how to smooth the data of array to get a smooth surface?

how i can remove outliers in data and get a smooth surface?

[William Rose]

@Abdullah, Please attach the data as a .mat file.

Answer 1

[William Rose]

@Abdullah,

Check this out:

https://www.mathworks.com/help/matlab/data_analysis/convolution-filter-to-smooth-data.html

Or do a median filter, in which each point is replaced by the median of a pxp array centered on that point.

Answer 2

[William Rose]

@Abdullah, an example of a median filter for a surface:

First, make a surface with some "noise":

A=repmat(-(-20:20).^2/400,31,1)+repmat([-(-15:15).^2/225]',1,41)+2+(rand(31,41)>.95)/5;
mesh(-20:20,-15:15,A)  %display the surface

Filter it with a pxp median filter

p=5;  p2=floor(p/2); [n,m]=size(A);
B=zeros(n,m);  %allocate array for smoothed surface
for i=1+p2:n-p2
    for j=1+p2:m-p2
        B(i,j)=median(median(A(i-p2:i+p2,j-p2:j+p2)));
    end
end
mesh(-20:20,-15:15,B)  %display the surface

The edges are zeros in my simple code, because, if the filter gets any closer to the edges, it will extend beyond the bounds of the original array, which would cause an error. You could improve this by adapting the filter as needed, when it gets near the edge.

[William Rose]

Simple median filter (same as the one in answer above), that stays clear of the edges. This leaves a rim of zeros around the edges:

for i=1+p2:n-p2
    for j=1+p2:m-p2
        B(i,j)=median(median(A(i-p2:i+p2,j-p2:j+p2)));
    end
end

A filter that goes right up to the edges is below.

for i=1:n
    for j=1:m
        B(i,j)=median(median(A(max(i-p2,1):min(i+p2,n),max(j-p2,1):min(j+p2,m))));
    end
end

[Abdullah]

Thank you your idea helped me further, but the right area in yallow could not be smoothed, any idea?

[William Rose]

@Abdullah, the area in yellow is elevated relative to the smooth contour of the other parts of the surface. You are correct that this elevated region is likely to remain elevated even after filtering. Filtering could make this region smoother, but the region will still be elevated. The behavior of the surface in the yellow area does not appear to be random variation. It looks more like a deterministic difference in the response of the system, when the RPM and torque are in this range of values. Therefore I recommend investigating why the system repsonse is different in this region.

[Abdullah]

actually this curve is the output of the optimization process in matlab, the optimization does not give accurate points in this area therefore i thought it might be possible to smooth this area somehow in matlab. but thank you anyway for your contribution William

[William Rose]

@Abdullah, you;re welcome. Good luck with your work.