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Effacer les filtres

Trying to adjust weighting on PART of a sigmoid fit

18 vues (au cours des 30 derniers jours)
ROBERTA le 13 Mar 2024
Modifié(e) : S0852306 le 25 Avr 2024 à 14:13
I included a picture of the current fit that I am getting, what is in black is the actual data. So far the fit is pretty good but my PI would like it to fit a bit better and he suggested weighting the first part of the fit less than the later parts since we really only care from about 500 seconds onwards. Any suggestions on how to do this? I can include the actual matlab file for the fit if that would be helpful for anyone

Réponses (2)

Image Analyst
Image Analyst le 14 Mar 2024
Then simply don't include that data in your training data set. Try
firstIndex = find(x > 500);
partialYData = y(firstIndex : end); % Extract out only y data where x is more than 500.
% Continue with however you did the fit, like with fitnlm or whatever (Demo attached).
Then just do whatever you did with partialYData instead of the full y data.

Sam Chak
Sam Chak le 14 Mar 2024
The data points do not exhibit a symmetrical sigmoidal trend, suggesting that the commonly used logistic function may not be suitable. You could consider fitting the data with asymmetrical sigmoidal models such as the Generalized logistic function, the Gompertz function, or the cumulative Gumbel distribution function.
Upon initial observation (based on experience), it appears that a 3rd-order dynamically-damped system with time delay could be a reasonably good fit. This type of trend also bears resemblance to the popular First-Order-Plus-Dead-Time (FOPDT) Model.
w = 0.01; % <-- tune this value only
amp = 6.5; % amplitude (measurable)
Td = 300; % time delay (measurable)
G = amp*tf(w^3, [1 3*w 3*w^2 w^3], 'InputDelay', Td)
G = 6.5e-06 exp(-300*s) * --------------------------------- s^3 + 0.03 s^2 + 0.0003 s + 1e-06 Continuous-time transfer function.
plotoptions = timeoptions('cstprefs');
plotoptions.Grid = 'on';
stepplot(G, 4000, plotoptions)
  6 commentaires
Sam Chak
Sam Chak le 21 Mar 2024
The coefficient 'd' in the Gompertz function represents the offset distance that shifts the function along the y-axis. The standard Gompertz function provided in the library models already includes this offset. If you wish to exclude the offset effect from the Gompertz function, you can either fix 'd = 0' at both lower and upper bounds, or manually remove the 'd' term from the equation. See Example below:
If you would like us to assist you in finding a better fit, please attach the data sheet (by clicking the paperclip icon). To save the variables 'xData' and 'yData' from the workspace to a mat-file, use the following syntax:
save myData.mat
%% data generation
a = 0.9911;
b = 0.0058;
c = 426.7144;
d =-0.1998;
f = @(x) (d + (a - d)*exp(-exp(-b*(x - c))));
x0 = fzero(f, 320);
x = x0:0.1:3500;
y = (d + (a - d)*exp(-exp(-b*(x - c)))); % Gompertz fcn with offset d
%% fitting preparation using Gompertz function
[xData, yData] = prepareCurveData(x, y);
fo = fitoptions('Method', 'NonlinearLeastSquares', ...
'Lower', [0.9, 0.005, 450], ... % lower bounds of {a, b, c}
'Upper', [1.0, 0.009, 500]); % upper bounds of {a, b, c}
ft = fittype('a*exp(-exp(-b*(x - c)))', 'options', fo); % Gompertz fcn with d = 0
%% fit the data
a0 = 0.95; % initial guess
b0 = 0.007;
c0 = 475;
[yfit, gof] = fit(xData, yData, ft, 'StartPoint', [a0, b0, c0])
yfit =
General model: yfit(x) = a*exp(-exp(-b*(x - c))) Coefficients (with 95% confidence bounds): a = 0.9897 (0.9896, 0.9898) b = 0.006504 (0.006497, 0.00651) c = 483.3 (483.2, 483.4)
gof = struct with fields:
sse: 1.5262 rsquare: 0.9988 dfe: 31729 adjrsquare: 0.9988 rmse: 0.0069
%% Plot result
plot(x(:,1:80:end), y(:,1:80:end), '.', 'markersize', 4), hold on
plot(yfit), grid on
grid on, xlabel('t'), ylabel('y')
legend('Data', 'Fitted Gompertz')
S0852306 le 25 Avr 2024 à 14:05
Modifié(e) : S0852306 le 25 Avr 2024 à 14:13
Most data measured from dynamics system do not have analytic solutions. so simple explicit model (such as Gompertz or logistic function) probably won't work.
There are 2 approaches,
  1. System identification: instead of finding the explicit function , (θ are the unknown parameters)find x implicitly by fitting the state function f, i.e. , θ could be found by dynamic programing (system identification toolbox is able to do this). once f is known you can evaluate x using ode solvers, this approach perform well when the "structure" of the dynamics system is well known, e.g. single pendulum: (find a and b).
  2. Universal approximator: using some complex black box model to fit the data; if your purpose is just to get a good fit this method usually works. however, the fitted black box function has no physical meaning. here's some results I got:
The underlying model is a neural net which is suitable to perform highly complex function approximation. the maximu absolute error (inf-norm) is about 0.02.
code: FEX
%% Generate data for fitting, follow Sam Chak's code.
clear; clc;
a = 0.9911;
b = 0.0058;
c = 426.7144;
d =-0.1998;
f = @(x) (d + (a - d)*exp(-exp(-b*(x - c))));
x0 = fzero(f, 320);
x = x0:0.1:3500;
y = (d + (a - d)*exp(-exp(-b*(x - c))));
x0 = linspace(0, 326, 10000);
y0 = zeros(1, 10000);
x1 = [x0 x];
y1 = [y0 y];
y1 = smooth(y1, 100);
y1 = y1.';
%% Initialize the model.
LayerStruct = [1, 8, 8, 8, 16, 1];
NN.InputAutoScaling = 'on';
NN.LabelAutoScaling = 'on';
NN.ActivationFunction = 'Sigmoid';
%% Perform least squares.
option.MaxIteration = 300;
NN = OptimizationSolver(x1, y1, NN, option);
%% Plot the results.
Prediction = NN.Evaluate(x1);
scatter(x1, y1, 3)
hold on
plot(x1, Prediction, 'LineWidth', 2)
legend('Fitting', 'Data')
%% Stats and error analysis
% R = FittingReport(x1, y1, NN);

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