环境系统评价模型的组合表示即可.理论分析和实例检验结果表明:该模型对任意广义环境系统的规范指标值皆普适、通用,因而使不同环境系统的评价变得简洁、统一.规范变换和优化算法相结合的建模思想和方法对简化广义环境系统评价的多元回归、投影寻踪回归、回归支持向量机和径向基神经网络建模亦有借鉴和启迪作用.

This study aims to set up two index formulae of fuzzy catastrophe used for seawater quality evaluation,which is not subject to the limitations of the number of indictors,and to set up grading standards on index values,which do not vary with the changes of index and index numbers. With properly setting the reference values and transforming forms for each seawater index,the difference in the same grade standard value with different indexes of seawater could be weakened,so the different indexes with normalized values were equivalent to a certain normalized index. Therefore,only two fuzzy catastrophe models of cusp catastrophe and swallowtail catastrophe were needed to build for seawater quality evaluation. Seawater quality evaluation for any indexes can be represented with multi-composition models of cusp catastrophe and(or) swallowtail catastrophe. Indexes formula of seawater quality evaluation with normalized index values based on catastrophe fuzzy applied to seawater quality evaluation of Pearl River Estuary and Qingdao sea area,and the results compared with BP artificial neural network and fuzzy comprehensive evaluation showed that the results are basically the same. Comparing with other traditional evaluation methods, indexes formula of fuzzy catastrophe based on normalized index values exhibit characteristics of universality and simplicity.

Water quality evaluation is an important issue in environmental management. Various methods have been used to evaluate the quality of surface water and groundwater. However, all previous studies have used different evaluation models for surface water and groundwater, and the models must be recalibrated due to changes in monitoring indicators in each evaluation. Water quality managers would benefit from a universal and effective model based on a simple expression that would be suitable for all cases of surface water and groundwater, and which could therefore serve as a standard method for a region or country. To meet this requirement, we attempted to develop a universal calibrated model based on the radial basis function neural network. In the new model, the units and values of the evaluation indicators for surface water and groundwater are normalized simultaneously to make the data directly comparable. The model's training inputs comprise the normalized value in each of a water quality indicator's grades (e.g., the nitrate contents defined in a regulatory standard for grades I to V) for all evaluation indicators. The central vector of the Gaussian function is used as the average of the evaluation indicators' normalized standard values for the five grades. The final calibrated model is expressed as an equation rather than in a programming language, and is therefore easier to use. We used the model in a Chinese case study, and found that the model was feasible (it compared well with the results of other models) and simple to use for the evaluation of surface water and groundwater quality.

应用集对分析法刻画历史样本之间的相似性,用多个最相似的历史样本的加权平均值作为当前样本预测值,建立了基于集对分析的降水酸度及水质相似预测模型(SFM-SPA),并运用该模型进行了降水酸度及水质预测的实例验证.结果表明,在主要影响因子选择适当、历史样本的代表性和相似性较好等限定条件下,利用模型进行环境预测是可行的,它较直观、计算简便,为环境污染预测提供了新的途径.

类比黑体辐射分布的普朗克公式,提出一维流场中污染物(或示踪剂)浓度的时间过程线分布或污染物浓度值的倒数沿程变化的时空迁移转换规律均可用与Plank分布相似的公式描述.结合实测的河水污染物监测数据,采用免疫进化算法对公式中的参数进行优化,得出优化后的一维流场中的污染物浓度时空迁移转换的Plank公式.实例分析表明该公式具有意义明确、形式简洁、所含参数较少、易于计算、方便实用的特点.

地下水位预测能为生态环境保护和地下水资源规划、管理提供科学依据.为了对地下水位动态变化进行准确预测,针对地下水位样本之间的相似性及影响因子与地下水位之间具有的确定、不确定性特征,提出将集对分析与相似预测相结合,从同、异、反三方面定量刻画地下水位的当前样本与历史样本之间的相似性,建立了基于集对分析的地下水位相似预测模型,并应用该模型计算地下水位预测值.实例检验结果表明:基于集对分析的地下水位相似预测模型的平均相对误差小于3％.与其他地下水位预测方法相比,该方法用于地下水位预测具有物理概念清晰,计算简便,预测精度较高的特点.