Monte Carlo analyses are generally considered the standard for uncertainty analysis. While accurate, these analyses can be expensive computationally. Recently, polynomial chaos has been proposed as an alternative approach to the estimation of uncertainty distributions (Hosder et al. A non-intrusive polynomial chaos method for uncertainty propagation in CFD simulations. In: 44th AIAA aerospace sciences meeting and exhibit, Reno, Nevada, 2006; Wu et al. Uncertainty analysis for parametric roll using non-intrusive polynomial chaos. In: Proceedings of the 12th international ship stability workshop, Washington, DC, USA, 2011). This approach works by representing the function as a series of orthogonal polynomials; the weights for which can be calculated via several methods. Previous studies have demonstrated the usefulness of this technique for comparatively simple systems such as parametric roll modeled by the Mathieu equation with normally distributed parameter values (Wu et al. Uncertainty analysis for parametric roll using non-intrusive polynomial chaos. In: Proceedings of the 12th international ship stability workshop, Washington, DC, USA, 2011). In the present work, a polynomial chaos method is applied to a nonlinear computational ship dynamics model with normally distributed input parameters. Test cases were selected where parametric roll was expected to potentially occur. The resulting probability distributions are compared to the results of a Monte Carlo analysis. In general, these results demonstrate good agreement between Monte Carlo simulation and polynomial chaos in the absence of capsize with significant computation gains found with polynomial chaos. Overall, we conclude that polynomial chaos is an effective tool for reducing simulation time costs when studying parametric roll, and potentially other ship dynamics phenomena, particularly in the absence of capsize-like bifurcations.
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The authors are extremely grateful for the advice provided by Mr. Kenneth Weems. The authors would also like to thank Drs. Pat Purtell, Ki-Han Kim, and Thomas Fu at the Office of Naval Research under Grant Number N00014-10-1-0398 and Eduardo Misawa at the National Science Foundation under Grant CMMI 0747973 for providing funding for this work.
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Cooper, M.D., Wu, W. & McCue, L.S. Non-intrusive polynomial chaos for efficient uncertainty analysis in parametric roll simulations. J Mar Sci Technol 21, 282–296 (2016). https://doi.org/10.1007/s00773-015-0351-0
- Parametric roll
- Non-intrusive polynomial chaos
- Monte Carlo
- Uncertainty analysis