摘要在我们赖以生存的大气环境，存在许多污染物危害着我们的身体健康，其中主要污染因子有、 、 。通过2005-2011年汉中市汉台区污染物浓度原始数据，分别运用MATLAB程序和最小二乘法的计算方法建立、 、 三个污染物的GM（1,1，）预测模型。86408

对得到的GM(1,1)模型用残差检验的方法检验后，发现预测模型精度符合预测要求，可以用来预测未来两年汉中市汉台区污染物浓度值。预测模型残差检验相对误差较大，然后经过残差修正得到新的模型精度更高的预测模型。在一定程度上，新的预测模型相对有所改善，用来预测未来两年汉中市污染物的浓度值，但预测值与检测值仍然偏差较大，所以污染物不适合用GM(1,1)模型。检验的GM（1,1）预测模型为残差不合格模型。

预测结果表明，模型修正后，模型精度在原来的程度上提高一点点，但模型的预测值与实际检测值仍然相差较大，所以修正结果不显著； 模型预测较准确，浓度逐渐下降，下降速度有所缓和，说明污染的防治措施生效且已经下降的一定程度，需要采取新的防治措施；浓度预测模型是不合格模型，可能数据量较少，不适合用GM（1,1）模型。

毕业论文关键词：灰色系统；GM（1,1）模型；残差检验；MATLAB

Abstract In atmospheric environment we live in, many pollutants are damaging our health, and the main pollution factors are PM_10, SO_2 and NO_2。 According to original date of pollutant concentration 2005-2011 in Hantai, Hanzhong, GM (1, 1) prediction model of three pollutants PM_10, SO_2 and NO_2 is establish by applying MATLAB program and the calculation method of least squares method。

After testing GM (1,1) model with residual analysis, it was found that accuracy of SO_2 prediction model meets the prediction requirement, so it can be used to predict concentrations of the pollutants in Hantai, Hanzhong in two years。 There is huge relative error in residual test of PM_10 prediction model, so it should be revised to get a new model—a more accurate prediction model。 To some extent, the new prediction model has improved, which has been used to predict concentrations of the pollutants in Hanzhong in two years。 However, the predicted value and measured values are still large, so it is not suitable to test pollutants with GM (1,1) model; that is GM (1,1) model, used to test NO_2, is a disqualification model。

Prediction results show that the revised PM_10 model has improved a little in precision, but predicted value and actual values of the model are still large, so the correction effect is not significant。 SO2 model is accurate, and SO_2 concentration gradually declines。 Besides, descent speed becomes slow, it means pollution prevention and control measures have taken effect and fallen to a certain extent, which needs to take new prevention and control measures。 NO_2 concentration prediction model is unqualified。 The amount of data is too little and maybe for this reason, it is not suitable to use GM (1, 1) model。

Keywords: Grey system; GM(1,1) model; Residual; MATLAB

目录

第一章  绪论 1

1。1 污染物浓度预测模型研究背景及国内外研究现状 1

1。1。1 研究背景 1

1。1。2 国内外研究现状 1

1。2 课题的提出与研究意义 2

1。3 主要研究内容 2

第二章  灰色预测模型理论及模型检验方法 4

2。1 灰色系统理论 4

2。2 ＧＭ（１,１）模型