Interpolating(or averaging) Time series curves

Question

Testscan 2022-7-18

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1763135-interpolating-or-averaging-time-series-curves

评论： Mathieu NOE 2022-7-20

Hi all, I have two time-series curves (blue and red as shown in the picture) corresponding to two different conditions (T=800, T=900). I would like to make an averaging of the two curves (or interpolation?) to get a curve like the black indicated in the picture corresponding to T=850. Do you have any suggestion how to do it? I was unable to get a code to reproduce the black curve numerically.

Do you think machine learning could be an option?

Many thanks

Input Data:

Red Curve:

0	0
5	0,0100000000000000
5,20000000000000	0,300000000000000
5,30000000000000	10
14	9,80000000000000
14,5000000000000	19
50	17

Blue Curve:

0	0
5	0,0100000000000000
5,20000000000000	0,300000000000000
5,30000000000000	10
10	9,80000000000000
10,5000000000000	19
50	17

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Answer 1

Mathieu NOE 2022-7-19

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在 MATLAB Online 中打开

hello

in your case it's fairly simple as both blue and red curves have exactly the same y values (but for different x)

so you simply need to do the mean of y blue and red and yu're done !

in case the two data sets would not share the same y values it would be a different situation (but it's also feasible)

%Red Curve:
rc = [0	0;
5	0.01;
5.2	0.30;
5.3	10;
14	9.80;
14.5	19;
50	17];
xr = rc(:,1);
yr = rc(:,2);
% Blue Curve:
bc = [0	0;
5	0.01;
5.2	0.30;
5.3	10;
10	9.80;
10.5	19;
50	17];
xb = bc(:,1);
yb = bc(:,2);
% plot red / blue / black curves
xk = (xr+xb)*0.5; % mean value
yk = (yr+yb)*0.5; % mean value
figure(1) 
plot(xb,yb,'b',xr,yr,'r',xk,yk,'k')

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Mathieu NOE 2022-7-19

在 MATLAB Online 中打开

here a better code that should work on your data

notice that I generates red and blue datas with different ranges and spacing to be more generic;

code :

 % create dummy data with different x spacings , start , end values :
%Red Curve:
xr = (0:1:50);
yr = sin(xr/50);
% Blue Curve:
xb = (1:0.5:55);
yb = sin(xb/50 +0.2);
% plot red / blue  original curves
figure(1) 
plot(xb,yb,'b',xr,yr,'r')
% create common x and y data
x_common = linspace(max(xb(1),xr(1)),min(xb(end),xr(end)),50);
% resample data on x_common
yr = interp1(xr,yr,x_common);
yb = interp1(xb,yb,x_common);
y_common = linspace(max(yb(1),yr(1)),min(yb(end),yr(end)),50);
%% main loop : search for horizontal intersections given by y_common data as threshold values
for ci = 1:numel(y_common)-1
    threshold = y_common(ci); % 
    [t0_pos1,s0_pos1,t0_neg1,s0_neg1]= crossing_V7(yr,x_common,threshold,'linear'); % positive (pos) and negative (neg) slope crossing points 
    [t0_pos2,s0_pos2,t0_neg2,s0_neg2]= crossing_V7(yb,x_common,threshold,'linear'); % positive (pos) and negative (neg) slope crossing points 
    % ind => time index (samples)
    % t0 => corresponding time (x) values 
    % s0 => corresponding function (y) values , obviously they must be equal to "threshold"
    tr = [t0_pos1 t0_neg1];
    tb = [t0_pos2 t0_neg2];
    xk(ci) = (tr+tb)/2;
    yk(ci) = threshold;
        
end
% plot red / blue / black curves aft
figure(2) 
plot(x_common,yb,'b',x_common,yr,'r',xk,yk,'k')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [t0_pos,s0_pos,t0_neg,s0_neg] = crossing_V7(S,t,level,imeth)
% [ind,t0,s0,t0close,s0close] = crossing_V6(S,t,level,imeth,slope_sign) % older format
% CROSSING find the crossings of a given level of a signal
%   ind = CROSSING(S) returns an index vector ind, the signal
%   S crosses zero at ind or at between ind and ind+1
%   [ind,t0] = CROSSING(S,t) additionally returns a time
%   vector t0 of the zero crossings of the signal S. The crossing
%   times are linearly interpolated between the given times t
%   [ind,t0] = CROSSING(S,t,level) returns the crossings of the
%   given level instead of the zero crossings
%   ind = CROSSING(S,[],level) as above but without time interpolation
%   [ind,t0] = CROSSING(S,t,level,par) allows additional parameters
%   par = {'none'|'linear'}.
%	With interpolation turned off (par = 'none') this function always
%	returns the value left of the zero (the data point thats nearest
%   to the zero AND smaller than the zero crossing).
%
% check the number of input arguments
error(nargchk(1,4,nargin));
% check the time vector input for consistency
if nargin < 2 | isempty(t)
	% if no time vector is given, use the index vector as time
    t = 1:length(S);
elseif length(t) ~= length(S)
	% if S and t are not of the same length, throw an error
    error('t and S must be of identical length!');    
end
% check the level input
if nargin < 3
	% set standard value 0, if level is not given
    level = 0;
end
% check interpolation method input
if nargin < 4
    imeth = 'linear';
end
% make row vectors
t = t(:)';
S = S(:)';
% always search for zeros. So if we want the crossing of 
% any other threshold value "level", we subtract it from
% the values and search for zeros.
S   = S - level;
% first look for exact zeros
ind0 = find( S == 0 ); 
% then look for zero crossings between data points
S1 = S(1:end-1) .* S(2:end);
ind1 = find( S1 < 0 );
% bring exact zeros and "in-between" zeros together 
ind = sort([ind0 ind1]);
% and pick the associated time values
t0 = t(ind); 
s0 = S(ind);
if ~isempty(ind)
    if strcmp(imeth,'linear')
        % linear interpolation of crossing
        for ii=1:length(t0)
            %if abs(S(ind(ii))) >= eps(S(ind(ii)))    % MATLAB V7 et +
            if abs(S(ind(ii))) >= eps*abs(S(ind(ii)))    % MATLAB V6 et -    EPS * ABS(X)
                % interpolate only when data point is not already zero
                NUM = (t(ind(ii)+1) - t(ind(ii)));
                DEN = (S(ind(ii)+1) - S(ind(ii)));
                slope =  NUM / DEN;
                slope_sign(ii) = sign(slope);
                t0(ii) = t0(ii) - S(ind(ii)) * slope;
                s0(ii) = level;
            end
        end
    end
    % extract the positive slope crossing points 
    ind_pos = find(sign(slope_sign)>0);
    t0_pos = t0(ind_pos);
    s0_pos = s0(ind_pos);
    % extract the negative slope crossing points 
    ind_neg = find(sign(slope_sign)<0);
    t0_neg = t0(ind_neg);
    s0_neg = s0(ind_neg);
else
    % empty output
    ind_pos = [];
    t0_pos = [];
    s0_pos = [];
    % extract the negative slope crossing points 
    ind_neg = [];
    t0_neg = [];
    s0_neg = [];
    
end
end

Mathieu NOE 2022-7-19

在 MATLAB Online 中打开

here we are

I am not saying here it's the ultimated code as it has been quite "customized" to work with your specific data.

Others approaches based on xcorr or dwt or other work done in the past have not been very satisfactory so for the time being this is the best answer I can supply in my limited time :

maybe it's good enough for a publication or a presentation

code :

load('export.mat'); %  (x_common, yr, yb) 
x_common = export(:,1);
dx = mean(diff(x_common));
yr = export(:,2);
yb = export(:,3);
ym = 0.5*(yb+yr);
%% main loop 
% some portion of the mean signal will be time shifted
% this will be done only on a limited x window around the big peaks located
% from the second derivative of the signal
% diff 
dyb = diff(yb)./dx;
dyb = [dyb(1); dyb];
dyr = diff(yr)./dx;
dyr = [dyr(1); dyr];
% diff diff
ddyb = diff(dyb)./dx;
ddyb = [ddyb(1); ddyb];
ddyr = diff(dyr)./dx;
ddyr = [ddyr(1); ddyr];
figure(1) 
subplot(211),plot(x_common,yb,'b*-',x_common,yr,'r*-')
subplot(212),plot(x_common,ddyb,'b*-',x_common,ddyr,'r*-')
% find first positive peaks for red curve second derivative
[mpr,indpr] = max(ddyr);
% find first positive peaks for blue curve second derivative
[mpb,indpb] = max(ddyb);
% find last negative peaks for blue curve second derivative
[mnb,indnb] = min(ddyb);
winlength = indnb-indpr;
yr_extract = yr(indpr-winlength:indpr+winlength);
yb_extract = yb(indpb-winlength:indpb+winlength);
ym_extract = 0.5*(yr_extract+yb_extract);
% replace ym section by ym_extract
center = round(0.5*(indpr+indpb));
ym(center-winlength:center+winlength) = ym_extract;
figure(2) 
plot(x_common,yb,'b',x_common,yr,'r',x_common,ym,'k')