Computational model without and with conditional expressions in Structural Reliability

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Hello everyone.

The UQLab V2.0 structural reliability module contains the approximation (FORM, SORM) and simulation (MCS, MCS-IS, MCS-SS) methods to estimate the probability of failure (P_f) and reliability index (\beta).

Initially I inserted a vectorized computational model as indicated in the manual. Then I added “if”, “elseif” and “else” conditional expressions as lines of code, since a deterministic parameter is determined with logical operations of two random parameters.

  • When the vectorized computational model does not include conditional expressions. I obtain agreement in the P_f and the \beta, between the approximation and simulation methods.
  • When the vectorized computational model includes conditional expressions. I get a discrepancy in the P_f and \beta, between the approximation and simulation methods.

My question is: In the presence of conditional expressions in the computational model, should I expect agreement or discrepancy in the results, between the approximation and simulation methods?

Thanks in advance for your answers.

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Hey @CsrCastillo,

Let me see if I understand your question correctly. You have a model of a limit-state function, and you perform reliability analysis on it using both simulation methods and approximation methods. However, because a set of parameters in your model depends on the input parameters, you have to introduce an ‘if’ statement. Once you do that, the approximation method no longer matches the results of the simulation methods. Is that right?

If this is the case, have you checked if the change in the parameters caused by the ‘if’ statements leads to some kind of bifurcation or some kind of discontinuity in the respose? I ask this because I believe that the approximation method has most likely converged to a wrong design point, or your model might have multiple failure regions, which are not captured by the approximation method.

Replying more directly to your question, I would say that yes, depending on how the changes in the parameters of your model affect the topology of your limit-state function, it is expected that a difference between the two approaches would appear. The question that remains is understanding how the ‘if’ statement affects the topology of your limit-state function.

If I misunderstood the question, please let me know!

Best regards,
Anderson

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