How to fit data!

I have experimental data and I need to represent it as a function of x using the MATLAB fitting tool.

However, the obtained experimental data were non-linear and were fitted by dividing the intervals.

The problem here is that the fitting is made so that the function values at the points connecting the sections do not match.

Is there a way or code to fix and fit the end value of the interval?

A data example is attached.

It's a long question, but I'll wait for an answer. Thank you.

(If there is an efficient way to represent it as a function, please let me know!)

- There may be some awkward parts using a translator! :)

[KSSV]

Did you try polyfit?

[재열 김]

@KSSV Yes. But the equation is badly conditioned and I don't want too high-order terms.

[Image Analyst]

You said "A data example is attached." but there is no attachment. Use the paperclip icon to attach your file, and give us the code to read it in and plot it.

[재열 김]

@Image Analyst Oh, I edited the post and attached the data. Thanks!

Answer 1

[Star Strider]

This is something similar to Curve Fitting of large Data Measurement? however with a different sort of envelope. I would begin by using the envelope function to get the general shape of the envelope, derive a function that describes it mathematically in terms of the other data (time, amplitude, frequency, perhaps others), then change the code in the Answer I linked to in order to fit the entire function to the data (unless the desired result is only to determine a function for the envelope, if so stop after the envelope determination step).

[재열 김]

Thanks for your reply!

I thought it was right to approach the data fitting like the page you linked to, so I modified the code to run it. But, as shown in the picture, I found that they are not very similar.

Should I use peak envelope (to get a function of x) to fit as closely as possible to the original data?

[Star Strider]

It ocurred to me that this could be a straighttforward system identification problem, and would automatically code for the envelope function as well, since that may not be possible to correctly estimate otherwise.

For best results, I need to know what the inputs were to the system that produced those outputs. It should be a vector (or matrix) of corresponding sample times. The system identification is not going to work well without knowing the inputs.

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/874645/h2_f_og_.csv', 'VariableNamingRule','preserve')

T1 = 251×4 table
      x           Fx             Fy            Fz    
    ______    ___________    ___________    _________

         0      0.0016495    -0.00014195    0.0053701
    1.0935      0.0014762     0.00023496    0.0051739
     2.187     0.00032598    -0.00015709    0.0054594
    3.2804     0.00029656     0.00070307    0.0056151
    4.3739      0.0012309      -8.01e-05     0.006997
    5.4674     0.00016371      -9.65e-05    0.0090012
    6.5609    -0.00035602      -9.09e-05    0.0082262
    7.6544     -0.0001414       1.35e-06    0.0081911
    8.7478      0.0012345     0.00030346    0.0098071
    9.8413      0.0015556     0.00011919     0.010114
    10.935    -0.00026018     0.00052635     0.015164
    12.028      0.0015505     0.00011503     0.016601
    13.122      0.0011482      -1.83e-05     0.021914
    14.215     0.00087075      -6.07e-05     0.022012
    15.309    -0.00092485       7.86e-05      0.02872
    16.402     -0.0023217      0.0007304     0.031215

x = T1.x;
Fx = T1.Fx;
Ts = mean(diff(x))                                  % Sampling Interval

Ts = 1.0935

% Tsd = std(diff(x))                                  % Check Sampling Time Consistency

Fx_data = iddata(Fx,[],Ts)

Fx_data =

Time domain data set with 251 samples.
Sample time: 1.09348 seconds           
                                       
Outputs      Unit (if specified)       
   y1                                  
                                       

Fxss_sys = ssest(Fx_data, 8)

Fxss_sys =
  Continuous-time identified state-space model:
      dx/dt = A x(t) + K e(t)
       y(t) = C x(t) + e(t)
 
  A = 
               x1          x2          x3          x4          x5          x6          x7          x8
   x1    0.009635      0.2412    0.006551     0.01099    -0.03323     -0.1819     -0.2486    -0.04133
   x2      -0.232     0.01263    -0.03631     0.02909     -0.1952    -0.04111  -0.0001147     0.04236
   x3   -0.008426     0.03976    -0.08719      0.3809    -0.03252     -0.1163     -0.3864      -0.743
   x4    -0.01136  -0.0002404     -0.2501     -0.1937      0.3994     -0.6713     -0.6635    -0.07726
   x5    -0.03699     0.01098     -0.2085    -0.01034     -0.2836    -0.03551      -1.613      -2.127
   x6    -0.02895     0.04372     -0.9473    0.008575     -0.7482      -6.161      -9.695      -7.186
   x7    -0.01104      0.1119     -0.7441    -0.04221     0.04838      -2.865      -5.675      -6.342
   x8    -0.02755     0.09637     -0.9548     0.04119      0.3045      -3.905      -4.536      -7.763
 
  C = 
               x1          x2          x3          x4          x5          x6          x7          x8
   y1       17.69      0.1826     -0.1761      0.2149    0.007997      0.4935      0.3214  -0.0009668
 
  K = 
           y1
   x1   0.334
   x2  0.5631
   x3  -6.595
   x4   2.645
   x5   1.094
   x6   7.102
   x7    1.62
   x8  -1.852
 
Parameterization:
   FREE form (all coefficients in A, B, C free).
   Disturbance component: estimate
   Number of free coefficients: 80
   Use "idssdata", "getpvec", "getcov" for parameters and their uncertainties.

Status:                                             
Estimated using SSEST on time domain data "Fx_data".
Fit to estimation data: 98.57% (prediction focus)   
FPE: 0.0002877, MSE: 0.0002532                      

figure
compare(Fx_data, Fxss_sys)

.