A Sensitivity-Based Approach for Reliability Analysis of Randomly Excited Structures With Interval Axial Stiffness

Abstract

Reliability assessment of linear discretized structures with interval parameters subjected to stationary Gaussian multi-correlated random excitation is addressed. The interval reliability function for the extreme value stress process is evaluated under the Poisson assumption of independent up-crossing of a critical threshold. Within the interval framework, the range of stress-related quantities may be significantly overestimated as a consequence of the so-called dependency phenomenon, which arises due to the inability of the Classical Interval Analysis (CIA) ([1],[2]) to treat multiple occurrences of the same interval variables as dependent ones. To limit undesirable conservatism in the context of interval reliability analysis, a novel sensitivity-based procedure relying on a combination of the Interval Rational Series Expansion [3] and the Improved Interval Analysis via Extra Unitary Interval [4] is proposed. This procedure allows us to detect suitable combinations of the endpoints of the uncertain parameters which yield accurate estimates of the lower bound and upper bound of the interval reliability function for the extreme value stress process. Furthermore, sensitivity analysis enables to identify the most influential parameters on structural reliability. A numerical application is presented to demonstrate the accuracy and efficiency of the proposed method as well as its usefulness in view of decision-making in engineering practice.

Reliability analysis of randomly excited FE modelled structures with interval mass and stiffness via sensitivity analysis

“…The chain rule of differentiation yields the following expression of the sensitivity of the CDF of the extreme value stress random process Y (h) j,max (α I , T) with respect to the uncertain parameters α i ∈ α I i (i = 1, 2, …, r) [50]:…”

“…For structures with uncertain-but-bounded parameters, the so-called fractile of order p, i.e. the response level which has a specified probability, p, of not being exceeded during the observation time [0, T], has an interval nature as well [46,50].…”

“…, of the interval stress random process Y (h) j (α I , t) can be computed by solving the following nonlinear equations [46,50]:…”

“…Indeed, stresses are more sensitive to the dependency phenomenon than displacements since their expression involves multiple occurrences of the same interval variables. Recently, this issue has been successfully addressed by Sofi et al [50] who proposed a sensitivity-based procedure for estimating the bounds of the interval reliability function for structures with interval axial stiffness assuming the axial stress at a critical location as responsible of structural failure. Recent efforts in literature have been devoted to the solution of the interval first-passage problem taking into account epistemic uncertainties in the stochastic loading model [51,52].…”

“…The main purpose of the present study is the extension of the sensitivity-based procedure proposed by Sofi et al [50] to general finite element models involving both mass and stiffness uncertainties subjected to stationary Gaussian multi-correlated random excitation with deterministic parameters. The formulation is developed in the context of the first-passage theory, under the Poisson assumption of independent up-crossings of a prescribed threshold [36,38].…”