第三问模型建立与求解doc.doc

基于最小加权距离和求污染源模型 因为每种元素的污染源应该在以该污染物浓度最大的点为圆心的圆内,且到其周围污染程度较大的点的总加权距离最小,所以本文建立模型(1),其中Wi为加权因子.具体实现步骤:(1)观察每个重金属元素的浓度分布图由观察可得出,As的污染源个数为3个,Cd的污染源个数为4个Cr为1个Cu2个,Hg3个,Ni1个,Pb2个,Zn2个.并将其周围污染程度大的点与其归为一组.(2) 因为权重因子主要与距离有关,离污染源越大,浓度梯度下降越大,所以本文以R=1000m为半径,画出每组的同心圆,确定权重因子Wi,(2). ASCdCrCu(3) 利用Lingo软件进行最优化求解,找出污染源坐标.模型求解:以As为例,其污染源个数为3个,具体分组如下表:组一编号Asxy浓度变化Wi8430.13 181341004608210.99 187381092119.140.018002257778.50 170871193321.630.010023172067.56 20282859022.570.0086974952567.34 151981010022.790.007760941968.67460.0070346821017.63 199681296122.50.0065332911957.56570.0057290082509.13 1406510987210.0050282543077.34 144821269222.790.005053439728.06070.0047463392847.12 166291448123.010.0049130972157.56 21018576422.570.0043717433088.23 143181356921.90.0042167282517.34 127341034422.790.0042139712927.12 174141547623.010.0042008221389.17960.0038186852479.58 12641956020.550.003726539927.41 23664979022.720.004104122678.67 121531233621.460.0033508212878.00 209831586222.130.003417075 组二 编号Asxy浓度变化Wi2921.87 474272933018.38 494872933.490.0169417483110.53 5567678211.340.011685421197.41 5481600414.460.0097321312218.67 5006884613.20.008379356239.39 3573621312.480.007841659229.84 3299601812.030.0062474034116.58 686972865.290.0024870711611.45 4777489710.420.00434837187.84 6534564114.030.00575637427.41 7056834814.460.00568575208.50 4592460313.370.0049625122378.90 7106946712.970.004038361528.23 5101408013.640.0042189921539.35 5438399412.520.0037133712237.12 63951044314.750.00414628778.94 2883361712.930.00313888389.62 2383369212.250.0028455951548.90 5382301212.970.002996351508.00 4020299013.870.0031788623310.27 77761061311.60.002579211 组三编号Asxy浓度变化Wi17823.72 1269630241747.56 11557158116.160.008790252507.20 10643447216.520.0065756481717.34 10225382116.520.0063626561389.17550.0042636111677.56 9663128816.160.004624145728.06660.0033483721657.78 8403107515.940.0033809153199.35 7653195214.370.0027872061957.56160.0029254161968.67050.0025046182479.58 12641956014.140.002163336187.84 6534564115.880.0023720263187.56 5985256716.160.0024024382418.23 10547959115.490.0022417764116.58 686972867.140.0009890161548.90 5382301214.820.0020262512517.34 127341034416.380.0022376741539.35 5438399414.370.0019624452567.34 151981010016.380.0021824581577.78 563613315.940.002089396将每组中的xi,yi,wi代入模型,用Lingo求解可得第一组的污染源为(17135,10506),第二组的污染源为5159,6484,第三组的污染源为10849,4464.5其余7种元素求解过程同上,具体结果为下表位置一位置二位置三位置四As(17135,10506)(10849,4464.5)(5159,6484)-Cd(19178,10081)(4956.6,5738.9)(3778.2,3375.8)(7194.2,9570.4)Cr(4177.6,5556.5)-Cu(3741.8,3912.5)(4633.