用matlab实现误差理论与数据处理的部分习题

误差理论与数据处理作业第一章Matlab代码：%题1-5%180度2分换算为clear all;clc;test5 = 180 + 2/60/60 ;absoluteError5 = (180 - test5) oppositeError5 = absoluteError5 / test5 * 100 % %1-7absouluteError7 = 100.2 -100.5 oppositeError7 = absouluteError7 / 100.5 * 100 %题目1-14比较测量方式的精度L1 = 110;L2 = 110;testError1 = 0.011;testError2 = 0.009;L3 = 150;testError3 = 0.012;%相对误差越小则越精确oppositeError1 = testError1 / L1;oppositeError2 = testError2 / L2;oppositeError3 = testError3 / L3;%寻找相对误差的最小值if oppositeError1 oppositeError2 if oppositeError2 oppositeError3 fprintf(精度最高的是第三种，相对误差为 %f,oppositeError3); else fprintf(精度最高的是第二种，相对误差为 %f,oppositeError2); endelse if oppositeError1 oppositeError3 fprintf(精度最高的是第三种，相对误差为 %f,oppositeError3); else fprintf(精度最高的是第一种，相对误差为 %f,oppositeError1); endend运行结果：absoluteError5 =-5.5556e-04oppositeError5 =-3.0864e-04absouluteError7 =-0.3000oppositeError7 = -0.2985精度最高的是第三种，相对误差为 0.第二章Matlab代码： 这章自己写了几个函数：function value = standardDeviation(n,v)%value是返回的标准差,n 是测量的值的矩阵，v是算术平均值% standardDeviation函数是求测量的标准差k = 1;for i = n residualError(k,:) = i - v ; %存放残差的向量 k = k+1;endvalue = (sum(residualError.2) / (numel(n) - 1)0.5;endfunction value = T_fenbubiao(a,v)%该函数实现T分布表的查询%v表示次数，a表示可信度m_005 = 12.71 4.30 3.18 2.78 2.57 2.45 2.36 2.31 2.26 2.23; 2.20 2.18 2.16 2.14 2.13 2.12 2.11 2.10 2.09 2.09; 2.08 2.07 2.07 2.06 2.06 2.06 2.05 2.05 2.05 2.04; 0 0 0 2.02 2.01 2.00 1.99 1.99 1.99 1.98 ; m_001 = 63.66 9.92 5.84 4.60 4.03 3.71 3.50 3.36 3.25 3.17; 3.11 3.05 3.01 2.98 2.95 2.92 2.90 2.88 2.86 2.85; 2.83 2.82 2.81 2.80 2.79 2.78 2.77 2.76 2.76 2.75; 0 0 0 2.70 2.68 2.66 2.65 2.64 2.63 2.63 ; m_00027= 235.80 19.21 9.21 6.62 5.51 4.90 4.53 4.28 4.09 3.96; 3.85 3.76 3.69 3.64 3.59 3.54 3.51 3.48 3.45 3.42; 3.40 3.38 3.36 3.34 3.33 3.32 3.30 3.29 3.28 3.27; 0 0 0 3.20 3.16 3.13 3.11 3.10 3.09 3.08 ; p = a ; switch p case double(0.05) index = lookup_index(v); row = index(1); column = index(2); if (row 0 & column 0) value = m_005(row,column); else value = 1.96; end case 0.0100; index = lookup_index(v); row = index(1); column = index(2); if (row 0 & column 0) value = m_001(row,column); else value = 2.58; end case 0.0027; index = lookup_index(v); row = index(1); column = index(2); if (row 0 & column 0) value = m_00027(row,column); else value =3.00; end otherwise value = 1.96; endendfunction value= lookup_index(v) if v 10 & v 20 & v 30 & v d3 value = findIndex(temp,vMax);else value =false;endendfunction value = findIndex(v,data)k = 1;for i = v if i = data; value = k; return ; end k = k+1;endvalue = false;end实现题目的主要代码：clear all;clc;%题目2-4 求平均误差和算数平均值test = 236.45,236.37,236.51,236.34,236.39,236.48,236.47,236.40 ;%8次测试值arithmeticAverageValue = sum(test) / numel(test) ; %算术平均值%根据贝塞公式求单次测量的标准差,d 为标准差，dd为算术平均标准差d = standardDeviation(test,arithmeticAverageValue);dd = d / (numel(test)0.5;fprintf(题目2-4 );fprintf(算术平均值为 %f ，单次测量的标准差为 %f,算术平均标准差为 %f n,arithmeticAverageValue,d,dd);%题目2-6 求算术平均值，标准差，或然误差，平均误差testValue2_6 = 168.41,168.54,168.59,168.40,168.50;arithmeticAverageValue2_6 = sum(testValue2_6) / numel(testValue2_6); %算术平均值d2_6 = standardDeviation(testValue2_6,arithmeticAverageValue2_6); %标准差dd2_6 = d2_6 / (numel(testValue2_6)0.5;p2_6 = 0.6745 * dd2_6; %或然误差averageError2_6 = 0.7979 * dd2_6; %平均误差fprintf(题目2-6 );fprintf(算术平均值为 %f ，单次测量的标准差为 %f,算术平均标准差为 %f n ,arithmeticAverageValue2_6,d2_6,dd2_6);fprintf( 或然误差 %f， 平均误差 %f n,p2_6,averageError2_6);%题目2-8 求置信限averageDeviation = 0.005 / (50.5);n = 5;P = 0.95; %置信限95% （1）按t分布计算a = 0.05;v = 4;t = T_fenbubiao(a,v); %根据t分布表查对应的t值x = t * averageDeviation;fprintf(题目2-12);fprintf(t分布下置信限为 -%f 到 %fn ,x,x);% (2)按正太分布做；t = 1.96;%根据表知t = 1.96x = t * averageDeviation;fprintf(正太分布下置信限为 -%f 到 %f n,x,x);%题目2-12 求加权算术平均值及其标准差xp = .85 .30 .97 .65 .33 .01 .69 .36; %测试的次数p = 1 3 5 7 8 6 4 2 ;averageXp = sum(xp) / numel(xp);k = 1;for i = xp temp = i - averageXp; residualError(:,k) = temp ; %存放残差的向量 k = k+1;endresidualErrorV2 = residualError.2;sum2_12 = sum(xp.*p);weightedAverage = sum2_12 / sum(p); %加权算术平均值value = (sum(p.*residualErrorV2)/(numel(xp)-1)*sum(p).0.5;%加权算术标准差fprintf(题目2-12);fprintf(加权算术平均值 %f ，加权算术标准差 %f n,weightedAverage,value);%题目2-17 判断是否有系统误差testValue2_17 = 14.7 15 15.2 14.8 15.5 14.6 14.9 14.8 15.1 15;averageValue = sum(testValue2_17) / numel(testValue2_17);%判断测量次数的奇偶cnt = numel(testValue2_17);if mod(cnt,2) = 0 K = cnt/2;else K = (cnt + 1) / 2;endv = calculationResiduals(testValue2_17); d2_17 = sum(v(1:K) - sum(v(K+1):cnt);fprintf(题目2-17);if abs(d2_17) abs(max(v) fprintf(%f 显著不为零,故测量中含有线性误差 ,d2_17);else fprintf(%f 不显著为零,故测量中不含有线性误差 ,d2_17);end%2-22莱以特准则判断粗大误差testValue2_22 = 28.53 28.52 28.50 28.52 28.53 28.53 28.50 28.49 28.49 28.51 28.53 28.52 28.49 28.40 28.50;n = numel(testValue2_22);averageValue2_22 = sum(testValue2_22) / n ;d2_22 = standardDeviation(testValue2_22,averageValue2_22) ; %计算标准差v2_22 = calculationResiduals(testValue2_22); %残差d3_2_22 = d2_22 * 3 ;while 1 index = judge(v2_22,d3_2_22); if index %如果有粗大误差剔除 fprintf(n值%f是粗大误差应该提除n,testValue2_22(index); testValue2_22(index) = ;%删除对应的值 %重复第一次的步骤 n = numel(testValue2_22); averageValue2_22 = sum(testValue2_22) / n ; d2_22 = standardDeviation(testValue2_22,averageValue2_22) ; %计算标准差 v2_22 = calculationResiduals(testValue2_22); %残差 d3_2_22 = d2_22 * 3 ; else break; end end代码的运行结果：题目2-4 算术平均值为 236. ，单次测量的标准差为 0.,算术平均标准差为 0. 题目2-6 算术平均值为 168. ，单次测量的标准差为 0.,算术平均标准差为 0. 或然误差 0.， 平均误差 0. 题目2-8 t分布下置信限为 -0. 到 0. 正太分布下置信限为 -0. 到 0. 题目2-12 加权算术平均值 . ，加权算术标准差 87. 题目2-17 0. 显著不为零,故测量中含有线性误差 题目2-22 值28.是粗大误差应该踢除第三章MATLAB代码：clear all;clc;%题目3-1 求测量误差test = 40 12 1.25 1.005;testOffset = -0.7 0.5 -0.3 0.1;limL = 0.35 0.25 0.20 0.20;testSum = sum(test);systemOffset = sum(testOffset);offsetValue = testSum - systemOffset * 1e-3;limLOffset = sum(limL.2)0.5;fprintf(题目3-1 );fprintf(系统误差 %f 修正值为 %f 测量误差 %f n ,systemOffset,offsetValue,limLOffset);%题目3-2 求立方体体积及其极限误差a = 161.6;b = 44.5;c = 11.2;da = 1.2;db = -0.8;dc = 0.5;%都是正负多少lima = 0.8;limb = 0.5;limc = 0.5;V = a*b*c;Vd = (da*b*c) + (a*db*c) + (a*b*dc);Vr = V - Vd;limV = (b*c)2*lima2 + (a*c)2*limb2 + (a*b)2*limc2).0.5;fprintf(题目3-2 测量体积最后结果表示为 %d +- %d n,Vr,limV);%题目3-4 求功耗global U;global I;%global f;syms U IP = U*I;fu = diff(P,U); %求偏导fi = diff(P,I);I = 22.5;U = 12.6;di = 0.5;du = 0.1;ss = vpa(subs(fu);zz = vpa(subs(fi);Dp = (ss2 * du2 + zz2 * di2 + 2*ss*zz*di*du)0.5;ui = vpa(subs(P);fprintf(题目3-4 功率P为 %sym 标准差为 %sym n,ui,Dp);%题目3-12 求误差global r;global h;syms r h%相对误差为1%,测量项目为2项 n = 2V3_12 = pi * h * r2;Vr = diff(V3_12 ,r);Vh = diff(V3_12,h);n = 20.5;e = 0.01;r = 2.0;h = 20.0;V0 = vpa(subs(V3_12);dv = V0 * e;rr = vpa(subs(Vr);hh = vpa(subs(Vh);dr = (dv / (n)*(1 / rr);dh = (dv / (n)*(1 / hh);ddr = vpa(dr);ddh = vpa(dh);fprintf(题目3-12 测定r的误差应为 %0.6sym 测定h的误差应为 %0.6sym n,vpa(ddr,4),vpa(ddh,5);代码的运行结果如下：题目3-1 系统误差 -0. 修正值为 54. 测量误差 0. 题目3-2 测量体积最后结果表示为 7.e+04 +- 3.e+03 题目3-4 功率P为 283.5ym 标准差为 8.55ym 题目3-12 测定r的误差应为 0.0070 测定h的误差应为 0.1414第四章MATLAB代码：clear all;clc ;%题目 4-1 求圆球的最大截面的圆周和面积及圆球的体积的测量不确定度%（1）求圆球的最大截面的圆周的测量不确定度global r;syms r;%求导D = 2*pi*r;f = diff(D,r);S = pi * r2 ;f1 = diff(S,r);V = (4/3)*pi*r3;f2 = diff(V,r);fprintf(题目 4-1 n)dr = 0.005;%标准差r = 3.132;fv = vpa(subs(f);Uc = (fv2*dr2)0.5; %标准不确定度n = 9;%测量次数减一t = 0.01;%置信度K = T_fenbubiao(t,n);U = K * Uc; %最大截面的圆周的测量不确定度fprintf(最大截面的圆周的测量不确定度为 %0.5s cmn,U);%(2) 求圆球的最大截面的面积的测量不确定度f1v = vpa(subs(f1);Uc1 = (f1v2 * dr2)0.5;U1 = K*Uc1;fprintf(最大截面的圆面积的测量不确定度为 %0.6s cmn,U1);%(3)圆球的体积的测量不确定度f2v