Second-Order Reliability Formulations in DAKOTA/UQ

Abstract

Reliability methods are probabilistic algorithms for quantifying the efiect of uncertainties in simulation input on response metrics of interest. In particular, they compute approximate response function distribution statistics (probability, reliability, and response levels) based on specifled probability distributions for input random variables. In this paper, second-order approaches are explored for both the forward reliability analysis of computing probabilities for specifled response levels (the reliability index approach (RIA)) and the inverse reliability analysis of computing response levels for specifled probabilities (the performance measure approach (PMA)). These new methods employ second-order Taylor series limit state approximations and second-order probability integrations using analytic, numerical, or quasi-Newton limit state Hessians, and are compared with the traditional second-order reliability method (SORM) as well as two-point limit state approximation methods. These reliability analysis methods are then employed within reliability-based design optimization (RBDO) studies using bi-level and surrogate-based formulations. These RBDO formulations employ analytic sensitivities of response, reliability, and second-order probability levels with respect to design variables that either augment or deflne distribution parameters for the uncertain variables. Relative performance of these reliability analysis and design algorithms are presented for a number of computational experiments performed using the DAKOTA/UQ software. Results indicate that second-order methods can be both more accurate through improved probability estimates and more e‐cient through accelerated convergence rates.