How to use RBF neural network to solve the following problems?

two question:

1. How to use the data with Curve Fitting in MATLAB, fitting it with cubic spline interpolation to add data points with limited test data? And draw the 3D surface after interpolation?

2. Although data points can be added after interpolation, it cannot describe all data points and data outside the test interval. For example, u=160, T? , so neural network fitting is adopted. What should be done if RBF neural network is used? (ay=1~8 is fixed,u can be increased to 200), is to find the interval ay=1~8,u=120-200 T?

Answer 1

[Purvaja]

Hi there,

I understand that you want to fit limited data using cubic spline interpolation in MATLAB and then generate a smooth 3D surface from the fitted data.

1. Cubic Spline Interpolation and 3D Surface Plotting: To perform cubic spline interpolation on your data and create a 3D surface plot, you can use the “csapi” function from the “Curve Fitting Toolbox”.

x = [40 60 80 100 120];  
y = [1.0 2.5 4.5 6.5 8.0];  
z = [... 
    1.69656 2.03469 2.28864 2.52846 2.53858; 
    2.24590 2.72092 3.04772 3.22486 3.41692; 
    ...]; 
    
% Generate a cubic spline approximation surface 
splineFunc = csapi({y, x}, z);  
[xq, yq] = meshgrid(40:1:120, 1:0.1:8); 
zq = fnval(splineFunc, {yq(:,1), xq(1,:)});  

% Plot the surface 
figure; 
surf(xq, yq, zq); 
xlabel('Speed (km/h)'); 
ylabel('Acceleration (m/s²)'); 
zlabel('Response Value'); 
title('3D Spline Surface using csapi'); 
shading interp; 
colorbar; 

2. RBF Neural Network Fitting: You can use MATLAB's “Neural Network Toolbox” to train an RBF network to predict the response for new values of speed and acceleration.

% Training inputs 
u = [40 60 80 100 120]; % speed 
ay = [1.0 2.5 4.5 6.5 8.0]; % acceleration 
[U, AY] = meshgrid(u, ay); 
inputs = [U(:)'; AY(:)'];  

targets = [... 
    1.69656 2.03469 2.28864 2.52846 2.53858; 
    2.24590 2.72092 3.04772 3.22486 3.41692; 
    ...]; 
targets = targets(:)';  

% Train RBF network 
net = newrb(inputs, targets, 0, 1, 100, 1); 

% Define prediction range 
[uq, ayq] = meshgrid(120:5:200, 1:1:8);  
test_inputs = [uq(:)'; ayq(:)']; 

% Predict using trained network 
predicted_T = net(test_inputs); 
predicted_T = reshape(predicted_T, size(uq)); 

% Plot the prediction surface 

Refer to the following official MathWorks documentation to learn more about the methods used:

1. Surf: https://www.mathworks.com/help/matlab/ref/surf.html
2. Meshgrid: https://www.mathworks.com/help/matlab/ref/meshgrid.html
3. Csapi: https://www.mathworks.com/help/curvefit/csapi.html
4. Newrb: https://www.mathworks.com/help/deeplearning/ref/newrb.html

Hope this helps you!