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Uncertainty quantification of Delft catamaran resistance, sinkage and trim for variable Froude number and geometry using metamodels, quadrature and Karhunen–Loève expansion

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Abstract

A framework for assessing convergence and validation of non-intrusive uncertainty quantification (UQ) methods is studied and applied to a complex industrial problem in ship design, namely the high-speed Delft Catamaran advancing in calm water, with variable Froude number and geometry. Relationship between UQ studies and deterministic verification and validation is discussed. Computations are performed using high- (URANS) and low- (potential flow) fidelity simulations. Froude number has expected value and standard deviation equal to 0.5 and 0.05, respectively, on a truncated normal distribution. Geometric uncertainty is related to the research space of a simulation-based design optimization, and assessed through the Karhunen–Loève expansion (KLE). Monte Carlo method with Latin hypercube sampling (MC-LHS) is used to compute expected value, standard deviation, distribution and uncertainty intervals for resistance, sinkage and trim. MC-LHS with CFD is used as a benchmark for validating less costly UQ methods, including MC-LHS with metamodels and standard quadrature formulas. Gaussian quadrature is found the most efficient method; however, MC-LHS with metamodels is preferred since provides with confidence intervals and distributions in a straightforward way and at reasonably small computational cost. UQ results are compared to earlier deterministic single- and multi-objective optimization; reduced-dimensional KLE studies for geometric variability indicate that stochastic optimization would not be of great benefit for the present problem.

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Acknowledgments

The present research is supported by the Office of Naval Research, Grant N00014-11-10237 and NICOP Grant N62909-11-17011, under the administration of Dr. Ki-Han Kim. The URANS computations were performed at the NAVY DoD Supercomputing Resource Center. Dr. Patrick Purtell provided support for the precursory research. The research was conducted in collaboration with NATO AVT-191: Application of Sensitivity Analysis and Uncertainty Quantification to Military Vehicle Design.

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Authors and Affiliations

  1. CNR-INSEAN, National Research Council-Marine Technology Research Institute, Via di Vallerano 139, 00128, Rome, Italy

    Matteo Diez & Emilio F. Campana

  2. IIHR-Hydroscience and Engineering, The University of Iowa, 100 C. Maxwell Stanley Hydraulics Laboratory, Iowa, IA, 52242-1585, USA

    Matteo Diez, Wei He & Frederick Stern

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  1. Matteo Diez
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  2. Wei He
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Correspondence to Frederick Stern.

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Diez, M., He, W., Campana, E.F. et al. Uncertainty quantification of Delft catamaran resistance, sinkage and trim for variable Froude number and geometry using metamodels, quadrature and Karhunen–Loève expansion. J Mar Sci Technol 19, 143–169 (2014). https://doi.org/10.1007/s00773-013-0235-0

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