how to plot the data and superimpose the mean of the data?

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Hydro 2014-10-18

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评论： Yuvarajendra A Reddy 2020-2-25

I am required to plot 20 second data of my veleocity. then i need to superimpose the mean of the velocity. Can somebody look into my codes. I dont know how to convert the velocity in Hz into second. The velocity is measure with a device that collect data 100 times in a second.

here is my code

U20=U(1:2000,:); % Selection of 20 seconds of data
Usec=U20/100; % 1 second =100 Hz (I think i am making mistake here)
plot(Usec);  % ploting of instantinous velocity
Umean=mean(Usec); % Mean of the sample
hold on
plot(Umean,'-','LineWidth',1); % Superimposing the mean velocity
xlabel('sample data length');
 ylabel('Stream wise velocity');

The graph should look like the attached picture where U is the mean and U' is the instantaneous velocity.

many thanks

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Hydro 2014-10-18

True, my U(velocity) is in m/sec however measured with a device that has sampling frequency of 100 per second that's why i need to convert my data into second and am therefore diving by 100. besides, lets say my location of interest is 3.0 m. I am still struggling to get the plot.

Guillaume 2014-10-18

编辑：Guillaume 2014-10-18

The sampling frequency has no bearing on the measured value, it only affects your x-axis.

What is the unit of the measured value?

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Answer 1

Mohammad Abouali 2014-10-18

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编辑：Mohammad Abouali 2014-10-18

在 MATLAB Online 中打开

% Generating some sample data
t=linspace(0,2*pi,100);
U=sin(t);
% Ploting velocity
plot(t, U);
axis tight
hold on
% Now plotting the mean value.
Umean = mean(U);
line(xlim, [Umean,Umean],'Color','r');

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Mohammad Abouali 2014-10-18

编辑：Mohammad Abouali 2014-10-18

在 MATLAB Online 中打开

I included two methods. (1) jumping window, which averages each 100 numbers together, (2) sliding window average (or moving window average).

Based on your description what you are looking is the first method though. But I included the second method too since it gives nicer mean graph.

U20_mean is array of 20x140 which averages each 100 row. Something along this should work:

load U2'0 second data';
%%Method 1: Jumping window
% Cell Array of size 20x1
U20_mean_cell=cellfun(@mean,mat2cell(U20,100*ones(20,1),140),'UniformOutput',false);
% Regular Array of size 20x140 which contains the average of each 100
% samples (or row)
U20_mean=cell2mat(U20_mean_cell);
% Sample plot
figure
tHighRes=linspace(0,20,2000);
plot(tHighRes,U20(:,1))
axis tight
hold on
tLowRes=linspace(0.5,19.5,20);
plot(tLowRes,U20_mean(:,1),'r','LineWidth',2);
%%Method 2: sliding window
s=ones(100,1)/100;
U20_mean_cell2=cellfun(@(x) conv(x,s,'valid') , ...
                       mat2cell(U20,2000,ones(140,1)), ...
                       'UniformOutput',false);
U20_mean_movingWindow=cell2mat(U20_mean_cell2);
%Sample plot
figure
tHighRes=linspace(0,20,2000);
plot(tHighRes,U20(:,1))
axis tight
hold on
plot(tHighRes(50:1950),U20_mean_movingWindow(:,1),'r','LineWidth',2);

Above figure is method 1

And this is method 2

Mohammad Abouali 2014-10-18

@ Guillaume In fluid mechanic quite often we decompose the velocity into its mean part and fluctuation part U=Ubar+U'. pretty much then the equation is solved for Ubar and then the turbulence equation is modeling the effect of U'. This is generally known as Reynolds Averaged Navier-Stokes' (RANS) equation.

I don't know why he wants to average these numbers, but this approach is used in many field. I applied the same techniques once on seismograph (yes, the techniques that are used in solving fluid motion applied on seisomograph) and I was able to detect some features much easier.

Yuvarajendra A Reddy 2020-2-25

在 MATLAB Online 中打开

Interesting answer by @Mohammad Abouali. There's a much simpler approach to this.

sample_data=rand(1,100);            % Your signal data array
mean_data = smoothdata(sample_data,'movmean'); % Calculating the average or mean, moving over each window
% Plotting graphs
figure
plot(sample_data)       % Original data
hold on
plot(mean_data,'linewidth',2)   % Average of the data
legend('Original signal','Mean of the signal')

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Answer 2

Guillaume 2014-10-18

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编辑：Guillaume 2014-10-18

在 MATLAB Online 中打开

Assuming you have a velocity U measured for 20 seconds (see comment to your question),

t = linspace(0, 20, numel(U)); %generate a time vector for 20 seconds with as many elements as U
plot(t, U);
hold on
Umean = mean(U);
plot(t, Umean);
xlabel('times (s)');
ylabel('velocity (m/s)');

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how to plot the data and superimpose the mean of the data?

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