线性度、迟滞、重复性matlab计算.doc

传感与测试线性度、迟滞、重复性 压力传感器知识点回顾：线性度(非线性误差）：输出输入校准曲线（实际）与所选定的拟合直线之间的吻合程度端点直线最佳直线最小二乘线xyxxyyDmaxyFSyxDHmaxyFS迟滞：正行程曲线与反行程曲线之间的不重合程度 重复性：正行程曲线或反行程曲线多次测量时曲线的一致程度.a：置信系数，a=2 (95.4%) a=3 (99.73%)xyyFSs 的算法：贝塞尔公式极 差 法线性度、迟滞反映系统误差重复性反映偶然误差三者的合成即反映 系统的总精度 测量范围和量程： ymax- ymin单边、双边、对称、不对称灵敏度：单位输入下的输出：分辨力（率）：在测量范围内，所能检测的最小的输入量的变化FS 灵敏阈：输出端产生可测变化的最小输入量的值，即零点附近的分辨力稳定性：长期稳定指标漂移：零漂，灵敏度漂移，温漂等压力传感器的静态标定AefpW活塞与油缸精密配合。这个缸塞系统将被计量介质的压力P，变换成作用于活塞底面上的力，该力使活塞浮起，并与作用在活塞上面的标准砝码（包括活塞自重）的重力W 相平衡，于是： 正行程U行程传感器的输入量(x)传感器的输出量(y)y1y2y3y4y500.660.650.780.670.802190.9191.1190.3190.8190.44382.8382.3383.5381.8382.86574.5576.4576.0576.2575.48769.4769.2770.4769.8771.510963.9963.1965.2964.7966.0反行程D10964.2965.1966.5965.7967.28770.6772.4771.0770.8772.16577.9577.4577.1578.1578.34384.0384.8384.2384.9384.22191.6192.2191.8191.5191.901.661.651.541.471.66Matlab程序：%求检测系统线性度，迟滞，重复性m=5;n=5; %m个测点，n个来回x1=2,4,6,8,10; %正行程的m个测点yu=190.9,382.8,575.8,769.4,963.9; 191.1,383.2,576.1,769.8,964.6; 191.3,383.5,576.6,770.4,965.2; 191.4,383.8,576.9,770.8,965.7; 191.4,383.8,577.0,771.0,966.0; %正行程测量数据yd=191.6,384.1,577.3,770.6,964.4; 191.6,384.2,577.4,771.0,965.1; 192.0,384.1,578.1,771.4,965.7; 191.9,384.9,578.1,771.4,965.7; 191.9,384.9,578.5,772.0,966.1 ; %反行程测量数据x2=x1; for i=1:(2*n-1) %扩展到全部的测点 x2=vertcat(x2,x1); i=i+1;end y=yu;yd; %所有测量数据组成nm矩阵xmean=mean(x2); %x2的列方向均值ymean=mean(y); %y的列方向均值,即每个测点对应的均值xmean=mean(xmean,2) %x2的总均值ymean=mean(ymean,2) %y的总均值%以下为求系统线性度部分lxx=sum(sum(x2-xmean).2) %lxy=sum(sum(x2-xmean).*(y-ymean) %k=lxy./lxx b=ymean-k*xmeanX=x1Y1=k.*X+b %拟合直线Y=Y1;for j=1:(2*n-1) Y=vertcat(Y,Y1); j=j+1;end %Y由一维扩展到2nm矩阵dLmax=max(max(abs(y-Y) %曲线与直线的最大差值yFS=max(max(y)-min(min(y) %满量程输出rL=dLmax./yFS %线性度%以下为求系统迟滞yumean=mean(yu)ydmean=mean(yd)DyiH=abs(yumean-ydmean) %正反行程的偏差DHmax=max(DyiH) %迟滞指标rH=DHmax./(2*yFS) %迟滞误差%以下求系统重复性dm0=1.41,1.91,2.24,2.48,2.67,2.83,2.96,3.08,3.18,3.26,3.33;%极差系数表，m=212dm=dm0(m-1); %dm表示m对应极差系数wu=max(yu)-min(yu) %正行程极差wd=max(yd)-min(yd) %反行程极差Su=wu./dm;Sd=wd./dm;Si=sqrt(Su.2+Sd.2)./2)+eps %第i个测点的子样标准差S=sqrt(1/n*sum(Si.2)+eps %整个测试过程的标准偏差rR=3*S/yFS %重复性指标M程序运行结果： System_Parametersxmean = 6ymean = 5.777280000000000e+02lxx = 400lxy = 3.868620000000000e+04k = 96.715499999999992b = -2.564999999999941X = 2 4 6 8 10Y1 = 1.0e+02 * Columns 1 through 2 1.908660000000001 3.842970000000000 Columns 3 through 4 5.777279999999999 7.711590000000000 Column 5 9.645900000000001dLmax = 1.927999999999997yFS = 7.752000000000001e+02rL = 0.002487100103199yumean = 1.0e+02 * Columns 1 through 2 1.912200000000000 3.834200000000000 Columns 3 through 4 5.764800000000000 7.702800000000000 Column 5 9.650799999999999ydmean = 1.0e+02 * Columns 1 through 2 1.918000000000000 3.844400000000001 Columns 3 through 4 5.778799999999999 7.712800000000000 Column 5 9.654000000000000DyiH = Columns 1 through 2 0.580000000000041 1.020000000000096 Columns 3 through 4 1.399999999999864 1.000000000000000 Column 5 0.320000000000050DHmax = 1.399999999999864rH = 9.029927760577035e-04wu = Columns 1 through 2 0.500000000000000 1.000000000000000 Columns 3 through 4 1.200000000000046 1.600000000000023 Column 5 2.100000000000023wd = Columns 1 through 2 0.400000000000006 0.799999999999955 Columns 3 through 4 1.200000000000046 1.399999999999977 Column 5 1.700000000000046Si = Columns 1 through 2 0.182568248752772 0.365136497505533 Columns 3 through 4 0.483870967741954 0.606181305579554 Column 5 0.770361821554159S = 0.521862060707458rR = 0.002019590018218由上运行结果知：线性度rL = 0.002487100103199迟滞误差rH = 9.029927760577035e-04重复性rR = 0.002019590018218 2015年4月26日星期日 北理 指导老师：2015-04-26 - 7 -