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[1stOpt] 1stopt参数拟合问题

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kingng3
发表于 2009-10-7 01:05:07 | 显示全部楼层 |阅读模式 来自 江苏镇江
constant  C=1.3;
function
y1=D1*sin(C1*Arctan(B1*Q1));
y2=D2*sin(C2*Arctan(B2*Q2));
Q1=(1-E1)*x1+(E1/B1)*Arctan(B1*x1);
Q2=(1-E2)*x2+(E2/B2)*Arctan(B2*x2);
D1=a1*F1^2+a2*F1;
D2=a1*F2^2+a2*F2;
E1=a6*F1^2+a7*F1+a8;
E2=a6*F2^2+a7*F2+a8;
B1=a3*sin(a4*Arctan(a5*F1))/C*D1;
B2=a3*sin(a4*Arctan(a5*F2))/C*D2;
data ;
//x1,x2,y1,y2,F1,F2
0 0 0.00623 0.00338 8500 10200
2.00E-05 1.00E-05 0.04353 0.0382 8500 10200
8.00E-05 5.00E-05 0.14941 0.16934 8500 10200
2.20E-04 1.40E-04 0.36694 0.46098 8500 10200
4.90E-04 3.50E-04 0.75778 0.96238 8500 10200
9.50E-04 7.00E-04 1.38456 1.74919 8500 10200
0.00167 0.00128 2.29213 2.94243 8500 10200
0.0027 0.00215 3.53554 4.71426 8500 10200
0.00412 0.00338 5.20226 7.27669 8500 10200
0.00601 0.00506 7.42113 10.82309 8500 10200
0.00844 0.00727 10.35209 15.50853 8500 10200
0.0115 0.01009 14.14065 21.48989 8500 10200
0.01529 0.0136 18.90052 28.95303 8500 10200
0.01988 0.01788 24.74298 38.11267 8500 10200
0.02535 0.02302 31.80531 49.17672 8500 10200
0.03179 0.02909 40.25924 62.31207 8500 10200
0.03928 0.03617 50.28468 77.66372 8500 10200
0.04789 0.04435 62.03036 95.37999 8500 10200
0.05771 0.0537 75.61252 115.63401 8500 10200
0.06879 0.06431 91.13844 138.63279 8500 10200
0.08121 0.07623 108.73974 164.56089 8500 10200
0.09502 0.08954 128.58368 193.54082 8500 10200
0.11028 0.10429 150.81816 225.66831 8500 10200


这是我要拟合的数据及方程，现在有几个问题需要解决，希望得到帮助
（1）要拟合方程是y,其中D,E,Q,B都是方程y的一个部分，用上面的程序进行拟合的时候都是单个的进行计算，也就是说把D,E,Q,B都当作单独的方程进行计算，改怎么改进？
（2）要得到的参数a1~a8应该同属于y1,y2，但是现在得到的a1~a8分别属于y1,y2，也就是说有两组a1~a8,该如何改进？我看了参数共享的帮助，但是做不出来！

希望上面的问题能得到解决，谢谢
参数, 拟合

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shamohu
发表于 2009-10-7 18:55:19 | 显示全部楼层 来自 北京
Simdroid开发平台
改成如下：

constant  C=1.3;
ConstStr Q1=(1-E1)*x1+(E1/B1)*Arctan(B1*x1),
         Q2=(1-E2)*x2+(E2/B2)*Arctan(B2*x2),
         D1=a1*F1^2+a2*F1,
         D2=a1*F2^2+a2*F2,
         E1=a6*F1^2+a7*F1+a8,
         E2=a6*F2^2+a7*F2+a8,
         B1=a3*sin(a4*Arctan(a5*F1))/C*D1,
         B2=a3*sin(a4*Arctan(a5*F2))/C*D2;
SharedModel;
Variable x1,x2,y1,y2,F1,F2;
function y1=D1*sin(C1*Arctan(B1*Q1));
         y2=D2*sin(C2*Arctan(B2*Q2));

data ;
//x1,x2,y1,y2,F1,F2
0 0 0.00623 0.00338 8500 10200
2.00E-05 1.00E-05 0.04353 0.0382 8500 10200
8.00E-05 5.00E-05 0.14941 0.16934 8500 10200
2.20E-04 1.40E-04 0.36694 0.46098 8500 10200
4.90E-04 3.50E-04 0.75778 0.96238 8500 10200
9.50E-04 7.00E-04 1.38456 1.74919 8500 10200
0.00167 0.00128 2.29213 2.94243 8500 10200
0.0027 0.00215 3.53554 4.71426 8500 10200
0.00412 0.00338 5.20226 7.27669 8500 10200
0.00601 0.00506 7.42113 10.82309 8500 10200
0.00844 0.00727 10.35209 15.50853 8500 10200
0.0115 0.01009 14.14065 21.48989 8500 10200
0.01529 0.0136 18.90052 28.95303 8500 10200
0.01988 0.01788 24.74298 38.11267 8500 10200
0.02535 0.02302 31.80531 49.17672 8500 10200
0.03179 0.02909 40.25924 62.31207 8500 10200
0.03928 0.03617 50.28468 77.66372 8500 10200
0.04789 0.04435 62.03036 95.37999 8500 10200
0.05771 0.0537 75.61252 115.63401 8500 10200
0.06879 0.06431 91.13844 138.63279 8500 10200
0.08121 0.07623 108.73974 164.56089 8500 10200
0.09502 0.08954 128.58368 193.54082 8500 10200
0.11028 0.10429 150.81816 225.66831 8500 10200
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kingng3
 楼主| 发表于 2009-10-12 09:47:25 | 显示全部楼层 来自 江苏镇江
原来我用的是1.5PJ版的，按楼主改的去做还是计算不了，算了，买不起软件，还是用MATLAB做吧
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wanglu
发表于 2009-10-12 10:17:25 | 显示全部楼层 来自 山东淄博
想用Forcal给你试一下，但C1、C2没有对应的数据，y1,y2在公式中又没有出现？
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wanglu
发表于 2009-10-12 10:19:53 | 显示全部楼层 来自 山东淄博
y1,y2找到了，还没看到C1、C2？
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kingng3
 楼主| 发表于 2009-10-12 15:19:36 | 显示全部楼层 来自 江苏镇江
楼主能不能帮我算一下a`~a8 ，谢谢了


constant  C=1.3;
ConstStr Q1=(1-E1)*x1+(E1/B1)*Arctan(B1*x1),
         Q2=(1-E2)*x2+(E2/B2)*Arctan(B2*x2),
         D1=a1*F1^2+a2*F1,
         D2=a1*F2^2+a2*F2,
         E1=a6*F1^2+a7*F1+a8,
         E2=a6*F2^2+a7*F2+a8,
         B1=a3*sin(a4*Arctan(a5*F1))/C*D1,
         B2=a3*sin(a4*Arctan(a5*F2))/C*D2;
SharedModel;
Variable x1,x2,y1,y2,F1,F2;
function y1=D1*sin(C*Arctan(B1*Q1));
         y2=D2*sin(C*Arctan(B2*Q2));
data ;
//x1,x2,y1,y2,F1,F2
0 0 0.00623 0.00338 8500 10200
2.00E-05 1.00E-05 0.04353 0.0382 8500 10200
8.00E-05 5.00E-05 0.14941 0.16934 8500 10200
2.20E-04 1.40E-04 0.36694 0.46098 8500 10200
4.90E-04 3.50E-04 0.75778 0.96238 8500 10200
9.50E-04 7.00E-04 1.38456 1.74919 8500 10200
0.00167 0.00128 2.29213 2.94243 8500 10200
0.0027 0.00215 3.53554 4.71426 8500 10200
0.00412 0.00338 5.20226 7.27669 8500 10200
0.00601 0.00506 7.42113 10.82309 8500 10200
0.00844 0.00727 10.35209 15.50853 8500 10200
0.0115 0.01009 14.14065 21.48989 8500 10200
0.01529 0.0136 18.90052 28.95303 8500 10200
0.01988 0.01788 24.74298 38.11267 8500 10200
0.02535 0.02302 31.80531 49.17672 8500 10200
0.03179 0.02909 40.25924 62.31207 8500 10200
0.03928 0.03617 50.28468 77.66372 8500 10200
0.04789 0.04435 62.03036 95.37999 8500 10200
0.05771 0.0537 75.61252 115.63401 8500 10200
0.06879 0.06431 91.13844 138.63279 8500 10200
0.08121 0.07623 108.73974 164.56089 8500 10200
0.09502 0.08954 128.58368 193.54082 8500 10200
0.11028 0.10429 150.81816 225.66831 8500 10200
0.12703 0.12053 175.53846 261.03966 8500 10200
0.14533 0.13829 202.82289 299.76409 8500 10200
0.16521 0.15764 232.75206 341.95888 8500 10200
0.18672 0.17859 265.41952 387.69722 8500 10200
0.20988 0.2012 300.93392 436.99755 8500 10200
0.23472 0.2255 339.36342 489.86172 8500 10200
0.26125 0.2515 380.7144 546.28968 8500 10200
0.2895 0.27922 424.97823 606.29491 8500 10200
0.31946 0.30868 472.15199 669.8986 8500 10200
0.35114 0.33987 522.24788 737.09155 8500 10200
0.38453 0.37281 575.29521 807.83014 8500 10200
0.41963 0.40748 631.29875 882.05666 8500 10200
0.45643 0.44388 690.21983 959.72229 8500 10200
0.49492 0.482 751.99825 1040.80552 8500 10200
0.53506 0.52181 816.5748 1125.28232 8500 10200
0.57683 0.56329 883.91445 1213.08131 8500 10200
0.6202 0.60641 953.99316 1304.08627 8500 10200
0.66514 0.65115 1026.75515 1398.16326 8500 10200
0.71162 0.69746 1102.10577 1495.20066 8500 10200
0.75961 0.74531 1179.93219 1595.13304 8500 10200
0.80907 0.79466 1260.13534 1697.8885 8500 10200
0.85997 0.84547 1342.65195 1803.3466 8500 10200
0.91225 0.89771 1427.41963 1911.36713 8500 10200
0.96589 0.95131 1514.33398 2021.80672 8500 10200
1.02083 1.00624 1603.25915 2134.53576 8500 10200
1.07703 1.06245 1694.05737 2249.45885 8500 10200
1.13443 1.11989 1786.62745 2366.47078 8500 10200
1.193 1.1785 1880.92679 2485.42446 8500 10200
1.25268 1.23825 1976.91522 2606.16356 8500 10200
1.31343 1.29907 2074.50055 2728.53608 8500 10200
1.37518 1.36091 2173.55602 2852.40203 8500 10200
1.43788 1.42373 2273.94347 2977.64586 8500 10200
1.50149 1.48747 2375.54104 3104.13495 8500 10200
1.56595 1.55207 2478.26747 3231.69703 8500 10200
1.6312 1.61749 2582.03418 3360.1586 8500 10200
1.6972 1.68367 2686.70601 3489.36608 8500 10200
1.76388 1.75056 2792.13168 3619.19972 8500 10200
1.8312 1.81811 2898.16582 3749.57778 8500 10200
1.89911 1.88626 3004.69665 3880.40485 8500 10200
1.96755 1.95497 3111.66401 4011.54555 8500 10200
2.03647 2.02419 3218.99955 4142.85723 8500 10200
2.10585 2.09386 3326.59179 4274.20857 8500 10200
2.17563 2.16395 3434.32646 4405.49946 8500 10200
2.24577 2.2344 3542.10727 4536.66485 8500 10200
2.31623 2.30519 3649.87114 4667.61732 8500 10200
2.38697 2.37626 3757.5994 4798.22733 8500 10200
2.45795 2.44758 3865.25711 4928.36086 8500 10200
2.52912 2.51911 3972.75293 5057.89492 8500 10200
2.60045 2.59081 4079.97352 5186.74079 8500 10200
2.6719 2.66265 4186.80342 5314.85607 8500 10200
2.74344 2.73461 4293.15505 5442.1913 8500 10200
2.81504 2.80664 4398.99856 5568.66246 8500 10200
2.88668 2.87873 4504.30268 5694.18442 8500 10200
2.95832 2.95084 4608.98932 5818.68751 8500 10200
3.02993 3.02294 4712.97148 5942.13638 8500 10200
3.10149 3.095 4816.174 6064.53894 8500 10200
3.17297 3.16702 4918.55243 6185.88021 8500 10200
3.24437 3.23895 5020.12767 6306.09473 8500 10200
3.31565 3.31079 5120.9459 6425.12421 8500 10200
3.38681 3.38253 5221.01669 6542.92696 8500 10200
3.45783 3.45413 5320.31031 6659.4762 8500 10200
3.52869 3.5256 5418.76991 6774.78437 8500 10200
3.59937 3.59693 5516.34484 6888.85425 8500 10200
3.66987 3.66809 5613.03077 7001.64722 8500 10200
3.74018 3.73907 5708.8359 7113.13221 8500 10200
3.81027 3.80987 5803.72882 7223.28991 8500 10200
3.88014 3.88047 5897.65245 7332.11045 8500 10200
3.94979 3.95087 5990.55304 7439.63392 8500 10200
4.01921 4.02106 6082.39783 7545.92994 8500 10200
4.0884 4.09103 6173.20863 7651.04157 8500 10200
4.15737 4.16078 6263.05016 7754.97918 8500 10200
4.22611 4.2303 6351.96204 7857.73983 8500 10200
4.29463 4.29959 6439.94749 7959.32975 8500 10200
4.36293 4.36865 6527.00805 8059.7877 8500 10200
4.43102 4.43749 6613.1408 8159.17045 8500 10200
4.49891 4.5061 6698.35404 8257.49956 8500 10200
4.56657 4.57449 6782.69143 8354.75604 8500 10200
4.63403 4.64266 6866.17854 8450.92397 8500 10200
4.70129 4.7106 6948.7898 8545.99616 8500 10200
4.76834 4.77832 7030.49227 8639.98452 8500 10200
4.83519 4.84582 7111.26373 8732.93858 8500 10200
4.90183 4.9131 7191.10171 8824.89146 8500 10200
4.96828 4.98016 7270.05347 8915.83866 8500 10200
5.03453 5.047 7348.18469 9005.79332 8500 10200
5.1006 5.11364 7425.52506 9094.78889 8500 10200
5.16649 5.18008 7502.07711 9182.86035 8500 10200
5.2322 5.24632 7577.83988 9270.06142 8500 10200
5.29775 5.31238 7652.82019 9356.444 8500 10200
5.36315 5.37826 7727.06391 9442.01051 8500 10200
5.4284 5.44397 7800.64867 9526.73097 8500 10200
5.49352 5.50951 7873.60639 9610.58595 8500 10200
5.5585 5.57489 7945.90721 9693.55725 8500 10200
5.62335 5.64013 8017.52094 9775.64222 8500 10200
5.6881 5.70522 8088.42244 9856.88388 8500 10200
5.75275 5.77019 8158.59209 9937.31916 8500 10200
5.81731 5.83503 8228.0546 10016.94601 8500 10200
5.88178 5.89975 8296.84742 10095.75888 8500 10200
5.94617 5.96436 8364.96327 10173.75753 8500 10200
6.01049 6.02886 8432.36873 10250.94765 8500 10200
6.07474 6.09327 8499.03771 10327.37093 8500 10200
6.13891 6.15759 8564.94949 10403.09748 8500 10200
6.20301 6.22183 8630.11652 10478.15378 8500 10200
6.26705 6.28598 8694.60518 10552.51463 8500 10200
6.33103 6.35006 8758.47244 10626.17792 8500 10200
6.39496 6.41408 8821.73046 10699.1582 8500 10200
6.45884 6.47803 8884.37821 10771.45413 8500 10200
6.52269 6.54191 8946.40322 10843.08258 8500 10200
6.58651 6.60574 9007.78494 10914.06792 8500 10200
6.65031 6.66951 9068.52802 10984.39172 8500 10200
6.71408 6.73324 9128.65481 11054.00725 8500 10200
6.77784 6.79694 9188.15416 11122.88753 8500 10200
6.84158 6.8606 9246.98237 11191.01588 8500 10200
6.90529 6.92424 9305.11454 11258.38284 8500 10200
6.96899 6.98786 9362.53694 11325.02332 8500 10200
7.03266 7.05147 9419.241 11390.98279 8500 10200
7.09632 7.11508 9475.26781 11456.26104 8500 10200
7.15996 7.1787 9530.67429 11520.84159 8500 10200
7.22361 7.24232 9585.46097 11584.73198 8500 10200
7.28725 7.30594 9639.6069 11647.93468 8500 10200
7.35089 7.36958 9693.12232 11710.44396 8500 10200
7.41453 7.43321 9746.01409 11772.28903 8500 10200
7.47818 7.49686 9798.289 11833.501 8500 10200
7.54183 7.56051 9850.00518 11894.06068 8500 10200
7.60548 7.62417 9901.23295 11953.92824 8500 10200
7.66913 7.68784 9951.98999 12013.08172 8500 10200
7.73278 7.75153 10002.25683 12071.50244 8500 10200
7.89645 7.81523 10052.36 12129.17739 8500 10200
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kingng3
 楼主| 发表于 2009-10-12 15:20:39 | 显示全部楼层 来自 江苏镇江
你好，程序写错了，C1C2就是C,能不能帮我算一下
constant  C=1.3;
ConstStr Q1=(1-E1)*x1+(E1/B1)*Arctan(B1*x1),
         Q2=(1-E2)*x2+(E2/B2)*Arctan(B2*x2),
         D1=a1*F1^2+a2*F1,
         D2=a1*F2^2+a2*F2,
         E1=a6*F1^2+a7*F1+a8,
         E2=a6*F2^2+a7*F2+a8,
         B1=a3*sin(a4*Arctan(a5*F1))/C*D1,
         B2=a3*sin(a4*Arctan(a5*F2))/C*D2;
SharedModel;
Variable x1,x2,y1,y2,F1,F2;
function y1=D1*sin(C*Arctan(B1*Q1));
         y2=D2*sin(C*Arctan(B2*Q2));
data ;
//x1,x2,y1,y2,F1,F2
0 0 0.00623 0.00338 8500 10200
2.00E-05 1.00E-05 0.04353 0.0382 8500 10200
8.00E-05 5.00E-05 0.14941 0.16934 8500 10200
2.20E-04 1.40E-04 0.36694 0.46098 8500 10200
4.90E-04 3.50E-04 0.75778 0.96238 8500 10200
9.50E-04 7.00E-04 1.38456 1.74919 8500 10200
0.00167 0.00128 2.29213 2.94243 8500 10200
0.0027 0.00215 3.53554 4.71426 8500 10200
0.00412 0.00338 5.20226 7.27669 8500 10200
0.00601 0.00506 7.42113 10.82309 8500 10200
0.00844 0.00727 10.35209 15.50853 8500 10200
0.0115 0.01009 14.14065 21.48989 8500 10200
0.01529 0.0136 18.90052 28.95303 8500 10200
0.01988 0.01788 24.74298 38.11267 8500 10200
0.02535 0.02302 31.80531 49.17672 8500 10200
0.03179 0.02909 40.25924 62.31207 8500 10200
0.03928 0.03617 50.28468 77.66372 8500 10200
0.04789 0.04435 62.03036 95.37999 8500 10200
0.05771 0.0537 75.61252 115.63401 8500 10200
0.06879 0.06431 91.13844 138.63279 8500 10200
0.08121 0.07623 108.73974 164.56089 8500 10200
0.09502 0.08954 128.58368 193.54082 8500 10200
0.11028 0.10429 150.81816 225.66831 8500 10200
0.12703 0.12053 175.53846 261.03966 8500 10200
0.14533 0.13829 202.82289 299.76409 8500 10200
0.16521 0.15764 232.75206 341.95888 8500 10200
0.18672 0.17859 265.41952 387.69722 8500 10200
0.20988 0.2012 300.93392 436.99755 8500 10200
0.23472 0.2255 339.36342 489.86172 8500 10200
0.26125 0.2515 380.7144 546.28968 8500 10200
0.2895 0.27922 424.97823 606.29491 8500 10200
0.31946 0.30868 472.15199 669.8986 8500 10200
0.35114 0.33987 522.24788 737.09155 8500 10200
0.38453 0.37281 575.29521 807.83014 8500 10200
0.41963 0.40748 631.29875 882.05666 8500 10200
0.45643 0.44388 690.21983 959.72229 8500 10200
0.49492 0.482 751.99825 1040.80552 8500 10200
0.53506 0.52181 816.5748 1125.28232 8500 10200
0.57683 0.56329 883.91445 1213.08131 8500 10200
0.6202 0.60641 953.99316 1304.08627 8500 10200
0.66514 0.65115 1026.75515 1398.16326 8500 10200
0.71162 0.69746 1102.10577 1495.20066 8500 10200
0.75961 0.74531 1179.93219 1595.13304 8500 10200
0.80907 0.79466 1260.13534 1697.8885 8500 10200
0.85997 0.84547 1342.65195 1803.3466 8500 10200
0.91225 0.89771 1427.41963 1911.36713 8500 10200
0.96589 0.95131 1514.33398 2021.80672 8500 10200
1.02083 1.00624 1603.25915 2134.53576 8500 10200
1.07703 1.06245 1694.05737 2249.45885 8500 10200
1.13443 1.11989 1786.62745 2366.47078 8500 10200
1.193 1.1785 1880.92679 2485.42446 8500 10200
1.25268 1.23825 1976.91522 2606.16356 8500 10200
1.31343 1.29907 2074.50055 2728.53608 8500 10200
1.37518 1.36091 2173.55602 2852.40203 8500 10200
1.43788 1.42373 2273.94347 2977.64586 8500 10200
1.50149 1.48747 2375.54104 3104.13495 8500 10200
1.56595 1.55207 2478.26747 3231.69703 8500 10200
1.6312 1.61749 2582.03418 3360.1586 8500 10200
1.6972 1.68367 2686.70601 3489.36608 8500 10200
1.76388 1.75056 2792.13168 3619.19972 8500 10200
1.8312 1.81811 2898.16582 3749.57778 8500 10200
1.89911 1.88626 3004.69665 3880.40485 8500 10200
1.96755 1.95497 3111.66401 4011.54555 8500 10200
2.03647 2.02419 3218.99955 4142.85723 8500 10200
2.10585 2.09386 3326.59179 4274.20857 8500 10200
2.17563 2.16395 3434.32646 4405.49946 8500 10200
2.24577 2.2344 3542.10727 4536.66485 8500 10200
2.31623 2.30519 3649.87114 4667.61732 8500 10200
2.38697 2.37626 3757.5994 4798.22733 8500 10200
2.45795 2.44758 3865.25711 4928.36086 8500 10200
2.52912 2.51911 3972.75293 5057.89492 8500 10200
2.60045 2.59081 4079.97352 5186.74079 8500 10200
2.6719 2.66265 4186.80342 5314.85607 8500 10200
2.74344 2.73461 4293.15505 5442.1913 8500 10200
2.81504 2.80664 4398.99856 5568.66246 8500 10200
2.88668 2.87873 4504.30268 5694.18442 8500 10200
2.95832 2.95084 4608.98932 5818.68751 8500 10200
3.02993 3.02294 4712.97148 5942.13638 8500 10200
3.10149 3.095 4816.174 6064.53894 8500 10200
3.17297 3.16702 4918.55243 6185.88021 8500 10200
3.24437 3.23895 5020.12767 6306.09473 8500 10200
3.31565 3.31079 5120.9459 6425.12421 8500 10200
3.38681 3.38253 5221.01669 6542.92696 8500 10200
3.45783 3.45413 5320.31031 6659.4762 8500 10200
3.52869 3.5256 5418.76991 6774.78437 8500 10200
3.59937 3.59693 5516.34484 6888.85425 8500 10200
3.66987 3.66809 5613.03077 7001.64722 8500 10200
3.74018 3.73907 5708.8359 7113.13221 8500 10200
3.81027 3.80987 5803.72882 7223.28991 8500 10200
3.88014 3.88047 5897.65245 7332.11045 8500 10200
3.94979 3.95087 5990.55304 7439.63392 8500 10200
4.01921 4.02106 6082.39783 7545.92994 8500 10200
4.0884 4.09103 6173.20863 7651.04157 8500 10200
4.15737 4.16078 6263.05016 7754.97918 8500 10200
4.22611 4.2303 6351.96204 7857.73983 8500 10200
4.29463 4.29959 6439.94749 7959.32975 8500 10200
4.36293 4.36865 6527.00805 8059.7877 8500 10200
4.43102 4.43749 6613.1408 8159.17045 8500 10200
4.49891 4.5061 6698.35404 8257.49956 8500 10200
4.56657 4.57449 6782.69143 8354.75604 8500 10200
4.63403 4.64266 6866.17854 8450.92397 8500 10200
4.70129 4.7106 6948.7898 8545.99616 8500 10200
4.76834 4.77832 7030.49227 8639.98452 8500 10200
4.83519 4.84582 7111.26373 8732.93858 8500 10200
4.90183 4.9131 7191.10171 8824.89146 8500 10200
4.96828 4.98016 7270.05347 8915.83866 8500 10200
5.03453 5.047 7348.18469 9005.79332 8500 10200
5.1006 5.11364 7425.52506 9094.78889 8500 10200
5.16649 5.18008 7502.07711 9182.86035 8500 10200
5.2322 5.24632 7577.83988 9270.06142 8500 10200
5.29775 5.31238 7652.82019 9356.444 8500 10200
5.36315 5.37826 7727.06391 9442.01051 8500 10200
5.4284 5.44397 7800.64867 9526.73097 8500 10200
5.49352 5.50951 7873.60639 9610.58595 8500 10200
5.5585 5.57489 7945.90721 9693.55725 8500 10200
5.62335 5.64013 8017.52094 9775.64222 8500 10200
5.6881 5.70522 8088.42244 9856.88388 8500 10200
5.75275 5.77019 8158.59209 9937.31916 8500 10200
5.81731 5.83503 8228.0546 10016.94601 8500 10200
5.88178 5.89975 8296.84742 10095.75888 8500 10200
5.94617 5.96436 8364.96327 10173.75753 8500 10200
6.01049 6.02886 8432.36873 10250.94765 8500 10200
6.07474 6.09327 8499.03771 10327.37093 8500 10200
6.13891 6.15759 8564.94949 10403.09748 8500 10200
6.20301 6.22183 8630.11652 10478.15378 8500 10200
6.26705 6.28598 8694.60518 10552.51463 8500 10200
6.33103 6.35006 8758.47244 10626.17792 8500 10200
6.39496 6.41408 8821.73046 10699.1582 8500 10200
6.45884 6.47803 8884.37821 10771.45413 8500 10200
6.52269 6.54191 8946.40322 10843.08258 8500 10200
6.58651 6.60574 9007.78494 10914.06792 8500 10200
6.65031 6.66951 9068.52802 10984.39172 8500 10200
6.71408 6.73324 9128.65481 11054.00725 8500 10200
6.77784 6.79694 9188.15416 11122.88753 8500 10200
6.84158 6.8606 9246.98237 11191.01588 8500 10200
6.90529 6.92424 9305.11454 11258.38284 8500 10200
6.96899 6.98786 9362.53694 11325.02332 8500 10200
7.03266 7.05147 9419.241 11390.98279 8500 10200
7.09632 7.11508 9475.26781 11456.26104 8500 10200
7.15996 7.1787 9530.67429 11520.84159 8500 10200
7.22361 7.24232 9585.46097 11584.73198 8500 10200
7.28725 7.30594 9639.6069 11647.93468 8500 10200
7.35089 7.36958 9693.12232 11710.44396 8500 10200
7.41453 7.43321 9746.01409 11772.28903 8500 10200
7.47818 7.49686 9798.289 11833.501 8500 10200
7.54183 7.56051 9850.00518 11894.06068 8500 10200
7.60548 7.62417 9901.23295 11953.92824 8500 10200
7.66913 7.68784 9951.98999 12013.08172 8500 10200
7.73278 7.75153 10002.25683 12071.50244 8500 10200
7.89645 7.81523 10052.36 12129.17739 8500 10200
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wanglu
发表于 2009-10-12 16:47:48 | 显示全部楼层 来自 山东淄博
Forcal代码：

  1. //这里是代码窗口，请将Forcal代码写在下面
  2. i: OutVector(p:k,i)= k=FCDLen(p),printff{"\r\n"},i=0,(i<k).while{printff{"{1,r,14.6}",get[p,i]},i++},printff{"\r\n"};    //输出一维数组
  3. !using("XSLSF");
  4. f(a1,a2,a3,a4,a5,a6,a7,a8:s,i,C,D1,D2,B1,B2,E1,E2,Q1,Q2,x1,x2,y1,y2,F1,F2:data,data_m,data_n)=    //函数定义
  5. {
  6.   C=1.3,i=0,s=0,
  7.   (i<data_m).while{
  8.     data.getra(i*data_n,&x1,&x2,&y1,&y2,&F1,&F2),
  9.     D1=a1*F1^2+a2*F1,
  10.     D2=a1*F2^2+a2*F2,
  11.     B1=a3*sin(a4*atan(a5*F1))/C*D1,
  12.     B2=a3*sin(a4*atan(a5*F2))/C*D2,
  13.     E1=a6*F1^2+a7*F1+a8,
  14.     E2=a6*F2^2+a7*F2+a8,
  15.     Q1=(1-E1)*x1+(E1/B1)*atan(B1*x1),
  16.     Q2=(1-E2)*x2+(E2/B2)*atan(B2*x2),
  17.     s=s+[y1-D1*sin(C*atan(B1*Q1))]^2+[y2-D2*sin(C*atan(B2*Q2))]^2,
  18.     i++
  19.   },
  20.   s
  21. };
  22. 验证(a1,a2,a3,a4,a5,a6,a7,a8:s,i,C,D1,D2,B1,B2,E1,E2,Q1,Q2,x1,x2,y1,y2,F1,F2:data,data_m,data_n)=    //函数定义
  23. {
  24.   printff{"\r\n           y1理论          y1拟合              y2理论          y2拟合\r\n\r\n"},
  25.   C=1.3,i=0,s=0,
  26.   (i<data_m).while{
  27.     data.getra(i*data_n,&x1,&x2,&y1,&y2,&F1,&F2),
  28.     D1=a1*F1^2+a2*F1,
  29.     D2=a1*F2^2+a2*F2,
  30.     B1=a3*sin(a4*atan(a5*F1))/C*D1,
  31.     B2=a3*sin(a4*atan(a5*F2))/C*D2,
  32.     E1=a6*F1^2+a7*F1+a8,
  33.     E2=a6*F2^2+a7*F2+a8,
  34.     Q1=(1-E1)*x1+(E1/B1)*atan(B1*x1),
  35.     Q2=(1-E2)*x2+(E2/B2)*atan(B2*x2),
  36.     s=s+[y1-D1*sin(C*atan(B1*Q1))]^2+[y2-D2*sin(C*atan(B2*Q2))]^2,
  37.     printff{"{1,r,18.10}{2,r,18.10}{3,r,18.10}{4,r,18.10}\r\n",y1,D1*sin(C*atan(B1*Q1)),y2,D2*sin(C*atan(B2*Q2))},
  38.     i++
  39.   },
  40.   s
  41. };
  42. main(:d,u,v,x,eps,k,xx,g,i,a1,a2,a3,a4,a5,a6,a7,a8:data,data_m,data_n)=
  43. {
  44.     data_m=150,data_n=6,
  45.     data=new{rtoi(real_s),rtoi(EndType),
  46. 0,0,0.00623,0.00338,8500,10200,
  47. 2.00E-05,1.00E-05,0.04353,0.0382,8500,10200,
  48. 8.00E-05,5.00E-05,0.14941,0.16934,8500,10200,
  49. 2.20E-04,1.40E-04,0.36694,0.46098,8500,10200,
  50. 4.90E-04,3.50E-04,0.75778,0.96238,8500,10200,
  51. 9.50E-04,7.00E-04,1.38456,1.74919,8500,10200,
  52. 0.00167,0.00128,2.29213,2.94243,8500,10200,
  53. 0.0027,0.00215,3.53554,4.71426,8500,10200,
  54. 0.00412,0.00338,5.20226,7.27669,8500,10200,
  55. 0.00601,0.00506,7.42113,10.82309,8500,10200,
  56. 0.00844,0.00727,10.35209,15.50853,8500,10200,
  57. 0.0115,0.01009,14.14065,21.48989,8500,10200,
  58. 0.01529,0.0136,18.90052,28.95303,8500,10200,
  59. 0.01988,0.01788,24.74298,38.11267,8500,10200,
  60. 0.02535,0.02302,31.80531,49.17672,8500,10200,
  61. 0.03179,0.02909,40.25924,62.31207,8500,10200,
  62. 0.03928,0.03617,50.28468,77.66372,8500,10200,
  63. 0.04789,0.04435,62.03036,95.37999,8500,10200,
  64. 0.05771,0.0537,75.61252,115.63401,8500,10200,
  65. 0.06879,0.06431,91.13844,138.63279,8500,10200,
  66. 0.08121,0.07623,108.73974,164.56089,8500,10200,
  67. 0.09502,0.08954,128.58368,193.54082,8500,10200,
  68. 0.11028,0.10429,150.81816,225.66831,8500,10200,
  69. 0.12703,0.12053,175.53846,261.03966,8500,10200,
  70. 0.14533,0.13829,202.82289,299.76409,8500,10200,
  71. 0.16521,0.15764,232.75206,341.95888,8500,10200,
  72. 0.18672,0.17859,265.41952,387.69722,8500,10200,
  73. 0.20988,0.2012,300.93392,436.99755,8500,10200,
  74. 0.23472,0.2255,339.36342,489.86172,8500,10200,
  75. 0.26125,0.2515,380.7144,546.28968,8500,10200,
  76. 0.2895,0.27922,424.97823,606.29491,8500,10200,
  77. 0.31946,0.30868,472.15199,669.8986,8500,10200,
  78. 0.35114,0.33987,522.24788,737.09155,8500,10200,
  79. 0.38453,0.37281,575.29521,807.83014,8500,10200,
  80. 0.41963,0.40748,631.29875,882.05666,8500,10200,
  81. 0.45643,0.44388,690.21983,959.72229,8500,10200,
  82. 0.49492,0.482,751.99825,1040.80552,8500,10200,
  83. 0.53506,0.52181,816.5748,1125.28232,8500,10200,
  84. 0.57683,0.56329,883.91445,1213.08131,8500,10200,
  85. 0.6202,0.60641,953.99316,1304.08627,8500,10200,
  86. 0.66514,0.65115,1026.75515,1398.16326,8500,10200,
  87. 0.71162,0.69746,1102.10577,1495.20066,8500,10200,
  88. 0.75961,0.74531,1179.93219,1595.13304,8500,10200,
  89. 0.80907,0.79466,1260.13534,1697.8885,8500,10200,
  90. 0.85997,0.84547,1342.65195,1803.3466,8500,10200,
  91. 0.91225,0.89771,1427.41963,1911.36713,8500,10200,
  92. 0.96589,0.95131,1514.33398,2021.80672,8500,10200,
  93. 1.02083,1.00624,1603.25915,2134.53576,8500,10200,
  94. 1.07703,1.06245,1694.05737,2249.45885,8500,10200,
  95. 1.13443,1.11989,1786.62745,2366.47078,8500,10200,
  96. 1.193,1.1785,1880.92679,2485.42446,8500,10200,
  97. 1.25268,1.23825,1976.91522,2606.16356,8500,10200,
  98. 1.31343,1.29907,2074.50055,2728.53608,8500,10200,
  99. 1.37518,1.36091,2173.55602,2852.40203,8500,10200,
  100. 1.43788,1.42373,2273.94347,2977.64586,8500,10200,
  101. 1.50149,1.48747,2375.54104,3104.13495,8500,10200,
  102. 1.56595,1.55207,2478.26747,3231.69703,8500,10200,
  103. 1.6312,1.61749,2582.03418,3360.1586,8500,10200,
  104. 1.6972,1.68367,2686.70601,3489.36608,8500,10200,
  105. 1.76388,1.75056,2792.13168,3619.19972,8500,10200,
  106. 1.8312,1.81811,2898.16582,3749.57778,8500,10200,
  107. 1.89911,1.88626,3004.69665,3880.40485,8500,10200,
  108. 1.96755,1.95497,3111.66401,4011.54555,8500,10200,
  109. 2.03647,2.02419,3218.99955,4142.85723,8500,10200,
  110. 2.10585,2.09386,3326.59179,4274.20857,8500,10200,
  111. 2.17563,2.16395,3434.32646,4405.49946,8500,10200,
  112. 2.24577,2.2344,3542.10727,4536.66485,8500,10200,
  113. 2.31623,2.30519,3649.87114,4667.61732,8500,10200,
  114. 2.38697,2.37626,3757.5994,4798.22733,8500,10200,
  115. 2.45795,2.44758,3865.25711,4928.36086,8500,10200,
  116. 2.52912,2.51911,3972.75293,5057.89492,8500,10200,
  117. 2.60045,2.59081,4079.97352,5186.74079,8500,10200,
  118. 2.6719,2.66265,4186.80342,5314.85607,8500,10200,
  119. 2.74344,2.73461,4293.15505,5442.1913,8500,10200,
  120. 2.81504,2.80664,4398.99856,5568.66246,8500,10200,
  121. 2.88668,2.87873,4504.30268,5694.18442,8500,10200,
  122. 2.95832,2.95084,4608.98932,5818.68751,8500,10200,
  123. 3.02993,3.02294,4712.97148,5942.13638,8500,10200,
  124. 3.10149,3.095,4816.174,6064.53894,8500,10200,
  125. 3.17297,3.16702,4918.55243,6185.88021,8500,10200,
  126. 3.24437,3.23895,5020.12767,6306.09473,8500,10200,
  127. 3.31565,3.31079,5120.9459,6425.12421,8500,10200,
  128. 3.38681,3.38253,5221.01669,6542.92696,8500,10200,
  129. 3.45783,3.45413,5320.31031,6659.4762,8500,10200,
  130. 3.52869,3.5256,5418.76991,6774.78437,8500,10200,
  131. 3.59937,3.59693,5516.34484,6888.85425,8500,10200,
  132. 3.66987,3.66809,5613.03077,7001.64722,8500,10200,
  133. 3.74018,3.73907,5708.8359,7113.13221,8500,10200,
  134. 3.81027,3.80987,5803.72882,7223.28991,8500,10200,
  135. 3.88014,3.88047,5897.65245,7332.11045,8500,10200,
  136. 3.94979,3.95087,5990.55304,7439.63392,8500,10200,
  137. 4.01921,4.02106,6082.39783,7545.92994,8500,10200,
  138. 4.0884,4.09103,6173.20863,7651.04157,8500,10200,
  139. 4.15737,4.16078,6263.05016,7754.97918,8500,10200,
  140. 4.22611,4.2303,6351.96204,7857.73983,8500,10200,
  141. 4.29463,4.29959,6439.94749,7959.32975,8500,10200,
  142. 4.36293,4.36865,6527.00805,8059.7877,8500,10200,
  143. 4.43102,4.43749,6613.1408,8159.17045,8500,10200,
  144. 4.49891,4.5061,6698.35404,8257.49956,8500,10200,
  145. 4.56657,4.57449,6782.69143,8354.75604,8500,10200,
  146. 4.63403,4.64266,6866.17854,8450.92397,8500,10200,
  147. 4.70129,4.7106,6948.7898,8545.99616,8500,10200,
  148. 4.76834,4.77832,7030.49227,8639.98452,8500,10200,
  149. 4.83519,4.84582,7111.26373,8732.93858,8500,10200,
  150. 4.90183,4.9131,7191.10171,8824.89146,8500,10200,
  151. 4.96828,4.98016,7270.05347,8915.83866,8500,10200,
  152. 5.03453,5.047,7348.18469,9005.79332,8500,10200,
  153. 5.1006,5.11364,7425.52506,9094.78889,8500,10200,
  154. 5.16649,5.18008,7502.07711,9182.86035,8500,10200,
  155. 5.2322,5.24632,7577.83988,9270.06142,8500,10200,
  156. 5.29775,5.31238,7652.82019,9356.444,8500,10200,
  157. 5.36315,5.37826,7727.06391,9442.01051,8500,10200,
  158. 5.4284,5.44397,7800.64867,9526.73097,8500,10200,
  159. 5.49352,5.50951,7873.60639,9610.58595,8500,10200,
  160. 5.5585,5.57489,7945.90721,9693.55725,8500,10200,
  161. 5.62335,5.64013,8017.52094,9775.64222,8500,10200,
  162. 5.6881,5.70522,8088.42244,9856.88388,8500,10200,
  163. 5.75275,5.77019,8158.59209,9937.31916,8500,10200,
  164. 5.81731,5.83503,8228.0546,10016.94601,8500,10200,
  165. 5.88178,5.89975,8296.84742,10095.75888,8500,10200,
  166. 5.94617,5.96436,8364.96327,10173.75753,8500,10200,
  167. 6.01049,6.02886,8432.36873,10250.94765,8500,10200,
  168. 6.07474,6.09327,8499.03771,10327.37093,8500,10200,
  169. 6.13891,6.15759,8564.94949,10403.09748,8500,10200,
  170. 6.20301,6.22183,8630.11652,10478.15378,8500,10200,
  171. 6.26705,6.28598,8694.60518,10552.51463,8500,10200,
  172. 6.33103,6.35006,8758.47244,10626.17792,8500,10200,
  173. 6.39496,6.41408,8821.73046,10699.1582,8500,10200,
  174. 6.45884,6.47803,8884.37821,10771.45413,8500,10200,
  175. 6.52269,6.54191,8946.40322,10843.08258,8500,10200,
  176. 6.58651,6.60574,9007.78494,10914.06792,8500,10200,
  177. 6.65031,6.66951,9068.52802,10984.39172,8500,10200,
  178. 6.71408,6.73324,9128.65481,11054.00725,8500,10200,
  179. 6.77784,6.79694,9188.15416,11122.88753,8500,10200,
  180. 6.84158,6.8606,9246.98237,11191.01588,8500,10200,
  181. 6.90529,6.92424,9305.11454,11258.38284,8500,10200,
  182. 6.96899,6.98786,9362.53694,11325.02332,8500,10200,
  183. 7.03266,7.05147,9419.241,11390.98279,8500,10200,
  184. 7.09632,7.11508,9475.26781,11456.26104,8500,10200,
  185. 7.15996,7.1787,9530.67429,11520.84159,8500,10200,
  186. 7.22361,7.24232,9585.46097,11584.73198,8500,10200,
  187. 7.28725,7.30594,9639.6069,11647.93468,8500,10200,
  188. 7.35089,7.36958,9693.12232,11710.44396,8500,10200,
  189. 7.41453,7.43321,9746.01409,11772.28903,8500,10200,
  190. 7.47818,7.49686,9798.289,11833.501,8500,10200,
  191. 7.54183,7.56051,9850.00518,11894.06068,8500,10200,
  192. 7.60548,7.62417,9901.23295,11953.92824,8500,10200,
  193. 7.66913,7.68784,9951.98999,12013.08172,8500,10200,
  194. 7.73278,7.75153,10002.25683,12071.50244,8500,10200,
  195. 7.89645,7.81523,10052.36,12129.17739,8500,10200
  196.     },
  197.     x=new[rtoi(real_s),rtoi(9)],
  198.     x=new[rtoi(real_s),rtoi(9)],
  199.     xx=new[rtoi(real_s),rtoi(8),rtoi(9)],
  200.     g=new[rtoi(real_s),rtoi(9)],
  201.     //eps=1e-50, d=0.0001,u=1.1,v=0.5,k=1000,
  202.     eps=1e-50, d=0.0002,u=1.6,v=0.4,k=2000,
  203.     i=XSLSF::jsim[HFor("f"),d,u,v,x,eps,k,xx,g],  //变换d、u、v进一步求解，k为允许的最大迭代次数
  204.     printff{"\r\n实际迭代次数={1,r}\r\n",i},
  205.     OutVector[x],
  206.     x.getra(0,&a1,&a2,&a3,&a4,&a5,&a6,&a7,&a8),
  207.     printff{"\r\n验证目标={1,r}\r\n",验证(a1,a2,a3,a4,a5,a6,a7,a8)},
  208.     delete[x],delete[xx],delete[g],delete[data]
  209. };
复制代码


结果：


  2. 实际迭代次数=779.
  3.   1.31183e-004  8.39228e-003  8.28998e-004  9.25637e-003  1.67914e-003  1.31872e-006  -1.3474e-002  1.00102e-002  2.55016e+007
  4.            y1理论          y1拟合              y2理论          y2拟合
  5.          6.23e-003                0.         3.38e-003                0.
  6.         4.353e-002   2.10032698e-002         3.82e-002  2.189030086e-002
  7.            0.14941  8.401307921e-002           0.16934      0.1094515043
  8.            0.36694      0.2310359682           0.46098      0.3064642119
  9.            0.75778      0.5145801152           0.96238      0.7661605292
  10.            1.38456      0.9976553527           1.74919       1.532321054
  11.            2.29213       1.753773231           2.94243       2.801958472
  12.            3.53554        2.83544228           4.71426       4.706414508
  13.            5.20226       4.326676626           7.27669       7.398921004
  14.            7.42113       6.311492035          10.82309       11.07648993
  15.           10.35209       8.863406056          15.50853        15.9142419
  16.           14.14065       12.07694641          21.48989       22.08729532
  17.           18.90052       16.05715554          28.95303       29.77076449
  18.           24.74298       20.87759259          38.11267       39.13975642
  19.           31.80531       26.62235442          49.17672       50.39125593
  20.           40.25924       33.38609745          62.31207       63.67844801
  21.           50.28468       41.25306307          77.66372       79.17637782
  22.           62.03036       50.29711598          95.37999        97.0819351
  23.           75.61252       60.61331076         115.63401       117.5481655
  24.           91.13844       72.25493167         138.63279       140.7718014
  25.          108.73974       85.30711551         164.56089       166.8618968
  26.          128.58368       99.82391742         193.54082       195.9930055
  27.          150.81816       115.8704669         225.66831       228.2738048
  28.          175.53846       133.4915751         261.03966       263.8127032
  29.          202.82289       152.7539786         299.76409       302.6740101
  30.          232.75206       173.6939297         341.95888       345.0091463
  31.          265.41952       196.3700487         387.69722       390.8377526
  32.          300.93392       220.8108934         436.99755       440.2882557
  33.          339.36342       247.0573626         489.86172       493.4227318
  34.           380.7144       275.1312989         546.28968       550.2587069
  35.          424.97823        305.078078         606.29491       610.8346393
  36.          472.15199       336.9033536          669.8986       675.1879041
  37.          522.24788       370.6368946         737.09155       743.2891505
  38.          575.29521       406.2904086         807.83014       815.1732184
  39.          631.29875       443.8897499         882.05666       890.7861812
  40.          690.21983       483.4538808         959.72229       970.1161963
  41.          751.99825       525.0058094        1040.80552       1053.127901
  42.           816.5748       568.5402728        1125.28232       1139.740611
  43.          883.91445       614.0778008        1213.08131       1229.893579
  44.          953.99316       661.6324661        1304.08627       1323.502387
  45.         1026.75515       711.2227791        1398.16326       1420.502316
  46.         1102.10577       762.8717765        1495.20066        1520.76158
  47.         1179.93219       816.6070749        1595.13304       1624.189754
  48.         1260.13534       872.4495441         1697.8885       1730.672729
  49.         1342.65195       930.4356383         1803.3466       1840.094398
  50.         1427.41963       990.5715616        1911.36713        1952.35814
  51.         1514.33398       1052.913069        2021.80672       2067.279516
  52.         1603.25915       1117.473124        2134.53576       2184.758258
  53.         1694.05737       1184.290656        2249.45885       2304.649466
  54.         1786.62745       1253.383034        2366.47078       2426.806758
  55.         1880.92679       1324.805362        2485.42446       2551.061247
  56.         1976.91522       1398.577649        2606.16356       2677.306433
  57.         2074.50055       1474.744738        2728.53608       2805.350163
  58.         2173.55602       1553.313276        2852.40203       2935.041974
  59.         2273.94347       1634.313107        2977.64586       3066.251671
  60.         2375.54104       1717.785106        3104.13495       3198.806848
  61.         2478.26747       1803.741034        3231.69703       3332.535345
  62.         2582.03418       1892.187791         3360.1586       3467.306652
  63.         2686.70601       1983.154184        3489.36608       3602.949364
  64.         2792.13168       2076.621579        3619.19972       3739.313514
  65.         2898.16582       2172.605623        3749.57778       3876.250086
  66.         3004.69665       2271.100374        3880.40485       4013.591199
  67.         3111.66401       2372.076148        4011.54555       4151.210907
  68.         3218.99955       2475.507585        4142.85723         4288.9647
  69.         3326.59179       2581.404839        4274.20857       4426.690409
  70.         3434.32646       2689.707084        4405.49946       4564.287409
  71.         3542.10727       2800.372088        4536.66485        4701.59826
  72.         3649.87114       2913.345789        4667.61732       4838.545983
  73.          3757.5994       3028.561729        4798.22733       4974.978354
  74.         3865.25711       3145.940575        4928.36086       5110.803882
  75.         3972.75293       3265.372868        5057.89492       5245.914453
  76.         4079.97352       3386.769019        5186.74079       5380.204927
  77.         4186.80342       3510.009479        5314.85607       5513.591781
  78.         4293.15505       3634.978786         5442.1913       5646.012422
  79.         4398.99856        3761.54902        5568.66246       5777.351856
  80.         4504.30268       3889.598028        5694.18442       5907.571174
  81.         4608.98932       4018.956276        5818.68751       6036.579584
  82.         4712.97148       4149.460548        5942.13638       6164.307598
  83.           4816.174       4280.955521        6064.53894       6290.688772
  84.         4918.55243        4413.25809        6185.88021       6415.711572
  85.         5020.12767       4546.232341        6306.09473       6539.279991
  86.          5120.9459        4679.66062        6425.12421       6661.387164
  87.         5221.01669       4813.393446        6542.92696       6782.010487
  88.         5320.31031       4947.238708         6659.4762       6901.079452
  89.         5418.76991       5080.999992        6774.78437       7018.609231
  90.         5516.34484       5214.477858        6888.85425       7134.582872
  91.         5613.03077       5347.508865        7001.64722       7248.953131
  92.          5708.8359       5479.910031        7113.13221       7361.707487
  93.         5803.72882       5611.461382        7223.28991       7472.850648
  94.         5897.65245       5742.001252        7332.11045       7582.357327
  95.         5990.55304       5871.370545        7439.63392       7690.235003
  96.         6082.39783       5999.395261        7545.92994       7796.476886
  97.         6173.20863       6125.924581        7651.04157       7901.077671
  98.         6263.05016       6250.830965        7754.97918       8004.048169
  99.         6351.96204        6373.95644        7857.73983       8105.385368
  100.         6439.94749       6495.185695        7959.32975        8205.10192
  101.         6527.00805       6614.392441         8059.7877       8303.211064
  102.          6613.1408       6731.475239        8159.17045       8399.740518
  103.         6698.35404       6846.339786        8257.49956       8494.690288
  104.         6782.69143       6958.833271        8354.75604       8588.088726
  105.         6866.17854       7068.912461        8450.92397       8679.950518
  106.          6948.7898       7176.492036        8545.99616        8770.27757
  107.         7030.49227        7281.48047        8639.98452       8859.098941
  108.         7111.26373       7383.827306        8732.93858       8946.430483
  109.         7191.10171       7483.460571        8824.89146       9032.288377
  110.         7270.05347       7580.362337        8915.83866       9116.689101
  111.         7348.18469       7674.478885        9005.79332       9199.649407
  112.         7425.52506       7765.807962        9094.78889       9281.210597
  113.         7502.07711       7854.326538        9182.86035       9361.388861
  114.         7577.83988       7940.020079        9270.06142         9440.2006
  115.         7652.82019       8022.907119          9356.444       9517.685695
  116.         7727.06391       8102.998772        9442.01051       9593.859903
  117.         7800.64867       8180.300322        9526.73097       9668.750455
  118.         7873.60639       8254.846569        9610.58595       9742.372922
  119.         7945.90721       8326.643182        9693.55725       9814.753994
  120.         8017.52094        8395.72451        9775.64222       9885.930664
  121.         8088.42244       8462.149199        9856.88388       9955.906745
  122.         8158.59209       8525.947524        9937.31916       10024.72884
  123.          8228.0546       8587.163994       10016.94601       10092.40034
  124.         8296.84742       8645.837205       10095.75888       10158.94575
  125.         8364.96327       8702.018416       10173.75753       10224.38903
  126.         8432.36873       8755.761122       10250.94765       10288.74371
  127.         8499.03771       8807.112899       10327.37093       10352.04288
  128.         8564.94949       8856.116836       10403.09748       10414.29929
  129.         8630.11652       8902.834232       10478.15378       10475.53523
  130.         8694.60518       8947.327215       10552.51463       10535.75378
  131.         8758.47244       8989.652019       10626.17792        10594.9862
  132.         8821.73046       9029.872597        10699.1582       10653.25358
  133.         8884.37821       9068.047101       10771.45413       10710.55871
  134.         8946.40322        9104.24574       10843.08258       10766.91373
  135.         9007.78494        9138.52667       10914.06792       10822.34802
  136.         9068.52802       9170.953571       10984.39172       10876.86444
  137.         9128.65481       9201.580038       11054.00725       10930.49145
  138.         9188.15416       9230.474103       11122.88753       10983.24823
  139.         9246.98237       9257.689232       11191.01588       11035.13728
  140.         9305.11454       9283.279717       11258.38284        11086.1855
  141.         9362.53694       9307.311378       11325.02332       11136.40311
  142.           9419.241       9329.833895       11390.98279       11185.80803
  143.         9475.26781       9350.910895       11456.26104       11234.41772
  144.         9530.67429        9370.59447       11520.84159        11282.2491
  145.         9585.46097       9388.947785       11584.73198       11329.30398
  146.          9639.6069         9406.0177       11647.93468       11375.59186
  147.         9693.12232       9421.858813       11710.44396       11421.13643
  148.         9746.01409       9436.521655       11772.28903       11465.92555
  149.           9798.289       9450.057651         11833.501       11509.98964
  150.         9850.00518       9462.512613       11894.06068       11553.32397
  151.         9901.23295       9473.933507       11953.92824       11595.94463
  152.         9951.98999       9484.366019       12013.08172        11637.8607
  153.        10002.25683       9493.854531       12071.50244       11679.08766
  154.           10052.36       9514.216335       12129.17739       11719.62791
  155. 验证目标=25501586.663172919
复制代码


a1,a2,a3,a4,a5,a6,a7,a8为：

1.31183e-004  8.39228e-003  8.28998e-004  9.25637e-003  1.67914e-003  1.31872e-006  -1.3474e-002  1.00102e-002

变换d、u、v进一步求解，看目标终值能否进一步减小。
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shamohu
发表于 2009-10-12 17:48:33 | 显示全部楼层 来自 北京海淀
1stOpt结果：

均方差(RMSE): 67.956848083656
残差平方和(RSS): 1385439.96043953
相关系数(R): 0.999942683378293
相关系数之平方(R^2): 0.999885370041782

参数                  最佳估算
--------------------        -------------
a1                 -0.00887308772200404
a2                 258.823175002446
a3                 -29166318.5879711
a4                 -1.79125288733091E-17
a5                 0.000359145287507015
a6                 -0.0129701924728399
a7                 241.97936429735
a8                 -1104114.89202431
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kingng3
 楼主| 发表于 2009-10-12 20:13:47 | 显示全部楼层 来自 江苏镇江
8# wanglu


朋友，谢谢你！但是现在将拟合的数据带到方程中，与原来数据的曲线很不吻合，是不是计算的问题？

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kingng3
 楼主| 发表于 2009-10-12 20:18:16 | 显示全部楼层 来自 江苏镇江
9# shamohu

谢谢楼主，但是拟合出来的曲线带入方程，与原来的数据曲线相差甚远，不知道是为什么？楼主能不能解释一下！

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kingng3
 楼主| 发表于 2009-10-12 20:25:01 | 显示全部楼层 来自 江苏镇江
11# kingng3

这是我用最小二乘拟合出来的图，但是也不是吻合的很好，特别是数据组数再增加时，拟合的效果就更不好了，还需要给出初值，所以觉得要是有个不用给初值就能比较精确的拟合出数据的方法就好了！问题还需要更多的讨论跟分析，谢谢各位的支持！

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kingng3
 楼主| 发表于 2009-10-12 20:36:18 | 显示全部楼层 来自 江苏镇江
12# kingng3

为了大家更直观的解决问题，我传上excel数据，这是要拟合的方程
C=1.3;
y1=D1*sin(C1*Arctan(B1*Q1));
y2=D2*sin(C2*Arctan(B2*Q2));
Q1=(1-E1)*x1+(E1/B1)*Arctan(B1*x1);
Q2=(1-E2)*x2+(E2/B2)*Arctan(B2*x2);
D1=a1*F1^2+a2*F1;
D2=a1*F2^2+a2*F2;
E1=a6*F1^2+a7*F1+a8;
E2=a6*F2^2+a7*F2+a8;
B1=a3*sin(a4*Arctan(a5*F1))/C*D1;
B2=a3*sin(a4*Arctan(a5*F2))/C*D2;

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