How to fit experimental data of three variables with 3 mathematical equations with 10 parameters(Have some constrains)??

I have expermental data for three variables and also have mathematical model with 10 parameters. I need to find out these parameters by curve fitting with some constraints. I tried all the functions like lsqcurvefit, lsqnonlin, fmincon etc. The problem is I am not able to get good fitting. Someone please help me to solve this.

[Anil Kumar Mekala]

tdata = [0.321760012464138 0.360371213959834 0.405417615704813 0.453681617574434 0.511598419817978 0.569515222061523 0.643520024928275 0.717524827795027 0.810835231409626 0.907363235148867 1.01997923951132 1.14224804424769 1.27738724948263 1.43504965559005 1.60880006232069 1.80829127004845 2.03674087889799 2.28127848837073 2.55477449896525 2.87331691130475 3.21760012464137 3.60371213959834 4.05417615704813 4.53681617574434 5.11598419817979 5.69515222061523 6.43520024928275 7.20742427919668 8.07617631284985 9.07363235148868 10.1676163938667 11.4224804424769 12.7738724948263 14.3504965559005 16.0880006232069 18.0829127004845 20.3674087889799 22.8127848837073 25.5477449896525 28.7331691130475 32.1760012464137 0.445924109299328 0.499435002415248 0.561864377717153 0.628752994112053 0.709019333785932 0.789285673459811 0.891848218598656 0.994410763737502 1.12372875543431 1.25750598822411 1.41357942647887 1.58303058801261 1.77031871391833 1.98882152747500 2.22962054649664 2.50609349426222 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3.70250000000000 3.73750000000000 3.76100000000000 3.78570000000000 3.83270000000000 3.84920000000000 3.88300000000000 3.91680000000000 3.95800000000000 3.98950000000000 4.01840000000000 4.05940000000000 4.09640000000000 4.13690000000000 4.17870000000000 4.20710000000000 4.27470000000000 4.30060000000000 4.31530000000000 4.39970000000000 4.52340000000000 3.34350000000000 3.36330000000000 3.38790000000000 3.43000000000000 3.43240000000000 3.45380000000000 3.46750000000000 3.49170000000000 3.50560000000000 3.53720000000000 3.55570000000000 3.58320000000000 3.61510000000000 3.63760000000000 3.65520000000000 3.68400000000000 3.71680000000000 3.74540000000000 3.77290000000000 3.80470000000000 3.83710000000000 3.86170000000000 3.90790000000000 3.93730000000000 3.97020000000000 4.00720000000000 4.04660000000000 4.08430000000000 4.12760000000000 4.16160000000000 4.24790000000000 4.25190000000000 4.29010000000000 4.34600000000000 4.37400000000000 4.46120000000000 4.52830000000000 4.53830000000000 4.56190000000000 4.65700000000000 4.78160000000000 3.45870000000000 3.45020000000000 3.52420000000000 3.52470000000000 3.55290000000000 3.56290000000000 3.57980000000000 3.60570000000000 3.64000000000000 3.66580000000000 3.69520000000000 3.72600000000000 3.74880000000000 3.77730000000000 3.80900000000000 3.84580000000000 3.88740000000000 3.91920000000000 3.95140000000000 3.98190000000000 4.01380000000000 4.07570000000000 4.09760000000000 4.13640000000000 4.18690000000000 4.23360000000000 4.27500000000000 4.32350000000000 4.37150000000000 4.41140000000000 4.46840000000000 4.52430000000000 4.57610000000000 4.63950000000000 4.68250000000000 4.76490000000000 4.82830000000000 4.87760000000000 4.90720000000000 5.03730000000000 5.14910000000000 3.57440000000000 3.60850000000000 3.63670000000000 3.67130000000000 3.69220000000000 3.74510000000000 3.78710000000000 3.78990000000000 3.84100000000000 3.86650000000000 3.91820000000000 3.94630000000000 3.97680000000000 4.01510000000000 4.05240000000000 4.08950000000000 4.12990000000000 4.16720000000000 4.21410000000000 4.25690000000000 4.30710000000000 4.36310000000000 4.39740000000000 4.45960000000000 4.51110000000000 4.57170000000000 4.62230000000000 4.68300000000000 4.75100000000000 4.80740000000000 4.87550000000000 4.94160000000000 5.01000000000000 5.09230000000000 5.16290000000000 5.22730000000000 5.33650000000000 5.40160000000000 5.46500000000000 5.59260000000000 5.76300000000000 3.27850000000000 3.32930000000000 3.30810000000000 3.34260000000000 3.35820000000000 3.37440000000000 3.38850000000000 3.42520000000000 3.42850000000000 3.45450000000000 3.47110000000000 3.48600000000000 3.51340000000000 3.53270000000000 3.56120000000000 3.57200000000000 3.59610000000000 3.62130000000000 3.64960000000000 3.67240000000000 3.70250000000000 3.73750000000000 3.76100000000000 3.78570000000000 3.83270000000000 3.84920000000000 3.88300000000000 3.91680000000000 3.95800000000000 3.98950000000000 4.01840000000000 4.05940000000000 4.09640000000000 4.13690000000000 4.17870000000000 4.20710000000000 4.27470000000000 4.30060000000000 4.31530000000000 4.39970000000000 4.52340000000000 3.81030000000000 3.81810000000000 3.85470000000000 3.91930000000000 3.94680000000000 3.99910000000000 4.03210000000000 4.06950000000000 4.11310000000000 4.15630000000000 4.20500000000000 4.24870000000000 4.30250000000000 4.34140000000000 4.40460000000000 4.44280000000000 4.50700000000000 4.56090000000000 4.61800000000000 4.68230000000000 4.74160000000000 4.79970000000000 4.87720000000000 4.94760000000000 5.02490000000000 5.09710000000000 5.17060000000000 5.25120000000000 5.33580000000000 5.42600000000000 5.51640000000000 5.61220000000000 5.70870000000000 5.81890000000000 5.92360000000000 6.02670000000000 6.17650000000000 6.28310000000000 6.38380000000000 6.55390000000000 6.77090000000000 4.13930000000000 4.22380000000000 4.26890000000000 4.30320000000000 4.34800000000000 4.40440000000000 4.46430000000000 4.52700000000000 4.58040000000000 4.63130000000000 4.70770000000000 4.75730000000000 4.83440000000000 4.89050000000000 4.96380000000000 5.04440000000000 5.12280000000000 5.20630000000000 5.29020000000000 5.38050000000000 5.47130000000000 5.57040000000000 5.66430000000000 5.75500000000000 5.88080000000000 5.99540000000000 6.12020000000000 6.24670000000000 6.38250000000000 6.52040000000000 6.66160000000000 6.80880000000000 6.95940000000000 7.12500000000000 7.30480000000000 7.48070000000000 7.70170000000000 7.87220000000000 8.05450000000000 8.30650000000000 8.61660000000000 4.71770000000000 4.78850000000000 4.87690000000000 4.94110000000000 5.02810000000000 5.12600000000000 5.21690000000000 5.32630000000000 5.41220000000000 5.50440000000000 5.59860000000000 5.72100000000000 5.82010000000000 5.94600000000000 6.05270000000000 6.17950000000000 6.31550000000000 6.45070000000000 6.58920000000000 6.74310000000000 6.89740000000000 7.05820000000000 7.24380000000000 7.40920000000000 7.60980000000000 7.79260000000000 8.01390000000000 8.22700000000000 8.45740000000000 8.69760000000000 8.95600000000000 9.21730000000000 9.49310000000000 9.88790000000000 10.0950000000000 10.4130000000000 10.8140000000000 11.1510000000000 11.5020000000000 11.9830000000000 12.4770000000000 5.99980000000000 6.13610000000000 6.29220000000000 6.41000000000000 6.55980000000000 6.68940000000000 6.85620000000000 7.00200000000000 7.18760000000000 7.35240000000000 7.54790000000000 7.74330000000000 7.95110000000000 8.16810000000000 8.40520000000000 8.63620000000000 8.90250000000000 9.16420000000000 9.44770000000000 9.74600000000000 10.0640000000000 10.3990000000000 10.7450000000000 11.1190000000000 11.5330000000000 11.9390000000000 12.4000000000000 12.8710000000000 13.3840000000000 13.9300000000000 14.4990000000000 15.0950000000000 15.7630000000000 16.4680000000000 17.2050000000000 18.0150000000000 18.9390000000000 19.8210000000000 20.7810000000000 21.9440000000000 23.1490000000000 8.88430000000000 9.25360000000000 9.53410000000000 9.82920000000000 10.1650000000000 10.5160000000000 10.9070000000000 11.2970000000000 11.7160000000000 12.1650000000000 12.6620000000000 13.1330000000000 13.6610000000000 14.2580000000000 14.8610000000000 15.5270000000000 16.2760000000000 17.0100000000000 17.7990000000000 18.6890000000000 19.6040000000000 20.6270000000000 21.6900000000000 22.8760000000000 24.1820000000000 25.5060000000000 27.0850000000000 28.6950000000000 30.3900000000000 32.3290000000000 34.3810000000000 36.5220000000000 38.8380000000000 41.5400000000000 44.3490000000000 47.4360000000000 50.8820000000000 54.2710000000000 57.9380000000000 62.2090000000000 66.7320000000000 19.9750000000000 21.2390000000000 22.4700000000000 23.7690000000000 25.3350000000000 26.8160000000000 28.6480000000000 30.2860000000000 32.3850000000000 34.5140000000000 37.0150000000000 39.3290000000000 41.8650000000000 44.8490000000000 48.0100000000000 51.5860000000000 55.7190000000000 59.8740000000000 64.2660000000000 69.2690000000000 74.5470000000000 80.1870000000000 86.2140000000000 92.5360000000000 99.8470000000000 107.150000000000 115.390000000000 123.780000000000 132.560000000000 142.690000000000 152.850000000000 163.280000000000 174.610000000000 187.510000000000 199.430000000000 212.690000000000 227.060000000000 241.200000000000 255.940000000000 272.470000000000 288.980000000000];

EI = [0.189610000000000 0.194000000000000 0.198300000000000 0.195680000000000 0.204100000000000 0.205470000000000 0.208420000000000 0.214890000000000 0.215720000000000 0.227350000000000 0.225450000000000 0.229630000000000 0.233730000000000 0.230290000000000 0.236300000000000 0.248440000000000 0.250890000000000 0.245770000000000 0.255020000000000 0.257260000000000 0.263270000000000 0.269290000000000 0.267240000000000 0.271630000000000 0.271350000000000 0.276140000000000 0.272440000000000 0.270680000000000 0.288850000000000 0.280520000000000 0.279320000000000 0.282180000000000 0.282200000000000 0.290980000000000 0.282970000000000 0.244180000000000 0.289510000000000 0.273220000000000 0.268060000000000 0.440370000000000 0.245710000000000 0.209060000000000 0.207650000000000 0.211340000000000 0.211650000000000 0.215390000000000 0.219490000000000 0.222630000000000 0.224080000000000 0.226050000000000 0.225680000000000 0.235380000000000 0.233710000000000 0.240230000000000 0.243720000000000 0.242390000000000 0.247710000000000 0.254140000000000 0.251380000000000 0.252190000000000 0.256240000000000 0.260600000000000 0.265140000000000 0.266260000000000 0.262870000000000 0.268290000000000 0.268140000000000 0.278720000000000 0.283820000000000 0.270750000000000 0.280640000000000 0.286930000000000 0.276530000000000 0.279750000000000 0.277500000000000 0.277360000000000 0.293180000000000 0.293510000000000 0.282560000000000 0.269250000000000 0.431930000000000 0.243300000000000 0.213740000000000 0.210040000000000 0.214960000000000 0.215440000000000 0.218920000000000 0.222970000000000 0.226470000000000 0.220180000000000 0.225940000000000 0.228220000000000 0.245300000000000 0.235040000000000 0.239780000000000 0.208770000000000 0.252530000000000 0.204290000000000 0.247320000000000 0.246460000000000 0.257140000000000 0.254360000000000 0.249710000000000 0.267670000000000 0.266220000000000 0.269540000000000 0.270720000000000 0.272860000000000 0.284300000000000 0.288820000000000 0.276020000000000 0.283390000000000 0.286430000000000 0.288940000000000 0.285320000000000 0.286380000000000 0.287120000000000 0.291930000000000 0.307910000000000 0.289620000000000 0.281780000000000 0.459270000000000 0.253110000000000 0.214360000000000 0.222300000000000 0.218800000000000 0.220090000000000 0.220390000000000 0.221930000000000 0.222080000000000 0.221160000000000 0.227200000000000 0.227800000000000 0.223570000000000 0.243620000000000 0.250360000000000 0.247230000000000 0.243870000000000 0.237030000000000 0.254270000000000 0.242030000000000 0.233960000000000 0.245090000000000 0.278170000000000 0.260370000000000 0.262280000000000 0.272430000000000 0.276070000000000 0.276170000000000 0.284230000000000 0.289760000000000 0.286330000000000 0.291670000000000 0.292450000000000 0.292610000000000 0.295400000000000 0.302070000000000 0.304010000000000 0.306290000000000 0.319330000000000 0.309280000000000 0.303350000000000 0.487360000000000 0.282100000000000 0.214490000000000 0.212000000000000 0.217930000000000 0.214300000000000 0.216510000000000 0.218570000000000 0.220440000000000 0.224400000000000 0.225540000000000 0.234290000000000 0.229120000000000 0.230970000000000 0.235120000000000 0.238630000000000 0.220880000000000 0.246320000000000 0.245900000000000 0.253820000000000 0.256090000000000 0.264720000000000 0.272230000000000 0.272970000000000 0.276500000000000 0.280540000000000 0.287320000000000 0.294990000000000 0.287130000000000 0.293920000000000 0.308830000000000 0.310760000000000 0.310760000000000 0.321270000000000 0.321350000000000 0.326420000000000 0.323480000000000 0.335790000000000 0.357390000000000 0.342500000000000 0.336390000000000 0.514560000000000 0.316360000000000 0.209060000000000 0.208350000000000 0.210170000000000 0.211700000000000 0.217830000000000 0.220900000000000 0.222340000000000 0.224590000000000 0.223350000000000 0.224980000000000 0.228990000000000 0.239950000000000 0.241480000000000 0.246470000000000 0.246090000000000 0.245200000000000 0.253490000000000 0.266610000000000 0.288030000000000 0.262090000000000 0.288440000000000 0.287250000000000 0.293680000000000 0.297500000000000 0.303130000000000 0.312910000000000 0.314540000000000 0.323340000000000 0.331880000000000 0.339150000000000 0.344280000000000 0.343300000000000 0.355530000000000 0.359170000000000 0.364760000000000 0.371150000000000 0.393090000000000 0.387500000000000 0.374850000000000 0.503150000000000 0.339660000000000 0.206950000000000 0.211570000000000 0.212590000000000 0.210940000000000 0.224830000000000 0.226430000000000 0.226560000000000 0.227110000000000 0.235060000000000 0.237760000000000 0.234850000000000 0.246520000000000 0.246450000000000 0.259590000000000 0.273830000000000 0.275530000000000 0.270780000000000 0.284270000000000 0.293140000000000 0.294410000000000 0.301960000000000 0.308220000000000 0.323380000000000 0.328880000000000 0.338440000000000 0.344130000000000 0.356510000000000 0.368510000000000 0.368770000000000 0.378580000000000 0.391360000000000 0.389250000000000 0.398220000000000 0.409910000000000 0.413030000000000 0.418810000000000 0.442630000000000 0.431550000000000 0.434390000000000 0.630770000000000 0.424160000000000 0.222120000000000 0.224230000000000 0.229340000000000 0.232250000000000 0.234750000000000 0.236940000000000 0.241270000000000 0.248860000000000 0.250870000000000 0.256170000000000 0.262810000000000 0.272820000000000 0.280380000000000 0.285780000000000 0.292660000000000 0.298250000000000 0.294380000000000 0.315370000000000 0.317470000000000 0.334740000000000 0.339010000000000 0.367940000000000 0.361180000000000 0.372980000000000 0.384420000000000 0.386580000000000 0.420920000000000 0.418390000000000 0.415580000000000 0.432460000000000 0.449360000000000 0.450280000000000 0.458170000000000 0.445440000000000 0.472910000000000 0.470260000000000 0.474390000000000 0.514890000000000 0.499380000000000 0.706440000000000 0.507650000000000 0.234780000000000 0.239950000000000 0.247540000000000 0.250960000000000 0.257340000000000 0.262690000000000 0.271420000000000 0.270480000000000 0.285710000000000 0.289230000000000 0.298410000000000 0.311120000000000 0.312740000000000 0.321320000000000 0.324280000000000 0.350500000000000 0.368550000000000 0.387760000000000 0.382630000000000 0.371410000000000 0.397550000000000 0.417420000000000 0.421830000000000 0.431230000000000 0.440030000000000 0.455760000000000 0.465850000000000 0.479710000000000 0.498430000000000 0.503120000000000 0.517150000000000 0.521850000000000 0.536770000000000 0.551530000000000 0.561880000000000 0.575550000000000 0.604600000000000 0.608380000000000 0.600140000000000 0.797040000000000 0.605120000000000 0.267920000000000 0.273880000000000 0.275240000000000 0.283130000000000 0.297460000000000 0.303980000000000 0.315000000000000 0.322940000000000 0.335250000000000 0.341080000000000 0.352830000000000 0.359560000000000 0.362360000000000 0.373600000000000 0.396540000000000 0.411940000000000 0.409870000000000 0.423740000000000 0.438310000000000 0.460380000000000 0.474540000000000 0.476810000000000 0.499330000000000 0.511480000000000 0.525000000000000 0.539220000000000 0.554710000000000 0.568130000000000 0.589070000000000 0.601750000000000 0.601500000000000 0.628310000000000 0.648390000000000 0.661430000000000 0.662750000000000 0.719050000000000 0.734360000000000 0.744030000000000 0.745770000000000 0.956120000000000 0.764040000000000 0.315920000000000 0.327700000000000 0.334370000000000 0.345800000000000 0.354230000000000 0.366110000000000 0.379400000000000 0.390260000000000 0.397780000000000 0.410180000000000 0.421730000000000 0.431740000000000 0.449890000000000 0.468410000000000 0.478930000000000 0.487610000000000 0.490100000000000 0.494100000000000 0.567310000000000 0.533990000000000 0.555870000000000 0.602680000000000 0.604460000000000 0.623070000000000 0.644470000000000 0.658540000000000 0.686940000000000 0.714880000000000 0.729940000000000 0.750470000000000 0.776390000000000 0.793490000000000 0.819750000000000 0.846040000000000 0.906580000000000 0.925980000000000 0.953100000000000 0.978350000000000 0.987600000000000 1.19830000000000 1.04430000000000 0.393330000000000 0.404100000000000 0.418440000000000 0.428310000000000 0.443780000000000 0.452810000000000 0.463570000000000 0.483970000000000 0.493190000000000 0.509780000000000 0.517860000000000 0.535730000000000 0.555290000000000 0.571510000000000 0.590580000000000 0.614080000000000 0.634580000000000 0.676570000000000 0.674560000000000 0.696320000000000 0.730540000000000 0.761450000000000 0.776850000000000 0.807320000000000 0.838780000000000 0.863020000000000 0.908630000000000 0.929160000000000 0.972570000000000 1.00170000000000 1.03720000000000 1.07440000000000 1.11330000000000 1.15420000000000 1.20550000000000 1.25090000000000 1.32080000000000 1.36970000000000 1.39540000000000 1.64870000000000 1.50590000000000 0.234780000000000 0.239950000000000 0.247540000000000 0.250960000000000 0.257340000000000 0.262690000000000 0.271420000000000 0.270480000000000 0.285710000000000 0.289230000000000 0.298410000000000 0.311120000000000 0.312740000000000 0.321320000000000 0.324280000000000 0.350500000000000 0.368550000000000 0.387760000000000 0.382630000000000 0.371410000000000 0.397550000000000 0.417420000000000 0.421830000000000 0.431230000000000 0.440030000000000 0.455760000000000 0.465850000000000 0.479710000000000 0.498430000000000 0.503120000000000 0.517150000000000 0.521850000000000 0.536770000000000 0.551530000000000 0.561880000000000 0.575550000000000 0.604600000000000 0.608380000000000 0.600140000000000 0.797040000000000 0.605120000000000 0.501560000000000 0.519350000000000 0.538690000000000 0.552860000000000 0.571650000000000 0.586870000000000 0.609830000000000 0.630050000000000 0.651910000000000 0.674570000000000 0.698120000000000 0.723360000000000 0.741370000000000 0.782150000000000 0.794470000000000 0.845490000000000 0.866650000000000 0.901940000000000 0.937540000000000 0.997880000000000 1.01430000000000 1.04720000000000 1.10060000000000 1.14310000000000 1.18860000000000 1.23210000000000 1.29250000000000 1.35150000000000 1.40910000000000 1.47040000000000 1.53630000000000 1.60080000000000 1.67180000000000 1.75200000000000 1.82530000000000 1.91560000000000 2.02670000000000 2.11270000000000 2.20110000000000 2.49750000000000 2.40550000000000 0.689860000000000 0.722090000000000 0.745920000000000 0.776520000000000 0.810450000000000 0.838840000000000 0.872290000000000 0.901720000000000 0.939700000000000 0.979940000000000 1.01480000000000 1.06040000000000 1.09550000000000 1.15710000000000 1.20480000000000 1.25120000000000 1.31720000000000 1.36450000000000 1.42500000000000 1.49830000000000 1.57260000000000 1.64260000000000 1.71530000000000 1.79710000000000 1.89260000000000 1.98150000000000 2.08720000000000 2.19320000000000 2.30230000000000 2.41740000000000 2.53860000000000 2.66270000000000 2.80460000000000 2.96360000000000 3.11480000000000 3.29320000000000 3.49140000000000 3.67770000000000 3.86240000000000 4.27430000000000 4.30520000000000 1.07080000000000 1.12130000000000 1.17340000000000 1.23070000000000 1.28840000000000 1.34870000000000 1.42240000000000 1.48370000000000 1.56240000000000 1.64170000000000 1.73490000000000 1.80530000000000 1.89830000000000 1.98660000000000 2.10170000000000 2.20850000000000 2.32230000000000 2.45100000000000 2.55910000000000 2.72110000000000 2.86490000000000 3.00850000000000 3.18570000000000 3.35190000000000 3.54650000000000 3.74080000000000 3.95790000000000 4.19420000000000 4.44010000000000 4.70260000000000 4.97780000000000 5.27840000000000 5.60060000000000 5.94170000000000 6.33630000000000 6.69980000000000 7.19630000000000 7.63460000000000 8.12740000000000 8.88130000000000 9.26890000000000 2.10180000000000 2.21960000000000 2.33840000000000 2.45590000000000 2.58980000000000 2.72040000000000 2.87070000000000 3.02360000000000 3.19140000000000 3.37210000000000 3.57450000000000 3.77540000000000 3.98590000000000 4.23870000000000 4.47820000000000 4.75670000000000 5.07210000000000 5.38980000000000 5.71890000000000 6.09100000000000 6.47470000000000 6.90420000000000 7.35330000000000 7.84950000000000 8.39330000000000 8.95620000000000 9.59180000000000 10.2520000000000 10.9870000000000 11.7710000000000 12.5750000000000 13.4760000000000 14.4640000000000 15.5200000000000 16.6470000000000 17.8500000000000 19.2550000000000 20.6680000000000 22.1730000000000 24.0950000000000 25.6750000000000 5.27680000000000 5.66670000000000 6.04000000000000 6.43370000000000 6.88980000000000 7.34980000000000 7.88640000000000 8.42120000000000 9.04170000000000 9.66280000000000 10.3750000000000 11.0880000000000 11.8620000000000 12.7670000000000 13.7070000000000 14.7130000000000 15.8320000000000 17.0110000000000 18.2570000000000 19.6690000000000 21.1500000000000 22.7710000000000 24.4450000000000 26.3170000000000 28.3660000000000 30.4310000000000 32.8370000000000 35.3650000000000 37.9820000000000 40.9110000000000 43.9670000000000 47.1680000000000 50.5280000000000 54.3800000000000 58.3830000000000 62.7340000000000 67.3980000000000 72.0530000000000 76.9100000000000 82.6860000000000 88.1110000000000 22.8750000000000 25.0400000000000 26.9660000000000 29.1240000000000 31.5720000000000 33.9470000000000 36.8390000000000 39.6250000000000 42.7050000000000 45.8710000000000 49.5040000000000 53.0470000000000 56.8290000000000 61.1740000000000 65.6780000000000 70.6770000000000 76.1360000000000 81.5340000000000 87.3020000000000 93.6960000000000 100.110000000000 106.990000000000 114.180000000000 121.630000000000 130.050000000000 138.150000000000 147.200000000000 156.350000000000 165.630000000000 175.930000000000 186 196.250000000000 207.100000000000 218.780000000000 229.650000000000 241.240000000000 253.430000000000 265.070000000000 276.790000000000 289.670000000000 301.690000000000];

eta = EI./ER;

E0 = 2.4;

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)))))));

eta = EI./ER;

constraints

lb = zeros(1,9);

ub = [0.01,1,1,1,inf,inf,inf,inf,1];

I have commented expermental data and equations someone please help me to solve this.

[Torsten]

Question has been discussed and answered here:

https://uk.mathworks.com/matlabcentral/answers/2070906-how-to-overcome-this-error-while-using-lsqnonlin-for-curvefitting?s_tid=prof_contriblnk

If you think the fit is bad, you can try changing your initial values for the parameters (maybe using "MultiStart") or make modifications to your model equation.

[Anil Kumar Mekala]

That answer is not serving the purpose. The parameters which we are getting there are not giving good curve fitting.

[Anil Kumar Mekala]

Model equations cannot be modified we have to use same equations.

[Torsten]

Then try different initial guesses for the parameters (maybe using "MultiStart") and see whether the solution parameters obtained give a better fit.

And for other forum members new to your question, you should at least tell which expressions you want to make almost equal.

[Anil Kumar Mekala]

What is this multistart and how to use it??

[Torsten]

All about the use of MultiStart can be found here:

https://uk.mathworks.com/help/gads/multistart.html

[Alex Sha]

How about the results below, seems to be good。

Sum Squared Error (SSE): 9538.72364923211
Root of Mean Square Error (RMSE): 2.84559106282007
Correlation Coef. (R): 0.998221682965744
R-Square: 0.996446528342961

Parameter	Best Estimate       
---------	-------------       
tr       	4.77923071824372E-7 
al       	1.97874148072177E-17
bta      	2.06284292411603E-17
g        	0.456257338085623   
p        	0.360589263851422   
l1       	133.444032158547    
l2       	2.2906607897617     
l3       	3.20014893227197E-24
o        	1 

[Anil Kumar Mekala]

Please try to fit them in log scale then only we will come to know how the fitting is.

[Anil Kumar Mekala]

And the values of al,bta,g, and p should be inbetween 0 to 1 can't be negligible values

[Star Strider]

‘Please try to fit them in log scale then only we will come to know how the fitting is.’

Not true. Transformations distort the data and errors. So keep them linear.

[Torsten]

@Alex Sha

Did you fit Ei against Einum together with Er against Ernum or Ei/Er against Einum/Ernum ?

[dpb]

"... the values of al,bta,g, and p should be inbetween 0 to 1 can't be negligible values"

If you constrain the model, then the magnitude of the parameters will be controlled by the data you provide. If you have no data which shows a significant variation of the response to a given variable, then the estimate for that variable will, inevitably, be near zero.

The form given also confounds variables by combining multiple coefficients in terms which makes estimation uniquely very difficult.

[Alex Sha]

@Torsten ER vs. tdata and EI vs. tdata simultaneously

[Alex Sha]

@Anil Kumar Mekala the values of al,bta,g, and p I given are all in the range of [0, 1].

If allow negative values, the result will be much better, even in log scale

Sum Squared Error (SSE): 69.3854274976025
Root of Mean Square Error (RMSE): 0.211033016869369
Correlation Coef. (R): 0.999978240096715
R-Square: 0.999956480666923

Parameter	Best Estimate      
---------	-------------      
tr       	9.96659032322083E-7
al       	0.0846648203798804 
bta      	0.237167900797157  
g        	-0.491630134017753 
p        	0.789887749532826  
l1       	156.797966147271   
l2       	14.9268893939603   
l3       	-4.61141192504551  
o        	-11.1885890017952

In normal scale:

In Log scale: