PCE for high-dimensional variables

UQ with UQLab Community Q&A and How To
1

I have 23 Gaussian variables and 605 CFD simulation results. I need to build a PCE model and settle the Sobol exponent, variance, mean to analyze the uncertainty, I also tried LARS, MC, OMP and other methods to solve, but the output of the OLOO error seems to be greater than 0.2 resulting in inaccurate results, I hope to get your help to help me solve this problem.

clearvars
uqlab
X=importdata('datafile\sample.txt');
Y=importdata('datafile\2.7.txt');
inputset={'X1','Gaussian',[1.45E+12,3.5875E+11];'X2','Gaussian',[181000000,44797500];'X3','Gaussian',[6.02E+10,1.48995E+10];'X4','Gaussian',[1.14E+7,2.82E+06];'X5','Gaussian',[3.63E+13,8.98E+12];'X6','Gaussian',[1.09E+9,2.7E+9];'X7','Gaussian',[3.63E+13,8.98E+12];'X8','Gaussian',[1.6E+15,1.6E+14];'X9','Gaussian',[1.69E+5,4.18E+4];'X10','Gaussian',[2.54E+10,6.29E+9];'X11','Gaussian',[2.5E+10,6.19E+9];'X12','Gaussian',[1.4E+12,3.47E+11];'X13','Gaussian',[9.4E+22,2.33E+22];'X14','Gaussian',[1.6E+7,3.96E+6];'X15','Gaussian',[2.3E+15,5.69E+14];'X16','Gaussian',[4E+11,9.9E+10];'X17','Gaussian',[2E+9,4.95E+8];'X18','Gaussian',[8.43E+7,2.09E+7];'X19','Gaussian',[3.01E+8,7.45E+7];'X20','Gaussian',[3.61E+7,8.93E+6];'X21','Gaussian',[9.03E+8,2.23E+8];'X22','Gaussian',[3.62E+3,8.96E+2];'X23','Gaussian',[1.45E+11,3.95E+10]}

for i=1:size(inputset,1)
 for i=1:size(inputset,1)
     InputOpts.Marginals(i).Name = inputset{i,1};
     InputOpts.Marginals(i).Type = inputset{i,2};
     InputOpts.Marginals(i).Parameters= inputset{i,3};
 end
end
myInput = uq_createInput(InputOpts);
MetaOpts.Type = 'Metamodel';
MetaOpts.MetaType = 'PCE';
MetaOpts.ExpDesign.X = X;
MetaOpts.ExpDesign.Y = Y;
MetaOpts.Degree = 2:10;
PCEOpts.TruncOptions.qNorm = 0.3:0.5;
PCEOpts.TruncOptions.MaxInteraction = 2
MetaOpts.Method = 'LARS';%LARS,BCS,OMP,OLS(求解器：稀疏，最小二回归，)
MetaOpts.ExpDesign.NSamples = size(X,1);
MetaOpts.truncOotions.Macinteraction=2;
myPCE = uq_createModel(MetaOpts);
myPCE = uq_createModel(MetaOpts);
uq_print(myPCE)
for i=1:size(Y,2)
    Mean(i)= myPCE.PCE(i).Moments.Mean;
    var(i)=myPCE.PCE(i).Moments.Var;
    std(i) = (myPCE.PCE(i).Moments.Var).^(0.5);
end
%%
SobolOpts.Type = 'Sensitivity';
SobolOpts.Method = 'Sobol';
SobolOpts.Sobol.Order = 2;
SobolOpts.Sobol.SampleSize = size(X,1);
mySobolAnalysisPCE = uq_createAnalysis(SobolOpts);
mySobolResultsPCE = mySobolAnalysisPCE.Results;
SobolTotal = mySobolResultsPCE.Total;
SobolFirstOrder =mySobolResultsPCE.FirstOrder;
2

Dear @MAJIE123

Before I dive into further details: I’m a little confused by this nested for loop:

for i=1:size(inputset,1)
 for i=1:size(inputset,1)
     InputOpts.Marginals(i).Name = inputset{i,1};
     InputOpts.Marginals(i).Type = inputset{i,2};
     InputOpts.Marginals(i).Parameters= inputset{i,3};
 end
end

The inner loop variable shadows the outer one. Is this really what you want?

Best regards
Styfen

3

This cycle is equivalent to reading the sample information, the sample name, the sample distribution type, and the sample size

4

I wanted to say that you can simply write this with a single loop:

for i = 1:size(inputset, 1)
    InputOpts.Marginals(i).Name = inputset{i, 1};
    InputOpts.Marginals(i).Type = inputset{i, 2};
    InputOpts.Marginals(i).Parameter = inputset{i, 3};
end

So I was wondering if there is a major logical error in your code.

There are a few other things I notice:

  • You have an unused structure PCEOpts. Should this be part of MetaOpts?
  • You have the line myPCE = uq_createModel(MetaOpts); twice
  • MetaOpts.truncOotions.Macinteraction=2 is not a valid field

I think the first step should be to clean up your code and make sure it does what you intend.