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Add BlackBoxChallenge problem for reliability
Add computeReliabilityIndex in FailureProbability Add beta value in the display Add support for parameter in RandomVariable Gumbel distribution Fix bug in ProbabilisticModel with Performance function but empty Evaluator Add Cinputnames in PerformanceFunction Fix but in Mio where Liomatrix and Lstructure where both were required
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‎COSSANXengine/examples/BlackBoxChallenge/RP14/RP14.m

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%% Problem Definition for the Reliability Problem 14
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% Get file name of this script
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Sfilename=mfilename;
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% Define random variables
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RV1=RandomVariable('Sdistribution','uniform', 'lowerbound',70,'upperbound',80);
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RV2=RandomVariable('Sdistribution','normal', 'mean',39, 'std',0.1);
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RV3=RandomVariable('Sdistribution','gumbel', 'parameter1',1342, 'parameter2',272.9);
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RV4=RandomVariable('Sdistribution','normal', 'mean',400, 'std',0.1);
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RV5=RandomVariable('Sdistribution','normal', 'mean',250000,'std',35000);
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% Define the RVset
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Xrvs = RandomVariableSet(...
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'Cmembers',{'RV1','RV2','RV3','RV4','RV5'},...
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'CXrv',{RV1 RV2 RV3 RV4 RV5}); %% Define the evaluator
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% Define Input object
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Xin = Input('Sdescription','Blackbox reliability challenge',...
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'CSmembers',{'Xrvs'},'CXmembers',{Xrvs});
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% Define a Model
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Xmdl=Model('Xevaluator',Evaluator,'Xinput',Xin);
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Xmio=Mio('Sdescription', 'Performance function', ...
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'Spath',pwd,'Sfile',strcat('g',Sfilename),...
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'Coutputnames',{'out'},...
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'Cinputnames',{'RV1','RV2','RV3','RV4','RV5'},...
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'Liomatrix',true,'Lfunction',true); % This flag specify if the .m file is a script or a function.
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% Construct a Mio object
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Xperfun=PerformanceFunction('Xmio',Xmio); % This flag specify if the .m file is a script or a function.
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% Construct the reliability model
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Xpm=ProbabilisticModel('Xmodel',Xmdl,'XperformanceFunction',Xperfun);
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% Define a Monte Carlo object
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% The montecarlo object defines the number of simulations to be used, the number of batches
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%assert(exists(Xsimilator),'No Simulator defined file: %s',mfilename('Fullpath'))
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‎COSSANXengine/examples/BlackBoxChallenge/RP14/gRP14.m

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function Moutput=gRP14(Minput)
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% This function defines the problem RP14.
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% Requires 5 inputs and provides 1 output
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% Performance function for reliability problem 14
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%
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% Parameters
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% ----------
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% Minput : Values of independent variables: columns are the
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% different parameters/random variables (x1, x2,...xn) and rows are
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% different parameter/random variables sets for different calls.
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%
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% Returns
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% -------
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% Moutput : Performance function value for the system.
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%
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% Reference: https://rprepo.readthedocs.io/en/latest/reliability_problems.html#sec-rp-14
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Moutput = Minput(:,1) - ...
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32./(pi.*Minput(:,2).^3) .* ...
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sqrt( (Minput(:,3).^2 .* Minput(:,4).^2)/16 + Minput(:,5).^2 );

‎COSSANXengine/examples/BlackBoxChallenge/RP24/RP24.m

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%% Problem Definition
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% Define random variables
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RV1=RandomVariable('Sdistribution','normal', 'mean',10, 'std',3.0);
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RV2=RandomVariable('Sdistribution','normal', 'mean',10, 'std',3.0);
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% Define the RVset
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Xrvs = RandomVariableSet(...
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'Cmembers',{'RV1','RV2'},...
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'CXrv',{RV1 RV2}); %% Define the evaluator
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% Construct a Mio object
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Xm=Mio( 'Sdescription', 'Performance function', ...
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...'Sscript','for j=1:length(Tinput), Toutput(j).out1=sqrt(Tinput(j).RV1^2+Tinput(j).RV2^2); end', ...
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'Spath',pwd,...
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'Sfile',[specs.Problem,'_mio'],...
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'Liostructure',true,...
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'Coutputnames',{'out'},...
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'Cinputnames',{'RV1','RV2'},...
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'Lfunction',false); % This flag specify if the .m file is a script or a function.
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% Construct the Evaluator
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Xeval = Evaluator('Xmio',Xm,'Sdescription','Evaluator xmio');
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% Define Input object
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Xin = Input('Sdescription','Blackbox reliability challenge');
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Xthreshold = Parameter('value',0);
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Xin = Xin.add('Xmember',Xrvs,'Sname','Xrvs');
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Xin = Xin.add('Xmember',Xthreshold,'Sname','Xthreshold');
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% Define a Model
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Xmdl=Model('Xevaluator',Xeval,'Xinput',Xin);
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% Define performance function
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Xpf=PerformanceFunction('Scapacity','out','Sdemand','Xthreshold','Soutputname','Vg');
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% Construct the model
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Xpm=ProbabilisticModel('Xmodel',Xmdl,'XperformanceFunction',Xpf);
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% Define a Monte Carlo object
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% The montecarlo object defines the number of simulations to be used, the number of batches
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Xsimulator = constructSimulator(specs,Xpm);
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%%
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[XpF, Xoutput] = Xpm.computeFailureProbability(Xsimulator);
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makePlots

‎COSSANXengine/examples/BlackBoxChallenge/RP24/RP24_mio.m

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for j=1:length(Tinput)
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Toutput(j).out = 2.5 - 0.2357 * (Tinput(j).RV1 - Tinput(j).RV2) + 0.00463 * (Tinput(j).RV1 + Tinput(j).RV2 - 20)^4;
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end

‎COSSANXengine/examples/BlackBoxChallenge/RP31/RP31.m

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%% Problem Definition
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% Define random variables
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RV1=RandomVariable('Sdistribution','normal', 'mean',0,'std',1);
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RV2=RandomVariable('Sdistribution','normal', 'mean',0,'std',1);
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% Define the RVset
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Xrvs = RandomVariableSet(...
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'Cmembers',{'RV1','RV2'},...
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'CXrv',{RV1 RV2}); %% Define the evaluator
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% Construct a Mio object
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Xm=Mio( 'Sdescription', 'Performance function', ...
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...'Sscript','for j=1:length(Tinput), Toutput(j).out1=sqrt(Tinput(j).RV1^2+Tinput(j).RV2^2); end', ...
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'Spath',pwd,...
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'Sfile',[specs.Problem,'_mio'],...
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'Liostructure',true,...
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'Coutputnames',{'out'},...
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'Cinputnames',{'RV1','RV2'},...
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'Lfunction',false); % This flag specify if the .m file is a script or a function.
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% Construct the Evaluator
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Xeval = Evaluator('Xmio',Xm,'Sdescription','Evaluator xmio');
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% Define Input object
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Xin = Input('Sdescription','Blackbox reliability challenge');
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Xthreshold = Parameter('value',0);
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Xin = Xin.add('Xmember',Xrvs,'Sname','Xrvs');
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Xin = Xin.add('Xmember',Xthreshold,'Sname','Xthreshold');
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% Define a Model
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Xmdl=Model('Xevaluator',Xeval,'Xinput',Xin);
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% Define performance function
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Xpf=PerformanceFunction('Scapacity','out','Sdemand','Xthreshold','Soutputname','Vg');
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% Construct the model
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Xpm=ProbabilisticModel('Xmodel',Xmdl,'XperformanceFunction',Xpf);
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% Define a Monte Carlo object
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% The montecarlo object defines the number of simulations to be used, the number of batches
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Xsimulator = constructSimulator(specs,Xpm);
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%%
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[XpF, Xoutput] = Xpm.computeFailureProbability(Xsimulator);
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makePlots

‎COSSANXengine/examples/BlackBoxChallenge/RP31/RP31_mio.m

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for j=1:length(Tinput)
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Toutput(j).out = 2 - Tinput(j).RV2 + ( 4 * Tinput(j).RV1 )^4;
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end

‎COSSANXengine/examples/BlackBoxChallenge/RP53/RP53.m

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%% Problem Definition
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RV1=RandomVariable('Sdistribution','normal', 'mean',1.5,'std',1);
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RV2=RandomVariable('Sdistribution','normal', 'mean',2.5,'std',1);
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% Define the RVset
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Xrvs = RandomVariableSet(...
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'Cmembers',{'RV1','RV2'},...
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'CXrv',{RV1 RV2}); %% Define the evaluator
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% Construct a Mio object
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Xm=Mio( 'Sdescription', 'Performance function', ...
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...'Sscript','for j=1:length(Tinput), Toutput(j).out1=sqrt(Tinput(j).RV1^2+Tinput(j).RV2^2); end', ...
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'Spath',pwd,...
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'Sfile',[specs.Problem,'_mio'],...
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'Liostructure',true,...
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'Coutputnames',{'out'},...
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'Cinputnames',{'RV1','RV2'},...
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'Lfunction',false); % This flag specify if the .m file is a script or a function.
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% Construct the Evaluator
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Xeval = Evaluator('Xmio',Xm,'Sdescription','Evaluator xmio');
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% Define Input object
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Xin = Input('Sdescription','Blackbox reliability challenge');
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Xthreshold = Parameter('value',0);
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Xin = Xin.add('Xmember',Xrvs,'Sname','Xrvs');
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Xin = Xin.add('Xmember',Xthreshold,'Sname','Xthreshold');
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% Define a Model
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Xmdl=Model('Xevaluator',Xeval,'Xinput',Xin);
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% Define performance function
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Xpf=PerformanceFunction('Scapacity','out','Sdemand','Xthreshold','Soutputname','Vg');
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% Construct the model
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Xpm=ProbabilisticModel('Xmodel',Xmdl,'XperformanceFunction',Xpf);
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Xsimulator = constructSimulator(specs,Xpm);
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%%
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[XpF, Xoutput] = Xpm.computeFailureProbability(Xsimulator);
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makePlots

‎COSSANXengine/examples/BlackBoxChallenge/RP53/RP53_mio.m

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for j=1:length(Tinput)
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Toutput(j).out = sin(5 * Tinput(j).RV1/2) + 2 - ...
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( Tinput(j).RV1^2 + 4) * ( Tinput(j).RV2 - 1 )/20;
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end

‎COSSANXengine/examples/BlackBoxChallenge/RP54/RP54.m

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%% Problem Definition
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RV1 = RandomVariable('Sdistribution','exponential', 'mean',1,'std',1);
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RV2 = RandomVariable('Sdistribution','exponential', 'mean',1,'std',1);
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RV3 = RandomVariable('Sdistribution','exponential', 'mean',1,'std',1);
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RV4 = RandomVariable('Sdistribution','exponential', 'mean',1,'std',1);
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RV5 = RandomVariable('Sdistribution','exponential', 'mean',1,'std',1);
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RV6 = RandomVariable('Sdistribution','exponential', 'mean',1,'std',1);
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RV7 = RandomVariable('Sdistribution','exponential', 'mean',1,'std',1);
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RV8 = RandomVariable('Sdistribution','exponential', 'mean',1,'std',1);
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RV9 = RandomVariable('Sdistribution','exponential', 'mean',1,'std',1);
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RV10 = RandomVariable('Sdistribution','exponential', 'mean',1,'std',1);
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RV11 = RandomVariable('Sdistribution','exponential', 'mean',1,'std',1);
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RV12 = RandomVariable('Sdistribution','exponential', 'mean',1,'std',1);
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RV13 = RandomVariable('Sdistribution','exponential', 'mean',1,'std',1);
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RV14 = RandomVariable('Sdistribution','exponential', 'mean',1,'std',1);
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RV15 = RandomVariable('Sdistribution','exponential', 'mean',1,'std',1);
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RV16 = RandomVariable('Sdistribution','exponential', 'mean',1,'std',1);
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RV17 = RandomVariable('Sdistribution','exponential', 'mean',1,'std',1);
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RV18 = RandomVariable('Sdistribution','exponential', 'mean',1,'std',1);
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RV19 = RandomVariable('Sdistribution','exponential', 'mean',1,'std',1);
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RV20 = RandomVariable('Sdistribution','exponential', 'mean',1,'std',1);
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% Define the RVset
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Xrvs = RandomVariableSet(...
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'Cmembers',{'RV1','RV2','RV3','RV4','RV5','RV6','RV7','RV8','RV9','RV10',...
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'RV11','RV12','RV13','RV14','RV15','RV16','RV17','RV18','RV19','RV20'},...
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'CXrv',{RV1 RV2 RV3 RV4 RV5 RV6 RV7 RV8 RV9 RV10 ...
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RV11 RV12 RV13 RV14 RV15 RV16 RV17 RV18 RV19 RV20}); %% Define the evaluator
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% Construct a Mio object
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Xm=Mio( 'Sdescription', 'Performance function', ...
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...'Sscript','for j=1:length(Tinput), Toutput(j).out1=sqrt(Tinput(j).RV1^2+Tinput(j).RV2^2); end', ...
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'Spath',pwd,...
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'Sfile',[specs.Problem,'_mio'],...
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'Liostructure',true,...
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'Coutputnames',{'out'},...
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'Cinputnames',{'RV1','RV2','RV3','RV4','RV5','RV6','RV7','RV8','RV9','RV10',...
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'RV11','RV12','RV13','RV14','RV15','RV16','RV17','RV18','RV19','RV20'},...
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'Lfunction',false); % This flag specify if the .m file is a script or a function.
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% Construct the Evaluator
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Xeval = Evaluator('Xmio',Xm,'Sdescription','Evaluator xmio');
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% Define Input object
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Xin = Input('Sdescription','Blackbox reliability challenge');
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Xthreshold = Parameter('value',0);
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Xin = Xin.add('Xmember',Xrvs,'Sname','Xrvs');
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Xin = Xin.add('Xmember',Xthreshold,'Sname','Xthreshold');
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% Define a Model
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Xmdl=Model('Xevaluator',Xeval,'Xinput',Xin);
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% Define performance function
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Xpf=PerformanceFunction('Scapacity','out','Sdemand','Xthreshold','Soutputname','Vg');
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% Construct the model
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Xpm=ProbabilisticModel('Xmodel',Xmdl,'XperformanceFunction',Xpf);
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Xsimulator = constructSimulator(specs,Xpm);
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%%
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[XpF, Xoutput] = Xpm.computeFailureProbability(Xsimulator);
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makePlots

‎COSSANXengine/examples/BlackBoxChallenge/RP54/RP54_mio.m

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for j=1:length(Tinput)
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Toutput(j).out=Tinput(j).RV1+...
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Tinput(j).RV2+...
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Tinput(j).RV3+...
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Tinput(j).RV4+...
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Tinput(j).RV5+...
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Tinput(j).RV6+...
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Tinput(j).RV7+...
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Tinput(j).RV8+...
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Tinput(j).RV9+...
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Tinput(j).RV10+...
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Tinput(j).RV11+...
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Tinput(j).RV12+...
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Tinput(j).RV13+...
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Tinput(j).RV14+...
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Tinput(j).RV15+...
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Tinput(j).RV16+...
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Tinput(j).RV17+...
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Tinput(j).RV18+...
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Tinput(j).RV19+...
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Tinput(j).RV20-8.951;
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end

‎COSSANXengine/examples/BlackBoxChallenge/RP75/RP75.m

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%% Problem Definition
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RV1=RandomVariable('Sdistribution','normal', 'mean',0,'std',1);
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RV2=RandomVariable('Sdistribution','normal', 'mean',0,'std',1);
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% Define the RVset
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Xrvs = RandomVariableSet(...
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'Cmembers',{'RV1','RV2'},...
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'CXrv',{RV1 RV2}); %% Define the evaluator
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% Construct a Mio object
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Xm=Mio( 'Sdescription', 'Performance function', ...
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...'Sscript','for j=1:length(Tinput), Toutput(j).out1=sqrt(Tinput(j).RV1^2+Tinput(j).RV2^2); end', ...
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'Spath',pwd,...
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'Sfile',[specs.Problem,'_mio'],...
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'Liostructure',true,...
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'Coutputnames',{'out'},...
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'Cinputnames',{'RV1','RV2'},...
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'Lfunction',false); % This flag specify if the .m file is a script or a function.
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% Construct the Evaluator
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Xeval = Evaluator('Xmio',Xm,'Sdescription','Evaluator xmio');
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% Define Input object
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Xin = Input('Sdescription','Blackbox reliability challenge');
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Xthreshold = Parameter('value',0);
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Xin = Xin.add('Xmember',Xrvs,'Sname','Xrvs');
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Xin = Xin.add('Xmember',Xthreshold,'Sname','Xthreshold');
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% Define a Model
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Xmdl=Model('Xevaluator',Xeval,'Xinput',Xin);
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% Define performance function
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Xpf=PerformanceFunction('Scapacity','out','Sdemand','Xthreshold','Soutputname','Vg');
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% Construct the model
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Xpm=ProbabilisticModel('Xmodel',Xmdl,'XperformanceFunction',Xpf);
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Xsimulator = constructSimulator(specs,Xpm);
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%%
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[XpF, Xoutput] = Xpm.computeFailureProbability(Xsimulator);
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makePlots

‎COSSANXengine/examples/BlackBoxChallenge/RP75/RP75_mio.m

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for j=1:length(Tinput)
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Toutput(j).out = 3 - Tinput(j).RV1 * Tinput(j).RV2;
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end

‎COSSANXengine/examples/BlackBoxChallenge/blackbox_challenge.mlx

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Binary file not shown.

‎COSSANXengine/examples/BlackBoxChallenge/computeFailureProbability.m

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function [outputArg1,outputArg2,outputArg4,outputArg5] = computeFailureProbability(inputArg1,inputArg2)
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%UNTITLED4 Summary of this function goes here
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% Detailed explanation goes here
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specs = inputArg1;
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problem = inputArg2;
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specs.Problem = problem;
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run(fullfile(problem,[problem,'.m']))
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outputArg1 = XpF.pfhat;
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outputArg2 = -norminv(XpF.pfhat);
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outputArg4 = XpF;
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outputArg5 = Xoutput;
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end
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‎COSSANXengine/examples/BlackBoxChallenge/constructSimulator.m

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function [outputArg1,outputArg2] = constructSimulator(inputArg1,inputArg2)
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%UNTITLED5 Summary of this function goes here
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% Detailed explanation goes here
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specs = inputArg1;
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Xpm = inputArg2;
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switch lower(specs.SimType)
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case 'mc'
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Xsimulator = MonteCarlo('Nsamples',specs.N,'Nbatches',1);
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case 'ls'
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Nlines = specs.N;
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XlsFD=LocalSensitivityFiniteDifference('Xtarget',Xpm,'Coutputnames',{'Vg'});
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XlsMC=LocalSensitivityMonteCarlo('Xtarget',Xpm,'Coutputnames',{'Vg'});
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XgFD = XlsFD.computeGradient;
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switch lower(specs.grad)
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case 'sns'
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XgSNS=XlsMC.computeGradientStandardNormalSpace;
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Xsimulator = LineSampling('Nlines',Nlines,'Xgradient',XgSNS,'Vset',specs.Vset);
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case 'phy'
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Xgrad = XlsFD.computeGradient;
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Xsimulator = LineSampling('Nlines',Nlines,'Xgradient',Xgrad,'Vset',specs.Vset);
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case 'ind'
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Xlsm=XlsFD.computeIndices;
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Xsimulator=LineSampling('Nlines',Nlines,'XlocalSensitivityMeasures',Xlsm,'Vset',specs.Vset);
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end
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case 'als'
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Xsimulator = AdaptiveLineSampling('Nlines',specs.N);
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case 'ss'
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Xsimulator = SubsetSimulation('Nsamples',specs.N,'Nbatches',1);
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end
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outputArg1 = Xsimulator;
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% outputArg2 = inputArg2;
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end
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‎COSSANXengine/examples/BlackBoxChallenge/formulas

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RP24
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\eqalign{
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& {g_{\mathrm{comp}}}({\bf X}) = 2.5 - 0.2357 \cdot ({X_1} - {X_2}) + 0.00463 \cdot {({X_1} + {X_2} - 20)^4} \cr
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& {g_{\mathrm{sys}}}({\bf X}) = {g_{\mathrm{comp}}}({\bf X}) \cr}

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