Research Papers: Ocean Renewable Energy

Efficient Dynamic Analysis of a Nonlinear Wave Energy Harvester Model

[+] Author and Article Information
Pol D. Spanos

Honorary Mem. ASME
G. R. Brown School of Engineering,
Rice University,
Houston, TX 77005;
Tongji University,
Shanghai 200092, China
e-mail: spanos@rice.edu

Felice Arena

DICEAM Department,
“Mediterranea” University of Reggio Calabria,
Loc. Feo di Vito,
Reggio Calabria 89122, Italy
e-mail: arena@unirc.it

Alessandro Richichi

DICEAM Department,
“Mediterranea” University of Reggio Calabria,
Loc. Feo di Vito,
Reggio Calabria 89122, Italy
e-mail: alessandro.richichi@unirc.it

Giovanni Malara

DICEAM Department,
“Mediterranea” University of Reggio Calabria,
Loc. Feo di Vito,
Reggio Calabria 89122, Italy
e-mail: giovanni.malara@unirc.it

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 October 9, 2015; final manuscript received February 10, 2016; published online April 7, 2016. Assoc. Editor: António Falcão.

J. Offshore Mech. Arct. Eng 138(4), 041901 (Apr 07, 2016) (8 pages) Paper No: OMAE-15-1104; doi: 10.1115/1.4032898 History: Received October 09, 2015; Revised February 10, 2016

In recent years, wave energy harvesting systems have received considerable attention as an alternative energy source. Within this class of systems, single-point harvesters are popular at least for preliminary studies and proof-of-concept analyses in particular locations. Unfortunately, the large displacements of a single-point wave energy harvester are described by a set of nonlinear equations. Further, the excitation is often characterized statistically and in terms of a relevant power spectral density (PSD) function. In the context of this complex problem, the development of efficient techniques for the calculation of reliable harvester response statistics is quite desirable, since traditional Monte Carlo techniques involve nontrivial computational cost. The paper proposes a statistical linearization technique for conducting expeditiously random vibration analyses of single-point harvesters. The technique is developed by relying on the determination of a surrogate linear system identified by minimizing the mean square error between the linear system and the nonlinear one. It is shown that the technique can be implemented via an iterative procedure, which allows calculating statistics, PSDs, and probability density functions (PDFs) of the response components. The reliability of the statistical linearization solution is assessed vis-à-vis data from relevant Monte Carlo simulations. This novel approach can be a basis for constructing computationally expeditious assessments of various design alternatives.

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Cruz, J. , 2008, Ocean Wave Energy: Current Status and Future Perspectives, Springer, Berlin.
Clément, A. , McCullen, P. , Falcão, A. , Fiorentino, A. , Gardner, F. , Hammarlund, K. , Lemonis, G. , Lewis, T. , Nielsen, K. , Petroncini, S. , Pontes, M. T. , Schild, P. , Sjöström, B.-O. , Sørensen, H. C. , and Thorpe, T. , 2002, “ Wave Energy in Europe: Current Status and Perspectives,” Renewable Sustainable Energy Rev., 6(5), pp. 405–431. [CrossRef]
Falnes, J. , 2007, “ A Review of Wave-Energy Extraction,” Mar. Struct., 20(4), pp. 185–201. [CrossRef]
Falcão, A. F. d. O. , 2010, “ Wave Energy Utilization: A Review of the Technologies,” Renewable Sustainable Energy Rev., 14(3), pp. 899–918. [CrossRef]
Budal, K. , Falnes, J. , Iversen, L. C. , Lillebekken, P. M. , Oltedal, G. , Hals, T. , Onshus, T. , and Høy, A. S. , 1982, “ The Norwegian Wave-Power Buoy Project,” 2nd International Symposium on Wave Energy Utilization, H. Berge , ed., Trondheim, Norway.
Nielsen, K. , and Smed, P. F. , 1998, “ Point Absorber—Optimization and Survival Testing,” 3rd European Wave Energy Conference, Patras, Greece.
Waters, R. , Stålberg, M. , Danielsson, O. , Svensson, O. , Gustafsson, S. , Strömstedt, E. , Eriksson, M. , Sundberg, J. , and Leijon, M. , 2007, “ Experimental Results From Sea Trials of an Offshore Wave Energy System,” Appl. Phys. Lett., 90(3), p. 034105. [CrossRef]
Elwood, D. , Schacher, A. , Rhinefrank, K. , Prudell, J. , Yim, S. , Amon, E. , Brekken, T. , and von Jouanne, A. , 2009, “ Numerical Modeling and Ocean Testing of a Direct-Drive Wave Energy Device Utilizing a Permanent Magnet Linear Generator for Power Take-Off,” ASME Paper No. OMAE2009-79146.
Elwood, D. , Yim, S. C. , Prudell, J. , Stillinger, C. , von Jouanne, A. , Brekken, T. , Brown, A. , and Paasch, R. , 2010, “ Design, Construction, and Ocean Testing of a Taut-Moored Dual-Body Wave Energy Converter With a Linear Generator Power Take-Off,” Renewable Energy, 35(2), pp. 348–354. [CrossRef]
Harleman, D. R. F. , and Shapiro, W. C. , 1960, “ The Dynamics of a Submerged Moored Sphere in Oscillatory Waves,” 7th Conference on Coastal Engineering, pp. 746–765.
Mavrakos, S. A. , Katsaounis, G. M. , and Apostolidis, M. S. , 2009, “ Effect of Floaters' Geometry on the Performance Characteristics of Tightly Moored Wave Energy Converters,” 28th International Conference on Ocean, Offshore and Arctic Engineering, Honolulu, HI.
Vicente, P. C. , Falcão, A. F. O. , and Justino, P. A. P. , 2013, “ Nonlinear Dynamics of a Tightly Moored Point-Absorber Wave Energy Converter,” Ocean Eng., 59, pp. 20–36. [CrossRef]
Yang, L. , Hals, J. , and Moan, T. , 2010, “ Analysis of Dynamic Effects Relevant for the Wear Damage in Hydraulic Machines for Wave Energy Conversion,” Ocean Eng., 37(13), pp. 1089–1102. [CrossRef]
Orazov, B. , O'Reilly, O. M. , and Savaş, Ö. , 2010, “ On the Dynamics of a Novel Ocean Wave Energy Converter,” J. Sound Vib., 329(24), pp. 5058–5069. [CrossRef]
Cummins, W. E. , 1962, “ The Impulse Response Function and Ship Motions,” Schiffstechnik, 9, pp. 101–109.
Zurkinden, A. S. , Ferri, F. , Beatty, S. , Kofoed, J. P. , and Kramer, M. M. , 2014, “ Non-Linear Numerical Modeling and Experimental Testing of a Point Absorber Wave Energy Converter,” Ocean Eng., 78, pp. 11–21. [CrossRef]
Zhang, X. , and Yang, J. , 2015, “ Power Capture Performance of an Oscillating-Body WEC With Nonlinear Snap Through PTO Systems in Irregular Waves,” Appl. Ocean Res., 52, pp. 261–273. [CrossRef]
Agamloh, E. B. , Wallace, A. K. , and von Jouanne, A. , 2008, “ Application of Fluid–Structure Interaction Simulation of an Ocean Wave Energy Extraction Device,” Renewable Energy, 33(4), pp. 748–757. [CrossRef]
Li, Y. , and Yu, Y.-H. , 2012, “ A Synthesis of Numerical Methods for Modeling Wave Energy Converter-Point Absorbers,” Renewable Sustainable Energy Rev., 16(6), pp. 4352–4364. [CrossRef]
Babarit, A. , Hals, J. , Muliawan, M. J. , Kurniawan, A. , Moan, T. , and Krokstad, J. , 2012, “ Numerical Benchmarking Study of a Selection of Wave Energy Converters,” Renewable Energy, 41, pp. 44–63. [CrossRef]
Babarit, A. , Hals, J. , Muliawan, M. J. , Kurniawan, A. , Moan, T. , and Krokstad, J. , 2015, “ Corrigendum to “Numerical Benchmarking Study of a Selection of Wave Energy Converters” [Renew Energy 41 (2012) 44–63],” Renewable Energy, 74, pp. 955–957. [CrossRef]
Goggins, J. , and Finnegan, W. , 2014, “ Shape Optimisation of Floating Wave Energy Converters for a Specified Wave Energy Spectrum,” Renewable Energy, 71, pp. 208–220. [CrossRef]
Falcão, A. F. d. O. , and Rodrigues, R. J. A. , 2002, “ Stochastic Modelling of OWC Wave Power Plant Performance,” Appl. Ocean Res., 24(2), pp. 59–71. [CrossRef]
Falcão, A. F. d. O. , 2002, “ Control of an Oscillating-Water-Column Wave Power Plant for Maximum Energy Production,” Appl. Ocean Res., 24(2), pp. 73–82. [CrossRef]
Falcão, A. F. d. O. , 2004, “ Stochastic Modelling in Wave Power-Equipment Optimization: Maximum Energy Production Versus Maximum Profit,” Ocean Eng., 31(11–12), pp. 1407–1421. [CrossRef]
Gomes, R. P. F. , Henriques, J. C. C. , Gato, L. M. C. , and Falcão, A. F. O. , 2012, “ Hydrodynamic Optimization of an Axisymmetric Floating Oscillating Water Column for Wave Energy Conversion,” Renewable Energy, 44, pp. 328–339. [CrossRef]
Falcão, A. F. O. , Henriques, J. C. C. , Gato, L. M. C. , and Gomes, R. P. F. , 2014, “ Air Turbine Choice and Optimization for Floating Oscillating-Water-Column Wave Energy Converter,” Ocean Eng., 75, pp. 148–156. [CrossRef]
Taghipour, R. , Perez, T. , and Moan, T. , 2008, “ Hybrid Frequency–Time Domain Models for Dynamic Response Analysis of Marine Structures,” Ocean Eng., 35(7), pp. 685–705. [CrossRef]
Perez, T. , and Fossen, T. I. , 2011, “ Practical Aspects of Frequency-Domain Identification of Dynamic Models of Marine Structures From Hydrodynamic Data,” Ocean Eng., 38(2–3), pp. 426–435. [CrossRef]
Duclos, G. , Clément, A. H. , and Chatry, G. , 2001, “ Absorption of Outgoing Waves in a Numerical Wave Tank Using a Self-Adaptive Boundary Condition,” Int. J. Offshore Pol. Eng., 11(3), pp. 168–175.
Vicente, P. C. , Falcão, A. F. , and Justino, P. A. P. , 2010, “ Nonlinear Dynamics of a Floating Wave Energy Converter Reacting Against the Sea Bottom Through a Tight Mooring Cable,” ASME Paper No. OMAE2010-20144.
Budal, K. , and Falnes, J. , 1975, “ A Resonant Point Absorber of Ocean-Wave Power,” Nature, 256, pp. 478–479. [CrossRef]
Budal, K. , and Falnes, J. , 1975, “ Power Generation From Ocean Waves Using a Resonant Oscillating System,” Mar. Sci. Commun., 1, pp. 269–288.
Falnes, J. , and Budal, K. , 1978, “ Wave-Power Conversion by Point Absorbers,” Norwegian Marit. Res., 6, pp. 2–11.
Evans, D. V. , 1981, “ Maximum Wave-Power Absorption Under Motion Constraints,” Appl. Ocean Res., 3(4), pp. 200–203. [CrossRef]
Budal, K. , and Falnes, J. , 1982, “ Wave Power Conversion by Point Absorbers: A Norwegian Project,” Int. J. Ambient Energy, 3(2), pp. 59–67. [CrossRef]
Pizer, D. J. , 1993, “ Maximum Wave-Power Absorption of Point Absorbers Under Motion Constraints,” Appl. Ocean Res., 15(4), pp. 227–234. [CrossRef]
Jordan, D. W. , and Smith, P. , 2007, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Oxford University Press, Oxford, UK.
Nayfeh, A. H. , and Mook, D. T. , 2008, Nonlinear Oscillations, Wiley, Weinheim, Germany.
Hagedorn, P. , and Stadler, W. , 1988, Non-Linear Oscillations, Oxford University Press, Oxford, UK.
Roberts, J. B. , and Spanos, P. D. , 2003, Random Vibration and Statistical Linearization, Dover Publications, Mineola, NY.
Spanos, P. D. , Ghosh, R. , Finn, L. D. , Botros, F. , and Halkyard, J. , 2005, “ Efficient Dynamic Analysis of a Combined Spar System Via a Frequency Domain Approach,” ASME Paper No. OMAE2005-67134.
Spanos, P. D. , Sofi, A. , Wang, J. , and Peng, B. , 2006, “ A Method for Fatigue Analysis of Piping Systems on Topsides of FPSO Structures,” ASME J. Offshore Mech. Arct. Eng., 128(2), pp. 162–168. [CrossRef]
Spanos, P. D. , Ghosh, R. , Finn, L. D. , and Halkyard, J. , 2005, “ Coupled Analysis of a Spar Structure: Monte Carlo and Statistical Linearization Solutions,” ASME J. Offshore Mech. Arct. Eng., 127(1), pp. 11–16. [CrossRef]
Spanos, P. D. , Nava, V. , and Arena, F. , 2010, “ Coupled Surge-Heave-Pitch Dynamic Modeling of Spar-Moonpool-Riser Interaction,” ASME J. Offshore Mech. Arct. Eng., 133(2), p. 021301. [CrossRef]
Low, Y. M. , 2009, “ Frequency Domain Analysis of a Tension Leg Platform With Statistical Linearization of the Tendon Restoring Forces,” Mar. Struct., 22(3), pp. 480–503. [CrossRef]
Hulme, A. , 1982, “ The Wave Forces Acting on a Floating Hemisphere Undergoing Forced Periodic Oscillations,” J. Fluid Mech., 121, pp. 443–463. [CrossRef]
Newman, J. N. , 1962, “ The Exciting Forces on Fixed Bodies in Waves,” J. Ship Res., 6(3), pp. 10–17.
Spanos, P. D. , Richichi, A. , and Arena, F. , 2014, “ Stochastic Analysis of a Nonlinear Energy Harvester Model,” ASME Paper No. OMAE2014-24489.
Atalik, T. S. , and Utku, S. , 1976, “ Stochastic Linearization of Multi-Degree-of-Freedom Non-Linear Systems,” Earthquake Eng. Struct. Dyn., 4(4), pp. 411–420. [CrossRef]
Priestley, M. B. , 1996, Spectral Analysis and Time Series, Elsevier Academic Press, Amsterdam, The Netherlands.
Shinozuka, M. , and Deodatis, G. , 1991, “ Simulation of Stochastic Processes by Spectral Representation,” ASME Appl. Mech. Rev., 44(4), pp. 191–204. [CrossRef]
Spanos, P. D. , and Tsavachidis, S. , 2001, “ Deterministic and Stochastic Analyses of Nonlinear System With a Biot Visco-Elastic Element,” Earthquake Eng. Struct. Dyn., 30(4), pp. 595–612. [CrossRef]
Hasselmann, K. , Barnett, T. P. , Bouws, E. , Carlson, H. , Cartwright, D. E. , Eake, K. , Euring, J. A. , Gienapp, A. , Hasselmann, D. E. , Kruseman, P. , Meerburg, A. , Mullen, P. , Olbers, D. J. , Richren, K. , Sell, W. , and Walden, H. , 1973, “ Measurements of Wind-Wave Growth and Swell Decay During the Joint North Sea Wave Project (JONSWAP),” Ergänzungsheft zur Deutschen Hydrographischen Zeitschrift, A8, pp. 1–95.


Grahic Jump Location
Fig. 1

Scheme of a single-point absorber with PTO and tight mooring line

Grahic Jump Location
Fig. 2

Short time history of excitation and response components of the single-point wave energy harvester

Grahic Jump Location
Fig. 3

Comparison between the PDFs of the surge (upper panel) and heave (lower panel) motions calculated via Monte Carlo data (dotted line) and a theoretical Gaussian distribution (continuous line)

Grahic Jump Location
Fig. 4

Comparison between the PSDs of the surge (upper panel) and heave (lower panel) motions calculated by statistical linearization (continuous line) and Monte Carlo data (dotted line)



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