Journal of the Computational Structural Engineering Institute of Korea (한국전산구조공학회논문집)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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State-Space Equation Model for Motion Analysis of Floating Structures Using System-Identification Methods

부유식 구조체 운동 해석을 위한 시스템 식별 방법을 이용한 상태공간방정식 모델

  • Jun-Sik Seong (Department of Civil Engineering, Mokpo National University) ;
  • Wonsuk Park (Department of Civil Engineering, Mokpo National University)
  • 성준식 (국립목포대학교 토목공학과) ;
  • 박원석 (국립목포대학교 토목공학과)
  • Received : 2023.12.18
  • Accepted : 2023.12.27
  • Published : 2024.04.30
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Abstract

In this paper, we propose a method for establishing a state-space equation model for the motion analysis of floating structures subjected to wave loads, by applying system-identification techniques. Traditionally, the motion of floating structures has been analyzed in the time domain by integrating the Cummins equation over time, which utilizes a convolution integral term to account for the effects of the retardation function. State-space equation models have been studied as a way to efficiently solve floating-motion equations in the time domain. The proposed approach outlines a procedure to derive the target transfer function for the load-displacement input/output relationship in the frequency domain and subsequently determine the state-space equation that closely approximates it. To obtain the state-space equation, the method employs the N4SID system-identification method and an optimization approach that treats the coefficients of the numerator and denominator polynomials as design variables. To illustrate the effectiveness of the proposed method, we applied it to the analysis of a single-degree-of-freedom model and the motion of a six-degree-of-freedom barge. Our findings demonstrate that the presented state-space equation model aligns well with the existing analysis results in both the frequency and time domains. Notably, the method ensures computational accuracy in the time-domain analysis while significantly reducing the calculation time.

이 논문에서는 파랑 하중을 받는 부유식 구조체의 운동 해석에 있어서 시스템 식별 방법을 이용한 상태공간방정식 모델을 수립하고 해석하는 방법을 제안하였다. 상태공간방정식 모델의 수립 방법으로는 주파수영역에서 하중-변위 입출력 관계에 대한 목표 전달함수를 구하고 이에 가장 근접하는 상태공간방정식을 구하는 절차를 제시하였다. 전통적으로 부유식 구조체 운동의 시간영역 해석은 지연함수의 합성곱적분을 포함하는 Cummins 방정식을 시간적분하여 이루어진다. 상태공간방정식 모델은 이러한 시간영역해석을 효과적으로 수행하기 위한 방법의 하나로서 연구되어 왔다. 제안하는 방법에서는 시스템 식별방법인 N4SID 와 전달함수의 분모 및 분자 다항식의 계수를 설계변수로 하는 최적화방법을 사용하여 목표 전달함수에 상응하는 상태공간방정식을 구한다. 제안하는 방법의 적용성을 보이는 예제로서 단자유도 수치모델 및 6자유도 바지의 운동을 해석하였다. 제시하는 상태공간방정식 모델은 주파수영역 및 시간영역에서 모두 기존의 해석결과와 잘 일치하고 시간영역해석에서는 계산의 정확도를 확보하면서 계산 시간을 크게 줄일 수 있음을 확인하였다.

Keywords

Acknowledgement

이 연구는 국토교통부/국토교통과학기술진흥원의 지원으로 수행되었음(과제번호RS-2023-00250727 다목적 해상 부유식 인프라 건설기술 개발).

References

  1. ANSYS, Inc. (2023) Ansys, Release 18.1.
  2. Chen, C.T. (1984) Linear System Theory and Design, Saunders College Publishing.
  3. Cho, J.-R., Jeon, S.-H., Jeong, W.-B. (2016) Numerical Analysis of Dynamic Response of Floating Offshore Wind Turbine to the Underwater Explosion using the PML Non-Reflecting Technique, J. Comput. Struct. Eng. Inst. Korea, 29(6), pp.521-527. https://doi.org/10.7734/COSEIK.2016.29.6.521
  4. Cummins, W.E. (1962) The Impulse Response Function and Ship Motions, Schiffstechnik, 9 (1661), pp.101-109.
  5. Duarte, T., Sarmento, A., Alves, M., Jonkman, J. (2013) State-Space Realization of the Wave-Radiation Force within FAST(No.NREL/CP-5000-58099), National Renewable Energy Lab.(NREL), Golden, CO (United States).
  6. Fossen, T.I. (2002) Marine Control Systems-Guidance, Navigation, and Control of Ships, Rigs and Underwater Vehicles, Marine Cybernetics, Trondheim, Norway, Org. Number NO 985 195 005 MVA, www.marinecybernetics.com, ISBN: 82 92356 00 2.
  7. Goupee, A.J., Koo, B.J., Kimball, R.W., Lambrakos, K.F., Dagher, H.J. (2014) Experimental Comparison of Three Floating Wind Turbine Concepts, J. Offshore Mech. & Arct. Eng., 136(2), p.020906.
  8. Jordan, M.A., Beltran-Aguedo, R. (2004) Optimal Identification of Potential-Radiation Hydrodynamics for Moored Floating Structures - a New General approach in State Space, Ocean Eng., 31(14-15), pp.1859-1914.
  9. Kashiwagi, M. (2004) Transient Responses of a VLFS during Landing and Take-off of an Airplane, J. Marine Sci. & Technol., 9, pp.14-23.
  10. Kim, H.S., Park, B., Lee, K. (2022) Parametric Study on Effect of Floating Breakwater for Offshore Photovoltaic System in Waves, J. Comput. Struct. Eng. Inst. Korea, 35(2), pp.109-117. https://doi.org/10.7734/COSEIK.2022.35.2.109
  11. Kim, H.S., Park, B., Sung, H.G., Lee, K. (2021) LMU Design Optimization for the Float-over Installation of Floating Offshore Platforms, J. Comput. Struct. Eng. Inst. Korea, 34(1), pp.43-50. https://doi.org/10.7734/COSEIK.2021.34.1.43
  12. Liu, F., Chen, J., Qin, H. (2017) Frequency Response Estimation of Floating Structures by Representation of Retardation Functions with Complex Exponentials, Mar. Struct., 54, pp.144-166.
  13. Lu, H., Chang, S., Chen, C., Fan, T., Chen, J. (2022) Replacement of Force-to-Motion Relationship with State-Space Model for Dynamic Response Analysis of Floating Offshore Structures, Appl. Ocean Res., 119, p.102977.
  14. Lu, H., Fan, T., Zhou, L., Chen, C., Yu, G., Li, X., Hou, F. (2020) A Rapid Response Calculation Method for Symmetrical Floating Structures based on State-Space Model Solving in Hybrid Time-Laplace Domain, Ocean Eng., 203, p.107227.
  15. Lu, H., Tian, Z., Zhou, L., Liu, F. (2019) An Improved Time-Domain Response Estimation Method for Floating Structures based on Rapid Solution of a State-Space Model, Ocean Eng., 173, pp.628-642.
  16. McKelvey, T., Akcay, H., Ljung, L. (1996) Subspace-based Multivariable System Identification from Frequency Response Data, IEEE Trans. Autom. Control, 41(7), pp.960-979. https://doi.org/10.1109/9.508900
  17. Moan, T., Eidem, M.E. (2020) Floating Bridges and Submerged Tunnels in Norway - The History and Future Outlook, Proc. World Conf. Float. Solut., Springer Singapore, pp.81-111.
  18. Orcina (2023) OrcaFlex (Version 11.0), Orcina Ltd.
  19. Pinkster, J.A. (1979) Mean and Low Frequency Wave Drifting Forces on Floating Structures, Ocean Eng., 6(6), pp.593-615.
  20. Schmiechen, M. (1973) On State Space Models and Their Application to Hydromechanic Systems, University of Tokyo, Department of Naval Architecture, Hongo, Bunkyo-Ku, NAUT Report 5002.
  21. Taghipour, R., Perez, T., Moan, T. (2008) Hybrid Frequency-Time Domain Models for Dynamic Response Analysis of Marine Structures, Ocean Eng., 35(7), pp.685-705.
  22. The MathWorks Inc. (2022) MATLAB version: 9.13.0 (R2022b), Natick, Massachusetts: The MathWorks Inc.
  23. Van Overschee, P., De Moor, B. (1994) N4SID: Subspace Algorithms for the Identification of Combined Deterministic-Stochastic Systems, Autom., 30(1), pp.75-93. https://doi.org/10.1016/0005-1098(94)90230-5
  24. Wang, K., Er, G.K., Zhu, Z. (2020) 3D Nonlinear Dynamic Analysis of Cable-Moored Offshore Structures, Ocean Eng., 213, p.107759.
  25. Yoon, J.S., Lee, P.S. (2017) Towards Hydro-Elastoplastic Analysis of Floating Plate Structures, J. Fluids & Struct., 71, pp.164-182.