Prediction of Structural Reliability Through an Alternative Variability-Based Methodology

Abstract

Abstract Astonishing increases in computational power have fueled the engineering community’s drive to seek increasingly optimized solutions to structural design problems. Although structural optimization can be critical to achieve a practical and cost-effective design, optimization often comes at a cost to reliability. The competing goals of optimization and reliability amplify the importance of validation, verification, and uncertainty quantification efforts to achieve sufficiently reliable performance. Evaluation of a structural system’s reliability presents a practical challenge to designers given the potentially large number of permutations of conditions that may exist over the full operational lifecycle. A direct prediction of performance and the prediction’s corresponding likelihood is often achieved via deterministic analysis techniques in conjunction with Monte Carlo analysis. Such methods can be overly cumbersome and often do not provide a complete picture of the system’s global reliability due to the practical limits of performing the necessary number of analyses. 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, but more expedient variability-based method. Non-hierarchical 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 structural response toward a failure condition. The utility of the proposed method is demonstrated through its application to a simple nonlinear dynamic single-degree-of-freedom structural model. A feedforward artificial neural network is trained from numerically-generated data to provide an expedient means of assessing the system’s behavior under perturbed conditions. 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.