How can I smooth this data before assigning a spline to it?

Question

Elias Kerstein 2024-4-17

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2108406-how-can-i-smooth-this-data-before-assigning-a-spline-to-it

评论： Mathieu NOE 2024-4-19

ag_gel_data.xlsx

I am attempting to fit a cubic spline to rheological data which can be found in the attached excel file. I need to smooth the data so that when plotting the derivative of the function, the curve does not jump up and down. I guess I am tryin to remove noise and smooth into a better looking line. The code and generated figures are below:

clc;
clear all;
%% --Variable Assignment--
osc_strain = xlsread("ag_gel_data.xlsx",1,'A31:A51');
stor_mod = xlsread("ag_gel_data.xlsx",1,'K31:K51');
loss_mod = xlsread("ag_gel_data.xlsx",1,'L31:L51');
tb1 = table(osc_strain,stor_mod,loss_mod);
%% --Fit: Cubic Spline Interpolant--
[xData, yData] = prepareCurveData( osc_strain, stor_mod );
%% --Plotting-- (Figure 1)
lg1 = loglog(tb1,"osc_strain","stor_mod",'LineWidth',1);
hold on;
lg2 = loglog(tb1,"osc_strain","loss_mod",'LineWidth',1);
% Plot fit with data on a log-log scale.
xup = linspace(xData(1) , xData(end),1e4);
yup = interp1(xData,yData,xup,'pchip');
s = plot(xup,yup ,'--');
%% --Figure Stylization--
lg1.LineStyle = "-";
lg1.Color = "magenta";
lg1.Marker = ".";
lg1.MarkerSize = 16;
lg2.LineStyle = "-";
lg2.Color = "magenta";
lg2.Marker = "o";
lg2.MarkerSize = 4;
s.LineStyle = "--";
s.Color = "black";
xlabel('Oscillation Stress, \gamma (%)')
ylabel("G',G'' (Pa)")
legend('Storage Modulus','Loss Modulus','Cubic Spline','Location','NW')
%% --Plotting-- (Figure 2)
figure;
semilogx( xup,gradient(yup,xup),'-.','color',"black")
xlabel('Oscillation Stress, \gamma (%)')
ylabel("Differential Modulus, K (Pa)")
%% --Tabulate Differential Modulus--
K = gradient(yup,xup);
Ktable0 = [xup; K].';
Ktable = Ktable0(K>=0,:);

Figure 1:

The data I would like to smooth are both pink curves.

Figure 2:

Smoothing the pink curves would result in a smoother curve of the derivative which is plotted above.

Any suggestions? Thank you!

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Mathieu NOE 2024-4-18

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2108406-how-can-i-smooth-this-data-before-assigning-a-spline-to-it#answer_1443826

在 MATLAB Online 中打开

hello

you could do this

just using basic interpolation (in log scale) and the regular smoothdata (use your own spline smoother if you prefer)

%% --Variable Assignment--
osc_strain = xlsread("ag_gel_data.xlsx",1,'A31:A51');
stor_mod = xlsread("ag_gel_data.xlsx",1,'K31:K51');
loss_mod = xlsread("ag_gel_data.xlsx",1,'L31:L51');
% log scale interpolate and smooth the data
Npoints = 200;
osc_strain2 = logspace(log10(min(osc_strain)),log10(max(osc_strain)),Npoints);
Nsmooth = 40;
method = 'lowess';
stor_mod2 = interp1(log(osc_strain),log(stor_mod),log(osc_strain2));
stor_mod2 = smoothdata(stor_mod2,method,Nsmooth);
stor_mod2 = exp(stor_mod2);
loss_mod2 = interp1(log(osc_strain),log(loss_mod),log(osc_strain2));
loss_mod2 = smoothdata(loss_mod2,method,Nsmooth);
loss_mod2 = exp(loss_mod2);
%% --Plotting-- (Figure 1)
loglog(osc_strain,stor_mod,'*-','LineWidth',2);
hold on
loglog(osc_strain2,stor_mod2,'*-','LineWidth',1);
loglog(osc_strain,loss_mod,'*-','LineWidth',2);
loglog(osc_strain2,loss_mod2,'*-','LineWidth',1);
hold off

6 个评论
显示 4更早的评论隐藏 4更早的评论

Mathieu NOE 2024-4-18

在 MATLAB Online 中打开

ag_gel_data.xlsx

well, I don't see a method where you could at the same time have a smoother curve AND have that curve go through the (raw data) peak point - unless you would either shift or stretch (anamorphosis) the curve so that a smoothed version of the curve would indeed go through that peak point, but that would simply mean we are manipulating the data and I don't think this is what you want

at the end , I wonder why we need to interpolate and smooth the curve , as this doesn't seem to be of some need when you compute the gradient (for my own fun I used both diff and gradient functions.

gradient on raw data seems to suffice, or ?

in this version of the code , I reduced a bit the amount of interpolation points (from 200 to 100) and also reduced the amount of smoothing , but , yes , there will always be a small difference between the peaks .

%% --Variable Assignment--

osc_strain = xlsread("ag_gel_data.xlsx",1,'A31:A51');

stor_mod = xlsread("ag_gel_data.xlsx",1,'K31:K51');

loss_mod = xlsread("ag_gel_data.xlsx",1,'L31:L51');

% log scale interpolate and smooth the data

Npoints = 100;

osc_strain2 = logspace(log10(min(osc_strain)),log10(max(osc_strain)),Npoints)';

Nsmooth = 5;

method = 'lowess';

stor_mod2 = interp1(log(osc_strain),log(stor_mod),log(osc_strain2));

stor_mod2 = smoothdata(stor_mod2,method,Nsmooth);

stor_mod2 = exp(stor_mod2);

% loss_mod2 = interp1(log(osc_strain),log(loss_mod),log(osc_strain2));

% loss_mod2 = smoothdata(loss_mod2,method,Nsmooth);

% loss_mod2 = exp(loss_mod2);

%% --Plotting-- (Figure 1)

figure(1);

loglog(osc_strain,stor_mod,'*-','LineWidth',2);

hold on

loglog(osc_strain2,stor_mod2,'*-','LineWidth',1);

% loglog(osc_strain,loss_mod,'*-','LineWidth',2);

% loglog(osc_strain2,loss_mod2,'*-','LineWidth',1);

hold off

%% --Plotting gradient -- (Figure 2)

figure(2);

% gradient computed with diff

gr = diff(stor_mod)./diff(osc_strain);

gr = [gr; NaN];

gr2 = diff(stor_mod2)./diff(osc_strain2);

gr2 = [gr2; NaN];

semilogx(osc_strain,gr,'*-','LineWidth',2);

hold on

semilogx(osc_strain2,gr2,'*-','LineWidth',2);

% compare with "gradient" function

semilogx(osc_strain,gradient(stor_mod)./gradient(osc_strain),'*-','LineWidth',2);

semilogx(osc_strain2,gradient(stor_mod2)./gradient(osc_strain2),'*-','LineWidth',1);

legend('raw data (diff)','interpol. & smoothed data (diff)','raw data (gradient)','interpol. & smoothed data (gradient)');

hold off

Elias Kerstein 2024-4-18

在 MATLAB Online 中打开

Hi, thank you for your answer! I am smoothing the data because my mentor and I are trying to emulate a data analysis method that we found in a literature review, but I agree that the gradient on the raw data is sufficient. It comes down to that smooth curves are easier to explain (and bring up less inquiries) when they are presented in a publication and more often than not, reducing jumps in the raw data down to "just being the data" doesn't quite satisfy reviewers or the principal investigator. I appreciate your work on this! I was able to use your smoothing method then apply my older code to create a cubic spline of the smoothed data, which is what I had set out to do. Here is the code for reference:

%% --Variable Assignment--
osc_strain = xlsread("ag_gel_data.xlsx",1,'A31:A51');
stor_mod = xlsread("ag_gel_data.xlsx",1,'K31:K51');
loss_mod = xlsread("ag_gel_data.xlsx",1,'L31:L51');
%% --Log Scale Interpolate and Smooth Data
Npoints = 200;
osc_strain2 = logspace(log10(min(osc_strain)),log10(max(osc_strain)),Npoints);
Nsmooth = 45;
method = 'lowess';
stor_mod2 = interp1(log(osc_strain),log(stor_mod),log(osc_strain2));
stor_mod2 = smoothdata(stor_mod2,method,Nsmooth);
stor_mod2 = exp(stor_mod2);
loss_mod2 = interp1(log(osc_strain),log(loss_mod),log(osc_strain2));
loss_mod2 = smoothdata(loss_mod2,method,Nsmooth);
loss_mod2 = exp(loss_mod2);
%% --Generating Curve Data for Differentiation
[xData1, yData1] = prepareCurveData( osc_strain2, stor_mod2 );
[xData2, yData2] = prepareCurveData( osc_strain2, loss_mod2 );
% Plot fit with data on a log-log scale.
xup1 = linspace(xData1(1) , xData1(end),1e4);
yup1 = interp1(xData1,yData1,xup1,'pchip');
s11 = plot(xup1,yup1 ,'--');
xup2 = linspace(xData2(1) , xData2(end),1e4);
yup2 = interp1(xData2,yData2,xup2,'pchip');
s22 = plot(xup2,yup2 ,'--');
%% --Plotting-- (Figure 1)
figure(1);
lg1 = loglog(osc_strain,stor_mod,'.-','LineWidth',1);
hold on
s1 = loglog(osc_strain2,stor_mod2,'--','LineWidth',1);
lg2 = loglog(osc_strain,loss_mod,'o-','LineWidth',1);
s2 = loglog(osc_strain2,loss_mod2,'--','LineWidth',1);
hold off
%% --Figure Stylization--
lg1.LineStyle = "-";
lg1.Color = "magenta";
lg1.Marker = ".";
lg1.MarkerSize = 16;
s1.LineStyle = "--";
s1.Color = "black";
lg2.LineStyle = "-";
lg2.Color = "magenta";
lg2.Marker = "o";
lg2.MarkerSize = 4;
s2.LineStyle = "--";
s2.Color = "blue";
xlabel('Oscillation Stress, \gamma (%)')
ylabel("G',G'' (Pa)")
legend('Storage Modulus','Smooth Storage Modulus','Loss Modulus','Smooth Loss Modulus','Location','NW')
%% --Plotting-- (Figure 2)
figure(2);
semilogx( xup1,gradient(yup1,xup1),'-.','color',"black")
hold on
semilogx( xup2,gradient(yup2,xup2),'-.','color',"blue")
hold off
xlabel('Oscillation Stress, \gamma (%)')
ylabel('Differential Modulus, K (Pa)')
legend('Storage Modulus','Loss Modulus','Location','NE')
%% --Tabulate Differential Modulus--
K1 = gradient(yup1,xup1);
Ktable01 = [xup1; K1].';
Ktable1 = Ktable01(K1>=0,:);
K2 = gradient(yup2,xup2);
Ktable02 = [xup2; K2].';
Ktable2 = Ktable02(K2>=0,:);

I'm certain it is bloated, but it works for my purposes as it smooths, applies a cubic spline interpolant, then tabulates the gradient in a table that I can export into a dedicated graphing software. If you have any more comments on the code above please let me know and again, thank you for your help!

Elias Kerstein 2024-4-19

prepareCurveData is not a function I have written and I do not have a file in the folder named as such for MATLAB to call. I believe it is a built in function into the software or at least Curve Fitter application. Anyway, thank you for your help!