A Bayesian analysis for the quantification of strength model uncertainty factor of ship structures in ultimate limit state

Abstract

The assessment of ship structural reliability involves the quantification of hull girder ultimate bending capacity. Traditionally, Smith’s method is employed for the probabilistic modeling of capacity. The modeling uncertainty associated with Smith’s method is considered by an independent multiplicative random variable Xr. As real-scale data from hull collapses are not available, the quantification of Xr is usually based on the combination of engineering judgment with more objective information, such as non-linear finite element analysis (NLFEA). In this paper, we propose a Bayesian analysis for the determination of Xr. Specifically, we use Bayesian statistical inference to estimate the parameters that characterize the probabilistic model of Xr based on expert judgment and a limited number of high-fidelity NLFEA data. We demonstrate the applicability of the method on container ships, for which two typical load scenarios are considered: (i) pure hogging moment and (ii) combined hogging moment with local bottom loads. For each load scenario, the corresponding Xr is determined. For cases where specific information from a target ship is available, a classical Bayesian updating scheme is proposed to adjust the distribution of Xr based on the individual ship’s structural characteristics. We present a numerical demonstration for the case of the MOL Comfort at the time of the accident. Finally, the impact of the proposed Xr on the failure probability estimate of a 4,400 TEU and a 9,400 TEU container ship is investigated. We show that using the proposed Xr the estimate of the uncertainty in Smith’s model prediction in pure hogging condition is considerably reduced. In addition, we demonstrate that the action of bottom local loads, which considerably decreases the hull girder ultimate strength and the reliability level of container ships in hogging, can be captured by the proposed Xr without any intervention in the conventional Smith method.