Gradient Intensity using principal component analysis

    I have a time series in which I have to detect the time where the gradient intensity is higher.

if true
% Create a time serie example
  x = linspace (1,10,50);
  noise = sin (2*x*25*(pi/180))
  x = x+noise ;

    % Calculate the gradient intensity for each point
    for i = 1:length(x);
        for j = 1:length(x);
            Grad (i, j) = (x(i) -x(j)) / abs(i-j);
        end

    end

    % Perform the PCA
    COV=nancov(Grad,'pairwise'); % Use of pairwise dut to the presence of NaN
    [Vecp,~] = eig(COV); 

    % Calculate the 1º-4º PC
    Q=COV*(Vecp(:,end ));  % 1ºPC
    Q1=COV*(Vecp(:,end-1 ));% 2ºPC
    Q2=COV*(Vecp(:,end-2 ));% 3ºPC
    Q3=COV*(Vecp(:,end-3 ));% 4ºPC

    % Plot
    figure
    subplot(211)
    plot(x) % Original sign
    hold on
    xlabel('Time')
    ylabel('Intensity')
    legend( 'Obs.')
    subplot(212)
    plot (Q,'.--r') % 1ºPC
    hold on
    plot (Q1,'.--m') % 2ºPC
    plot (Q2,'.--k') % 3ºPC
    plot (Q3,'.--c') % 4ºPC
    legend ( '1PC', '2PC','3PC','4PC')
    xlabel('Time')
    ylabel('Arb. Units')

end

Through principal components analysis of the gradient for each point, you can see 1PC (red line) increases the signal in the area of higher gradient (time until 21 until ~ 43). Does anyone have an idea how to do automatically because I have to applied the methodology to various segments of a series. Or what kind of technique to use? Have already tried eg inflection points, adjust to a normal distribution but not with good results for other segments of the series. For better understanding I let an example of the code I am using.

 Thank you in advance for any answer.