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Reliability analysis by AkMCS.PCK

Hello everyone,

I try to solve the reliability problem with more random variables (>10) with ‘AKMCS’ based on ‘PCK’. The options are used follows as:

APCKMCSOpts.Type = ‘Reliability’;
APCKMCSOpts.Method = ‘AKMCS’;
APCKMCSOpts.AKMCS.MetaModel = ‘PCK’;
APCKMCSOpts.AKMCS.IExpDesign.Sampling = ‘LHS’;
APCKMCSOpts.AKMCS.MaxAddedED = 20;
APCKMCSOpts.AKMCS.IExpDesign.N = 20;
APCKMCSOpts.AKMCS.PCK.Kriging.Corr.Family = ‘Gaussian’;
% APCKMCSOpts.LARS.LarsEarlyStop=50;
APCKMCSOpts.AKMCS.Convergence=‘stopPf’;
APCKMCSOpts.Simulation.MaxSampleSize = 1e6;
myAPCKMCSAnalysis = uq_createAnalysis(APCKMCSOpts);

I get this warning:

Warning: Warning: numerical instability!! Gamma for LAR
iteration 17 was set to 0 to prevent crashes.

In uq_lar (line 269)
In uq_PCE_lars (line 60)
In uq_PCE_calculate_coefficients_regression (line 197)
In uq_PCE_calculate_coefficients (line 47)
In uq_calculateMetamodel (line 18)
In uq_initialize_uq_metamodel (line 358)
In uq_core_module/run_initialization_script
In uq_core_model/add_module
In uq_createModel
In uq_PCK_calculate_coefficients (line 88)
In uq_calculateMetamodel (line 24)
In uq_initialize_uq_metamodel (line 358)
In uq_core_module/run_initialization_script
In uq_core_model/add_module
In uq_createModel
In uq_akmcs (line 110)
In uq_reliability (line 62)
In uq_analysis/run
In uq_runAnalysis
In uq_initialize_uq_reliability (line 633)
In uq_core_module/run_initialization_script
In uq_core_analysis/add_module
In uq_createAnalysis
In DARMM_ver1_Temporal_1 (line 303)

I did a change in uq_lar.m based on @nluethen comments:

After line 224 of uq_lar, I added the line:
Pinv(Psi(:,a_coeff)’*Psi(:,a_coeff));

But my problem is not solved.
Also, I used this option “LarsEarlyStop” and it was not worked for reliability analysis.
Could anyone help me to understand my mistake?

Best Regards,

Hi @Abdollahi,

The warning can sometimes appear, typically when your data does not contain enough information for LARS to select the regressors properly. Can you find out when the warning appears, is it already in the first iteration of AKMCS? It seems you are specifying 20 initial points and 20 additional points for AKMCS in more than 10 dimensions, so only 40 points in total, that might be too little to get a reasonable answer!

The change in uq_lar.m that you mention also had to do with data/design matrix problems, but doesn’t have to do with this warning, so it won’t change anything in your case.

Regarding your second question,

I am not sure what you mean with that (how did you notice it was not used?) But can it be that LARS should be a field of APCKMCSOPTS.AKMCS.PCK instead of being a field of APCKMCSOpts?

By the way, the line APCKMCSOpts.Simulation.MaxSampleSize = 1e6; is only valid for MC-based reliability and will probably be ignored. Sorry, I was wrong about that, see Reliability Analysis manual, p. 40.

Let us know whether this helped solve your problems. Good luck! :slight_smile: