三元线性回归方程.docx

1、三元线性回归方程对于一个稳定生产的水泥厂家来说,其主要工艺条件,原、燃料状况,在某一较长的时间内,是基本稳定的。在此前提条件下,出厂水泥28d抗压强度与熟料3d强度、混合材掺量、水泥3d强度之间,具有线性相关关系。应用三元线性回归分析方法,可直接预报水泥28d强度。 现列举工作中的一个实例,说明此预报方法的操作步骤。1 设立关系式 水泥28d强度y与熟料3d强度x1、混合材(煤渣)掺量x2、水泥3d强度x3之间具有直接相关关系,其回归关系式为: y=a0+a1x1+a2x2+a3x3 (1) 其中:a0、a1、a2、a3为回归系数。求得并验证了这些系数,就会使以后的预报来得十分方便。 2 选取

2、样本 选取某一段时间内的连续实际数据,剔除个别明显异常值后即为样本。一般选取30组以上的数据为好,样本数据越多,回归分析结果越准确,见表1。 表1 样本数据 序号i熟料3d强度x1混合材掺量x2水泥3d强度x3水泥28d强度y132.810.529.250.1234.011.530.651.9334.512.030.950.9434.812.031.251.4535.313.030.251.0635.013.030.149.9733.711.528.447.9831.710.528.348.5932.310.529.250.01034.111.530.150.21133.211.029.951

3、.81233.211.029.649.51333.711.529.051.81432.111.028.849.71533.311.030.149.41633.610.530.651.61734.313.028.949.51833.912.529.351.01932.211.028.448.42033.211.027.750.02133.612.528.749.72233.612.528.350.42331.510.528.349.02433.612.527.649.22536.814.528.951.32634.612.530.251.62730.08.028.148.02833.111.02

4、9.750.72930.68.527.849.23034.712.530.150.83133.011.029.650.13232.811.027.547.93334.512.530.450.43433.412.028.649.63535.013.529.550.63633.811.530.450.53733.011.030.250.23831.69.528.249.53933.311.030.950.34033.411.029.449.74136.014.527.650.54232.410.527.848.74333.410.530.550.64435.014.030.351.14534.41

5、3.030.749.74634.613.030.449.64732.711.028.349.14833.311.527.749.24934.412.530.950.65034.412.531.452.1 3 参数计算 4 求解回归系数 依最小二乘法原理所得方程组 及解: 得:a1=0.597;a2=-0.282;a3=0.397;a0=21.680 5 整理检验 将所求得的回归系数代入(1)式即得水泥28d强度预报值为: =21.680+0.597x1-0.282x2+0.397x3 (1)检验其相关性 r接近1,说明相关性良好。 (2)检验其精度 剩余标准偏差 S值较小,说明回归方程精度良好

6、。 (3)检验其可靠性 预报值与实测值y的比较见表2,其相对误差几乎全部落于5%的范围内,说明可靠性良好。 表228d强度预报值与实测值的比较 序号i实测y(MPa)预报 (MPa)相对误差(%)150.149.9-0.4251.950.9-1.9350.951.20.6451.451.50.2551.051.10.2649.951.94.0747.949.84.0848.548.90.8950.049.6-0.81050.250.71.01151.850.3-2.91249.550.11.21351.850.1-3.31449.749.2-1.01549.450.42.01651.650.9

7、-1.41749.550.01.01851.050.0-2.01948.449.11.42050.049.4-1.82149.749.6-0.22250.449.4-2.02349.048.8-0.42449.249.202551.351.0-0.62651.650.8-1.62748.048.51.02850.750.1-1.22949.248.6-1.23050.850.803150.150.0-0.23247.949.12.53350.450.80.83449.649.603550.650.5-0.23650.550.70.43750.250.30.23849.549.1-0.83950

8、.350.70.84049.750.21.04150.550.0-1.04248.749.10.84350.650.80.44451.150.7-0.84549.750.72.04649.650.72.04749.149.30.44849.249.30.24950.651.00.85052.151.2-1.7 6 结语 (1)出厂水泥28d抗压强度与熟料3d强度、混合材掺量、水泥3d强度之间具有三元线性相关关系。 (2)采用三元线性回归分析比一元或二元线性回归分析方法更能直接预报水泥28d强度。 (3)采用三元线性回归分析方法预报水泥28d强度,相对误差小,可靠性高。 (4)利用三元线性回归方程良好的可靠性、精度、相关程度,如果将混合材掺量视为因变量,则可很好地指导水泥粉磨配料。此时方程式改写为: 即:x2=3.546-2.120x1-1.408x3-76.879式中:x2需预测的混合材掺量; 期望的水泥28d强度; x1已知的熟料3d强度; x3期望的水泥3d强度。