Identification of Lagrangian Drifting by Sparse Nonlinear Dynamic System Algorithm
Year 2024,
Volume: 29 Issue: 3, 675 - 682, 24.12.2024
Ali Rıza Alan
,
Cihan Bayındır
Abstract
In this study, the applicability of the approach known as sparse identification of nonlinear dynamics (SINDy) for the simulation of the mechanisms controlling coastal and harbor hydrodynamic processes was examined. The main goal of the SINDy approach is to use ordinary differential equations (ODEs) with as few sparse components as possible to describe the drift trajectories of particles and objects determined by computational or measurement techniques. Using Lagrangian drift device data obtained using a floating buoy in the Caribbean Sea in the Atlantic Ocean, the possible use of the drift route and time series of the SINDy algorithm with and without trigonometric terms to model hydrodynamic effects in coastal and harbor hydrodynamics is investigated. It has been shown that Lagrangian drifter equations can be reconstructed from data with SINDy. It has been suggested that, for specified types of events and disasters, the SINDy-based algorithmic technique can reliably and quickly estimate the coastal and harbor hydrodynamic equations specific to a region. An evaluation of possible study areas, usage areas, and practical applications of our findings is also included.
Project Number
TÜBA GEBİP-2022, İTÜ BAP MDA-2023-45117, İTÜ BAP FHD-2023-44985, İTÜ BAP MGA-2022-43528, İTÜ BAP MYL-2022-43642, İTÜ BAP MDK-2021-42849
References
- Bayındır, C. ve Namlı, B. (2021) Efficient sensing of von Kármán vortices using compressive sensing, Computers and Fluids, 226(104975), 4195. doi: 10.1016/j.compfluid.2021.104975
- Bayındır, C. (2015) Compressive split-step Fourier method, TWMS Journal of Applied and Engineering Mathematics, 52, 298-306.
- Brunton, S. L., Proctor, J. L. ve Kutz, J. N. (2016a) Discovering governing equations from data by sparse identification of nonlinear dynamical systems, Proceedings of the National Academy of Sciences, 113(15), 3932-3937. doi: 10.1073/pnas.1517384113
- Brunton, S. L., Proctor, J. L. ve Kutz, J. N. (2016b) Sparse identification of nonlinear dynamics with control (SINDYc), IFAC-Online Papers, 49(18), 710-715. doi: 10.1016/j.ifacol.2016.10.249
- Davis, R. (1991) Lagrangian ocean studies, Annual Review of Fluid Mechanics, 23, 43-64.
- Elipot, S., Lumpkin, R., Perez, R. C., Lilly, J. M., Early, J. J. ve Sykulski, A. M. (2016) A global surface drifter data set at hourly resolution, Journal of Geophysical Research: Oceans, 121(5), 2937-2966. doi: 10.1002/2016JC011716
- Fukami, K., Murata, T., Zhang, K. ve Fukagata, K. (2021) Sparse identification of nonlinear dynamics with low-dimensionalized flow representations, Journal of Fluid Mechanics, 926, A10. doi: 10.1017/jfm.2021.697
- Goldberg, D. E. (1989) Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, New York.
- Holland, J. (1975) Adaptation in Natural and Artificial Systems, MIT Press, Massachusetts.
- Lin, L., Zhuang, W. ve Huang, Y. (2017) Lagrangian Statistics and Intermittency in Gulf of Mexico, Scientific Reports, 7, 17463. doi: 10.1038/s41598-017-17513-9
- Liu, Y. ve Weisberg, R. H. (2011) Evaluation of trajectory modeling in different dynamic regions using normalized cumulative Lagrangian separation, Journal of Geophysical Research: Oceans, 116, C9. doi: 10.1029/2010JC006837
- MacMahan, J., Brown, J. ve Thornton, E. (2009) Low-cost handheld global positioning system for measuring surf-zone currents, Journal of Coastal Research, 25(3), 744-754. doi: 10.2112/08-1000.1
- McCarroll, R. J., Brander, R. W., Turner, I. L., Power, H. E. ve Mortlock, T. R. (2014) Lagrangian observations of circulation on an embayed beach with headland rip currents, Marine Geology, 355, 173-188. doi: 10.1016/j.margeo.2014.05.020
- Purnomo, A. ve Hayashibe, M. (2023) Sparse identification of Lagrangian for nonlinear dynamical systems via proximal gradient method, Scientific Reports, 13, 7919. doi: 10.1038/s41598-023-34931-0
- Shea, D. E., Brunton, S. L. ve Kutz, J. N. (2021) SINDy-BVP: Sparse identification of nonlinear dynamics for boundary value problems, Physical Review Research, 3(2), 023255. doi: 10.1103/PhysRevResearch.3.023255
- Spydell, M., Feddersen, F., Guza, R. T. ve Schmidt, W. E. (2007) Observing surf-zone dispersion with drifters, Journal of Physical Oceanography, 37(12), 2920-2939. doi: 10.1175/2007JPO3580.1
KIYI VE LİMANLARDAKİ LAGRANGE SÜRÜKLENMESİNİN SEYREK DOĞRUSAL OLMAYAN DİNAMİK SİSTEM ALGORİTMASIYLA BELİRLENMESİ
Year 2024,
Volume: 29 Issue: 3, 675 - 682, 24.12.2024
Ali Rıza Alan
,
Cihan Bayındır
Abstract
Bu çalışmada, doğrusal olmayan dinamiklerin seyrek tanımlanması veya SINDy (sparse identification of nonlinear dynamics) olarak bilinen yaklaşımın, kıyı ve liman hidrodinamik süreçlerini kontrol eden mekanizmaların benzeşimi için uygulanabilirliği incelenmiştir. SINDy yaklaşımının temel amacı, hesaplamalı veya ölçüm teknikleriyle belirlenen parçacıkların ve nesnelerin sürüklenme rotalarını açıklamak için mümkün olan en az seyrek bileşenli adi diferansiyel denklemleri (ADD) kullanmaktır. Atlas Okyanusu'nda Karayip Denizi’nde yüzen bir şamandıra kullanılarak elde edilen Lagrange sürüklenme cihazı verilerinden yararlanılarak, sürüklenme rotası ve zaman serilerinin SINDy algoritmasının trigonometrik bileşenlerinin hem olması hem de olmaması durumlarında kıyı ve liman hidrodinamiğindeki hidrodinamik etkileri modellemek için olası kullanımı araştırılmıştır. SINDy ile Lagrange sürüklenicisi denklemlerinin verilerden geriçatılabileceği gösterilmiştir. Belirlenen türden olay ve afetlerde, SINDy tabanlı algoritmik tekniğin, bir bölgeye özgü kıyı ve liman hidrodinamiği denklemlerini güvenilir ve hızlı bir şekilde tahmin edebileceği önerilmiştir. Ayrıca bulgularımızın olası çalışma alanları, kullanım konuları ve pratik uygulamalarına ilişkin bir değerlendirmeye de yer verilmiştir.
Supporting Institution
Türkiye Bilimler Akademisi (TÜBA)-Üstün Başarılı Genç Bilim İnsanlarını Ödüllendirme Programı (GEBİP), İstanbul Teknik Üniversitesi (İTÜ)-Bilimsel Araştırma Projeleri (BAP) Fonu
Project Number
TÜBA GEBİP-2022, İTÜ BAP MDA-2023-45117, İTÜ BAP FHD-2023-44985, İTÜ BAP MGA-2022-43528, İTÜ BAP MYL-2022-43642, İTÜ BAP MDK-2021-42849
References
- Bayındır, C. ve Namlı, B. (2021) Efficient sensing of von Kármán vortices using compressive sensing, Computers and Fluids, 226(104975), 4195. doi: 10.1016/j.compfluid.2021.104975
- Bayındır, C. (2015) Compressive split-step Fourier method, TWMS Journal of Applied and Engineering Mathematics, 52, 298-306.
- Brunton, S. L., Proctor, J. L. ve Kutz, J. N. (2016a) Discovering governing equations from data by sparse identification of nonlinear dynamical systems, Proceedings of the National Academy of Sciences, 113(15), 3932-3937. doi: 10.1073/pnas.1517384113
- Brunton, S. L., Proctor, J. L. ve Kutz, J. N. (2016b) Sparse identification of nonlinear dynamics with control (SINDYc), IFAC-Online Papers, 49(18), 710-715. doi: 10.1016/j.ifacol.2016.10.249
- Davis, R. (1991) Lagrangian ocean studies, Annual Review of Fluid Mechanics, 23, 43-64.
- Elipot, S., Lumpkin, R., Perez, R. C., Lilly, J. M., Early, J. J. ve Sykulski, A. M. (2016) A global surface drifter data set at hourly resolution, Journal of Geophysical Research: Oceans, 121(5), 2937-2966. doi: 10.1002/2016JC011716
- Fukami, K., Murata, T., Zhang, K. ve Fukagata, K. (2021) Sparse identification of nonlinear dynamics with low-dimensionalized flow representations, Journal of Fluid Mechanics, 926, A10. doi: 10.1017/jfm.2021.697
- Goldberg, D. E. (1989) Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, New York.
- Holland, J. (1975) Adaptation in Natural and Artificial Systems, MIT Press, Massachusetts.
- Lin, L., Zhuang, W. ve Huang, Y. (2017) Lagrangian Statistics and Intermittency in Gulf of Mexico, Scientific Reports, 7, 17463. doi: 10.1038/s41598-017-17513-9
- Liu, Y. ve Weisberg, R. H. (2011) Evaluation of trajectory modeling in different dynamic regions using normalized cumulative Lagrangian separation, Journal of Geophysical Research: Oceans, 116, C9. doi: 10.1029/2010JC006837
- MacMahan, J., Brown, J. ve Thornton, E. (2009) Low-cost handheld global positioning system for measuring surf-zone currents, Journal of Coastal Research, 25(3), 744-754. doi: 10.2112/08-1000.1
- McCarroll, R. J., Brander, R. W., Turner, I. L., Power, H. E. ve Mortlock, T. R. (2014) Lagrangian observations of circulation on an embayed beach with headland rip currents, Marine Geology, 355, 173-188. doi: 10.1016/j.margeo.2014.05.020
- Purnomo, A. ve Hayashibe, M. (2023) Sparse identification of Lagrangian for nonlinear dynamical systems via proximal gradient method, Scientific Reports, 13, 7919. doi: 10.1038/s41598-023-34931-0
- Shea, D. E., Brunton, S. L. ve Kutz, J. N. (2021) SINDy-BVP: Sparse identification of nonlinear dynamics for boundary value problems, Physical Review Research, 3(2), 023255. doi: 10.1103/PhysRevResearch.3.023255
- Spydell, M., Feddersen, F., Guza, R. T. ve Schmidt, W. E. (2007) Observing surf-zone dispersion with drifters, Journal of Physical Oceanography, 37(12), 2920-2939. doi: 10.1175/2007JPO3580.1