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Research Papers: Ocean Engineering

On the Development of an Efficient Surrogate Model for Predicting Long-Term Extreme Loads on a Wave Energy Converter

[+] Author and Article Information
Phong T. T. Nguyen

Department of Civil, Architectural and Environmental Engineering,
The University of Texas at Austin,
Austin, TX 78712
e-mail: phongnguyen@utexas.edu

Lance Manuel

Department of Civil, Architectural and Environmental Engineering,
The University of Texas at Austin,
Austin, TX 78712
e-mail: lmanuel@utexas.edu

Ryan G. Coe

Water Power Technologies,
Sandia National Laboratories,
Albuquerque, NM 87185
e-mail: rcoe@sandia.gov

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the Journal of Offshore Mechanics and Arctic Engineering. Manuscript received November 22, 2018; final manuscript received February 8, 2019; published online March 21, 2019. Assoc. Editor: Zhen Gao. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.

J. Offshore Mech. Arct. Eng 141(6), 061103 (Mar 21, 2019) (11 pages) Paper No: OMAE-18-1199; doi: 10.1115/1.4042944 History: Received November 22, 2018; Accepted February 08, 2019

Accurate prediction of long-term extreme loads is essential for the design of wave energy converters (WECs), but it is also computationally demanding due to the low probabilities associated with their occurrence. Although a full long-term probabilistic analysis using integration over all sea states or Monte Carlo simulation (MCS) may be used, these methods can be prohibitively expensive when individual response simulations are complex and time-consuming. The application of polynomial chaos expansion (PCE) schemes to allow the propagation of uncertainty from the environment through the stochastic sea surface elevation process and ultimately to WEC extreme load response prediction is the focus in this study. A novel approach that recognizes the role of long-term ocean climate uncertainty (in sea state variables such as significant wave height and spectral peak period) as well as short-term response uncertainty arising from the unique random phasing in irregular wave trains is presented and applied to a single-body point-absorber WEC device model. Stochastic simulation results in time series realizations of various response processes for the case-study WEC. We employ environmental data from a possible deployment site in Northern California (NDBC 46022) to assess long-term loads. MCS computations are also performed and represent the “truth” system against which the efficiency and accuracy of the PCE surrogate model are assessed. Results suggest that the PCE approach requires significantly less effort to obtain comparable estimates to MCS.

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References

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Figures

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Fig. 1

A schematic diagram of the case-study WEC device [7]

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Fig. 2

Example WEC response time series Hs = 7 m and Tp = 18 s: (a) PTO extension and (b) heave force

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Fig. 3

Flowchart for predicting the WEC long-term extreme response using PCE

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Fig. 4

Selected sea states (environmental variables) (a) derived from 72 Gauss–Laguerre quadrature points (b) used to obtain training data for a PCE order-6 model

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Fig. 5

WEC response extremes from the ten training data sets for Ngp = 7 values of Hs (when for Q2 = 0.19, 2.57, 12.7): (a) PTO extension, Q2 = 0.19; (b) heave force, Q2 = 0.19; (c) PTO extension, Q2 = 2.57; (d) heave force, Q2 = 2.57; (e) PTO extension, Q2 = 12.7; and (f) heave force, Q2 = 12.7

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Fig. 6

Estimated polynomial coefficients for the ten PCE order-6 models (28 terms): (a) PTO extension and (b) heave force

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Fig. 7

Cumulate contributions from order-6 polynomial expansion terms toward the long-term WEC response extreme: (a) PTO extension and (b) heave force

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Fig. 8

Comparisons of ten repetitions of loads resulting from the truth system and the PCE surrogate (p = 5, 6, 7) for the seven selected sea states: (a) and (b) p = 5; (c) and (d) p = 6; (e) and (f) p = 7

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Fig. 9

Sampled 100,000 Hs and Tp values and associated WEC response extreme for the MCS and PCE order-6 model: (a) PTO extension, MCS; (b) PTO extension, PCE; (c) heave force, MCS; and (d) heave force, PCE

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Fig. 10

WEC long-term response probability of exceedance plots based on MCS and PCE (N = 10): (a) PTO extension and (b) heave force

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Fig. 11

WEC long-term response probability of exceedance plots based on MCS and PCE (N = 15): (a) PTO extension and (b) heave force

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Fig. 12

WEC long-term response probability of exceedance plots based on MCS and PCE (N = 20): (a) PTO extension and (b) heave force

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