Reliability Assessment of Structures Using Interval Uncertainty Analysis

Reliability assessment of a structure is crucial in the evaluation of the structure's feasibility, integrity and safety. Moreover, conventional structural reliability assessment methods mostly employ traditional probability theories. The First Order Reliability Method (FORM) is one of the probabilistic-based methods that is widely accepted and used. However, because of its inherent approximation, the FORM may not always accurately consider the presence of uncertainties in the structure. This is especially true when the system consists of interconnected modes of failure. One of the methods to quantify the presence of uncertainty is interval or (unknown-but-bounded) analysis. In this paper, a new method for reliability assessment of structures is developed that enhances FORM for consideration of uncertainties using interval analysis. This method will hereafter be referred to as the Interval First Order Reliability Method (IFORM). IFORM benefits from the simplicity of both FORM and interval analysis by avoiding the requirement for the prior knowledge of joint probability density function for the input parameters. Using IFORM, first, uncertain input parameters are quantified by independent interval variables. Then, the first order reliability analysis is performed using input interval parameters leading to the determination of the bounds on the probability of failure (damage) for the entire structure. Several numerical examples that illustrate the capability and feasibility of this method are presented. The results are then compared with those using the FORM and Monte Carlos Simulations, in which the advantage of IFORM over the traditional FORM is demonstrated.