Reliability-Based Topology, Shape, and Size Optimization to Find the Optimal Four-Legged Jacket Offshore Platform
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This study aims to establish a comprehensive reliability-oriented optimization framework for a four-legged offshore platform jacket without batter, addressing the persistent issue of material overuse in conventional deterministic design. The proposed methodology sequentially integrates topology, shape, and reliability-based size optimization to achieve a lightweight yet safe structural configuration. Topology optimization is first performed using the Solid Isotropic Material with Penalization (SIMP) method to minimize strain energy under prescribed volume constraints, generating an optimal load-transfer mechanism. The obtained layout is refined through shape optimization to improve joint configuration and stress redistribution. Finally, reliability-based design optimization (RBDO) is implemented using a Kriging surrogate model coupled with Sequential Quadratic Programming (SQP) and Monte Carlo simulation to minimize structural weight under probabilistic constraints, including strength, displacement, and target reliability index (β 3). The optimized jacket achieves a 53.71% weight reduction while satisfying safety requirements with a maximum unity check of 0.77 and a reliability index of β = 3.11. The proposed surrogate-assisted RBDO significantly reduces computational effort compared to direct reliability analysis. The primary novelty lies in the unified integration of topology, shape, and probabilistic size optimization for a non-battered platform jacket, which has not been comprehensively reported in previous offshore structural optimization studies.
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[1] Liu, S., Yin, X., Li, H., Yang, J., Li, P., & Li, P. (2025). Effectiveness of MTMD for jacket offshore platform under wave and earthquake excitations. Soil Dynamics and Earthquake Engineering, 199(July), 109654. doi:10.1016/j.soildyn.2025.109654.
[2] Sarker, S., Kim, D., Azad, M. S., Sinsabvarodom, C., & Guk, S. (2021). Influence of optimal intensity measures selection in engineering demand parameter of fixed jacket offshore platform. Applied Sciences (Switzerland), 11(22), 10745. doi:10.3390/app112210745.
[3] Moradi, H., Karimi, H. R., KaramZadeh, N. S., & O’Din Rabei Golami, E. (2020). Effects of leg slope on the failure of fixed jacket platforms: A case study of south pars gas Field’s platforms. Ocean Engineering, 210. doi:10.1016/j.oceaneng.2020.107401.
[4] Li, N., Shi, W., Han, X., Li, X., Verma, A. S., & Liu, C. (2023). Dynamic analysis of an integrated offshore structure comprising a jacket-supported offshore wind turbine and aquaculture steel cage. Ocean Engineering, 274, 274. doi:10.1016/j.oceaneng.2023.114059.
[5] Ju, S. H. (2022). Increasing the fatigue life of offshore wind turbine jacket structures using yaw stiffness and damping. Renewable and Sustainable Energy Reviews, 162. doi:10.1016/j.rser.2022.112458.
[6] Bai, J., Jiao, C., Ai, F., Wang, Y., & Yang, Q. (2025). Dynamic response of the jacket offshore wind turbines subjected to coupled wind, wave, and earthquake loads under scour conditions. Ocean Engineering, 328. doi:10.1016/j.oceaneng.2025.120901.
[7] Zhang, P., Li, J., Gan, Y., Zhang, J., Qi, X., Le, C., & Ding, H. (2020). Bearing capacity and load transfer of brace topological in offshore wind turbine jacket structure. Ocean Engineering, 199. doi:10.1016/j.oceaneng.2020.107037.
[8] Nassiraei, H., & Rezadoost, P. (2021). SCFs in tubular X-joints retrofitted with FRP under out-of-plane bending moment. Marine Structures, 79. doi:10.1016/j.marstruc.2021.103010.
[9] Pan, Z., Wu, G., Si, F., Shang, J., Zhou, H., Li, Q., & Zhou, T. (2022). Parametric study on SCF distribution along the weld toe of internally ring-stiffened two-planar tubular KK joints under axial loading. Ocean Engineering, 248. doi:10.1016/j.oceaneng.2022.110826.
[10] Nassiraei, H., & Rezadoost, P. (2022). Stress concentration factors in tubular T-joints reinforced with external ring under in-plane bending moment. Ocean Engineering, 266. doi:10.1016/j.oceaneng.2022.112551.
[11] Wang, S., Meng, X., Ji, S., Fang, H., Liu, Y., & Duan, L. Y. (2019). All-metal brace with hysteresis dissipation for impact protection of jacket platforms. Marine Structures, 66, 1–15. doi:10.1016/j.marstruc.2019.02.009.
[12] Siriwardane, S. C., Adasooriya, N. D., & Pavlou, D. (2021). Fatigue Strength Curve for Tubular Joints of Offshore Structures under Dynamic Loading. Dynamics, 1(1), 125–133. doi:10.3390/dynamics1010007.
[13] Fang, H., Meng, X., Duan, L., Liu, Y., & Wu, R. (2020). Enhanced dissipation of a jacket platform provided by a steel brace containing a multistable bilayered column. Ocean Engineering, 203. doi:10.1016/j.oceaneng.2020.107244.
[14] Ahmadi, H., & Zavvar, E. (2020). Degree of bending (DoB) in offshore tubular KT-joints under the axial, in-plane bending (IPB), and out-of-plane bending (OPB) loads. Applied Ocean Research, 95. doi:10.1016/j.apor.2019.102015.
[15] Chatziioannou, K., Karamanos, S. A., & Huang, Y. (2019). Ultra low-cycle fatigue performance of S420 and S700 steel welded tubular X-joints. International Journal of Fatigue, 129. doi:10.1016/j.ijfatigue.2019.105221.
[16] Tian, X., Wang, Q., Liu, G., Liu, Y., Xie, Y., & Deng, W. (2019). Topology optimization design for offshore platform jacket structure. Applied Ocean Research, 84, 38–50. doi:10.1016/j.apor.2019.01.003.
[17] Martens, J. H., Zwick, D., & Muskulus, M. (2015, June). Topology optimization of a jacket structure for an offshore wind turbine with a genetic algorithm. 11th World Congress on Structural and Multidisciplinary Optimization, 1, 2-7.
[18] Zhang, C., Long, K., Zhang, J., Lu, F., Bai, X., & Jia, J. (2022). A topology optimization methodology for the offshore wind turbine jacket structure in the concept phase. Ocean Engineering, 266(P4), 112974. doi:10.1016/j.oceaneng.2022.112974.
[19] Cui, Y., Yu, Y., Cheng, S., Wei, M., Pan, Y., & Dong, Z. (2024). Multi-performance reliability-based concept-detailed co-design of offshore structures using modified conjugate FR algorithm. Ocean Engineering, 300, 117275. doi:10.1016/j.oceaneng.2024.117275.
[20] Zhou, Y., Zhang, J., Long, K., Saeed, A., Tao, T., & Chen, J. (2025). Topology optimization on a jacket structure for offshore wind turbines by altering structural design domain. Applied Ocean Research, 154(January), 104421. doi:10.1016/j.apor.2025.104421.
[21] Mei, Z., Huang, Y., & Chen, J. (2025). Direct mesh-free topology optimization using random feature method. CAD Computer Aided Design, 189(June), 103939. doi:10.1016/j.cad.2025.103939.
[22] Lei, Z., Deng, Z., Liang, Y., Chen, G., Li, R., & Yang, D. (2025). Hybrid method of SIMP and SAIP for reliability-based topology optimization considering strength failure under load uncertainty. Computer Methods in Applied Mechanics and Engineering, 441(March), 117975. doi:10.1016/j.cma.2025.117975.
[23] Zhao, Q., Wang, C., Zuo, T., Wang, Q., & Liu, Z. (2025). A domain evolution method to suppress the eigen-frequency and eigenmode errors caused by low-density elements in dynamic topology optimization. Advances in Engineering Software, 210(April), 104011. doi:10.1016/j.advengsoft.2025.104011.
[24] Cao, Y., Yang, J., Gao, X., & Wang, Y. (2025). An efficient self-filtering topology optimization method based on Free Element Method. Engineering Analysis with Boundary Elements, 179(PB), 106429. doi:10.1016/j.enganabound.2025.106429.
[25] Liu, J., Zhang, H., Min, Q., Li, P., Yang, J., & Xia, Z. (2025). Geometrically nonlinear isogeometric topology optimization via extended finite element method. Computers and Structures, 316(June), 107871. doi:10.1016/j.compstruc.2025.107871.
[26] Zhu, J. H., Zhang, W. H., & Xia, L. (2016). Topology Optimization in Aircraft and Aerospace Structures Design. Archives of Computational Methods in Engineering, 23(4), 595–622. doi:10.1007/s11831-015-9151-2.
[27] Li, J., Wu, Z., Xie, C., Xiao, L., Garg, A., & Mei, G. (2025). The optimization design for the truss substructure of the novel truss-type submerged floating tunnel using the topology optimization method. Ocean Engineering, 340(P3), 122409. doi:10.1016/j.oceaneng.2025.122409.
[28] Lan, R., Long, K., Saeed, A., Geng, R., Chen, Y., Zhang, J., Tao, T., & Liu, J. (2024). Fail-safe topology optimization for a four-leg jacket structure of offshore wind turbines. Structures, 62(January), 106183. doi:10.1016/j.istruc.2024.106183.
[29] Zhu, S. P., Keshtegar, B., Trung, N. T., Yaseen, Z. M., & Bui, D. T. (2021). Reliability-based structural design optimization: hybridized conjugate mean value approach. Engineering with Computers, 37(1), 381–394. doi:10.1007/s00366-019-00829-7.
[30] Lavaei, M. H., Mohammadi Dehcheshmeh, E., Safari, P., Broujerdian, V., & Gandomi, A. H. (2023). Reliability-based design optimization of post-tensioned self-centering rocking steel frame structures. Journal of Building Engineering, 75. doi:10.1016/j.jobe.2023.106955.
[31] Liu, X., Li, T., Zhou, Z., & Hu, L. (2022). An efficient multi-objective reliability-based design optimization method for structure based on probability and interval hybrid model. Computer Methods in Applied Mechanics and Engineering, 392. doi:10.1016/j.cma.2022.114682.
[32] Jerez, D. J., Jensen, H. A., & Beer, M. (2022). Reliability-based design optimization of structural systems under stochastic excitation: An overview. Mechanical Systems and Signal Processing, 166. doi:10.1016/j.ymssp.2021.108397.
[33] Kaveh, A., & Zaerreza, A. (2022). Reliability-based design optimization of the frame structures using the force method and SORA-DM framework. Structures, 45, 814–827. doi:10.1016/j.istruc.2022.09.057.
[34] Yu, Y., Wei, M., Yu, J., Cui, Y., Gao, R., Dong, Z., & Wang, X. (2023). Reliability-based design method for marine structures combining topology, shape, and size optimization. Ocean Engineering, 286. doi:10.1016/j.oceaneng.2023.115490.
[35] Meng, D., Yang, H., Yang, S., Zhang, Y., Jesus, A. M. P. D., Correia, J., Fazeres-Ferradosa, T., Macek, W., Branco, R., & Zhu, S. P. (2024). Kriging-assisted hybrid reliability design and optimization of offshore wind turbine support structure based on a portfolio allocation strategy. Ocean Engineering, 295(February), 116842. doi:10.1016/j.oceaneng.2024.116842.
[36] Jiang, Z., Huang, X., Wang, B., Liao, X., Liu, H., & Ding, P. (2024). Time-dependent reliability-based design optimization of main shaft bearings in wind turbines involving mixed-integer variables. Reliability Engineering and System Safety, 243(November 2023), 109817. doi:10.1016/j.ress.2023.109817.
[37] Jiang, Z., Huang, X., Ding, P., Liu, H., & Ge, Y. (2023). Reliability-based design optimization of the spiral water jacket for motorized spindle. Case Studies in Thermal Engineering, 51(July), 103665. doi:10.1016/j.csite.2023.103665.
[38] Cui, Y., Zhang, B., Yu, Y., Cheng, S., Wei, M., Jin, Z., & Song, L. (2024). A novel BACG inverse reliability algorithm for efficient and robust reliability-based topology optimization of marine structures. Ocean Engineering, 298(February), 117165. doi:10.1016/j.oceaneng.2024.117165.
[39] Rajput, S. P. S., & Datta, S. (2019). A review on optimization techniques used in civil engineering material and structure design. Materials Today: Proceedings, 26, 1482–1491. doi:10.1016/j.matpr.2020.02.305.
[40] Mei, L., & Wang, Q. (2021). Structural Optimization in Civil Engineering: A Literature Review. Buildings, 11(2), 66. doi:10.3390/buildings11020066.
[41] Deng, W., Tian, X., Han, X., Liu, G., Xie, Y., & Li, Z. (2021). Topology optimization of jack-up offshore platform leg structure. Proceedings of the Institution of Mechanical Engineers Part M: Journal of Engineering for the Maritime Environment, 235(1), 165–175. doi:10.1177/1475090220928736.
[42] López, C., Baldomir, A., & Hernández, S. (2018). The relevance of reliability-based topology optimization in early design stages of aircraft structures. Structural and Multidisciplinary Optimization, 57(1), 417–439. doi:10.1007/s00158-017-1740-2.
[43] Tian, X., Sun, X., Liu, G., Deng, W., Wang, H., Li, Z., & Li, D. (2022). Optimization design of the jacket support structure for offshore wind turbine using topology optimization method. Ocean Engineering, 243. doi:10.1016/j.oceaneng.2021.110084.
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