Second-Order Inverse Reliability Analysis: A New Methodology to the Treatment of Reliability in Engineering System

Abstract

Reliability-based methods have been established to take into account, in a rigorous manner, the uncertainties involved in analysis of engineering systems. The failure probability and reliability index are used to quantify risks and therefore evaluate the consequences of failure. First/second-order reliability method (FORM/SORM) is considered to be one of the most reliable computational methods to deal with reliability in engineering systems. Basically, the idea is to overcome the computational difficulties in determination of the reliability index and approximating the constraints. In this contribution, a new methodology to deal with uncertainties in engineering systems is proposed. This approach, called Second-Order Inverse Reliability Analysis (SOIRA), consists in the use of first and second order derivatives to find the solution associated with the highest probability value (inverse reliability analysis). In order to evaluate the proposed methodology, three reliability approaches (FORM, SORM and IRA - Inverse Reliability Analysis) are applied in two test cases: (i) W16X31 steel beam problem and (ii) beam problem. The obtained results demonstrated that the proposed strategy represents an interesting alternative to reliability design of engineering systems.