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

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 X_r. As real-scale data from hull collapses are not available, the quantification of X_r 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 X_r. Specifically, we use Bayesian statistical inference to estimate the parameters that characterize the probabilistic model of X_r 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 X_r 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 X_r 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 X_r 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 X_r 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 X_r without any intervention in the conventional Smith method.