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Integral curve fitting in origin

  1. Feb 17, 2015 #1
    Dear users,

    I deal with following problem.

    I've got a data of Intenzity of chemiluminezcence as a function of temperature. The data should be fitted by following equation:

    upload_2015-2-17_16-1-35.png

    I found that in origin one can fit also data with integral function, with fittin parameters P, A, i, E.
    The beta and R are constants that I already know.

    So my question is. Is it possible to make this kind of curve fitting in Origin, and Is it correct to make this kind of curve fitting or it is impossible to obtain correct physical results.

    Thank you in advance

    PN
     

    Attached Files:

  2. jcsd
  3. Feb 18, 2015 #2
    Hi ! Your question concerns the fitting of an "integral equation" to experimental data.
    I cannot say, a-priori, if it's relevant to the kind of method used in the paper : https://fr.scribd.com/doc/14674814/Regressions-et-equations-intégrales
    To answer to this question, it is important to know how the experimental data are distributed (regularly or non-regularly spaced, range, order of magnitude of scatter, ...).
    If you post an example of data, I could check and say if the method described in the referenced paper can be addapted to become convenient in your case.
     
  4. Feb 18, 2015 #3
    Hi!
    Thank you for your answer,
    Of course, I can show you the data,

    so, here's the plot of a data and data below
    upload_2015-2-18_9-54-27.png

    303,143 0,40355
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    303,143 1,21065
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    420,594 22,51816
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    420,924 23,08313
    421,089 24,29379
    421,254 21,30751
    421,419 25,50444
    421,584 22,51816
    421,748 23,80952
    421,913 22,27603
    422,078 22,59887
    422,243 23,56739
    422,408 25,35432
    422,573 24,3745
    422,737 24,29379
    422,902 25,58515
    423,067 27,19935
    423,232 28,16788
    423,396 24,45521
    423,561 27,28006
    423,726 27,84504
    423,891 28,65214
    424,055 30,18563
    424,22 30,6699
    424,385 30,34705
    424,549 32,92978
    424,714 29,9435
    424,879 31,39629
    425,043 31,63842
    425,208 29,86279
    425,373 31,63842
    425,537 31,71913
    425,702 31,31558
    425,867 32,2841
    426,031 35,02825
    426,196 31,96126
    426,36 34,6247
    426,525 37,61098
    426,69 32,60694
    426,854 33,65617
    427,019 31,15416
    427,183 34,94754
    427,348 35,99677
    427,512 38,66021
    427,677 36,31961
    427,841 37,046
    428,006 39,3866
    428,17 39,30589
    428,335 41,56578
    428,499 40,67797
    428,664 40,03228
    428,828 41,40436
    428,993 43,17998
    429,157 46,16626
    429,321 40,1937
    429,486 43,98709
    429,65 40,67797
    429,815 43,50282
    429,979 41,96933
    430,143 43,98709
    430,308 45,60129
    430,472 44,0678
    430,636 46,73123
    430,801 51,49314
    430,965 47,2155
    431,129 49,47538
    431,294 46,89266
    431,458 51,57385
    431,622 49,31396
    431,787 50,60533
    431,951 54,88297
    432,115 52,38095
    432,279 52,46166
    432,444 56,33575
    432,608 57,54641
    432,772 60,37127
    432,936 54,72155
    433,1 57,38499
    433,265 59,24132
    433,429 57,30428
    433,593 60,29056
    433,757 62,06618
    433,921 63,68039
    434,085 65,29459
    434,249 68,11945
    434,414 64,97175
    434,578 64,24536
    434,742 68,84584
    434,906 67,63519
    435,07 69,3301
    435,234 71,18644
    435,398 70,37934
    435,562 72,80065
    435,726 76,67474
    435,89 81,03309
    436,054 73,93059
    436,218 73,12349
    436,382 79,09605
    436,546 74,73769
    436,71 81,9209
    436,874 86,27926
    437,038 84,82647
    437,202 82,56659
    437,366 89,50767
    437,53 94,10815
    437,694 91,12187
    437,858 94,83454
    438,022 93,94673
    438,186 98,30508
    438,35 99,03148
    438,513 96,0452
    438,677 95,39952
    438,841 104,7619
    439,005 105,08475
    439,169 104,7619
    439,333 107,82889
    439,496 110,73446
    439,66 108,23245
    439,824 115,65779
    439,988 115,65779
    440,152 118,8862
    440,315 120,90395
    440,479 119,28975
    440,643 118,72478
    440,807 123,24455
    440,97 124,53592
    441,134 130,34705
    441,298 130,10492
    441,462 135,67393
    441,625 133,17191
    441,789 132,12268
    441,953 140,75868
    442,116 144,14851
    442,28 149,55609
    442,444 143,90638
    442,607 150,68604
    442,771 149,39467
    442,934 158,59564
    443,098 158,99919
    443,262 156,49718
    443,425 163,59968
    443,589 164,24536
    443,752 165,94027
    443,916 170,13721
    444,08 167,07022
    444,243 179,4996
    444,407 179,90315
    444,57 178,45036
    444,734 192,81679
    444,897 190,5569
    445,061 195,64165
    445,224 198,14366
    445,388 193,86602
    445,551 199,83858
    445,715 198,78935
    445,878 196,93301
    446,041 207,50605
    446,205 221,2268
    446,368 205,73043
    446,532 213,96287
    446,695 218,96691
    446,858 215,98063
    447,022 217,99839
    447,185 218,15981
    447,349 234,8749
    447,512 230,26634
    447,675 241,64649
    447,839 232,92978
    448,002 244,8749
    448,165 248,91041
    448,329 252,7845
    448,492 250,84746
    448,655 257,70783
    448,818 253,5109
    448,982 253,10734
    449,145 265,94027
    449,308 263,92252
    449,471 257,54641
    449,635 283,53511
    449,798 276,99758
    449,961 291,52542
    450,124 294,26957
    450,287 287,4092
    450,451 283,4544
    450,614 286,19855
    450,777 308,55529
    450,94 298,14366
    451,103 309,36239
    451,266 310,49233
    451,429 306,77966
    451,593 318,0791
    451,756 324,69734
    451,919 322,841
    452,082 322,841
    452,245 337,69169
    452,408 340,43584
    452,571 342,5343
    452,734 342,45359
    452,897 354,88297
    453,06 361,50121
    453,223 360,77482
    453,386 376,59403
    453,549 377,9661
    453,712 385,55287
    453,875 386,11784
    454,038 388,70056
    454,201 414,68927
    454,364 412,42938
    454,527 412,75222
    454,69 429,53995
    454,853 439,79015
    455,016 432,84907
    455,179 452,62308
    455,341 462,06618
    455,504 462,954
    455,667 480,79096
    455,83 483,93866
    455,993 495,2381
    456,156 495,56094
    456,319 504,19693
    456,481 520,33898
    456,644 536,31961
    456,807 557,14286
    456,97 556,33575
    457,133 570,94431
    457,295 576,3519
    457,458 591,84826
    457,621 595,88378
    457,784 622,92171
    457,946 622,27603
    458,109 657,86925
    458,272 664,32607
    458,435 673,68846
    458,597 687,48991
    458,76 698,14366
    458,923 720,5004
    459,085 745,76271
    459,248 762,63115
    459,411 773,76917
    459,573 785,23002
    459,736 798,38579
    459,898 810,16949
    460,061 851,41243
    460,24 861,82405
    460,386 883,05085
    460,549 896,20662
    460,711 928,00646
    460,874 942,85714
    461,037 965,94027
    461,215 991,92897
    461,378 1026,55367
    461,54 1031,63842
    461,703 1068,44229
    461,865 1073,12349
    462,028 1099,1929
    462,19 1117,91768
    462,353 1132,76836
    462,515 1142,13075
    462,678 1203,38983
    462,84 1220,5004
    463,003 1234,54399
    463,165 1256,98144
    463,328 1267,47377
    463,49 1285,95642
    463,652 1323,80952
    463,815 1345,84342
    463,977 1335,51251
    464,14 1351,08959
    464,302 1384,74576
    464,464 1387,97417
    464,627 1431,71913
    464,789 1431,88055
    464,951 1464,5682
    465,114 1464,5682
    465,276 1472,55851
    465,438 1490,07264
    465,6 1511,21872
    465,763 1528,00646
    465,925 1540,51655
    466,087 1582,80872
    466,249 1564,81033
    466,412 1595,15738
    466,574 1613,15577
    466,736 1623,56739
    466,898 1636,40032
    467,061 1671,50928
    467,223 1674,41485
    467,385 1682,48588
    467,547 1706,86037
    467,709 1757,4657
    467,871 1768,20016
    468,034 1780,06457
    468,196 1766,66667
    468,358 1815,98063
    468,52 1812,75222
    468,682 1829,78208
    468,844 1864,89104
    469,006 1859,48345
    469,168 1883,53511
    469,33 1887,00565
    469,492 1899,03148
    469,654 1955,52865
    469,816 1970,54076
    469,978 1954,56013
    470,14 2005,40759
    470,302 2013,47861
    470,464 2045,52058
    470,626 2077,159
    470,788 2060,45198
    470,95 2111,0573
    471,112 2093,13963
    471,274 2186,68281
    471,436 2180,87167
    471,598 2195,40032
    471,76 2231,71913
    471,922 2239,14447
    472,084 2267,07022
    472,246 2287,73204
    472,408 2294,26957
    472,57 2337,69169
    472,731 2358,91848
    472,893 2413,64003
    473,055 2433,0912
    473,063 2452,46166

    I don't know if you mean this kind of data example, do you?
     
  5. Feb 18, 2015 #4
    At first sight, it does'nt work.
    What is the value of Troom corresponding to the data ?
    Is the unknown coefficient (A/i) negative ?
     
  6. Feb 20, 2015 #5
    Hi,
    The Troom is the initial temperature so it start in first column Troo=303,143 Kelvin
    A/i is pozitive parameter and parameter Beta is also pozitive (beta value is known, so it is not fit).

    Thank you for your help.

    P.

    Here is a similar plot where the data was fitted on this type of file using equastion writes above
    1-s2.0-S0141391010003496-gr1.jpg
     
  7. Feb 20, 2015 #6
    When T is increassing, the integral is increassing, the denominator of the function is increassing, the function is decreassing, which is not consistent with the data. This seems to be the main cause of failure of the fitting.
     
  8. Feb 25, 2015 #7
    Since the issue remained outstanding for enough time, I will close it, as far I am concerned.
    I cannot help more because the function proposed is not convenient to fit with the given data : any fitting method fails if the general shape of the function is in contradiction with the experimental data.
    This is clear on the joint figure : The 1080 experimental points are drawn on logarithmic scale. This is necessary to make visible the scatter in case of large range of magnitude.
    The kind of shape of the functions I(T) is sketched (red curve) It is not possible to compute the values of the parameters because there is no experimental point in the convenient range. So, the curve drawn is purely symbolic, only for explanation.
    Probably, reconsidering the physical model will lead to a more convenient function.

    Figure.JPG
     
  9. Mar 9, 2015 #8
    I´m so sorry, that I haven't replied earlier. Thank you for sharing your answer, but If you look at my first contribution you have used different formula from my formula in your plot. The denominator is power of 2. But you are right this function has decrease character. And therefore we have to used different physical model.

    Thank's a lot for your time, and again I am very sorry that I haven't replied earlier.
     
  10. Mar 9, 2015 #9
    Hi Pavol Namer !
    I used the formula with denominator at power 2. In fact, there is a typo on the figure attached to my answer : I forgot to write the power. It doesn't matter since it was only a skeched graph.
     
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