StartPoint on Curve Fitting Toolbox
I am trying to fit a linear resonance curve of a 2nd order mechanical system to get the Q-factor.
The instrument that I am using to obtain the frequency response function has an in-built curve fitting software that uses the following equation to fit the curve.
denominator = sqrt(f^2 + (Q / f0)^2 * (f^2 – f0^2)^2);
X=A * f / denominator;
(C=0) *image q2.png
A is the amplitude, š¯‘„ is the quality factor and š¯‘“0 is the center frequency.
My goal is to use MATLAB’s Curve Fitting tool to obtain the Q-factor value; first I want to match the Q-factor value obtained from the instrument (as a validation step, so I can fit more data without requiring the instrument’s curve fitting tool).
Below is the FRF obtained from the instrument–the Q factor value I obtain is 8705.9559
*image q1.png
Center Frequency (f0) = 1496.26
A = 2.4216e-3 (amplitude)
I saved this sweep and plotted and tried to recreate the this fit using the CurveFitting tool box–using the same cut-off range as above (1453 kHz to 1548 kHz)
However, I am having an issue with converging to the value for the Q-factor from the instrument–it varies as I change my StartPoint and Lower and Upper values. I understand this is the case, sensitive to inital conditions–however, I was under the assumption that it may converge to the value as I refine my StartPoint and Lower and Upper bounds—this is not the case.
For example:
With StartPoint= 0; Lower= 10; Upper= 10e3 Q=8052 (7994, 8110) with R-square of 0.9961
moving the StartPoint closer to 8000 (which is around the actual value), it drops
With StartPoint = 7000; Lower=10; Upper= 10e3 Q=8278 (8228, 8329) with R-square of 0.9973
With StartPoint= 8000; Lower= 10; Upper= 10e3 Q=8000 (7940, 8060) with R-square of 0.9961
(varying the Upper and Lower bounds also causes the Q factor value to change–and not converge–to different values that is around value obtained from the instrument)
–I was hoping to get closer and improve the goodness of fit, but the fit is very sensitive to the StartPoint—any pointers on how to get an accurate value?
Is this method, fitting this curve using the CurveFitting Toolbox the best method to get the value for Q?
I have shared my data, code and image snippets. Any pointers appreciated.
clc;clear;close all
data = load(‘data.mat’);
f=data.d(:,1);
A=data.d(:,2);
[fitresult, gof] = createFit(f, A)
function [fitresult, gof] = createFit(f, A)
%CREATEFIT(F,A)
% Create a fit.
%
% Data for ‘untitled fit 1’ fit:
% X Input: f
% Y Output: A
% Output:
% fitresult : a fit object representing the fit.
% gof : structure with goodness-of fit info.
%
% See also FIT, CFIT, SFIT.
% Auto-generated by MATLAB on 12-Jun-2024 17:27:38
%% Fit: ‘untitled fit 1’.
[xData, yData] = prepareCurveData( f, A );
% Set up fittype and options.
ft = fittype( ‘2.4216e-3*f./(sqrt(f^2+(Q/1496.26)^2*(f^2-1496.26^2)^2))’, ‘independent’, ‘f’, ‘dependent’, ‘A’ );
excludedPoints = (xData < 1426.9) | (xData > 1570.4);
opts = fitoptions( ‘Method’, ‘NonlinearLeastSquares’ );
opts.Display = ‘Off’;
opts.Lower = 10;
opts.MaxFunEvals = 1000;
opts.MaxIter = 1000;
opts.StartPoint = 7000;
opts.TolFun = 1e-07;
opts.Upper = 10000;
opts.Exclude = excludedPoints;
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );
% Plot fit with data.
figure( ‘Name’, ‘untitled fit 1’ );
h = plot( fitresult, xData, yData, excludedPoints );
legend( h, ‘A vs. f’, ‘Excluded A vs. f’, ‘untitled fit 1’, ‘Location’, ‘NorthEast’, ‘Interpreter’, ‘none’ );
% Label axes
xlabel( ‘f’, ‘Interpreter’, ‘none’ );
ylabel( ‘A’, ‘Interpreter’, ‘none’ );
grid on
end
TL;DR–I am trying to understand why the value of Q, obtained from my fit, does not converge to a value (and improve the fit) as I use a guess that is around the accurate value, and reduce the size of the bounds (Lower and Upper)I am trying to fit a linear resonance curve of a 2nd order mechanical system to get the Q-factor.
The instrument that I am using to obtain the frequency response function has an in-built curve fitting software that uses the following equation to fit the curve.
denominator = sqrt(f^2 + (Q / f0)^2 * (f^2 – f0^2)^2);
X=A * f / denominator;
(C=0) *image q2.png
A is the amplitude, š¯‘„ is the quality factor and š¯‘“0 is the center frequency.
My goal is to use MATLAB’s Curve Fitting tool to obtain the Q-factor value; first I want to match the Q-factor value obtained from the instrument (as a validation step, so I can fit more data without requiring the instrument’s curve fitting tool).
Below is the FRF obtained from the instrument–the Q factor value I obtain is 8705.9559
*image q1.png
Center Frequency (f0) = 1496.26
A = 2.4216e-3 (amplitude)
I saved this sweep and plotted and tried to recreate the this fit using the CurveFitting tool box–using the same cut-off range as above (1453 kHz to 1548 kHz)
However, I am having an issue with converging to the value for the Q-factor from the instrument–it varies as I change my StartPoint and Lower and Upper values. I understand this is the case, sensitive to inital conditions–however, I was under the assumption that it may converge to the value as I refine my StartPoint and Lower and Upper bounds—this is not the case.
For example:
With StartPoint= 0; Lower= 10; Upper= 10e3 Q=8052 (7994, 8110) with R-square of 0.9961
moving the StartPoint closer to 8000 (which is around the actual value), it drops
With StartPoint = 7000; Lower=10; Upper= 10e3 Q=8278 (8228, 8329) with R-square of 0.9973
With StartPoint= 8000; Lower= 10; Upper= 10e3 Q=8000 (7940, 8060) with R-square of 0.9961
(varying the Upper and Lower bounds also causes the Q factor value to change–and not converge–to different values that is around value obtained from the instrument)
–I was hoping to get closer and improve the goodness of fit, but the fit is very sensitive to the StartPoint—any pointers on how to get an accurate value?
Is this method, fitting this curve using the CurveFitting Toolbox the best method to get the value for Q?
I have shared my data, code and image snippets. Any pointers appreciated.
clc;clear;close all
data = load(‘data.mat’);
f=data.d(:,1);
A=data.d(:,2);
[fitresult, gof] = createFit(f, A)
function [fitresult, gof] = createFit(f, A)
%CREATEFIT(F,A)
% Create a fit.
%
% Data for ‘untitled fit 1’ fit:
% X Input: f
% Y Output: A
% Output:
% fitresult : a fit object representing the fit.
% gof : structure with goodness-of fit info.
%
% See also FIT, CFIT, SFIT.
% Auto-generated by MATLAB on 12-Jun-2024 17:27:38
%% Fit: ‘untitled fit 1’.
[xData, yData] = prepareCurveData( f, A );
% Set up fittype and options.
ft = fittype( ‘2.4216e-3*f./(sqrt(f^2+(Q/1496.26)^2*(f^2-1496.26^2)^2))’, ‘independent’, ‘f’, ‘dependent’, ‘A’ );
excludedPoints = (xData < 1426.9) | (xData > 1570.4);
opts = fitoptions( ‘Method’, ‘NonlinearLeastSquares’ );
opts.Display = ‘Off’;
opts.Lower = 10;
opts.MaxFunEvals = 1000;
opts.MaxIter = 1000;
opts.StartPoint = 7000;
opts.TolFun = 1e-07;
opts.Upper = 10000;
opts.Exclude = excludedPoints;
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );
% Plot fit with data.
figure( ‘Name’, ‘untitled fit 1’ );
h = plot( fitresult, xData, yData, excludedPoints );
legend( h, ‘A vs. f’, ‘Excluded A vs. f’, ‘untitled fit 1’, ‘Location’, ‘NorthEast’, ‘Interpreter’, ‘none’ );
% Label axes
xlabel( ‘f’, ‘Interpreter’, ‘none’ );
ylabel( ‘A’, ‘Interpreter’, ‘none’ );
grid on
end
TL;DR–I am trying to understand why the value of Q, obtained from my fit, does not converge to a value (and improve the fit) as I use a guess that is around the accurate value, and reduce the size of the bounds (Lower and Upper)Ā I am trying to fit a linear resonance curve of a 2nd order mechanical system to get the Q-factor.
The instrument that I am using to obtain the frequency response function has an in-built curve fitting software that uses the following equation to fit the curve.
denominator = sqrt(f^2 + (Q / f0)^2 * (f^2 – f0^2)^2);
X=A * f / denominator;
(C=0) *image q2.png
A is the amplitude, š¯‘„ is the quality factor and š¯‘“0 is the center frequency.
My goal is to use MATLAB’s Curve Fitting tool to obtain the Q-factor value; first I want to match the Q-factor value obtained from the instrument (as a validation step, so I can fit more data without requiring the instrument’s curve fitting tool).
Below is the FRF obtained from the instrument–the Q factor value I obtain is 8705.9559
*image q1.png
Center Frequency (f0) = 1496.26
A = 2.4216e-3 (amplitude)
I saved this sweep and plotted and tried to recreate the this fit using the CurveFitting tool box–using the same cut-off range as above (1453 kHz to 1548 kHz)
However, I am having an issue with converging to the value for the Q-factor from the instrument–it varies as I change my StartPoint and Lower and Upper values. I understand this is the case, sensitive to inital conditions–however, I was under the assumption that it may converge to the value as I refine my StartPoint and Lower and Upper bounds—this is not the case.
For example:
With StartPoint= 0; Lower= 10; Upper= 10e3 Q=8052 (7994, 8110) with R-square of 0.9961
moving the StartPoint closer to 8000 (which is around the actual value), it drops
With StartPoint = 7000; Lower=10; Upper= 10e3 Q=8278 (8228, 8329) with R-square of 0.9973
With StartPoint= 8000; Lower= 10; Upper= 10e3 Q=8000 (7940, 8060) with R-square of 0.9961
(varying the Upper and Lower bounds also causes the Q factor value to change–and not converge–to different values that is around value obtained from the instrument)
–I was hoping to get closer and improve the goodness of fit, but the fit is very sensitive to the StartPoint—any pointers on how to get an accurate value?
Is this method, fitting this curve using the CurveFitting Toolbox the best method to get the value for Q?
I have shared my data, code and image snippets. Any pointers appreciated.
clc;clear;close all
data = load(‘data.mat’);
f=data.d(:,1);
A=data.d(:,2);
[fitresult, gof] = createFit(f, A)
function [fitresult, gof] = createFit(f, A)
%CREATEFIT(F,A)
% Create a fit.
%
% Data for ‘untitled fit 1’ fit:
% X Input: f
% Y Output: A
% Output:
% fitresult : a fit object representing the fit.
% gof : structure with goodness-of fit info.
%
% See also FIT, CFIT, SFIT.
% Auto-generated by MATLAB on 12-Jun-2024 17:27:38
%% Fit: ‘untitled fit 1’.
[xData, yData] = prepareCurveData( f, A );
% Set up fittype and options.
ft = fittype( ‘2.4216e-3*f./(sqrt(f^2+(Q/1496.26)^2*(f^2-1496.26^2)^2))’, ‘independent’, ‘f’, ‘dependent’, ‘A’ );
excludedPoints = (xData < 1426.9) | (xData > 1570.4);
opts = fitoptions( ‘Method’, ‘NonlinearLeastSquares’ );
opts.Display = ‘Off’;
opts.Lower = 10;
opts.MaxFunEvals = 1000;
opts.MaxIter = 1000;
opts.StartPoint = 7000;
opts.TolFun = 1e-07;
opts.Upper = 10000;
opts.Exclude = excludedPoints;
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );
% Plot fit with data.
figure( ‘Name’, ‘untitled fit 1’ );
h = plot( fitresult, xData, yData, excludedPoints );
legend( h, ‘A vs. f’, ‘Excluded A vs. f’, ‘untitled fit 1’, ‘Location’, ‘NorthEast’, ‘Interpreter’, ‘none’ );
% Label axes
xlabel( ‘f’, ‘Interpreter’, ‘none’ );
ylabel( ‘A’, ‘Interpreter’, ‘none’ );
grid on
end
TL;DR–I am trying to understand why the value of Q, obtained from my fit, does not converge to a value (and improve the fit) as I use a guess that is around the accurate value, and reduce the size of the bounds (Lower and Upper)Ā curve fittingĀ MATLAB Answers ā€” New Questions
ā€‹
