I am designing a battery model with an internal resistance which is dependant on two variables: SoC and temperature.
I have interpolated the data I have (x,y and z basically - a total of 131 points each) with MATLAB's curve fitting toolbox and was able to generate the desired 3D map of that dependence (see the picture below):
My question is how can I use that map now for my Simulink model? As input parameters I will have SoC and temperature and the resistance in ohm should be the output. However, I have not been able to find a convenient way to export the data in a suitable lookup table (or similarly useful, my first guess was that I should use a 2-D lookup table in this case) in Simulink. However, I am quite new to this and I do not know how to generate the the table data for the Simulink LUT.
Simulink LUT:
Table data is your interpolated z-data from curve fitting. I guess it will have a value for every combination of breakpoints (i.e. it covers every grid intersection in your first diagram). So if Breakpoint 1 is 100 elements and Breakpoint 2 is 40 elements, Table data is 100x40.
If you can't get the data out from the GUI-based interactive curve fit, I guess you can extract the data from the command line. The following is an excerpt of Mathworks' curve fitting documentation. It would be good to verify this because I don't have the toolbox to test it though.
•Interpolation: fittedmodel = fit([Time,Temperature], Energy, 'cubicinterp');
•Evaluation: fittedmodel(80, 40)
Based on your LUT inputs u1 and u2, the table will interpolate or extrapolate the grid to get your output value.
Hope that helps.
I did find a solution after all, thanks Tom for your help, the fittedmodel() function was indeed the key of it. I then used two FOR loops to populate my matrix which was 49x51 (as seen by the grid in the image) after the cftool interpolation. After that it was all a matter of two for loops in one another to populate my matrix with the z values of my T and SoC parameters.
for x = 1:49
for y = 1:51
TableData(x,y)=fittedmodel(B_SoC(x),B_Temp(y));
end
end
Where TableData is the 49x51 matrix required for my LUT, B_SoC and B_Temp being [0:2.083:100] and [-10:1.1:45] respectively (determined as the desired start and end of my x and y axis with the spacing taken from the image with the data cursor).
Related
I am trying trying to graph the polynomial fit of a 2D dataset in Matlab.
This is what I tried:
rawTable = readtable('Test_data.xlsx','Sheet','Sheet1');
x = rawTable.A;
y = rawTable.B;
figure(1)
scatter(x,y)
c = polyfit(x,y,2);
y_fitted = polyval(c,x);
hold on
plot(x,y_fitted,'r','LineWidth',2)
rawTable.A and rawTable.A are randomly generated numbers. (i.e. the x dataset cannot be represented in the following form : x=0:0.1:100)
The result:
second-order polynomial
But the result I expect looks like this (generated in Excel):
enter image description here
How can I graph the second-order polynomial fit in MATLAB?
I sense some confusion regarding what the output of each of those Matlab function mean. So I'll clarify. And I think we need some details as well. So expect some verbosity. A quick answer, however, is available at the end.
c = polyfit(x,y,2) gives the coefficient vectors of the polynomial fit. You can get the fit information such as error estimate following the documentation.
Name this polynomial as P. P in Matlab is actually the function P=#(x)c(1)*x.^2+c(2)*x+c(3).
Suppose you have a single point X, then polyval(c,X) outputs the value of P(X). And if x is a vector, polyval(c,x) is a vector corresponding to [P(x(1)), P(x(2)),...].
Now that does not represent what the fit is. Just as a quick hack to see something visually, you can try plot(sort(x),polyval(c,sort(x)),'r','LineWidth',2), ie. you can first sort your data and try plotting on those x-values.
However, it is only a hack because a) your data set may be so irregularly spaced that the spline doesn't represent function or b) evaluating on the whole of your data set is unnecessary and inefficient.
The robust and 'standard' way to plot a 2D function of known analytical form in Matlab is as follows:
Define some evenly-spaced x-values over the interval you want to plot the function. For example, x=1:0.1:10. For example, x=linspace(0,1,100).
Evaluate the function on these x-values
Put the above two components into plot(). plot() can either plot the function as sampled points, or connect the points with automatic spline, which is the default.
(For step 1, quadrature is ambiguous but specific enough of a term to describe this process if you wish to communicate with a single word.)
So, instead of using the x in your original data set, you should do something like:
t=linspace(min(x),max(x),100);
plot(t,polyval(c,t),'r','LineWidth',2)
I have got a matrix of AirFuelRatio values at certain engine speeds and throttlepositions. (eg. the AFR is 14 at 2500rpm and 60% throttle)
The matrix is now 25x10, and the engine speed ranges from 1200-6000rpm with interval 200rpm, the throttle range from 0.1-1 with interval 0.1.
Say i have measured new values, eg. an AFR of 13.5 at 2138rpm and 74,3% throttle, how do i merge that in the matrix? The matrix closest values are 2000 or 2200rpm and 70 or 80% throttle. Also i don't want new data to replace the older data. How can i make the matrix take this value in and adjust its values to take the new value in account?
Simplified i have the following x-axis values(top row) and 1x4 matrix(below):
2 4 6 8
14 16 18 20
I just measured an AFR value of 15.5 at 3 rpm. If you interpolate the AFR matrix you would've gotten a 15, so this value is out of the ordinary.
I want the matrix to take this data and adjust the other variables to it, ie. average everything so that the more data i put in the more reliable and accurate the matrix becomes. So in the simplified case the matrix would become something like:
2 4 6 8
14.3 16.3 18.2 20.1
So it averages between old and new data. I've read the documentation about concatenation but i believe my problem can't be solved with that function.
EDIT: To clarify my question, the following visual clarification.
The 'matrix' keeps the same size of 5 points whil a new data point is added. It takes the new data in account and adjusts the matrix accordingly. This is what i'm trying to achieve. The more scatterd data i get, the more accurate the matrix becomes. (and yes the green dot in this case would be an outlier, but it explains my case)
Cheers
This is not a matter of simple merge/average. I don't think there's a quick method to do this unless you have simplifying assumptions. What you want is a statistical inference of the underlying trend. I suggest using Gaussian process regression to solve this problem. There's a great MATLAB toolbox by Rasmussen and Williams called GPML. http://www.gaussianprocess.org/gpml/
This sounds more like a data fitting task to me. What you are suggesting is that you have a set of measurements for which you wish to get the best linear fit. Instead of producing a table of data, what you need is a table of values, and then find the best fit to those values. So, for example, I could create a matrix, A, which has all of the recorded values. Let's start with:
A=[2,14;3,15.5;4,16;6,18;8,20];
I now need a matrix of points for the inputs to my fitting curve (which, in this instance, lets assume it is linear, so is the set of values 1 and x)
B=[ones(size(A,1),1), A(:,1)];
We can find the linear fit parameters (where it cuts the y-axis and the gradient) using:
B\A(:,2)
Or, if you want the points that the line goes through for the values of x:
B*(B\A(:,2))
This results in the points:
2,14.1897 3,15.1552 4,16.1207 6,18.0517 8,19.9828
which represents the best fit line through these points.
You can manually extend this to polynomial fitting if you want, or you can use the Matlab function polyfit. To manually extend the process you should use a revised B matrix. You can also produce only a specified set of points in the last line. The complete code would then be:
% Original measurements - could be read in from a file,
% but for this example we will set it to a matrix
% Note that not all tabulated values need to be present
A=[2,14; 3,15.5; 4,16; 5,17; 8,20];
% Now create the polynomial values of x corresponding to
% the data points. Choosing a second order polynomial...
B=[ones(size(A,1),1), A(:,1), A(:,1).^2];
% Find the polynomial coefficients for the best fit curve
coeffs=B\A(:,2);
% Now generate a table of values at specific points
% First define the x-values
tabinds = 2:2:8;
% Then generate the polynomial values of x
tabpolys=[ones(length(tabinds),1), tabinds', (tabinds').^2];
% Finally, multiply by the coefficients found
curve_table = [tabinds', tabpolys*coeffs];
% and display the results
disp(curve_table);
I want to carry out hierarchical clustering in Matlab and plot the clusters on a scatterplot. I have used the evalclusters function to first investigate what a 'good' number of clusters would be using different criteria values eg Silhouette, CalinskiHarabasz. Here is the code I used for the evaluation (x is my data with 200 observations and 10 variables):
E = evalclusters(x,'linkage','CalinskiHarabasz','KList',[1:10])
%store kmean optimal clusters
optk=E.OptimalK;
%save the outouts to a structure
clust_struc(1).Optimalk=optk;
clust_struc(1).method={'CalinskiHarabasz'}
I then used code similar to what I have found online:
gscatter(x(:,1),x(:,2),E.OptimalY,'rbgckmr','xod*s.p')
%OptimalY is a vector 200 long with the cluster numbers
and this is what I get:
My question may be silly, but I don't understand why I am only using the first two columns of data to produce the scatter plot? I realise that the clusters themselves are being incorporated through the use of the Optimal Y, but should I not be using all of the data in x?
Each row in x is an observation with properties in size(x,2) dimensions. All this dimensions are used for clustering x rows.
However, when plotting the clusters, we cannot plot more than 2-3 dimensions so we try to represent each element with its key properties. I'm not sure that x(:,1),x(:,2) are the best option, but you have to choose 2 for a 2-D plot.
Usually you would have some property of interest that you want to plot. Have a look at the example in MATLAB doc: the fisheriris data has 4 different variables - the length and width measurements from the sepals and petals of three species of iris flowers. It is up to you to decide which you want to plot against each other (in the example they choosed Petal Length and Petal Width).
Here is a comparison between taking Petals measurements and Sepals measurements as the axis for plotting the grouping:
I want to use the following signal (red) in Simulink as input.
All I have is this picture. Any advice on the simplest way to implement this signal?
Your question has two parts: bringing the data to work space of Matlab and feeding the data to Simulink.
For the first part I think the simplest thing is to put about 30 points on the figure and write their estimated (x,y) values in vectors X and Y. it should not be hard because the first part of it is periodic.
Then use plot(X,Y) to plot this vector in Matlab and update your estimated values till you are satisfied that your plot is similar to the figure.
For the second part you can create a structure where time is the same as your X axis and Y as the values:
input.time = X;
input.signals.values = Y;
where X and Y should have the same length.
you can find good examples of how to import signals from work space to Simulink at this page: https://www.mathworks.com/help/simulink/slref/fromworkspace.html
I have a time series of temperature profiles that I want to interpolate, I want to ask how to do this if my data is irregularly spaced.
Here are the specifics of the matrix:
The temperature is 30x365
The time is 1x365
Depth is 30x1
Both time and depth are irregularly spaced. I want to ask how I can interpolate them into a regular grid?
I have looked at interp2 and TriScatteredInterp in Matlab, however the problem are the following:
interp2 works only if data is in a regular grid.
TriscatteredInterp works only if the vectors are column vectors. Although time and depth are both column vectors, temperature is not.
Thanks.
Function Interp2 does not require for a regularly spaced measurement grid at all, it only requires a monotonic one. That is, sampling positions stored in vectors depths and times must increase (or decrease) and that's all.
Assuming this is indeed is the situation* and that you want to interpolate at regular positions** stored in vectors rdepths and rtimes, you can do:
[JT, JD] = meshgrid(times, depths); %% The irregular measurement grid
[RT, RD] = meshgrid(rtimes, rdepths); %% The regular interpolation grid
TemperaturesOnRegularGrid = interp2(JT, JD, TemperaturesOnIrregularGrid, RT, RD);
* : If not, you can sort on rows and columns to come back to a monotonic grid.
**: In fact Interp2 has no restriction for output grid (it can be irregular or even non-monotonic).
I would use your data to fit to a spline or polynomial and then re-sample at regular intervals. I would highly recommend the polyfitn function. Actually, anything by this John D'Errico guy is incredible. Aside from that, I have used this function in the past when I had data on a irregularly spaced 3D problem and it worked reasonably well. If your data set has good support, which I suspect it does, this will be a piece of cake. Enjoy! Hope this helps!
Try the GridFit tool on MATLAB central by John D'Errico. To use it, pass in your 2 independent data vectors (time & temperature), the dependent data matrix (depth) along with the regularly spaced X & Y data points to use. By default the tool also does smoothing for overlapping (or nearly) data points. If this is not desired, you can override this (and other options) through a wide range of configuration options. Example code:
%Establish regularly spaced points
num_points = 20;
time_pts = linspace(min(time),max(time),num_points);
depth_pts = linspace(min(depth),max(depth),num_points);
%Run interpolation (with smoothing)
Pest = gridfit(depth, time, temp, time_pts, depth_pts);