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How to overcome this error while using lsqnonlin for curvefitting??

2 Ansichten (letzte 30 Tage)
Anil Kumar Mekala
Anil Kumar Mekala am 17 Jan. 2024
Bearbeitet: Torsten am 17 Jan. 2024
Solver stopped prematurely.
fmincon stopped because it exceeded the function evaluation limit,
options.MaxFunctionEvaluations = 3.000000e+03.
Please help me to change maxfunctionevaluations to 10000.
  2 Kommentare
Mann Baidi
Mann Baidi am 17 Jan. 2024
Bearbeitet: Mann Baidi am 17 Jan. 2024
Hi,
Can you share the code where you are using the function "lsqnonlin".
Anil Kumar Mekala
Anil Kumar Mekala am 17 Jan. 2024
Bearbeitet: Torsten am 17 Jan. 2024
clc
clear all
close all
warning off
%25wt.%
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0.556704212312915 0.565751138088012 0.575688551436653 0.584204362465232 0.592854575515779 0.604083074314778 0.616119858500382 0.624238724991523 0.633536136925854 0.645193565262883 0.653932728792848 0.674337517433752 0.680741692674867 0.682720057720058 0.629864445072014 0.643539094650206 0.656698821007503 0.669802691754868 0.685059964276601 0.698657384385878 0.712665291762708 0.726557415843342 0.740196078431373 0.753536147283341 0.767104542966612 0.781058466130150 0.795474596502154 0.809367586937869 0.821952179474565 0.835643280443510 0.849528761780955 0.862949900524507 0.874917651192411 0.888732873797975 0.902163999668353 0.914614055531000 0.929578013080038 0.940381138897258 0.951863863280254 0.964085853934972 0.975826057181989 0.987624829965827 1.00318307504341 1.00693054058217 1.01735053455175 0.978635014836795 0.994113475177305 1.00823885881592 1.02135464430761 1.03449470766129 1.04707306005143 1.05837164639469 1.06887376410946 1.07891482039148 1.08820568419422 1.09557179066647 1.10325788177929 1.11123869012079 1.11780520052887 1.12314342013264 1.12825093899097 1.13413353046456 1.13800074878323 1.14086912745644 1.14501593865771 1.14679340433297 1.14813694267516 1.14853824345334 1.15085904628331 1.15073076492328 1.15158667008321 1.15180928715639 1.15060810306663 1.15303398494080 1.14859382677957 1.14500631417120 1.16559676039939 1.16312816517335 1.15901685131738 1.15366178428762 1.14910266224377 1.14576160026234 1.14021790620559 1.13606219986279 1.13073192239859 1.12594851428977 1.12003294214536 1.11489898989899 1.11072463768116 1.10684213809019 1.10092631833868 1.09521570471377 1.09022470628493 1.08534013982910 1.07878298330641 1.07368750652333 1.06778370144707 1.06134122287968 1.05619969336911 1.04920775056921 1.04179427130247 1.03647616539373 1.03099782246702 1.02342095427931 1.01902140920312 1.01105448843591 1.00370073633207];
ydata = [sm;lm;lf];
tdata = freq;
% scatter(freq,ydata);
fun = @(x)nlsqfun(x,tdata,ydata);
x0 = [1e-5,0.1,0.1,0.1,0,0,0,0,0.01];
% x0 = [7.1066e-08;0.5235;0.6678;0.0192;8.3181e+03;2.7365e+03;1.6327e+03;543.8365;0.1859];
% x0 = zeros(1,9);
A = [];
b = [];
Aeq = [];
beq = [];
lb = zeros(1,9);
ub = [0.01,1,1,1,inf,inf,inf,inf,1];
x = lsqnonlin(fun,x0,lb,ub,A,b,Aeq,beq);
Solver stopped prematurely. fmincon stopped because it exceeded the function evaluation limit, options.MaxFunctionEvaluations = 3.000000e+03.
function E = nlsqfun(x,tdata,ydata)
E0 = 3.73;
Tr = x(1); al = x(2); bta = x(3); g = x(4); p = x(9); l1 = x(5); l2 = x(6); l3 = x(7); o = x(8);
ER = (E0 + ((l1*(((tdata).*Tr).^(g+p)).*(cos(0.5*pi*(g+p)) + l2*cos(0.5*pi*p)*(((tdata).*Tr).^(g))))./(1+ l2*(((tdata).*Tr).^(g)).*(2*cos(0.5*pi*g) + l2*(((tdata).*Tr).^(g))))) + ((E0*o*(((tdata).*Tr).^(al+bta)).*(cos(0.5*pi*(al+bta)) + l3*cos(0.5*pi*bta)*(((tdata).*Tr).^(al)) + (((tdata).*Tr).^(al+bta))))./(1 + (((tdata).*Tr).^(al)).*(2*l3*cos(0.5*pi*al) + 2*cos(0.5*pi*(al+bta)*(((tdata).*Tr).^(bta))) + (((tdata).*Tr).^(al)).*(l3^2 + 2*l3*cos(0.5*pi*bta)*(((tdata).*Tr).^(bta)) + (((tdata).*Tr).^(2*bta)))))));
EI = (((l1.*(((tdata).*Tr).^(g+p)).*(sin(0.5*pi*(g+p)) + l2*sin(0.5*pi*p)).*(((tdata).*Tr).^(g)))./(1 + l2*(((tdata).*Tr).^(g)).*(2*cos(0.5*pi*g) + l2*(((tdata).*Tr).^(g))))) + ((E0*o*(((tdata).*Tr).^(al+bta)).*(sin(0.5*pi*(al+bta)) + l3*sin(0.5*pi*bta)*(((tdata).*Tr).^(al))))./(1 + (((tdata).*Tr).^(al)).*(2*l3*cos(0.5*pi*al) + 2*cos(0.5*pi*(al+bta))*(((tdata).*Tr).^(bta)) + (((tdata).*Tr).^(al)).*(l3^2 + 2*l3*cos(0.5*pi*bta).*(((tdata).*Tr).^(bta)) + (((tdata).*Tr).^(2*bta)))))));
% gs = ((E0*o*(((tdata).*Tr).^(al+bta)).*(sin(0.5*pi*(al+bta)) + l3*sin(0.5*pi*bta)*(((tdata).*Tr).^(al))).*(1 + l2*(((tdata).*Tr).^(g)).*(2*cos(0.5*pi*g) + l2*(((tdata).*Tr).^(g)))) + l1*(((tdata).*Tr).^(g+p)).*(sin(0.5*pi*(g+p)) + l2*sin(0.5*pi*p)*(((tdata).*Tr).^(g))).*(1 + (((tdata).*Tr).^(al)).*(2*l3*cos(0.5*pi*al) + 2*cos(0.5*pi*(al+bta))*(((tdata).*Tr).^(bta))) + (((tdata).*Tr).^(2*al)).*(l3^2 + 2*l3*cos(0.5*pi*bta).*(((tdata).*Tr).^(bta)) + (((tdata).*Tr).^(2*bta)))))./(E0*(1 + l2*(((tdata).*Tr).^(g)).*(2*cos(0.5*pi*g) + l2*(((tdata).*Tr).^(g)))).*(1 + (1+o)*(((tdata).*Tr).^(2*al + 2*bta)) + l3*(((tdata).*Tr).^(al)).*(2*cos(0.5*pi*al) + l3*(((tdata).*Tr).^(al))) + (2+o)*(((tdata).*Tr).^(al+bta)).*(cos(0.5*pi*(al+bta)) + l3*cos(0.5*pi*bta)*(((tdata).*Tr).^(al)))) + l1*(((tdata).*Tr).^(g+p)).*(cos(0.5*pi*(g+p)) + l2*cos(0.5*pi*p)*(((tdata).*Tr).^(g))).*(1 + 2*l3*cos(0.5*pi*al)*(((tdata).*Tr).^(al)) + 2*cos(0.5*pi*(al+bta))*(((tdata).*Tr).^(al+bta)) + (((tdata).*Tr).^(2*al)).*(l3^2 + 2*l3*cos(0.5*pi*bta)*(((tdata).*Tr).^(bta)) + (((tdata).*Tr).^(2*bta))))));
gs = EI./ER;
sm_exp = ydata(1,:);
lm_exp = ydata(2,:);
lf_exp = ydata(3,:);
E = sum((gs.*sm_exp - lm_exp).^2);
ya = EI./ER;
%clf;
%loglog(sm_exp,lf_exp,'*');
%hold on;
%loglog(sm_exp,ya,"r");
%drawnow;
end

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Antworten (3)

Hassaan
Hassaan am 17 Jan. 2024
you can set various options including the maximum number of function evaluations using the optimoptions function. If you're reaching the function evaluation limit, you can increase it as follows:
% Create an options structure for fmincon where you set the MaxFunctionEvaluations to 10000
options = optimoptions('fmincon', 'MaxFunctionEvaluations', 10000);
% Then you pass these options to the fmincon function
% For example, if you were minimizing a function 'myFunction' starting at an initial point 'x0'
[x, fval, exitflag, output] = fmincon(@myFunction, x0, [], [], [], [], [], [], [], options);
In this code, replace @myFunction with the handle to your actual objective function and x0 with your actual initial point for the optimization. The rest of the parameters [] should be replaced with any constraints you have.
Make sure to include this options structure when you call fmincon. The solver will then use the specified limit for function evaluations.
-----------------------------------------------------------------------------------------------------------------------------------------------------
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It's important to note that the advice and code are based on limited information and meant for educational purposes. Users should verify and adapt the code to their specific needs, ensuring compatibility and adherence to ethical standards.
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Mann Baidi
Mann Baidi am 17 Jan. 2024
Hi Anil,
As per my understanding of the question, you would like to change the "options.MaxFunctionEvaluations" from 3000 to 10000.
You can accomplish this using the below code:
% Assuming you have an existing options structure
options = optimoptions('fmincon')
options =
fmincon options: Options used by current Algorithm ('interior-point'): (Other available algorithms: 'active-set', 'sqp', 'sqp-legacy', 'trust-region-reflective') Set properties: No options set. Default properties: Algorithm: 'interior-point' BarrierParamUpdate: 'monotone' ConstraintTolerance: 1.0000e-06 Display: 'final' EnableFeasibilityMode: 0 FiniteDifferenceStepSize: 'sqrt(eps)' FiniteDifferenceType: 'forward' HessianApproximation: 'bfgs' HessianFcn: [] HessianMultiplyFcn: [] HonorBounds: 1 MaxFunctionEvaluations: 3000 MaxIterations: 1000 ObjectiveLimit: -1.0000e+20 OptimalityTolerance: 1.0000e-06 OutputFcn: [] PlotFcn: [] ScaleProblem: 0 SpecifyConstraintGradient: 0 SpecifyObjectiveGradient: 0 StepTolerance: 1.0000e-10 SubproblemAlgorithm: 'factorization' TypicalX: 'ones(numberOfVariables,1)' UseParallel: 0 Options not used by current Algorithm ('interior-point') Default properties: FunctionTolerance: 1.0000e-06
% Set the 'MaxFunctionEvaluations' option to 10000
options.MaxFunctionEvaluations = 10000;
options
options =
fmincon options: Options used by current Algorithm ('interior-point'): (Other available algorithms: 'active-set', 'sqp', 'sqp-legacy', 'trust-region-reflective') Set properties: MaxFunctionEvaluations: 10000 Default properties: Algorithm: 'interior-point' BarrierParamUpdate: 'monotone' ConstraintTolerance: 1.0000e-06 Display: 'final' EnableFeasibilityMode: 0 FiniteDifferenceStepSize: 'sqrt(eps)' FiniteDifferenceType: 'forward' HessianApproximation: 'bfgs' HessianFcn: [] HessianMultiplyFcn: [] HonorBounds: 1 MaxIterations: 1000 ObjectiveLimit: -1.0000e+20 OptimalityTolerance: 1.0000e-06 OutputFcn: [] PlotFcn: [] ScaleProblem: 0 SpecifyConstraintGradient: 0 SpecifyObjectiveGradient: 0 StepTolerance: 1.0000e-10 SubproblemAlgorithm: 'factorization' TypicalX: 'ones(numberOfVariables,1)' UseParallel: 0 Options not used by current Algorithm ('interior-point') Default properties: FunctionTolerance: 1.0000e-06
Hope this works!

Torsten
Torsten am 17 Jan. 2024
Bearbeitet: Torsten am 17 Jan. 2024
clc
clear all
close all
warning off
%25wt.%
freq = [3.21760012464137 3.47500813461269 3.73241614458399 4.05417615704813 4.37593616951227 4.72987218322282 5.11598419817979 5.50209621313675 5.95256023058654 6.43520024928275 6.95001626922537 7.49700829041440 8.07617631284985 8.75187233902454 9.39539236395281 10.1676163938667 11.0041924262735 11.8407684586803 12.7738724948263 13.8678565372043 14.8974885770896 16.0880006232069 17.4072166743098 18.8229607291520 20.3674087889799 21.8796808475613 23.6493609161141 25.5477449896525 27.5426570669302 29.7949771541791 32.1760012464137 4.45924109299328 4.81598038043274 5.17271966787221 5.61864377717153 6.06456788647086 6.55508440670012 7.09019333785932 7.62530226901851 8.24959602203757 8.91848218598656 9.63196076086549 10.3900317466743 11.1926951434131 12.1291357729417 13.0209839915404 14.0912018538588 15.2506045380370 16.4100072222153 17.7031871391833 19.2193291108010 20.6462862605589 22.2962054649664 24.1244943130937 26.0865603940107 28.2269961186475 30.3228394323543 32.7754220335006 35.4063742783666 38.1711037560225 41.2925725211178 44.5924109299328 6.35302312594096 6.86126497601624 7.36950682609151 8.00480913868561 8.64011145127970 9.33894399513321 10.1013067702461 10.8636695453590 11.7530927829908 12.7060462518819 13.7225299520325 14.8025438834424 15.9460880461118 17.2802229025594 18.5508275277476 20.0755530779734 21.7273390907181 23.3791251034627 25.2215018099856 27.3815296728055 29.4144970731066 31.7651156297048 34.3698551113406 37.1651852867546 40.2146363872063 43.2005572563985 46.6947199756660 50.4430036199712 54.3818779580546 58.8289941462133 63.5302312594096 9.33854849802655 10.0856323778687 10.8327162577108 11.7665711075135 12.7004259573161 13.7276662920990 14.8482921118622 15.9689179316254 17.2763147213491 18.6770969960531 20.1712647557374 21.7588180004019 23.4397567300466 25.4008519146322 27.2685616142375 29.5098132537639 31.9378358632508 34.3658584727377 37.0740375371654 40.2491440264944 43.2374795458629 46.6927424901328 50.5215473743237 54.6305087134553 59.1130119925081 63.5021297865806 68.6383314604952 74.1480750743309 79.9379751431073 86.4749590917259 93.3854849802655 14.2246087642848 15.3625774654276 16.5005461665704 17.9230070429989 19.3454679194273 20.9101748834987 22.6171279352128 24.3240809869270 26.3155262139269 28.4492175285696 30.7251549308552 33.1433384207836 35.7037679983549 38.6909358388547 41.5358575917116 44.9497636951400 48.6481619738540 52.3465602525681 56.4716967942107 61.3080637740675 65.8599385786386 71.1230438214241 76.9551334147808 83.2139612710661 90.0417734779228 96.7273395971367 104.550874417493 112.943393588421 121.762651022278 131.719877157277 142.246087642848 22.5689147806216 24.3744279630713 26.1799411455210 28.4368326235832 30.6937241016453 33.1763047275137 35.8845745011883 38.5928442748629 41.7524923441499 45.1378295612431 48.7488559261426 52.5855714388482 56.6479760993601 61.3874482032906 65.9012311594149 71.3177707067641 77.1856885497257 83.0536063926873 89.5985916790675 97.2720227044789 104.494075434278 112.844573903108 122.097828963163 132.028151466636 142.861230561334 153.468620508227 165.881523637568 179.197183358135 193.189910522121 208.988150868556 225.689147806216 37.5314651371578 40.5339823481304 43.5364995591030 47.2896460728188 51.0427925865346 55.1712537516219 59.6750295680809 64.1788053845398 69.4332105037419 75.0629302743155 81.0679646962608 87.4483137695776 94.2039774942659 102.085585173069 109.591878200501 118.599429833419 128.357610769080 138.115791704741 148.999916594516 161.760614741150 173.770683585040 187.657325685789 203.045226392024 219.559071052373 237.574174318209 255.213962932673 275.856268758110 297.999833189033 321.269341574071 347.541367170081 375.314651371578 65.9144223994882 71.1875761914472 76.4607299834063 83.0521722233551 89.6436144633039 96.8942009272476 104.803931615186 112.713662303125 121.941681439053 131.828844798976 142.375152382894 153.580604190807 165.445200222715 179.287228926608 192.470113406506 208.289574782383 225.427324606249 242.565074430116 261.680256925968 284.091160541794 305.183775709630 329.572111997441 356.597025181231 385.599371037006 417.238293788760 448.218072316519 484.471004636238 523.360513851936 564.227455739619 610.367551419261 659.144223994882 123.394584773911 133.266151555824 143.137718337737 155.477176815128 167.816635292519 181.390039617649 196.197389790519 211.004739963388 228.279981831736 246.789169547823 266.532303111648 287.509382523213 309.720407782517 335.633270585039 360.312187539821 389.926887885560 422.009479926776 454.092071967993 489.876501552428 531.830660375557 571.316927503209 616.972923869556 667.564703626860 721.858320927381 781.087721618858 839.083176462596 906.950198088247 979.753003104856 1056.25764566468 1142.63385500642 1233.94584773911 249.081801127179 269.008345217354 288.934889307528 313.843069420246 338.751249532964 366.150247656954 396.040063792215 425.929879927477 460.801332085282 498.163602254359 538.016690434708 580.360596626328 625.195320829220 677.502499065928 727.318859291364 787.098491561887 851.859759854953 916.621028148020 988.854750474903 1073.54256285814 1153.24873921884 1245.40900563590 1347.53254409804 1457.12853659400 1576.68780113505 1693.75624766482 1830.75123828477 1977.70950094981 2132.14021764866 2306.49747843768 2490.81801127179 550.042592950819 594.046000386884 638.049407822950 693.053667118032 748.057926413113 808.562611637703 874.567722791802 940.572833945900 1017.57879695901 1100.08518590164 1188.09200077377 1281.59924157541 1380.60690830655 1496.11585282623 1606.12437141639 1738.13459372459 1881.14566789180 2024.15674205901 2183.66909401475 2370.68357561803 2546.69720536229 2750.21296475409 2975.73042786393 3217.74916876229 3481.76961337868 3740.28963206557 4042.81305818852 4367.33818802950 4708.36459565901 5093.39441072458 5500.42592950819 1353.48236219729 1461.76095117307 1570.03954014885 1705.38777636858 1840.73601258831 1989.61907243001 2152.03695589369 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lf = [0.0813203663249874 0.0829161241547314 0.0756621511274890 0.0844390630871363 0.0858648648648649 0.0830068072389175 0.0905037244331042 0.0821627716277163 0.0811676738707365 0.0809901231557127 0.0825699977698031 0.0825778351346991 0.0833072446317480 0.0809307263912817 0.0810627326843059 0.0789664461434853 0.0806887171804778 0.0762506882718477 0.0770021095398078 0.0783805415113124 0.0773940987437920 0.0759945715393563 0.0752230558167201 0.0833073172611821 0.0803478756772170 0.0764118843499915 0.0767312810252732 0.0752477315008163 0.0861751416756012 0.110655557991668 0.0641779830300365 0.0775835443819878 0.0763103448275862 0.0779068343267739 0.0741511877301607 0.0954281167758125 0.0779522625760424 0.0793627776770789 0.0784340080646779 0.0795655112100493 0.0783211213762345 0.0779685548307790 0.0791626345413252 0.0765824279641001 0.0769061200812144 0.0790046382370785 0.0752735399863959 0.0800289967137058 0.0773174441214408 0.0761919409412488 0.0750350523384231 0.0729586446668331 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0.0844240233774223 0.0767251439612787 0.0761964711492609 0.0763965844402277 0.0727394697556643 0.0776117434235321 0.0773805057402266 0.0769288291488288 0.0773382968822708 0.0753082071151814 0.0745145093406188 0.0775069496861135 0.0789375446044614 0.0827701831312871 0.0823609028057212 0.0760765550239235 0.0738675580449905 0.0873362683743269 0.108859287451105 0.0712709604995440 0.0725441304519908 0.0735743761053252 0.0734371945736737 0.0745646911845085 0.0775926178285670 0.0751002304816874 0.0785379767571839 0.0758360592649606 0.0767462795196415 0.0766401343793544 0.0770124781252378 0.0788785507191450 0.0769900803023146 0.0787360748436062 0.0790334976662230 0.0775221403933998 0.0782314317069995 0.0795949348341232 0.0800819157964651 0.0803039759168839 0.0793909594399459 0.0790381323524056 0.0807064330031566 0.0829064930367155 0.0846050534534319 0.0814588302813996 0.0802989932225819 0.0814849171379132 0.0970915220197963 0.113462236903547 0.0769464962203117 0.0752944612089945 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0.0844057201725131 0.108111179092737 0.100382886347709 0.0986451925070851 0.103339218677683 0.0942343640136509 0.112751539688803 0.122542033825450 0.0949588750331653 0.0842517912743370 0.0842660857908847 0.0886030925905126 0.0919501006936675 0.0952914756593233 0.0935352229711015 0.0867274197104432 0.0903598807106135 0.0939240460371056 0.0955121685434072 0.0867990340756641 0.111315789473684 0.0924378341526427 0.0980559448001845 0.0978868511254815 0.0998872266567990 0.100604838709677 0.102178048482522 0.101902891700264 0.105841077185663 0.102381319755182 0.104667795972144 0.112200335145857 0.112798643493006 0.113860157913265 0.105372585096596 0.110873944822764 0.110651182082124 0.124268776025553 0.137273178622335 0.105345608792056 0.0940439217127630 0.0955146856986000 0.0967746645979739 0.0948798120368697 0.0976672019052087 0.101159321302754 0.0984558612783033 0.103928476114225 0.104240339369742 0.104711075159146 0.108562148876405 0.108273393854749 0.111793172830084 0.110539406186849 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0.136740336037652 0.141773203263684 0.142413876563130 0.148363519278757 0.146380585688496 0.150297406614323 0.154043442069388 0.154606076734029 0.158060658767257 0.160489257014175 0.161429771633697 0.165161093761901 0.166087875585082 0.169187188057375 0.172387615361715 0.176018526713278 0.162559705525774 0.184039632153182 0.175665158110173 0.182901281192549 0.188516296370192 0.207246891651865 0.220513381861967 0.196585526135648 0.152787171728613 0.155664827055124 0.161433468969274 0.160442687747036 0.166024138093814 0.168721710629000 0.171137247609750 0.173574969975056 0.178239750717908 0.180951660488691 0.184788325994500 0.187152627736139 0.190987663440940 0.194529498805983 0.197483691941131 0.200556099809831 0.206041562522317 0.208654281830539 0.212536508649742 0.217108463880124 0.220825407327764 0.224502614941352 0.228444949843642 0.234822482033680 0.239375610786826 0.242421455133175 0.247609023338011 0.251908298353245 0.271188843635614 0.280369206404197 0.260834700650144 0.0940439217127630 0.0955146856986000 0.0967746645979739 0.0948798120368697 0.0976672019052087 0.101159321302754 0.0984558612783033 0.103928476114225 0.104240339369742 0.104711075159146 0.108562148876405 0.108273393854749 0.111793172830084 0.110539406186849 0.111468339204399 0.114715335954864 0.113358278765201 0.115386045568251 0.116290056827735 0.118573864206198 0.118582098241762 0.120387691697515 0.121334671514832 0.124648625626577 0.127040684115056 0.124566053592785 0.128712394705174 0.125448516691228 0.143081250502290 0.156767752053540 0.125017400046400 0.200900537031220 0.203092888688073 0.207970238267566 0.213058172143525 0.215114955611200 0.220177270930955 0.224447523477628 0.231996681415929 0.235981725136170 0.239479870103401 0.245073378082081 0.250186616902159 0.254258533560279 0.259998172061262 0.265145646110939 0.270654033761524 0.275293879973232 0.282457044457572 0.287573555717299 0.326917260486105 0.297982983280776 0.294397130266424 0.314828273355996 0.313021400072543 0.316549887411844 0.328378118676449 0.337538761208566 0.340782735516980 0.365435845925408 0.348328614292355 0.352622606598615 0.286298205082637 0.292537463668734 0.296142705058057 0.303276176935616 0.309824684686868 0.315101297954883 0.318921415375870 0.331229698375870 0.334131002751381 0.340232741032860 0.347505662546061 0.352246466980713 0.357738016927597 0.368435817481469 0.374087201605671 0.380805702150922 0.388194444444444 0.395360003269042 0.402658074909384 0.411471025260030 0.418812268021098 0.426336024605921 0.434715516425258 0.444980443285528 0.453576642335766 0.460709462501125 0.470049548752433 0.478629945964790 0.498492289135866 0.506957459159134 0.501416291444945 0.403464784663324 0.413694621051569 0.422310440651052 0.430199513381995 0.442824273799252 0.451436375623999 0.459811093619780 0.456362467866324 0.478715612718828 0.484229453556706 0.494534903862810 0.505510064824292 0.513446223488977 0.521862381540997 0.530001621271077 0.540019125029883 0.548405297390487 0.556704212312915 0.565751138088012 0.575688551436653 0.584204362465232 0.592854575515779 0.604083074314778 0.616119858500382 0.624238724991523 0.633536136925854 0.645193565262883 0.653932728792848 0.674337517433752 0.680741692674867 0.682720057720058 0.629864445072014 0.643539094650206 0.656698821007503 0.669802691754868 0.685059964276601 0.698657384385878 0.712665291762708 0.726557415843342 0.740196078431373 0.753536147283341 0.767104542966612 0.781058466130150 0.795474596502154 0.809367586937869 0.821952179474565 0.835643280443510 0.849528761780955 0.862949900524507 0.874917651192411 0.888732873797975 0.902163999668353 0.914614055531000 0.929578013080038 0.940381138897258 0.951863863280254 0.964085853934972 0.975826057181989 0.987624829965827 1.00318307504341 1.00693054058217 1.01735053455175 0.978635014836795 0.994113475177305 1.00823885881592 1.02135464430761 1.03449470766129 1.04707306005143 1.05837164639469 1.06887376410946 1.07891482039148 1.08820568419422 1.09557179066647 1.10325788177929 1.11123869012079 1.11780520052887 1.12314342013264 1.12825093899097 1.13413353046456 1.13800074878323 1.14086912745644 1.14501593865771 1.14679340433297 1.14813694267516 1.14853824345334 1.15085904628331 1.15073076492328 1.15158667008321 1.15180928715639 1.15060810306663 1.15303398494080 1.14859382677957 1.14500631417120 1.16559676039939 1.16312816517335 1.15901685131738 1.15366178428762 1.14910266224377 1.14576160026234 1.14021790620559 1.13606219986279 1.13073192239859 1.12594851428977 1.12003294214536 1.11489898989899 1.11072463768116 1.10684213809019 1.10092631833868 1.09521570471377 1.09022470628493 1.08534013982910 1.07878298330641 1.07368750652333 1.06778370144707 1.06134122287968 1.05619969336911 1.04920775056921 1.04179427130247 1.03647616539373 1.03099782246702 1.02342095427931 1.01902140920312 1.01105448843591 1.00370073633207];
ydata = [sm;lm;lf];
tdata = freq;
% scatter(freq,ydata);
fun = @(x)nlsqfun(x,tdata,ydata);
x0 = [1e-5,0.1,0.1,0.1,0,0,0,0,0.01];
% x0 = [7.1066e-08;0.5235;0.6678;0.0192;8.3181e+03;2.7365e+03;1.6327e+03;543.8365;0.1859];
% x0 = zeros(1,9);
A = [];
b = [];
Aeq = [];
beq = [];
lb = zeros(1,9);
ub = [0.01,1,1,1,inf,inf,inf,inf,1];
x = lsqnonlin(fun,x0,lb,ub,A,b,Aeq,beq)
Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance.
x = 1×9
0.0000 0.0022 0.4468 0.4948 55.2736 0.3729 17.7596 76.0509 0.0023
E = fun(x);
%[tdata,idx] = sort(tdata);
%plot(tdata,E(idx),'o')
plot(tdata,E,'o')
function E = nlsqfun(x,tdata,ydata)
E0 = 3.73;
Tr = x(1); al = x(2); bta = x(3); g = x(4); p = x(9); l1 = x(5); l2 = x(6); l3 = x(7); o = x(8);
ER = (E0 + ((l1*(((tdata).*Tr).^(g+p)).*(cos(0.5*pi*(g+p)) + l2*cos(0.5*pi*p)*(((tdata).*Tr).^(g))))./(1+ l2*(((tdata).*Tr).^(g)).*(2*cos(0.5*pi*g) + l2*(((tdata).*Tr).^(g))))) + ((E0*o*(((tdata).*Tr).^(al+bta)).*(cos(0.5*pi*(al+bta)) + l3*cos(0.5*pi*bta)*(((tdata).*Tr).^(al)) + (((tdata).*Tr).^(al+bta))))./(1 + (((tdata).*Tr).^(al)).*(2*l3*cos(0.5*pi*al) + 2*cos(0.5*pi*(al+bta)*(((tdata).*Tr).^(bta))) + (((tdata).*Tr).^(al)).*(l3^2 + 2*l3*cos(0.5*pi*bta)*(((tdata).*Tr).^(bta)) + (((tdata).*Tr).^(2*bta)))))));
EI = (((l1.*(((tdata).*Tr).^(g+p)).*(sin(0.5*pi*(g+p)) + l2*sin(0.5*pi*p)).*(((tdata).*Tr).^(g)))./(1 + l2*(((tdata).*Tr).^(g)).*(2*cos(0.5*pi*g) + l2*(((tdata).*Tr).^(g))))) + ((E0*o*(((tdata).*Tr).^(al+bta)).*(sin(0.5*pi*(al+bta)) + l3*sin(0.5*pi*bta)*(((tdata).*Tr).^(al))))./(1 + (((tdata).*Tr).^(al)).*(2*l3*cos(0.5*pi*al) + 2*cos(0.5*pi*(al+bta))*(((tdata).*Tr).^(bta)) + (((tdata).*Tr).^(al)).*(l3^2 + 2*l3*cos(0.5*pi*bta).*(((tdata).*Tr).^(bta)) + (((tdata).*Tr).^(2*bta)))))));
% gs = ((E0*o*(((tdata).*Tr).^(al+bta)).*(sin(0.5*pi*(al+bta)) + l3*sin(0.5*pi*bta)*(((tdata).*Tr).^(al))).*(1 + l2*(((tdata).*Tr).^(g)).*(2*cos(0.5*pi*g) + l2*(((tdata).*Tr).^(g)))) + l1*(((tdata).*Tr).^(g+p)).*(sin(0.5*pi*(g+p)) + l2*sin(0.5*pi*p)*(((tdata).*Tr).^(g))).*(1 + (((tdata).*Tr).^(al)).*(2*l3*cos(0.5*pi*al) + 2*cos(0.5*pi*(al+bta))*(((tdata).*Tr).^(bta))) + (((tdata).*Tr).^(2*al)).*(l3^2 + 2*l3*cos(0.5*pi*bta).*(((tdata).*Tr).^(bta)) + (((tdata).*Tr).^(2*bta)))))./(E0*(1 + l2*(((tdata).*Tr).^(g)).*(2*cos(0.5*pi*g) + l2*(((tdata).*Tr).^(g)))).*(1 + (1+o)*(((tdata).*Tr).^(2*al + 2*bta)) + l3*(((tdata).*Tr).^(al)).*(2*cos(0.5*pi*al) + l3*(((tdata).*Tr).^(al))) + (2+o)*(((tdata).*Tr).^(al+bta)).*(cos(0.5*pi*(al+bta)) + l3*cos(0.5*pi*bta)*(((tdata).*Tr).^(al)))) + l1*(((tdata).*Tr).^(g+p)).*(cos(0.5*pi*(g+p)) + l2*cos(0.5*pi*p)*(((tdata).*Tr).^(g))).*(1 + 2*l3*cos(0.5*pi*al)*(((tdata).*Tr).^(al)) + 2*cos(0.5*pi*(al+bta))*(((tdata).*Tr).^(al+bta)) + (((tdata).*Tr).^(2*al)).*(l3^2 + 2*l3*cos(0.5*pi*bta)*(((tdata).*Tr).^(bta)) + (((tdata).*Tr).^(2*bta))))));
gs = EI./ER;
sm_exp = ydata(1,:);
lm_exp = ydata(2,:);
lf_exp = ydata(3,:);
E = gs.*sm_exp - lm_exp;
%E = sum((gs.*sm_exp - lm_exp).^2);
%ya = EI./ER;
%clf;
%loglog(sm_exp,lf_exp,'*');
%hold on;
%loglog(sm_exp,ya,"r");
%drawnow;
end
  7 Kommentare
Torsten
Torsten am 17 Jan. 2024
You can do that by yourself. Use MATLAB online if your MATLAB supplies a different or no solution.
Torsten
Torsten am 17 Jan. 2024
I added the error plot in the code above.

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