Compressive Sensing–Based Reconstruction of Sea Free-Surface Elevation on a Vertical Wall
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 144, Issue 5
Abstract
Measuring the free-surface displacement on a vertical wall of a marine structure is not a trivial problem. In this context, the efficacy of ultrasonic probes is affected by the interaction between the signal emitted by the sensor and the vertical wall, whereas image-based techniques are computationally demanding, especially if long-time series are utilized. Considering these difficulties, this paper proposes a novel approach for measuring the sea surface elevation on vertical breakwaters. The proposed methodology involves the use of pressure measurements and a reconstruction algorithm based on a compressive sensing (CS) technique in conjunction with a generalized harmonic wavelet (GHW) basis. In particular, a constrained CS optimization approach is proposed by utilizing the known values of the free-surface data to reconstruct all other missing data while adhering at the same time to prescribed upper and lower bounds at all time instants. The reliability of the methodology was assessed against field data pertaining to a vertical wall equipped with pressure transducers recorded at the Natural Ocean Engineering Laboratory of Reggio Calabria. It was shown that direct application of an unconstrained GHW-based CS optimization approach yielded physically inconsistent minima and maxima values; thus, it was inadequate for reliably reconstructing the free surface. These drawbacks were removed by the constrained GHW-based CS. Furthermore, examination of the reconstructed sea surface profiles in the vicinity of extremely high wave crests or wave troughs showed that they are in agreement with pertinent theoretical data obtained by using the nonlinear quasi-determinism theory.
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Acknowledgments
This paper was developed during the Marie Curie IRSES project “Large Multi Purpose Platforms for Exploiting Renewable Energy in Open Seas (PLENOSE)” funded by the European Union (Grant Agreement Number PIRSES-GA-2013–612581). I. A. Kougioumtzoglou gratefully acknowledges the support by the Civil, Mechanical, and Manufacturing Innovation (CMMI) Division of the National Science Foundation, USA (Award Number 1724930).
References
Baquerizo, A., and M. A. Losada. 1995. “Transfer function between wave height and wave pressure for progressive waves, by Y.-Y. Kuo and J.-F. Chiu: Comments.” Coastal Eng. 24 (3): 351–353. https://doi.org/10.1016/0378-3839(94)00038-Y.
Bishop, C. T., and M. A. Donelan. 1987. “Measuring waves with pressure transducers.” Coastal Eng. 11 (4): 309–328. https://doi.org/10.1016/0378-3839(87)90031-7.
Boccotti, P. 1981. “On the highest waves in a stationary Gaussian process.” Atti Acc. Ligure di Scienze e Lettere. 38: 271–302.
Boccotti, P. 1982. “On ocean waves with high crests.” Meccanica. 17 (1): 16–19. https://doi.org/10.1007/BF02156003.
Boccotti, P. 1983. “Some new results on statistical properties of wind waves.” Appl. Ocean Res. 5 (3): 134–140. https://doi.org/10.1016/0141-1187(83)90067-6.
Boccotti, P. 1989. “Quasi-determinism of sea wave groups.” Meccanica. 24 (1): 3–14. https://doi.org/10.1007/BF01575998.
Boccotti, P. 2014. Wave mechanics and wave loads on marine structures, butterworth. Oxford: Butterworth-Heinemann.
Boccotti, P., F. Arena, V. Fiamma, A. Romolo, and G. Barbaro. 2011. “Estimation of mean spectral directions in random seas.” Ocean Eng. 38 (2–3): 509–518. https://doi.org/10.1016/j.oceaneng.2010.11.018.
Boccotti, P., F. Arena, V. Fiamma, A. Romolo, and G. Barbaro. 2012. “Small-scale field experiment on wave forces on upright breakwaters.” J. Waterway, Port, Coastal, Ocean Eng. 138 (2): 97–114. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000111.
Boccotti, P., G. Barbaro, and L. Mannino. 1993. “A field experiment on the mechanics of irregular gravity waves.” J. Fluid Mech. 252 (1): 173–186. https://doi.org/10.1017/S0022112093003714.
Byrd, R. H., J. C. Gilbert, and J. Nocedal. 2000. “A trust region method based on interior point techniques for nonlinear programming.” Math. Program. 89 (1): 149–185. https://doi.org/10.1007/PL00011391.
Candes, E. J., J. Romberg, and T. Tao. 2006a. “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information.” IEEE Trans. Inf. Theory. 52 (2): 489–509. https://doi.org/10.1109/TIT.2005.862083.
Candes, E. J., J. K. Romberg, and T. Tao. 2006b. “Stable signal recovery from incomplete and inaccurate measurements.” Commun. Pure Appl. Math. 59 (8): 1207–1223. https://doi.org/10.1002/cpa.20124.
Candes, E. J., and T. Tao. 2005. “Decoding by linear programming.” IEEE Trans. Inf. Theory. 51 (12): 4203–4215. https://doi.org/10.1109/TIT.2005.858979.
Candes, E. J., and T. Tao. 2006. “Near-optimal signal recovery from random projections: Universal encoding strategies?” IEEE Trans. Inf. Theory. 52 (12): 5406–5425. https://doi.org/10.1109/TIT.2006.885507.
Candes, E. J., and M. B. Wakin. 2008. “An introduction to compressive sampling.” IEEE Signal Process Mag. 25 (2): 21–30. https://doi.org/10.1109/MSP.2007.914731.
Claerbout, J. F., and F. Muir. 1973. “Robust modeling with erratic data.” Geophys. 38 (5): 826–844. https://doi.org/10.1190/1.1440378.
Comerford, L. A., M. Beer, and I. A. Kougioumtzoglou. 2014. “Compressive sensing based power spectrum estimation from incomplete records by utilizing an adaptive basis.” Proc., IEEE Symp. on Computational Intelligence for Engineering Solutions (CIES), 117–124. New York: Institute of Electrical and Electronics Engineers.
Comerford, L., H. A. Jensen, F. Mayorga, M. Beer, and I. A. Kougioumtzoglou. 2017. “Compressive sensing with an adaptive wavelet basis for structural system response and reliability analysis under missing data.” Comput. Struct. 182: 26–40. https://doi.org/10.1016/j.compstruc.2016.11.012.
Comerford, L., I. A. Kougioumtzoglou, and M. Beer. 2015. “On quantifying the uncertainty of stochastic process power spectrum estimates subject to missing data.” Int. J. Sustainable Mater. Struct. Syst. 2 (1/2): 185–206. https://doi.org/10.1504/IJSMSS.2015.078358.
Comerford, L., I. A. Kougioumtzoglou, and M. Beer. 2016. “Compressive sensing based stochastic process power spectrum estimation subject to missing data.” Probab. Eng. Mech. 44: 66–76. https://doi.org/10.1016/j.probengmech.2015.09.015.
Constantin, A. 2012. “On the recovery of solitary wave profiles from pressure measurements.” J. Fluid Mech. 699: 376–384. https://doi.org/10.1017/jfm.2012.114.
de Boor, C. 1978. A practical guide to splines. New York: Springer-Verlag.
Dean, R. G., and R. A. Dalrymple. 1991. Water wave mechanics for engineers and scientists. Singapore: World Scientific.
Deconinck, B., K. L. Oliveras, and V. Vasan. 2012. “Relating the bottom pressure and the surface elevation in the water wave problem.” J. Nonlinear Math. Phys. 19 (sup1): 179–189. https://doi.org/10.1142/S1402925112400141.
Donoho, D. L. 2006. “Compressed sensing.” IEEE Trans. Inf. Theory. 52 (4): 1289–1306. https://doi.org/10.1109/TIT.2006.871582.
Escher, J., and T. Schlurmann. 2008. “On the recovery of the free surface from the pressure within periodic traveling water waves.” J. Nonlinear Math. Phys. 15 (sup2): 50–57. https://doi.org/10.2991/jnmp.2008.15.s2.4.
Haile, M., and A. Ghoshal. 2012. “Application of compressed sensing in full-field structural health monitoring.” Proc., SPIE 8346, Smart Sensor Phenomena, Technology, Networks, and Systems Integration, 834618. https://www.spiedigitallibrary.org/conference-proceedings-of-spie/8346/834618/Application-of-compressed-sensing-in-full-field-structural-health-monitoring/10.1117/12.915429.short?SSO=1&tab=ArticleLink.
Harley, J. B., A. C. Schmidt, and J. M. F. Moura. 2012. “Accurate sparse recovery of guided wave characteristics for structural health monitoring.” Proc., 2012 IEEE International Ultrasonics Symp., 158–161. New York: Institute of Electrical and Electronics Engineers.
Hasselmann, K., et al. 1973. “Measurements of wind-wave growth and swell decay during the joint North Sea wave project (JONSWAP).” Ergänzungsheft zur Deutschen Hydrographischen Zeitschrift. A8: 1–95.
Huang, Y., J. L. Beck, S. Wu, and H. Li. 2014. “Robust Bayesian compressive sensing for signals in structural health monitoring.” Comput.-Aided Civ. Infrastruct. Eng. 29 (3): 160–179. https://doi.org/10.1111/mice.12051.
Klis, R., and E. N. Chatzi. 2017. “Vibration monitoring via spectro-temporal compressive sensing for wireless sensor networks.” Struct. Infrastruct. Eng. 13 (1): 195–209. https://doi.org/10.1080/15732479.2016.1198395.
Kougioumtzoglou, I. A., K. R. M. dos Santos, and L. Comerford. 2017. “Incomplete data based parameter identification of nonlinear and time-variant oscillators with fractional derivative elements.” Mech. Syst. Sig. Process. 94: 279–296. https://doi.org/10.1016/j.ymssp.2017.03.004.
Kundu, P. K., I. M. Cohen, and D. R. Dowling. 2015. Fluid mechanics. London: Elsevier Science.
Kuo, Y.-Y., and J.-F. Chiu. 1995. “Transfer function between wave height and wave pressure for progressive waves: Reply to the comments of A. Baquerizo and M.A. Losada.” Coastal Eng. 24 (3): 355–356. https://doi.org/10.1016/0378-3839(94)00039-Z.
Kuo, Y.-Y., and Y.-F. Chiu. 1994. “Transfer function between wave height and wave pressure for progressive waves.” Coastal Eng. 23 (1): 81–93. https://doi.org/10.1016/0378-3839(94)90016-7.
Laface, V., I. A. Kougioumtzoglou, G. Malara, and F. Arena. 2017. “Efficient processing of water wave records via compressive sensing and joint time-frequency analysis via harmonic wavelets.” Appl. Ocean Res. 69: 1–9. https://doi.org/10.1016/j.apor.2017.09.011.
Lee, H. S., and S. H. Kwon. 2003. “Wave profile measurement by wavelet transform.” Ocean Eng. 30 (18): 2313–2328. https://doi.org/10.1016/S0029-8018(03)00114-8.
Levine, R. M., J. E. Michaels, and S. J. Lee. 2012. “Guided wave localization of damage via sparse reconstruction.” AIP Conf. Proc. 1430 (1): 647–654.
Mascareñas, D., A. Cattaneo, J. Theiler, and C. Farrar. 2013. “Compressed sensing techniques for detecting damage in structures.” Struct. Health Monit. 12 (4): 325–338. https://doi.org/10.1177/1475921713486164.
Newland, D. E. 1994. “Wavelet analysis of vibration: Part 1—Theory.” J. Vib. Acoust. 116 (4): 409–416. https://doi.org/10.1115/1.2930443.
Nyquist, H. 1928. “Certain topics in telegraph transmission theory.” Trans. Am. Inst. Electr. Eng. 47 (2): 617–644. https://doi.org/10.1109/T-AIEE.1928.5055024.
O'Connor, S. M., J. P. Lynch, and A. C. Gilbert. 2013. “Implementation of a compressive sampling scheme for wireless sensors to achieve energy efficiency in a structural health monitoring system.” In Proc., SPIE 8694, Nondestructive Characterization for Composite Materials, Aerospace Engineering, Civil Infrastructure, and Homeland Security, 86941L-86941L-86911. Bellingham, WA: SPIE. https://www.spiedigitallibrary.org/conference-proceedings-of-spie/8694/1/Implementation-of-a-compressive-sampling-scheme-for-wireless-sensors-to/10.1117/12.2010128.short.
Oliveras, K. L., V. Vasan, B. Deconinck, and D. Henderson. 2012. “Recovering the water-wave profile from pressure measurements.” SIAM J. Appl. Math. 72 (3): 897–918. https://doi.org/10.1137/110853285.
Perelli, A., L. De Marchi, L. Flamigni, A. Marzani, and G. Masetti. 2015. “Best basis compressive sensing of guided waves in structural health monitoring.” Digital Signal Process. 42: 35–42. https://doi.org/10.1016/j.dsp.2015.04.001.
Phillips, O. M., D. Gu, and M. Donelan. 1993a. “Expected structure of extreme waves in a Gaussian sea. Part I: Theory and SWADE buoy measurements.” J. Phys. Oceanogr. 23 (5): 992–1000. https://doi.org/10.1175/1520-0485(1993)023%3C0992:ESOEWI%3E2.0.CO;2.
Phillips, O. M., D. Gu, and E. J. Walsh. 1993b. “On the expected structure of extreme waves in a Gaussian sea. Part II: SWADE scanning radar altimeter measurements.” J. Phys. Oceanogr. 23 (10): 2297–2309. https://doi.org/10.1175/1520-0485(1993)023%3C2297:OTESOE%3E2.0.CO;2.
Romolo, A., and F. Arena. 2013. “Three-dimensional non-linear standing wave groups: Formal derivation and experimental verification.” Int. J. Non Linear Mech. 57: 220–239. https://doi.org/10.1016/j.ijnonlinmec.2013.08.005.
Romolo, A., F. Arena, and V. Laface. 2014. “A generalized approach to the mechanics of three-dimensional nonlinear ocean waves.” Probab. Eng. Mech. 35: 96–107. https://doi.org/10.1016/j.probengmech.2013.10.009.
Shannon, C. 1949. “Comunication in the presence of noise.” Proc. Inst. Radio Eng. 37 (1): 10–21.
Tau Siesakul, B., K. Gkoktsi, and A. Giaralis. 2015. “Compressive power spectrum sensing for vibration-based output-only system identification of structural systems in the presence of noise.” In Proc., SPIE Sensing Technology + Applications, International Society for Optics and Photonics, 94840K. Bellingham, WA: SPIE. https://www.spiedigitallibrary.org/conference-proceedings-of-spie/9484/94840K/Compressive-power-spectrum-sensing-for-vibration-based-output-only-system/10.1117/12.2177162.short.
Tsai, C.-H., M.-C. Huang, F.-J. Young, Y.-C. Lin, and H.-W. Li. 2005. “On the recovery of surface wave by pressure transfer function.” Ocean Eng. 32 (10): 1247–1259. https://doi.org/10.1016/j.oceaneng.2004.10.020.
Tsai, J.-C., and C.-H. Tsai. 2009. “Wave measurements by pressure transducers using artificial neural networks.” Ocean Eng. 36 (15–16): 1149–1157. https://doi.org/10.1016/j.oceaneng.2009.08.007.
Viriyakijja, K., and C. Chinnarasri. 2015. “Wave flume measurement using image analysis.” Aquat. Procedia. 4: 522–531. https://doi.org/10.1016/j.aqpro.2015.02.068.
Waltz, R. A., J. L. Morales, J. Nocedal, and D. Orban. 2006. “An interior algorithm for nonlinear optimization that combines line search and trust region steps.” Math. Program. 107 (3): 391–408. https://doi.org/10.1007/s10107-004-0560-5.
Wang, Y., and H. Hao. 2015. “Damage identification scheme based on compressive sensing.” J. Comput. Civ. Eng. 29 (2): 04014037. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000324.
Yang, Y., and S. Nagarajaiah. 2015. “Output-only modal identification by compressed sensing: Non-uniform low-rate random sampling.” Mech. Syst. Sig. Process. 56–57: 15–34. https://doi.org/10.1016/j.ymssp.2014.10.015.
Zhang, Y., L. Comerford, M. Beer, and I. Kougioumtzoglou. 2015. “Compressive sensing for power spectrum estimation of multi-dimensional processes under missing data.” In Proc., 2015 Int. Conf. on Systems, Signals and Image Processing (IWSSIP), 162–165. London: IEEE.
Zhang, Y., L. Comerford, I. Kougioumtzoglou, and M. Beer. 2018. “Lp-norm minimization for stochastic process power spectrum estimation subject to incomple data.” Mech. Syst. Sig. Process. 101: 361–376. https://doi.org/10.1016/j.ymssp.2017.08.017.
Zou, Z., Y. Bao, H. Li, B. F. Spencer, and J. Ou. 2015. “Embedding compressive sensing-based data loss recovery algorithm into wireless smart sensors for structural health monitoring.” IEEE Sens. J. 15 (2): 797–808.
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Received: Jun 22, 2017
Accepted: Jan 18, 2018
Published online: Jun 18, 2018
Published in print: Sep 1, 2018
Discussion open until: Nov 18, 2018
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