How do I fit a damped sine wave to my data?

How do I fit a damped sine wave to my data?

Hello,

I'm very new to matlab (joined a day ago) and am trying to fit a damped sine wave to my data from google sheets. I found out how to fit polynomials, etc. using the pre-installed program on Matlab; however, this pre-installed program doesn't have a damped sine wave of best fit. I've been trying to figure out how to fit my data with a damped sine wave for some time now but nothing has worked out. Attached to this question are two data sets, the (1,1) data set represents the x-axis data whereas the (1,2) data set represents the y-axis data. If someone could help me fit my data to a damped sine wave I would much appreciate it..

[Jan]

What is " the pre-installed program on Matlab"?

[Edison Doko]

The pre-installed program i'm referring to can be accessed by going to the apps section of matlab, then clicking curve fitting. Sorry if the terminology I used was incorrect, didn't mean to cause any confusion.

[Jan]

Confusions and questions for clarifications belong to the nature of this forum.

[Stephen23]

Original question by Edison Doko retrieved from Google Cache:

https://web.archive.org/web/20230530153048/https://webcache.googleusercontent.com/search?q=cache:Noe5YnAxySoJ:https://www.mathworks.com/matlabcentral/answers/807962-how-do-i-fit-a-damped-sine-wave-to-my-data

How do I fit a damped sine wave to my data?

Hello,

I'm very new to matlab (joined a day ago) and am trying to fit a damped sine wave to my data from google sheets. I found out how to fit polynomials, etc. using the pre-installed program on Matlab; however, this pre-installed program doesn't have a damped sine wave of best fit. I've been trying to figure out how to fit my data with a damped sine wave for some time now but nothing has worked out. Attached to this question are two data sets, the (1,1) data set represents the x-axis data whereas the (1,2) data set represents the y-axis data. If someone could help me fit my data to a damped sine wave I would much appreciate it.

Answer 1

[Jan]

x = csvread('PH 1140 - 3R (1,1) - Sheet1.csv');
y = csvread('PH 1140 - 3R (1,2) - Sheet1.csv');
plot(x, y);
hold on;

This is the equation of a damped sine:

f = @(p) p(1) * sin(p(2) * x - p(3)) .* exp(-p(4) * x);

A fair start value for p found manually:

p0 = [0.17, 6, 1.2, 0.13];
h = plot(x, f(p0), 'r');

Now it matters, if you are wanted to write your own parameter estimation tool or if you can use Matlab's toolbox functions for this job. In the latter you can use fminsearch :

p0 = [0.17, 6, 1.2, 0.13];
p  = fminsearch(@(p) norm(f(p) - y), p0)
% 0.1659, 5.935, 1.783, 0.1512
h2 = plot(x, f(p), 'r');

Not satisfying. My initial guess looked nicer. The final part does not oscillate around 0, so a vertical shift might solve the problem:

f2  = @(p) p(1) * sin(p(2) * x - p(3)) .* exp(-p(4) * x) + p(5);
p20 = [0.17, 6, 1.2, 0.13, -0.006];
%                         mean(y)
format long g
p2  = fminsearch(@(p) norm(f2(p) - y), p20);
% [0.165487, 5.934186, 1.777052, 0.150949, -0.005647]

Well, I'm still not satisfied. Modifying the frequency and the damping looks better:

p2_guess = [0.165487, 6.0, 1.777052, 0.130949, -0.005647]

Any ideas, what I'm doing wrong?

[Edison Doko]

Thank you! I will take into consideration the fminsearch tool as I'm going to have to repeat this process five more times for five more sets of data.

[Alex Sha]

Hi, Edison, if you don't mind the length, the fitting function below should be much better:

y=p1*sin(p2*x-p3)*exp(-p4*x)+p6*cos(p7*x-p8)*exp(p9*x)+p10;

Root of Mean Square Error (RMSE): 0.00297794529932042
Sum of Squared Residual: 0.00259837035428316
Correlation Coef. (R): 0.99744510981767
R-Square: 0.994896747099183

Parameter	Best Estimate
----------	-------------
p1	0.0736813934626548
p2	6.10084592065804
p3	9.7061325271986
p4	0.0811845187962298
p6	0.216025844636208
p7	-5.86321132404066
p8	28.7124412480121
p9	-0.302318685948081
p10	-0.00587533278341315

[Durva Naik]

Hi Alex, can you please share how to obtain the R2 value for the fitted curve?