灰色系统GM（1,1）残差模型在水质预测中的应用与探讨

近年来，灰色系统理论在环境预测方面已被较为广泛地应用，本文以青格达湖水质污染指标COD近十余年的监测数据作为原始数据．预测来来水质污染指标浓度值，探讨GM（1，1）模型在水质预测中的适用条件。1方法概述按X（0）的原始数据列得到下述GM（1，1）模型的时间响应函数。从模型得到的还原数据列为已知原始数据列为定义残差为如果取k—i．i＋1…·．n，便有残差列q（）一（q（0）（i）．q（0（i＋l）…·，q’0’（n》·对十”建立GM（1，1）模型．得时！司响应函数2计算步骤2．1建立GM（1，1）模型对原始数据列X”’作一次累加主成…     

灰色理论及其模型在北京典型城市区域声环境研究中的应用

以北京市某典型区域作为研究对象,在收集大量相关资料与实测历史噪声数据的基础上,对研究区域内的声环境质量影响因素进行灰色关联度分析,并运用灰色理论建立GM（1,1）模型进行预测。结果表明,影响城市区域声环境质量因素从大到小的排序依次为：机动车辆﹥常住人口数量﹥平均车流量﹥地区生产总值﹥城市道路桥梁﹥基础设施投资﹥治理噪声环保投资;以研究区域内噪声污染实测历史数据建立的GM（1,1）模型精度符合要求标准,根据GM（1,1）模型预测北京市“十二五”期间声环境质量达标且有轻微下降趋势。     

运用灰色系统的GM（1，1）模型对城市噪声的综合预测

应用GM（1，1）模型，对大同市各功能区环境噪声进行综合预测，得出了大同市未来几年城市噪声的变化趋势。     

1976-2005年唐山地区降水变化规律及干旱预测

利用唐山市1976-2005年各县年降水序列,分析了该市降水的空间分布规律和时间变化特点。采用灰色系统的灾变预测方法,对各县分别建立了GM（1,1）模型,进行未来25年唐山市各站的干旱年预测。利用残差检验、后验差检验和关联度检验对各模型分别进行了精度检验。结果表明,预测模型精度较高,可以对唐山市各县未来的干旱年进行预测,从而为科学决策提供依据。     

基于GM（1,1）模型的城镇生活污水排放量预测

根据2000--2012年全国城镇生活污水排放量数据,建立了相应的GM（1,1）模型和预测函数。通过后验差检验等对预测函数进行了评估,并对2013--2017年城镇生活污水排放量进行了预测,结果表明,2013--2017年全国城镇生活污水的排放量逐年增加,呈上升趋势,从2013年的477．2736亿t上升到2017年的624．1022亿t;灰色预测模型和方法简单易用,利用较少的数据即可进行精度较高的预测。     

应用GM（1，1）模型的简化算法预测废水排放量

从GM（1，1）的建模原理和模型结构特征出发，通过一系列的推导、变换、给出了直接从原始序列出发求解模型的方法，通过对某市废水排放量预测的应用建模计算比较，表明该方法是切实可行的。     

北京市城市道路交通噪声的灰色预测

以北京市1991~2002年城市道路交通噪声监测数据为基础,运用灰色系统理论,建立了灰色GM(1,1)预测模型,并采用残差、均方差比值、小误差概率检验等3种办法对所建模型的拟合精度进行了检验.结果表明,此模型精度为一级灰色预测模型.预测精度较高,平均拟合偏差为0.40%.对2003~2005年噪声的预测精度平均高达99.9%.利用常规GM(1,1)模型、新陈代谢GM(1,1)模型和多维灰数递补GM(1,1)模型等三种预测模型对本市未来3年(2006~2008年)的城市道路交通噪声进行了预测.     

“3S”技术的城市环境监测与管理系统研究

基于遥感（ＲＳ）、地理信息系统（ＧＩＳ）、全球定位系统（ＧＰＳ）（简称“３Ｓ”技术）,辅以常规环境监测与分析手段建立的城市环境监测缠环境保护与区域可持续发展强有力的技术支持,对以“３Ｓ”技术建立的城市环境监测与管理系统的构成及其应用进行了探讨。     

灰色模型在岩溶地下水水质预测中的应用研究

运用灰色理论建立水质预测模型,通过对水质指标拟合值与实测值差异性分析,判断模型精密度,并预测山东省东阿县下马头水源地未来2年的水质变化趋势,结果表明:在4项水质指标预测模型中,总硬度、氟化物指标的GM(1,1)时间响应预测模型拟合结果较好;溶解性总固体、硝酸盐指标的GM(1,1)时间响应预测模型精密度均为3级,不适合指标的预测;未来2年下马头水源地岩溶地下水水质良好。     

地表水COD浓度灰色预测的GPPM（1）模型

根据地表水中ＣＯＤ浓度的时序数据,建立了ＧＰＰＭ（１）预测模型,结果表明ＧＰＰＭ（１）模型的预测精度优于常规灰色ＧＭ（１,１）模型,它为环境系统的拟合,预测和决策提供了新的方法途径。     

GM（1,1）模型简化算法及其在噪声影响预测中的应用

对ＧＭ（１，１）模型经差分形式化及令定写成直线方程形式。据最小二乘法原理，原方程的参数辨识可借助线性回归方法来实现。从而使ＧＭ（１，１）模型的应用更显普及和实用化。     

基于MATLAB的灰色模型在广州市降尘预测中的应用

用MATLAB语言将灰色系统理论中的GM(1,1)模型,从建模到模型的检验过程编制成一个普适程序。将该程序应用于广州市降尘量的预测分析,结果令人满意。     

Prediction of the effluent from a domestic wastewater treatment plant of CASP using gray model and neural network

When a domestic wastewater treatment plant (DWWTP) is put into operation, variations of the wastewater quantity and quality must be predicted using mathematical models to assist in operating the wastewater treatment plant such that the treated effluent will be controlled and meet discharge standards. In this study, three types of gray model (GM) including GM (1, N), GM (1, 1), and rolling GM (1, 1) were used to predict the effluent biochemical oxygen demand (BOD), chemical oxygen demand (COD), and suspended solids (SS) from the DWWTP of conventional activated sludge process. The predicted results were compared with those obtained using backpropagation neural network (BPNN). The simulation results indicated that the minimum mean absolute percentage errors of 43.79%, 16.21%, and 30.11% for BOD, COD, and SS could be achieved. The fitness was higher when using BPNN for prediction of BOD (34.77%), but it required a large quantity of data for constructing model. Contrarily, GM only required a small amount of data (at least four data) and the prediction results were analogous to those of BPNN, even lower than that of BPNN when predicting COD (16.21%) and SS (30.11%). According to the prediction, results suggested that GM could predict the domestic effluent variation when its effluent data were insufficient.     

Modified grey model for estimating traffic tunnel air quality

This study compared three forecasting models based on the mean absolute percentage errors (MAPE) of their accuracy in forecasting air pollution in a traffic tunnel: the Grey model (GM), the combination model used four sample point and five sample point prediction with GM (1,1)(GM(1,1)^4 + 5), and the modified grey model (MGM). An MGM was combined using the four points of the original sequence using the original grey prediction GM (1,1) for short-term forecasting. The proposed method cannot only enhance the prediction accuracy of the original grey model, but can also solve the jump data forecasting problem something for which the original grey model is inappropriate. The MAPE was applied to the models, and the MGM found the proposed method to be simple and efficient. The MAPE of MGM, calculated over 3 h of forecasts, were as follows: 10.12 (Upwind), 10.07 (Middle) and 7.68 (Downwind) for CO; 10.79 (Upwind), 6.05 (Middle) and 5.98 (Downwind) for NO _x , and 11.67 (Upwind), 7.32 (Middle) and 4.56 (Downwind) for NMHC. The MGM model results reveal that the combined forecasts can significantly decrease the overall forecasting error. Results of this demonstrate that MGM can accurately forecast air pollution in the Kaohsiung Chung–Cheng Tunnel.     

Forest cover change and fragmentation using Landsat data in Maçka State Forest Enterprise in Turkey

In this study, Grey model (GM) and artificial neural network (ANN) were employed to predict suspended solids (SSeff) and chemical oxygen demand (CODeff) in the effluent from a wastewater treatment plant in industrial park of Taiwan. When constructing model or predicting, the influent quality or online monitoring parameters were adopted as the input variables. ANN was also adopted for comparison. The results indicated that the minimum MAPEs of 16.13 and 9.85% for SSeff and CODeff could be achieved using GMs when online monitoring parameters were taken as the input variables. Although a good fitness could be achieved using ANN, they required a large quantity of data. Contrarily, GM only required a small amount of data (at least four data) and the prediction results were even better than those of ANN. Therefore, GM could be applied successfully in predicting effluent when the information was not sufficient. The results also indicated that these simple online monitoring parameters could be applied on prediction of effluent quality well.     

Modelling Gene Flow between Fields of White Clover with Honeybees as Pollen Vectors

The portion-dilution model is a parametric restatement of the conventional view of animal pollination; it predicts the level of pollinator-mediated gene dispersal. In this study, the model was applied to white clover (Trifolium repens) and its most frequent pollinator, the honeybee (Apis mellifera). One of the three parameters in the portion-dilution model is the mean number of flowers a pollinator visits in one foraging bout. An alternative method to estimate this parameter was developed that was not depending on pollinator hive-seeking behaviour. The new estimation method, based on nectar collection, seems to be a good alternative, when reliable observation on visiting behaviour of pollinators is not possible. The gene flow in white clover was modelled. Where fields were assumed to be well separated, and only a low fraction of bees travelled between fields, the gene flow was estimated to be 0.7%, but subjected to large uncertainty. In a worst case scenario with adjacent fields—one with a genetically modified (GM) T. repens cultivar and the other with a conventional T. repens cultivar—and where all arriving bees were expected to transfer GM pollen, the median gene flow was modelled to be 7% with an estimated 95% percentile of 70%. The results show that the European Union threshold limit of 0.9% GM admixture for food and feed will likely be exceeded at times and especially organic farmers that do not accept GM admixture and often have clover and clover–grass fields might face challenges with admixture of GM.     

环境预测中的GAM模型

当原始序列属代数曲线型时，应用ＧＡＭ模型可以提高精度，从而避免进行ＧＭ（１，１）模型的残差修正二次建模。从分析ＧＭ（１，１）模型的缺陷着手，结合实例详细介绍了ＧＡＭ模型的思想形成和计算方法。