|Table of Contents|

Citation:
　Fuxuan Ma,Fan Zhu,Meng Zhang,et al.Fuzzy Optimization Method for Wind Load Monitoring of Fixed Offshore Wind Turbines[J].Journal of Marine Science and Application,2026,(4):1042-1061.[doi:10.1007/s11804-025-00707-3]
Click and Copy

Fuzzy Optimization Method for Wind Load Monitoring of Fixed Offshore Wind Turbines

Info

Title:
Fuzzy Optimization Method for Wind Load Monitoring of Fixed Offshore Wind Turbines
Author(s):
Fuxuan Ma1;  Fan Zhu2;  Meng Zhang1; 2; 3;  Zhihua Li2;  Xianqiang Qu2
Affilations:
Author(s):
Fuxuan Ma1;  Fan Zhu2;  Meng Zhang1; 2; 3;  Zhihua Li2;  Xianqiang Qu2
1. College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China;
2. Yantai Research Institute, Harbin Engineering University, Yantai 264000, China;
3. College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, China
Keywords:
Wind load monitoring; Fixed offshore wind turbines; Fuzzy optimization; Ill-posedness index of mathematical models; Error index of monitoring data
分类号:
-
DOI:
10.1007/s11804-025-00707-3
Abstract:
Fixed offshore wind turbines generally use statistical parameters of sea conditions in or near the target sea area as design benchmarks during the design phase. However, these sea state statistical parameters vary substantially from the actual sea state parameters experienced by offshore wind turbines. This situation brings uncertainty to the structural safety of offshore wind turbines. Online monitoring of wind loads exerted on the wind tower topside, which uses monitoring the structural response of the wind tower to determine wind load online, provides another technical approach for accurately measuring the wind loads exerted on the wind tower topside. However, online monitoring of wind loads can be affected by factors such as the ill-posedness of mathematical models and errors in monitoring data. The mathematical model for wind load monitoring is usually optimized only with the ill-posedness index as the objective function to reduce or overcome model ill-posedness. The error level of monitoring data is not considered in optimization, which likely leads to a high proportion of monitoring data error and then reduces the quality of monitoring data. Hence, a fuzzy optimization method was developed in this study to reduce the ill-posedness index of mathematical models and the influence of monitoring data errors on the monitoring results, in which the ill-posedness index of the mathematical models is weighted and unified with the error index of the monitoring data. In addition, the effectiveness and reliability of the method developed were demonstrated through numerical examples of jacket wind turbines, and structural damage can be accurately analyzed using the monitored wind loads.

References:

[1] Bartlett FD, Flannelly WG (1979) Model verification of force determination for measuring vibratory loads. Journal of the American Helicopter Society 24(2): 10-18
[2] Bertsekas D (2009) Convex optimization theory. Athena Scientific, Nashua, USA
[3] Bozyigit B, Bozyigit I, Prendergast LJ (2023) Analytical approach for seismic analysis of onshore wind turbines considering soil-structure interaction. Structures 51: 226-241. https://doi.org/10.1016/ j.istruc.2023.03.048
[4] Bozyigit B, Bozyigit I, Prendergast LJ (2025) Rapid assessment of seismic performance of large monopile-supported offshore wind turbines under scour. European Journal of Mechanics-A/Solids 109: 105451. https://doi.org/10.1016/j.euromechsol.2024.105451
[5] Chen T, Kusche J, Shen Y, Chen Q (2020) A combined use of TSVD and tikhonov regularization for mass flux solution in tibetan plateau. Remote Sensing 12(12): 2045. https://doi.org/10.3390/rs12122045
[6] Choi EC (2004) Field measurement and experimental study of wind speed profile during thunderstorms. Journal of Wind Engineering and Industrial Aerodynamics 92(3-4): 275-290
[7] Dirlik T (1985) Application of computers in fatigue analysis. PhD thesis, University of Warwick, Coventry
[8] Giansante N, Jones R, Calapodas NJ (1982) Determination of in-flight helicopter loads. Journal of the American Helicopter Society 27(3): 58-64
[9] Gupta DK, Dhingra AK (2013) Input load identification from optimally placed strain gages using D-optimal design and model reduction. Mechanical Systems and Signal Processing 40(2): 556-570. https://doi.org/10.1016/j.ymssp.2013.06.011
[10] He ZC, Zhang Z, Li E (2019) Multi-source random excitation identification for stochastic structures based on matrix perturbation and modified regularization method. Mech. Syst. Sig. Process 119: 266-292. https://doi.org/10.1016/j.ymssp.2018.09.021
[11] He ZC, Zhang Z, Li E (2020) Random dynamic load identification for stochastic structural-acoustic system using an adaptive regularization parameter and evidence theory. J. Sound Vibration 471: 115188. https://doi.org/10.1016/j.jsv.2020.115188
[12] Jeong S, Kim EJ, Shin DH, Park JW, Sim SH (2020) Data fusion-based damage identification for a monopile offshore wind turbine structure using wireless smart sensors. Ocean Eng. 195: 106728. https://doi.org/10.1016/j.oceaneng.2019.106728
[13] Jiang J, Tang H, Mohamed MS, Luo S, Chen J (2020) Augmented tikhonov regularization method for dynamic load identification. Applied Sciences 10(18): 6348. https://doi.org/10.3390/app10186348
[14] Karlsson SES (1996) Identification of external structural loads from measured harmonic responses. Journal of Sound and Vibration 196(1): 59-74
[15] Kong S, Cui H, Tian Y, Ji S (2020) Identification of ice loads on shell structure of ice-going vessel with green kernel and regularization method. Mar. Struct. 74: 102820. https://doi.org/10.1016/j.marstruc. 2020.102820
[16] Liu M, Liao H, Li M, Ma C, Yu M (2012) Long-term field measurement and analysis of the natural wind characteristics at the site of Xi-hou-men Bridge. J. Zhejiang Univ. Sci. A 13(3): 197-207. https://doi.org/10.1631/jzus.A1100178
[17] Liu R, Dobriban E, Hou Z, Qian K (2022a) Dynamic load identification for mechanical systems: A review. Arch. Comput. Methods Eng. 29(2): 831-863. https://doi.org/10.1007/s11831-021-09594-7
[18] Liu Y, Wang L, Li M, Wu Z (2022b) A distributed dynamic load identification method based on the hierarchical-clustering-oriented radial basis function framework using acceleration signals under convex-fuzzy hybrid uncertainties. Mech. Syst. Sig. Process 172: 108935. https://doi.org/10.1016/j.ymssp.2022.108935
[19] Lutes LD, Larsen CE (1990) Improved spectral method for variable amplitude fatigue prediction. Journal of Structural Engineering 116(4): 1149-1164
[20] Ma F, Zhang M, Qu X, Zhu F, Li Z (2024a) A monitoring method for wind loads exerted on offshore gravity wind turbine through optimised mathematical model. Ocean Engineering 309: 118606. https://doi.org/10.1016/j.oceaneng.2024.118606
[21] Ma F, Zhang M, Wang D, Zhang K, Qu X (2024b) A reconstruction method of stress fields, bending moments and wave parameters for floating nuclear power plants through regular wave identification. Ocean Engineering 310: 118703. https://doi.org/10.1016/j.oceaneng. 2024.118703
[22] Ma F, Zheng K, Li Z, Zhang M, Zhu F, Qu X (2025) A high-fidelity monitoring method for stress distribution in gravity-based offshore wind turbine towers using a well-conditioned orthogonal basis expansion model. Ocean Engineering 325: 120884. https://doi.org/10.1016/j.oceaneng.2025.120884
[23] Miao B, Zhou F, Jiang C, Luo Y, Chen H (2020) A load identification application technology based on regularization method and finite element modified model. Shock Vib. 2020: 1-12. https://doi.org/10.1155/2020/8875697
[24] Ortiz K, Chen NK (1987) Fatigue damage prediction for stationary wideband processes. Proceedings of 5th International Conference on Applications of Statistics and Probability in Soil and Structural Engineering, St. Petersburg
[25] Starkey JM, Merrill GL (1989) On the ill-conditioned nature of indirect force measurement techniques. Journal of Modal Analysis 4(3): 103-108
[26] Tamura Y, Iwatani Y, Hibi K, Suda K, Nakamura O, Maruyama T, Ishibashi R (2007) Profiles of mean wind speeds and vertical turbulence intensities measured at seashore and two inland sites using Doppler sodars. Journal of Wind Engineering and Industrial Aerodynamics 95(6): 411-427
[27] Tian B, Ren H, Yi X, Du G, Jiang C (2019) Noise suppression method for magnetic resonance sounding signals based on double singular value decomposition. Radio. Sci. 54(6): 517-530. https://doi.org/10.1029/2018RS006687
[28] Wang L, Han X, Liu J, Chen J (2011) An improved iteration regularization method and application to reconstruction of dynamic loads on a plate. J. Comput. Appl. Math. 235(14): 4083-4094. https://doi.org/10.1016/j.cam.2011.02.034
[29] Wang L, Huang Yang, Xie Youxiang, Du Yixian (2020) A new regularization method for dynamic load identification. Sci. Prog. 103(3): 1-15. https://doi.org/10.1177/0036850420931283
[30] Wang Z, Qiao D, Tang G, Wang B, Yan J, Ou J (2022) An identification method of floating wind turbine tower responses using deep learning technology in the monitoring system. Ocean Eng. 261: 112105. https://doi.org/10.1016/j.oceaneng.2022.112105
[31] Wirsching PH, Light MC (1980) Fatigue under wide band random stresses. Journal of the Structural Division 106(7): 1593-1607
[32] Xiao Y, Chen J, Li JZ, Luo YJ, Zhang YB (2013) A joint method of denoising correction and regularization preconditioned iteration for dynamic load identification in time domain. Journal of Vibration Engineering 26(6): 854-862. (in Chinese)
[33] Xu M, Au FTK, Wang S, Wang Z, Peng Q, Tian H (2022) Dynamic response analysis of a real-world operating offshore wind turbine under earthquake excitations. Ocean Eng. 266: 112791. https://doi.org/10.1016/j.oceaneng.2022.112791
[34] Zhang C, Xu Y (2016) Comparative studies on damage identification with tikhonov regularization and sparse regularization. Structural Control and Health Monitoring 23(3): 560-579. https://doi.org/10.1002/stc.1785
[35] Zhang M, Qiu B, Wei Q, Qu X, Shi D (2019a) Indirect ice load monitoring and strength analysis of a steel gate considering uncertainties. Measurement 148: 106919. https://doi.org/10.1016/j.measurement.2019.106919
[36] Zhang M, Qiu B, Zhu M, Qu X (2019b) Novel computation method of reducing ill-posedness for structural static distributed load identification by optimising strain gauge locations. Mechanical Systems and Signal Processing 124: 83-110. https://doi.org/10.1016/j.ymssp.2019.01.051
[37] Zhi L, Li Q, Fang M (2016) Identification of wind loads and estimation of structural responses of super‐tall buildings by an inverse method. Computer‐Aided Civil and Infrastructure Engineering 31(12): 966-982. https://doi.org/10.1111/mice.12241
[38] Zhu F, Zhang M, Ma F, Li Z, Qu X (2024) Identification of wind load exerted on the jacket wind turbines from optimally placed strain gauges using C-optimal design and mathematical model reduction. Journal of Marine Science and Engineering 12(4): 563. https://doi.org/10.3390/jmse12040563

Memo

Memo:
Received date:2025-2-28;Accepted date:2025-4-16。<br>Foundation item:Funding Supported by the National Natural Science Foundation of China (52301365), Shandong Provincial Natural Science Foundation (ZR2022QE106), Heilongjiang Provincial Natural Science Foundation of China (LH2023E075), Science and Technology Plan Project of Yantai City (2023JMRH004), and Special fund for Taishan Industrial Leading Talent Project (tsls20230605).<br>Corresponding author:Meng Zhang，E-mail:zhangmeng@hrbeu.edu.cn
Last Update: 2026-10-16