三元二次回归正交组合设计(下)

三元二次回归正交组合设计(下)——在消除试验机摩擦振动中的应用吉林大学农机**x32x22x12x2x3x1x3x1x2x3x2x1x0ji1234567891011121314151617111111111111111111111-1-1-1-1r-r000000011-1-111-1-100r-r000001-11-11-11-10000r-r00011-1-1-1-1110000000000000000000000000001-11-1-11-111-1-111-1-1111111111r2r200000001111111100r2r200000111111110000r2r2000353.1rx1′0.3140.3140.3140.3140.3140.3140.3140.3141.1451.145-0.686-0.686-0.686-0.686-0.686-0.686-0.686x2′0.3140.3140.3140.3140.3140.3140.3140.314-0.686-0.6861.1451.145-0.686-0.686-0.686-0.686-0.686x3′0.3140.3140.3140.3140.3140.3140.3140.314-0.686-0.686-0.686-0.6861.1451.145-0.686-0.686-0.686中心化处理17.522210.5151918.585182.54.518668yi三元二次回归正交设计试验方案及计算格式表686.02ijijxx三、回归计算及统计检验P因素二次回归模型在编码空间中的回归方程为pjjhpjjjjjhhjjjxbxxbxbby1120ˆ相应，三因素二次回归模型在编码空间中的回归方程为2333222221113223311321123322110ˆxbxbxbxxbxxbxxbxbxbxbbyNyi0yb17N3,2,1jjjijNiiijjDBxyxb21hjhjijjhNiiijNiijDBxxyxxb211hh)(jjjjijNiiNiijjDBxyxb2'11'jjh1.计算回归系数X0X1(Z1)X2(Z2)X3(Z3)x1x2x1x3x2x3X12(x1′)X22(x2′)X32(x3′)YiDj1711.66211.66211.6628886.7056.7056.705Bj171.512.5672.47-42.772.5-1.57.51.65415.3919.05bj10.0881.0776.215-3.6770.313-0.1880.9380.2472.2252.841SjFjaj三元二次回归正交设计计算格式表jjjDBbiijjyxB21ijNijxD计算步骤：2.显著性检验eejjjfSfSF),(ejffFRRfSfSF回回回eelflffSfSFlf【1】回归系数检验【2】回归方程检验【3】失拟检验),(RffF回),(elfffF～～～0120067.2)(miiieyyS210mfejjjBbS主要计算Fj，αj，计算过程如下1jfeejjjfSfSF),(ejffF～【1】回归系数检验X0X1(Z1)X2(Z2)X3(Z3)x1x2x1x3x2x3X12(x1′)X22(x2′)X32(x3′)YiDj1711.66211.66211.6628886.7056.7056.705S=733f=16Se=2.67Fe=2S回=717f回=6SR=16fR=10Slf=13.33flf=8Bj171.512.5672.47-42.772.5-1.57.51.65415.3919.05bj10.0881.0776.215-3.6770.313-0.1880.9380.2472.2252.841Sj173013.54501570.7810.2817.0310.40835.354.1Fj10.14337.8117.60.5860.2115.2730.30626.4840.59aj0.250.010.010.250.050.0549.98)21(01.0，F),(ejffF51.18)21(05.0，F57.2)21(25.0，FeejjjfSfSF三元二次回归正交设计计算格式表～经过检验发现，b12、b13、b11不显著，应该剔除；b1、b23的显著性水平为α=0.25，考虑到其F比接近于，因此保留在方程中。于是得到回归方程53.8)21(10.0，F3232321841.2225.2938.0677.3215.6077.1088.10xxxxxxxy161nf【2】回归方程检验及失拟检验717332223321SSSSSSS回6f332223321ffffff回733)(17121711712iiiiyyS16回SSSR10f回ffR0120067.2)(miiieyyS210mfe33.13elfSSSR8ffelffR7.74RRfSfSF回回回25.1lfeelflffSfSF39.5)10,6(01.0F35.3)2,8(25.0F回归平方和总平方和剩余平方和误差平方和失拟平方和方程检验失拟检验3.方程转换jjjjZZx03232321841.2225.2938.0677.3215.6077.1088.10xxxxxxxy686.0222xx2322323210027.00070.00016.0499.0521.0431.0218.26zzzzzzzy686.02ijijxx6.14.05.2)4(111zzx111.30556.018)56(222zzx703.10316.06.31)8.53(333zzx686.0233xx四、结果分析由方程可见，消除摩擦振动所需的激振力与系统参数之间呈明显的非线性关系。利用所求的方程能对试验机在各种系统参数组合下需要的激振力作出比较准确的预报，从而大大缩短了调整激振力所需的时间，显著提高了设备的利用率。五、致谢