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Bayesian Reliability Analysis Using Kriging Dimension Reduction Method (KDRM)

A technique for reliability-based design optimization(RBDO) is developed based on the Bayesian approach, which can deal with the epistemic uncertainty arising due to the limited number of data. Until recently, the conventional RBDO was implemented mostly by assuming the uncertainty as aleatory which means the statistical properties are completely known. In practice, however, this is not the case due to the insufficient data for estimating the statistical information, which makes the existing RBDO methods less useful. In this study, a Bayesian reliability is introduced to take account of the epistemic uncertainty, which is defined as the lower confidence bound of the probability distribution of the original reliability. In this case, the Bayesian reliability requires double loop of the conventional reliability analyses, which can be computationally expensive. Kriging based dimension reduction method(KDRM), which is a new efficient tool for the reliability analysis, is employed to this end. The proposed method is illustrated using a couple of numerical examples.