How to interpolate my data to produce a variable tolerance band

I have 2 seperate in input arrays, containing x and y values which when plotted give me a black line in the graph similar to the following:

I am looking to apply upper and lower tolerance limits to my data to produce a graph with tighter tolerancing for small Y values (e.g 2x) than large values with a cap of 5x max(Y) and -1/5 max(Y) for the upper and lower tolerances as shown.

My initial thoughts were that interpolation of each Y value based on proximity of the X value to max(Y) would be the best approach however I can't seem to get my data into the correct format for the "interp1" command to produce the graph similar to the one i've drawn above as the Y values are not based on a mathematical function!

Any thoughts?

Answer 1

[Mathieu NOE]

hello

maybe this ? your 2 and 5 factors are my a and b in the code below :

clc
clearvars

% dummy signal
n=300;
x=linspace(0,2*pi,n);
y = 0.25*ones(size(x));
y = max(y,-cos(x));

% min / max coefficients
a = 2;
b = 5;
bell_factor = length(y)/7; % tune the bell shape (narrow or wider)

%% main code
a_min1 = a*min(y);
a_max1 = b*max(y);
a_min2 = (1-1/a)*min(y);
a_max2 = (1-1/b)*max(y);

% find peak point
[val,ind] = max(y);
for ci = 1:n
    dist = abs(ci-ind);
    limit_upper(ci) = a_min1 + (a_max1 - a_min1)*exp(-(dist/bell_factor)^2);
    limit_lower(ci) = a_min2 + (a_max2 - a_min2)*exp(-(dist/bell_factor)^2);
end
    
    

figure(1)
plot(x,y,'k',x,limit_upper,'g--',x,limit_lower,'b--','linewidth',2,'markersize',12);

[Chris Swain-Phipps]

Looks promising but the down side of this approach is that it doesn't take into account the impact of the surrounding Y values and assumes data is symmetrical about the maximum point.

[Mathieu NOE]

hello

1/ not sure to understand what you mean by " surrounding Y values" - maybe if you would share some data that would help ?

2/ was not sure either what the shape of the tolerance curve should be ? follow the y data shape or ? I was guesing from the posted graph that the uppel / lower curves would hape a gaussian shape , but that was my idea.

[Chris Swain-Phipps]

Hi Mathieu,

Basically, I'm looking for a way for the limits to be set based on the values of some reference data.

So in your graph that you produced above, I want the limits curves to have a similar shape but scaled differently in the Y-axis based on the distance away from the maximum value, something like this:

I've added a feature to the reference signal you created to empahsise that this should also be visible on the tolerance curve.

Hope that clarifies things.

[Mathieu NOE]

hello Cristopher

a new attempt here below :

clc
clearvars

% dummy signal
n=300;
x=linspace(0,2*pi,n);
y = 0.25*ones(size(x));
y = max(y,-cos(x));
y(200:220) = 0.5;

% min / max coefficients
a = 2;
b = 5;

%% main code

% find peak point
[val,ind] = max(y);

for ci = 1:n
    dist = abs(ci-ind)./ind;
    limit_upper(ci) = (a + (b - a)*(1-dist)).*y(ci);
    limit_lower(ci) = (1/a + (1/b - 1/a)*(1-dist)).*y(ci);
end
    
figure(1)
plot(x,y,'k',x,limit_upper,'g--',x,limit_lower,'b--','linewidth',2,'markersize',12);