Overview of Reliability Analysis and Design Capabilities in DAKOTA

Reliability methods are probabilistic algorithms for quantifying the effect of uncertainties in simulation input on response metrics of interest. In particular, they compute response function distribution statistics (probability, reliability, and response levels) based on specified probability distributions for input random variables. Thus, these reliability methods provide a capability for uncertainty quantification, which may be used either for stand-alone probabilistic analysis or as a foundation for reliabilitybased design optimization algorithms. In this paper, capabilities developed at Sandia National Laboratories for reliability analysis and design [1, 2] are overviewed. From the reliability analysis side, both the forward reliability analysis of computing probabilities for specified response levels (the reliability index approach (RIA)) and the inverse reliability analysis of computing response levels for specified probabilities (the performance measure approach (PMA)) are of interest. Algorithm options include the use of limit state approximations with first-order local (AMV, AMV+), second-order local (AMV, AMV+), or multipoint (TANA) surrogate models in x-space or u-space; first-order or second-order probability integrations; analytic, numerical, or quasi-Newton limit state Hessians; most probable point search algorithm selections; and warm-starting approaches. From the reliability-based design optimization side, design formulations may be broadly characterized as bi-level (in which the reliability analysis is nested within the optimization), sequential (in which iteration occurs between optimization and reliability analysis), or unilevel (in which the design and reliability searches are combined into a Principal Member of Technical Staff, Optimization and Uncertainty Estimation Department. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed-Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000. NSF IGERT Fellow, Department of Civil and Environmental Engineering.