无约束重力模式.doc

无约束重力模式 根据无约束重力模型公式：两边取对数得 Ln(Tij)=lnk+lnGi+lnAj-lntijTij 交通区i到交通区j的出行分布量：Gi 交通区i的出行产生总量：Aj 交通区j的出行吸引总量：K， 模型参数；公式转换为:Y=K+x1+x2-x3参数的确定是通过拟合现状OD调查资料，用最小二乘法确定。现有一规划区域，共划分为5个交通区，经调查其现状OD分布见表1，各交通区间的出行时间见表2，通过对各交通区的交通生成进行预测，得到各交通区未来交通产生、吸引量见表3，分析计算得到未来各交通区间的交通出行时间见表4。表A1（现状OD分布）交通区1234518006002003004002200210050020015054502409001005041101002407005059050100120600表B2（各交通区间的出行时间）交通区123451510182030212410252031510815354202515103053525353512表C2（各交通区未来交通产生，吸引量）交通区产生量吸引量152004400245004100333003400421002700523002200 表D1（未来各交通区间的交通出行时间）交通区1234515101215202104820203101071030415201082053020303010解： 选用出行时间的函数形式，将无约束重力模型变为：Ln(Tij)=lnk+lnGi+lnAj-lntij格式LN(number)：number是用于计算其自然对数的正实数。Ln是exp函数的反函数计算步骤：打开数据文件，在定下的单元格中输入公式 Ln(number),按下number之后选择要计算的数字，然后按下Entre键后公式将返回计算结果如下表：ijTGATlnTlnGlnAlnt118005200440056.6846128.5564148.389361.6094381260052004100106.396938.5564148.3187422.3025851320052003400125.2983178.5564148.1315312.4849071430052002700155.7037828.5564147.9010072.708051540052002200205.9914658.5564147.6962132.9957322120045004400105.2983178.4118338.389362.3025852221004500410047.6496938.4118338.3187421.386294235004500340086.2146088.4118338.1315312.0794422420045002700205.2983178.4118337.9010072.9957322515045002200205.0106358.4118337.6962132.9957323145033004400106.1092488.1016788.389362.3025853224033004100105.4806398.1016788.3187422.302585339003300340076.8023958.1016788.1315311.945913410033002700104.605178.1016787.9010072.302585355033002200303.9120238.1016787.6962133.4011974111021004400154.700487.6496938.389362.708054210021004100204.605177.6496938.3187422.9957324324021003400105.4806397.6496938.1315312.302585447002100270086.551087.6496937.9010072.079442455021002200203.9120237.6496937.6962132.995732519023004400304.499817.7406648.389363.401197525023004100203.9120237.7406648.3187422.9957325310023003400304.605177.7406648.1315313.4011975412023002700304.7874927.7406647.9010073.4011975560023002200106.396937.7406647.6962132.302585YX1X2X3Y=K+x1+x2-x3此方程为线性回归方程，k, ，是用最小二乘法标定。计算步骤：cccy=c=(1 x)： YX1X2X36.684618.55648.38941.60946.396918.55648.31872.30265.298318.55648.13152.48495.703818.55647.90102.70815.991518.55647.69622.99575.298318.41188.38942.30267.649718.41188.31871.38636.214618.41188.13152.07945.298318.41187.90102.99575.010618.41187.69622.99576.109218.10178.38942.30265.480618.10178.31872.30266.802418.10178.13151.94594.605218.10177.90102.30263.912018.10177.69623.40124.700517.64978.38942.70814.605217.64978.31872.99575.480617.64978.13152.30266.551117.64977.90102.07943.912017.64977.69622.99574.499817.74078.38943.40123.912017.74078.31872.99574.605217.74078.13153.40124.787517.74077.90103.40126.396917.74077.69622.3026将C=( 1 x)转置的步骤是：按矩阵c选择行列数，在单元格中输入:=TRANSPOSE(B2:E26)，然后按Cntrl+Shift+Enter组合键最后得出的结果是如下表（C）:11111111111111111111111118.5564148.5564148.5564148.5564148.5564148.4118338.4118338.4118338.4118338.4118338.1016788.10178.101688.1016788.1016787.6496937.6496937.6496937.6496937.6496937.7406647.7406647.7406647.7406647.7406648.389368.3187428.1315317.9010077.6962138.389368.3187428.1315317.9010077.6962138.389368.31878.131537.9010077.6962138.389368.3187428.1315317.9010077.6962138.389368.3187428.1315317.9010077.6962131.6094382.3025852.4849072.708052.9957322.3025851.3862942.0794422.9957322.9957322.3025852.30261.945912.3025853.4011972.708052.9957322.3025852.0794422.9957323.4011972.9957323.4011973.4011972.302585下一步的步骤是C.c；依据C425C254C44 选择单元格区域的行列数，在单元格区域中输入为=MMULT(A28:Y31,B2:E26)，然后然后按Cntrl+Shift+Enter组合键最后得出的结果是如下表C.c：25202.3014202.184364.69881202.30141640.221636.086521.8098202.18431636.0861636.811522.016864.69881521.8098522.0168175.021下一步是算C.c ；先选择单元格区域的行列数，在单元格区域中输入： =MINVERSE(B34:E37)然后按Cntrl+Shift+Enter组合键。得出的结果是如下表C.c ：88.85468-3.7687-6.4898-2.2538-3.76870.3656950.0696880.095011-6.48980.0696880.6918240.12784-2.25380.0950110.127840.174296下一步是算C.c .C；依据C44C425C425选择单元格区域中的行列数，在单元格区域中输入为：=MMULT(B39:E42,A28:Y31)，按Cntrl+Shift+Enter组合键。得出的结果是如下表C.c .C：-1.4645-2.56842-1.76437-0.77124-0.09055-2.481830.041599-0.30565-0.874740.454338-1.31295-0.8551.164181.8563620.709383-0.52339-0.713472.0637084.062683.326618-2.42845-1.05632-0.755190.7408614.5459880.0978880.1588240.16310.1682370.1812980.1108730.0188930.0717040.1426970.128426-0.00255-0.007-0.0544-0.036580.053527-0.12931-0.1069-0.18581-0.22307-0.15029-0.03019-0.07363-0.04816-0.06422-0.182870.116190.1559470.049738-0.08122-0.186120.1947260.028733-0.01217-0.05452-0.19620.1731120.1243-0.0509-0.16474-0.165980.1934490.181372-0.03676-0.22477-0.249310.2884010.1877110.110029-0.04945-0.33158-0.087830.023960.0318040.0412270.0651880.01925-0.14948-0.05260.0776320.051451-0.01022-0.019-0.1053-0.072650.0926540.0175090.058623-0.08612-0.15449-0.020960.1469650.0672670.1140040.084534-0.13313下一步是算C.c .CY：依据C425C251C41选择单元格区域中的行列数，在单元格区域中输入为：=MMULT(A45:Y48,A2:A26) 。然后按Cntrl+Shift+Enter组合键。得出的结果是如下表C.c .CY：LNK8.2227040.481022-0.3757-1.4067经过最小二乘法标定后，得到 K=2.106，=0.481, =-0.375, =-1.406则所求的无约束重力模型为：将预测各交通区发生，吸引量和预测各交通区间出行时间代入公式得到的交通分布预测结果如下表：交通区12345产生总量153.21145.21201.3300485.20 118