Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design

By Xiaoping Du, Wei Chen. Design Automation Conference, 2004

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Design sensitivity and reliability-based structural optimization by univariate decomposition (2008, background): “Of the two remaining gradients, the partial derivative of the reliability index βk, with respect to design variable, di is (Ditlevsen and Madsen 1996) @βk @di ¼ rhk u; dð Þ T rhk u; dð Þk k @u @di " # u¼u k ð12Þ where rhk ¼ @hk=@u1; ;@hk=@uNf gT , k k is the L2 norm, and the vector derivative…”
Reliability-based design optimization for problems with interval distribution parameters (2016, methodology): “A conventional RBDO problem with precise distributions can generally be formulated as follows (Du and Chen 2004):”
Second‐order reliability method‐based inverse reliability analysis using Hessian update for accurate and efficient reliability‐based design optimization (2014, methodology): “In this way, the reliability index can be efficiently updated without sacrificing efficiency Most of the RBDO methods such as decoupled methods [25–28] and single-loop methods [29–31] are based on FORM for the simplicity and efficiency of computation.”
Reliability-Based Design With the Mixture of Random and Interval Variables (2005, methodology): “It was extended to the general probabilistic design through shifting the deterministic boundary in design space by Du and Chen [9].”