Structural reliability under monotony: Properties of FORM, simulation or response surface methods and a new class of Monotonous Reliability Methods (MRM)

In many mechanical or physical systems, the failure function, albeit complex and computationally intensive, happens to be monotonous with respect to its uncertain model inputs. In that case, some properties can be derived on the partial robustness of classical methods such as FORM, Monte–Carlo or response surfaces to estimate rare failure probabilities under the constraint of the number of expensive model runs, such as robust probability bounds, saved number of model runs or guaranteed variance reduction. A new formulation taking full advantage of monotony is introduced along with a family of associated Monotonous Reliability Methods (MRM). They consist in narrowing progressively some robust upper and lower bounds on the failure probability through an adaptive design of experiment. A number of variants can be considered: they comprise adaptive Monte–Carlo, dedicated response surfaces and deterministic design of experiments or hybrid variants with classical FORM or simulation methods. Their common advantages are that the prediction accuracy of the failure probability is guaranteed with certainty; additional model runs always ameliorate the accuracy; a change of the uncertainty model is possible without additional runs. Performance is compared on benchmarks including a nuclear finite-element mechanical study and a simple flooding model. Simple MRM variants appear quite promising in low input dimensions with highly efficient computation of a bounding established with certainty. Research perspectives are given to extend the efficiency of the methods in higher dimensions and address the relaxing of full monotony hypotheses.