How to randomly sample output times in Simbiology?

In the Simbiology Model Analyzer, 1) how to specify output time point of each run of the model as a random number from a normal distribution? E.g. a random number from a mean of 15min and SD 2min. 2) How to incorporate the output time as one input variable in global sensitivity analysis (Sobol index)? Thank you very much!

Answer 1

[Sulaymon Eshkabilov]

To randomly generate values using MEAN and STD values, normrnd() fcn can be used:

MEAN_val = 15;   % Mean in minutes
STD_dev = 2;     % Standard deviation in minutes

Random_Number = normrnd(MEAN_val, STD_dev, 10, 1);
fprintf('Random number generated:  %f \n', Random_Number);

Random number generated:  16.088707 
Random number generated:  15.394483 
Random number generated:  13.774981 
Random number generated:  12.427133 
Random number generated:  16.101281 
Random number generated:  14.156724 
Random number generated:  14.321607 
Random number generated:  14.717372 
Random number generated:  13.227484 
Random number generated:  13.669566 

Answer 2

[Jeremy Huard]

Hi @Wang,

Since your ultimate goal is to run a GSA on the model output, I would recommend the following:

1. Create parameter outTimeScalar in your model with the relevant unit
2. Create a parameter that converts the simulation time (which can be different for every simulation program) into the same unit as the parameter outTimeScalar. This can be achieved with a repeated assignment: timeInUnitOfInterest = time
3. Create an observable that will call an external function that you will implement in the next step, for example: out = getOutput(timeInUnitOfInterest, speciesOfinterest, outTimeScalar)
4. Create the external function that gives you the output at this specific time:

function out = getOutput(time, speciesOfinterest, outTime)

if all(time==0)

out = speciesOfinterest(end);

else

[time,idx] = unique(time,'last');

speciesOfinterest = speciesOfinterest(idx);

outTime = outTime(1);

out = interp1(time, speciesOfinterest, outTime,'pchip');

end

end

Please note that for this to provide meaningful results, you will need to make sure that timeInUnitOfInterest(1) < outTimeScalar < timeInUnitOfInterest(end).

Now, you can use Sobol GSA or MPGSA with outTimeScalar as an input that is sampled from a normal distribution.

I hope this helps.

Best regards,

Jérémy

Edit: Corrected function.