Hello everyone,
I am working on evaluating the reliability index (β) and the probability of failure (pf) of a beam using both the Monte Carlo Simulation (MCS) and the First Order Reliability Method (FORM) with the following limit state function:
g(P, L, W, T) = W * T - (P * L) / 4
The random variables and their properties are defined as follows:
- Beam length (L) : Normal distribution (8m, 0.1m)
- Force (P): ∼ N(10 kN, 2kN)
- Plastic section modulus (W): ∼ N(100*10^-6 m^3, 2.10^-5 m^3)
- Yield stress (T):∼ N(600*10^3 kN/m^2, 10^5 kN/m^2)
I implemented the following MATLAB code to set up the reliability analysis in UQLab:
%% Initialize UQLab
uqlab;
% Remove existing models and inputs to avoid the "Multiple model definitions" error
uq_removeModel('all'); % Remove all existing models
uq_removeInput('all'); % Remove all existing input objects
%% Define the probabilistic model (INPUT object)
InputOpts.Marginals(1).Name = 'L'; % Beam length
InputOpts.Marginals(1).Type = 'Gaussian';
InputOpts.Marginals(1).Parameters = [8, 0.1]; % Mean 8m, Std 0.1m
InputOpts.Marginals(2).Name = 'P'; % Force
InputOpts.Marginals(2).Type = 'Gaussian';
InputOpts.Marginals(2).Parameters = [10, 2]; % Mean 10kN, Std 2kN
InputOpts.Marginals(3).Name = 'W'; % Plastic section modulus
InputOpts.Marginals(3).Type = 'Gaussian';
InputOpts.Marginals(3).Parameters = [100e-6, 2e-5]; % Mean 100x10^-6, Std 2x10^-5
InputOpts.Marginals(4).Name = 'T'; % Yield stress
InputOpts.Marginals(4).Type = 'Gaussian';
InputOpts.Marginals(4).Parameters = [600e3, 1e5]; % Mean 600x10^3 kN/m^2, Std 10^5 kN/m^2
% Create the INPUT object
myInput = uq_createInput(InputOpts);
%% Define the limit state function (MODEL object)
ModelOpts.mString = 'X(:,3) .* X(:,4) - (X(:,2) .* X(:,1)) / 4'; % MATLAB function for g(P, L, W, T)
ModelOpts.isVectorized = true; % To handle vectorized operations
% Create the MODEL object
myModel = uq_createModel(ModelOpts);
%% Set up the reliability analysis (ANALYSIS object)
% Monte Carlo Simulation (MCS) setup
ReliabilityOpts.Type = 'Reliability';
ReliabilityOpts.Method = 'MCS'; % Monte Carlo Simulation
ReliabilityOpts.Simulation.BatchSize = 1e4; % Number of samples per batch
ReliabilityOpts.Simulation.MaxSampleSize = 1e6; % Maximum number of samples
% Assign the limit state function and input
ReliabilityOpts.Model = myModel;
ReliabilityOpts.Input = myInput;
% Run the reliability analysis using MCS
MCSAnalysis = uq_createAnalysis(ReliabilityOpts);
%% Output the MCS results
uq_print(MCSAnalysis);
uq_display(MCSAnalysis);
%% Set up FORM analysis
ReliabilityOpts.Method = 'FORM'; % First Order Reliability Method
% Run the reliability analysis using FORM
FORMAnalysis = uq_createAnalysis(ReliabilityOpts);
%% Output the FORM results
uq_print(FORMAnalysis);
uq_display(FORMAnalysis);
However, I encounter the following error:
Error using uq_initialize_uq_default_model
Multiple model definitions found!
Error in uq_core_module/run_initialization_script (line 201)
initHandle(obj);
Error in uq_core_model/add_module (line 91)
success = this.run_initialization_script(obj);
Error in uq_createModel (line 107)
eval(str);
Error in Question_5_MC_FORM (line 35)
myModel = uq_createModel(ModelOpts);
I have attempted to remove existing models and inputs using uq_removeModel and uq_removeInput, but the error persists. Could anyone advise me on how to resolve this issue?
Thank you in advance for your help!