How to convert trajectory of the current vector to grayscale.

Dear sir,

Could you make help for coding. I attached the data.mat

First, I read the three phase current. After I use clarke transform and I get current vector (Is).

1. I established a 60×60 2D matrix to depict the trajectory, with (30,30) as the origin and 1 step size.

2. I calculate the trajectory of the current vector on the α-β plane. But it is not like the below picture.

why is it that picture?

3. The probability that each point in the current vector trajectory falls into a certain grid is calculated as the grayscale of the point.

4. I want use mean value filtering algorithm to filter out the points with low probability,

5. I want normalize the value of each pixel in the 2D matrix according to the min-max normalization.

But ı get very bad result like that. The circle should be large.

The circle should be large, like below picture

load("data.mat")
Ia = data(:,1);
Ib = data(:,2);
Ic = data(:,3);
 
%%  Clarke (3 phase → αβ)
I_alpha = Ia; 
I_beta  = (1/sqrt(3))*(Ia + 2*Ib);   % Clarke formülü

% Current vector
Is = I_alpha + 1j*I_beta;
plot(Is)

%% 1⃣ 60×60 2D matrix
grid_size = 60;          % 60x60 matrix
origin = [30, 30];       % (30,30) origin
step = 1;                % 1

traj_matrix = zeros(grid_size, grid_size);

%% 2⃣ Place the current vector on 2D matrix
for i = 1:length(Is)
    Ia_val = real(Is(i));
    Ib_val = imag(Is(i));
    
    xi = round(Ia_val/step + origin(1));
    yi = round(Ib_val/step + origin(2));
    
    if xi >= 1 && xi <= grid_size && yi >= 1 && yi <= grid_size
        traj_matrix(yi, xi) = traj_matrix(yi, xi) + 1;
    end
end
plot(traj_matrix)

●

%%3⃣ Probability matrix (grayscale intensity)
traj_prob = traj_matrix / sum(traj_matrix(:));

%%4⃣  Mean Value filtering (noise reduction)
kernel = fspecial('average', [3 3]);  % 3x3 mean filter
traj_filtered = imfilter(traj_prob, kernel, 'replicate');

%%5⃣  Min–max normalization
min_val = min(traj_filtered(:));
max_val = max(traj_filtered(:));
traj_norm = (traj_filtered - min_val) / (max_val - min_val);

%%6⃣  visualization
figure;
imshow(traj_norm, []);
title('Normalized 2D Current Vector Trajectory (αβ plane)');
xlabel('\alpha axis');
ylabel('\beta axis');
colormap('gray');
colorbar;

Answer 1

[Matt J]

Maybe this is what you wanted?

load("data.mat")
Ia = data(:,1);
Ib = data(:,2);
Ic = data(:,3);
 
%%  Clarke (3 phase → αβ)
I_alpha = Ia; 
I_beta  = (1/sqrt(3))*(Ia + 2*Ib);   % Clarke formülü

plot(I_alpha, I_beta,'.'); axis equal

%% 1⃣ 60×60 2D matrix
grid_size = 60;          % 60x60 matrix3

traj_prob = histcounts2(I_alpha,I_beta, grid_size, Norm="prob");


%%4⃣  Mean Value filtering (noise reduction)
kernel = fspecial('average', [3 3]);  % 3x3 mean filter
traj_norm = rescale( imfilter(traj_prob, kernel, 'rep')  );

%%6⃣  visualization
figure;
imagesc(traj_norm)
title('Normalized 2D Current Vector Trajectory (αβ plane)');
xlabel('\alpha axis');
ylabel('\beta axis');
colormap gray; colorbar;

[Bahadir]

@Matt J Thank you,

The circle you drew at above is exactly the graph I wanted. Because it is not contain any error data, it shuold be perfectly circle.

But I have some questions.

1) My matrix is 60x60. How do I draw the radius of the circle as 25 within this matrix?

Because the circle is fixed to edge of matrix.

2) Although the circle drawn above is perfectly circular, when I look at the matrix values on the right and left sides of the circle, I see that the circle is not circular.

How can ı make perfectly circular?

3) The Plot of "Normalized 2D Current Vector Trajectory (αβ plane)" is grey scale picture.

How can I make it more distinct? In other words, how can I make the values of the gray pixels more distinct?

4) I attached new data which s3 fault.

load("data_s3.mat")
Ia = data(:,1);
Ib = data(:,2);
Ic = data(:,3);

%%  Clarke (3 phase → αβ)
I_alpha = Ia; 
I_beta  = (1/sqrt(3))*(Ia + 2*Ib);   % Clarke formülü
plot(I_alpha, I_beta,'.'); axis equal

This graph is incorrect because it should not be a perfect circle.

It should be like below. Because The semicircle should contain error information; the semicircle should be without error.

Thank you

[Matt J]

(1) You can use padarray and imresize to adjust the proportions of the circle, relative to the surrounding grid area.

(2) The spatial distribution of (I_alpha, I_beta) is not uniform around the circumference of the circle. Therefore, the image values will not be either.

(3) Use clim.

(4) If the graph is showing a perfect circle, then your data is a perfect circle.