Prediction of Structural Reliability Through an Alternative Variability-Based Methodology

The often-competing goals of optimization and reliability design amplify the importance of verification, validation, and uncertainty quantification (VVUQ) to achieve sufficient reliability. Evaluation of a system's reliability presents practical challenges given the large number of permutations of conditions that may exist over the system's operational lifecycle. Uncertainty and variability sources are not always well defined and are sometimes not possible to predict, yielding traditional uncertainty quantification (UQ) techniques insufficient. A variability-based method is proposed to bridge this gap in state-of-the-art UQ practice where sources of uncertainty and variability cannot be readily quantified. At the point of incipient structural failure, the structural response becomes highly variable and sensitive to minor perturbations in conditions. This characteristic provides a powerful opportunity to determine the critical failure conditions and to assess the resulting structural reliability through an alternative variability-based method. Nonhierarchical clustering, proximity analysis, and the use of stability indicators are combined to identify the loci of conditions that lead to a rapid evolution of the response toward a failure condition. The method's utility is demonstrated through its application to a simple nonlinear dynamic single-degree-of-freedom structural model. In addition to the L2 norm, a new stability indicator is proposed called the “instability index,” which is a function of both the L2 norm and the calculated proximity to adjacent loci of conditions with differing structural response. The instability index provides a rapidly achieved quantitative measure of the relative stability of the system for all possible loci of conditions.