New Multidimensional Visualization Technique for Limit-State Surfaces in Nonlinear Finite-Element Reliability Analysis

Structural reliability problems involving the use of advanced finite-element models of real-world structures are usually defined by limit-states expressed as functions referred to as limit-state functions of basic random variables used to characterize the pertinent sources of uncertainty. These limit-state functions define hyper-surfaces referred to as limit-state surfaces in the high-dimensional spaces of the basic random variables. The hyper-surface topology is of paramount interest, particularly in the failure domain regions with highest probability density. In fact, classical asymptotic reliability methods, such as the firstand second-order reliability method FORM and SORM , are based on geometric approximations of the limit-state surfaces near the so-called design point s DP . This paper presents a new efficient tool, the multidimensional visualization in the principal planes MVPP method, to study the topology of high-dimensional nonlinear limit-state surfaces LSSs near their DPs. The MVPP method allows the visualization, in particularly meaningful twodimensional subspaces denoted as principal planes, of actual high-dimensional nonlinear limit-state surfaces that arise in both timeinvariant and time-variant mean out-crossing rate computation structural reliability problems. The MVPP method provides, at a computational cost comparable with SORM, valuable insight into the suitability of FORM/SORM approximations of the failure probability for various reliability problems. Several application examples are presented to illustrate the developed MVPP methodology and the value of the information provided by visualization of the LSS. DOI: 10.1061/ ASCE EM.1943-7889.0000183 CE Database subject headings: Finite element method; Structural reliability; Limit states; Imaging techniques. Author keywords: Nonlinear finite-element method; Structural reliability analysis; Limit-state surface; Hyper-surface topology; Multidimensional visualization.