Simple MATLAB Nonlinear Fitting Example Using nlinfit Function

This example demonstrates a straightforward MATLAB nonlinear fitting approach using the nlinfit function. Suppose we have experimental data representing the concentration variation of a substance over time. Nonlinear fitting helps us identify the optimal function that best approximates this dataset. Here we assume the concentration-time relationship follows an exponential decay pattern. First, let's generate synthetic data for demonstration purposes. We'll simulate an exponential decay function and introduce random Gaussian noise to mimic real experimental measurements. MATLAB code for data generation: t = linspace(0,10,101)'; y = exp(-0.5*t) + 0.1*randn(size(t)); Now we'll employ nonlinear fitting to determine the optimal parameters for our model function. We hypothesize that the concentration-time relationship can be expressed using the following exponential form: y = Ae^(-λt) where A and λ represent the parameters we need to estimate through fitting. The nlinfit function from MATLAB's Statistics and Machine Learning Toolbox will perform the nonlinear regression. MATLAB implementation for nonlinear fitting: f = @(p,x) p(1)*exp(-p(2)*x); p0 = [1 1]; [p,resid,J,cov] = nlinfit(t,y,f,p0); In this implementation, we define an anonymous function f that accepts parameter vector p and independent variable x, returning the predicted y values. The initial parameter guesses p0 provide starting values for the optimization algorithm. The nlinfit function returns the fitted parameters p, residuals resid, Jacobian matrix J, and covariance matrix cov for statistical analysis. We can visualize the fitting results by comparing the original data with our fitted curve: MATLAB plotting code: plot(t,y,'o',t,f(p,t),'-') legend('Original Data','Fitted Curve') xlabel('Time') ylabel('Concentration') The visualization demonstrates that our fitted curve closely approximates the experimental data points. This example serves as a fundamental introduction to nonlinear fitting in MATLAB, illustrating key concepts in parameter estimation, model definition, and result validation using MATLAB's statistical toolbox functions.