curve fitting of a complex equation

omega=[0 500	1000	1500	2000	2500	3000	3500	4000	4500	5000	5500	6000	6500	7000	7500	8000	8500	9000	9500	10000	10500	11000	11500	12000	12500	13000	13500	14000	14500	15000];
ydata1=[0	2.773974956	9.859008802	19.20487131	29.60850853	40.54661158	51.7216818	62.90316231	73.8967491	84.55521774	94.77825113	104.5075664	113.7172145	122.4051971	130.5842098	138.2785508	145.5166646	152.3241086	158.7410015	164.7940864	170.5138742	175.9234703	181.0507873	185.9164421	190.5396332	194.9419395	199.1392141	203.1447385	206.9756021	210.6403678	214.1499578];
ydata2=[0	23.23166979	43.89101766	61.37336819	76.13374067	88.63427978	99.17236163	107.96827	115.2289659	121.1585778	125.9542122	129.7976768	132.8504967	135.2544369	137.1234954	138.5545735	139.6310041	140.4137722	140.960863	141.3115956	141.5020398	141.5603911	141.5098635	141.3688178	141.150192	140.8714973	140.5392011	140.1625248	139.7464364	139.3025573	138.8344027];

I want to curve fit the above equation to this data

ydata1 is for real part, and ydata2 is for imaginary part, my doubt is whether i should separate real and imaginary part, and solve it separately. Or should i try to solve it together, i have tried both the ways and i am not getting the proper answer.

ANSWER FOR K1 IS 204419 AND K2 IS 160380, C1 =102.884 AND C2=326.123

any hints in this regard would be appreciated

[Supreeth D K]

q is 0.01

[Alex Sha]

@Supreeth D K，does your fitting function look like below? where k1, k2, c1, c2, w1, w2 are parameters needed to be estimated, q is a constant of 0.01

if the above is corrected, the best result will then be:

Sum Squared Error (SSE): 46.424449856966
Root of Mean Square Error (RMSE): 0.865321587218246
Correlation Coef. (R): 0.999869229000882
R-Square: 0.999738475102819

Parameter	Best Estimate    
---------	-------------    
k1       	181.203558111029 
k2       	13247.6132403486 
c1       	-1.42262791216218
c2       	-2.96730197634771
w1       	-14713.9170455795
w2       	-4222.15402974947

[Supreeth D K]

the fit is proper, but the solution is K1 =204419 AND K2 IS 160380, C1 =102.884 AND C2=326.123, Did you solve both real and imaginary part at same time or separately.

[Alex Sha]

Yes, simultaneously.

If you think "K1 =204419 AND K2 IS 160380, C1 =102.884 AND C2=326.123" being right answers, how about another two parameters w1 and w2?

[Supreeth D K]

I dnt the value of w1 and w2. Just that w1=k1/c1 w2=k2/c2. also unit of k is N/m and c is Ns/m.

[Alex Sha]

if w1=k1/c1 w2=k2/c2, then:

Sum Squared Error (SSE): 318.329366755648
Root of Mean Square Error (RMSE): 2.26590922701928
Correlation Coef. (R): 0.999027013165415
R-Square: 0.998054973034211

Parameter	Best Estimate     
---------	-------------     
k1       	1761183.84910946  
k2       	20644.014228873   
c1       	-0.505604385784565
c2       	-3.67185412002803 

"K1 =204419 AND K2 IS 160380, C1 =102.884 AND C2=326.123" are complete far away from right solution.

[Supreeth D K]

is it possible to share the code?? so that i can once go through it.

[Alex Sha]

Hi, @Supreeth D K, the result provided above was obtaind by using a package other than Matlab, the code likes below, very simple. It is easy to make a judgement of goodness by taking the results back to Matlab.

ConstStr w1=k1/c1, w2=k2/c2;
ComplexStr = j;
Parameter k(2),c(2);
Variable omega,y[realPart],y[imagPart];
Function y=(k1/(1+(w1/omega)^2))+(k2/(1+(w2/omega)^2))*q-j*((c1*omega/(1+(omega/w1)^2)+(c2*omega/(1+(omega/w2)^2))))*q;
Data;
omega=[0,500,1000,1500,2000,2500,3000,3500,4000,4500,5000,5500,6000,6500,7000,7500,8000,8500,9000,9500,10000,10500,11000,11500,12000,12500,13000,13500,14000,14500,15000];
y_real=[0,2.773974956,9.859008802,19.20487131,29.60850853,40.54661158,51.7216818,62.90316231,73.8967491,84.55521774,94.77825113,104.5075664,113.7172145,122.4051971,130.5842098,138.2785508,145.5166646,152.3241086,158.7410015,164.7940864,170.5138742,175.9234703,181.0507873,185.9164421,190.5396332,194.9419395,199.1392141,203.1447385,206.9756021,210.6403678,214.1499578];
y_image=[0,23.23166979,43.89101766,61.37336819,76.13374067,88.63427978,99.17236163,107.96827,115.2289659,121.1585778,125.9542122,129.7976768,132.8504967,135.2544369,137.1234954,138.5545735,139.6310041,140.4137722,140.960863,141.3115956,141.5020398,141.5603911,141.5098635,141.3688178,141.150192,140.8714973,140.5392011,140.1625248,139.7464364,139.3025573,138.8344027];