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bella_虫虫

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注册: 2012-09-19
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[求助] MATLAB或者1stOpt自定义公式曲线拟合已有1人参与

自定义公式是y^2-1=A*x^2/(x^2-B^2)+C*x^2/(x^2-D^2)
其中x是波长，y是折射率。求参数A,B,C,D.万分感谢！数据如下：
x y
0.4 1.76854
0.401 1.76835
0.402 1.76817
0.403 1.768
0.404 1.76782
0.405 1.76764
0.406 1.76747
0.407 1.7673
0.408 1.76713
0.409 1.76696
0.41 1.76679
0.411 1.76662
0.412 1.76646
0.413 1.76629
0.414 1.76613
0.415 1.76597
0.416 1.76581
0.417 1.76565
0.418 1.76549
0.419 1.76533
0.42 1.76518
0.421 1.76502
0.422 1.76487
0.423 1.76472
0.424 1.76457
0.425 1.76442
0.426 1.76427
0.427 1.76412
0.428 1.76398
0.429 1.76383
0.43 1.76369
0.431 1.76355
0.432 1.76341
0.433 1.76327
0.434 1.76313
0.435 1.76299
0.436 1.76285
0.437 1.76272
0.438 1.76258
0.439 1.76245
0.44 1.76232
0.441 1.76218
0.442 1.76205
0.443 1.76192
0.444 1.76179
0.445 1.76167
0.446 1.76154
0.447 1.76141
0.448 1.76129
0.449 1.76116
0.45 1.76104
0.451 1.76092
0.452 1.7608
0.453 1.76068
0.454 1.76056
0.455 1.76044
0.456 1.76032
0.457 1.7602
0.458 1.76009
0.459 1.75997
0.46 1.75986
0.461 1.75974
0.462 1.75963
0.463 1.75952
0.464 1.75941
0.465 1.7593
0.466 1.75919
0.467 1.75908
0.468 1.75897
0.469 1.75886
0.47 1.75875
0.471 1.75865
0.472 1.75854
0.473 1.75844
0.474 1.75833
0.475 1.75823
0.476 1.75813
0.477 1.75803
0.478 1.75793
0.479 1.75783
0.48 1.75773
0.481 1.75763
0.482 1.75753
0.483 1.75743
0.484 1.75733
0.485 1.75724
0.486 1.75714
0.487 1.75705
0.488 1.75695
0.489 1.75686
0.49 1.75677
0.491 1.75667
0.492 1.75658
0.493 1.75649
0.494 1.7564
0.495 1.75631
0.496 1.75622
0.497 1.75613
0.498 1.75604
0.499 1.75596
0.5 1.75587
0.501 1.75578
0.502 1.7557
0.503 1.75561
0.504 1.75553
0.505 1.75544
0.506 1.75536
0.507 1.75528
0.508 1.75519
0.509 1.75511
0.51 1.75503
0.511 1.75495
0.512 1.75487
0.513 1.75479
0.514 1.75471
0.515 1.75463
0.516 1.75455
0.517 1.75447
0.518 1.75439
0.519 1.75432
0.52 1.75424
0.521 1.75416
0.522 1.75409
0.523 1.75401
0.524 1.75394
0.525 1.75386
0.526 1.75379
0.527 1.75372
0.528 1.75364
0.529 1.75357
0.53 1.7535
0.531 1.75343
0.532 1.75336
0.533 1.75329
0.534 1.75321
0.535 1.75315
0.536 1.75307
0.537 1.75301
0.538 1.75294
0.539 1.75287
0.54 1.7528
0.541 1.75273
0.542 1.75267
0.543 1.7526
0.544 1.75253
0.545 1.75247
0.546 1.7524
0.547 1.75234
0.548 1.75227
0.549 1.75221
0.55 1.75215
0.551 1.75208
0.552 1.75202
0.553 1.75196
0.554 1.75189
0.555 1.75183
0.556 1.75177
0.557 1.75171
0.558 1.75165
0.559 1.75159
0.56 1.75153
0.561 1.75147
0.562 1.75141
0.563 1.75135
0.564 1.75129
0.565 1.75123
0.566 1.75117
0.567 1.75111
0.568 1.75106
0.569 1.751
0.57 1.75094
0.571 1.75088
0.572 1.75083
0.573 1.75077
0.574 1.75072
0.575 1.75066
0.576 1.75061
0.577 1.75055
0.578 1.7505
0.579 1.75044
0.58 1.75039
0.581 1.75034
0.582 1.75028
0.583 1.75023
0.584 1.75018
0.585 1.75012
0.586 1.75007
0.587 1.75002
0.588 1.74997
0.589 1.74992
0.59 1.74987
0.591 1.74981
0.592 1.74977
0.593 1.74971
0.594 1.74966
0.595 1.74961
0.596 1.74957
0.597 1.74952
0.598 1.74947
0.599 1.74942
0.6 1.74937
0.601 1.74932
0.602 1.74927
0.603 1.74923
0.604 1.74918
0.605 1.74913
0.606 1.74909
0.607 1.74904
0.608 1.74899
0.609 1.74895
0.61 1.7489
0.611 1.74886
0.612 1.74881
0.613 1.74877
0.614 1.74872
0.615 1.74868
0.616 1.74863
0.617 1.74859
0.618 1.74854
0.619 1.7485
0.62 1.74845
0.621 1.74841
0.622 1.74837
0.623 1.74833
0.624 1.74828
0.625 1.74824
0.626 1.7482
0.627 1.74816
0.628 1.74811
0.629 1.74807
0.63 1.74803
0.631 1.74799
0.632 1.74795
0.633 1.74791
0.634 1.74787
0.635 1.74783
0.636 1.74779
0.637 1.74775
0.638 1.74771
0.639 1.74767
0.64 1.74763
0.641 1.74759
0.642 1.74755
0.643 1.74751
0.644 1.74747
0.645 1.74743
0.646 1.7474
0.647 1.74736
0.648 1.74732
0.649 1.74728
0.65 1.74725
0.651 1.74721
0.652 1.74717
0.653 1.74714
0.654 1.7471
0.655 1.74706
0.656 1.74703
0.657 1.74699
0.658 1.74695
0.659 1.74692
0.66 1.74688
0.661 1.74685
0.662 1.74681
0.663 1.74678
0.664 1.74674
0.665 1.74671
0.666 1.74667
0.667 1.74664
0.668 1.7466
0.669 1.74657
0.67 1.74653
0.671 1.7465
0.672 1.74647
0.673 1.74643
0.674 1.7464
0.675 1.74637
0.676 1.74633
0.677 1.7463
0.678 1.74627
0.679 1.74623
0.68 1.7462
0.681 1.74617
0.682 1.74614
0.683 1.74611
0.684 1.74607
0.685 1.74604
0.686 1.74601
0.687 1.74598
0.688 1.74595
0.689 1.74592
0.69 1.74588
0.691 1.74585
0.692 1.74582
0.693 1.74579
0.694 1.74576
0.695 1.74573
0.696 1.7457
0.697 1.74567
0.698 1.74564
0.699 1.74561
0.7 1.74558
0.701 1.74555
0.702 1.74552
0.703 1.74549
0.704 1.74547
0.705 1.74544
0.706 1.74541
0.707 1.74538
0.708 1.74535
0.709 1.74532
0.71 1.74529
0.711 1.74526
0.712 1.74524
0.713 1.74521
0.714 1.74518
0.715 1.74515
0.716 1.74513
0.717 1.7451
0.718 1.74507
0.719 1.74504
0.72 1.74502
0.721 1.74499
0.722 1.74496
0.723 1.74493
0.724 1.74491
0.725 1.74488
0.726 1.74486
0.727 1.74483
0.728 1.7448
0.729 1.74478
0.73 1.74475
0.731 1.74472
0.732 1.7447
0.733 1.74467
0.734 1.74465
0.735 1.74462
0.736 1.7446
0.737 1.74457
0.738 1.74455
0.739 1.74452
0.74 1.7445
0.741 1.74447
0.742 1.74445
0.743 1.74442
0.744 1.7444
0.745 1.74437
0.746 1.74435
0.747 1.74433
0.748 1.7443
0.749 1.74428
0.75 1.74425
0.751 1.74423
0.752 1.74421
0.753 1.74418
0.754 1.74416
0.755 1.74414
0.756 1.74411
0.757 1.74409
0.758 1.74407
0.759 1.74404
0.76 1.74402
0.761 1.744
0.762 1.74398
0.763 1.74395
0.764 1.74393
0.765 1.74391
0.766 1.74389
0.767 1.74386
0.768 1.74384
0.769 1.74382
0.77 1.7438
0.771 1.74377
0.772 1.74375
0.773 1.74373
0.774 1.74371
0.775 1.74369
0.776 1.74367
0.777 1.74364
0.778 1.74362
0.779 1.7436
0.78 1.74358
0.781 1.74356
0.782 1.74354
0.783 1.74352
0.784 1.7435
0.785 1.74348
0.786 1.74346
0.787 1.74344
0.788 1.74342
0.789 1.7434
0.79 1.74337
0.791 1.74335
0.792 1.74333
0.793 1.74331
0.794 1.74329
0.795 1.74327
0.796 1.74326
0.797 1.74323
0.798 1.74322
0.799 1.7432
0.8 1.74318
0.801 1.74316
0.802 1.74314
0.803 1.74312
0.804 1.7431
0.805 1.74308
0.806 1.74306
0.807 1.74304
0.808 1.74302
0.809 1.743
0.81 1.74299
0.811 1.74297
0.812 1.74295
0.813 1.74293
0.814 1.74291
0.815 1.74289
0.816 1.74287
0.817 1.74286
0.818 1.74284
0.819 1.74282
0.82 1.7428
0.821 1.74278
0.822 1.74276
0.823 1.74275
0.824 1.74273
0.825 1.74271
0.826 1.74269
0.827 1.74268
0.828 1.74266
0.829 1.74264
0.83 1.74262
0.831 1.74261
0.832 1.74259
0.833 1.74257
0.834 1.74255
0.835 1.74254
0.836 1.74252
0.837 1.7425
0.838 1.74249
0.839 1.74247
0.84 1.74245
0.841 1.74244
0.842 1.74242
0.843 1.7424
0.844 1.74239
0.845 1.74237
0.846 1.74235
0.847 1.74234
0.848 1.74232
0.849 1.74231
0.85 1.74229
0.851 1.74227
0.852 1.74226
0.853 1.74224
0.854 1.74222
0.855 1.74221
0.856 1.74219
0.857 1.74218
0.858 1.74216
0.859 1.74215
0.86 1.74213
0.861 1.74212
0.862 1.7421
0.863 1.74208
0.864 1.74207
0.865 1.74205
0.866 1.74204
0.867 1.74202
0.868 1.74201
0.869 1.74199
0.87 1.74198
0.871 1.74196
0.872 1.74195
0.873 1.74193
0.874 1.74192
0.875 1.7419
0.876 1.74189
0.877 1.74187
0.878 1.74186
0.879 1.74185
0.88 1.74183
0.881 1.74182
0.882 1.7418
0.883 1.74179
0.884 1.74177
0.885 1.74176
0.886 1.74174
0.887 1.74173
0.888 1.74172
0.889 1.7417
0.89 1.74169
0.891 1.74167
0.892 1.74166
0.893 1.74165
0.894 1.74163
0.895 1.74162
0.896 1.7416
0.897 1.74159
0.898 1.74158
0.899 1.74156
0.9 1.74155

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1楼 2018-10-22 17:07:50

已阅回复此楼关注TA 给TA发消息送TA红花 TA的回帖

独孤神宇

版主 (知名作家)

应助: 490 (硕士)
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金币: 31014.8
散金: 802
红花: 122
沙发: 1
帖子: 5600
在线: 855.5小时
虫号: 3522474
注册: 2014-11-06
性别: GG
专业: 机械动力学
管辖: 计算模拟

【答案】应助回帖

★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★
感谢参与，应助指数 +1
bella_虫虫: 金币+20, ★★★很有帮助, 大神，有拟合后的数据吗？我还需要画出拟合曲线。谢谢！ 2018-10-23 09:30:04

结果不唯一，模型和数据匹配度太高了，如果是实验数据，感觉就有点假了，。

模型公式: y = sqrt(a*x^2/(x^2-b^2)+c*x^2/(x^2-d^2)+1)
y = sqrt((-1.18379266454923)*x^2/(x^2-18.1057685843^2)+2.00785118048099*x^2/(x^2-0.0945636570305277^2)+1)

迭代数: 515
计算用时(时:分:秒:微秒): 00:00:08:244
优化算法: 标准简面体爬山法 + 通用全局优化算法(SM1)
计算结束原因: 达到收敛判断标准
均方差(RMSE): 3.2249045091751E-5
残差平方和(SSR): 5.21040455574223E-7
相关系数(R): 0.999989750571742
相关系数之平方(R^2): 0.999979501248535
修正R平方(Adj. R^2): 0.999979418924232
确定系数(DC): 0.999979501177371
卡方系数(Chi-Square): 1.48486804223232E-7
F统计(F-Statistic): 8081713.58220345

参数最佳估算
---------- -------------
a -1.18379266454923
b 18.1057685843
c 2.00785118048099
d 0.0945636570305277

**********************

迭代数: 727
计算用时(时:分:秒:微秒): 00:00:09:450
优化算法: 标准简面体爬山法 + 通用全局优化算法(SM1)
计算结束原因: 达到收敛判断标准
均方差(RMSE): 3.22347590799856E-5
残差平方和(SSR): 5.20578926165303E-7
相关系数(R): 0.999989759928103
相关系数之平方(R^2): 0.999979519961065
修正R平方(Adj. R^2): 0.999979437711913
确定系数(DC): 0.999979519334905
卡方系数(Chi-Square): 1.48357855659539E-7
F统计(F-Statistic): 8089167.49117066

参数最佳估算
---------- -------------
a 2.00784753166354
b 0.094565365438321
c -1.88301602220581
d 22.8151229510075