Nonlinear Grey Bernoulli Model for Long-Term Marine Corrosion Forecasting of Steel Pipe under Sparse-data Conditions
References
- Andrade, C., & Alonso, C. (1996). Corrosion rate monitoring in the laboratory and on-site. Construction and Building Materials, 10(5), 315–328.
https://doi.org/10.1016/0950-0618(95)00043-7 . - Cavanaugh, M., Buchheit, R., & Birbilis, N. (2010). Modeling the environmental dependence of pit growth using neural network approaches. Corrosion Science, 52(9), 3070–3077.
- Chen, C.-I. (2008). Application of the novel nonlinear grey Bernoulli model for forecasting unemployment rate. Chaos, Solitons & Fractals, 37(1), 278–287.
- Chen, C.-I., Chen, H. L., & Chen, S.-P. (2008). Forecasting of foreign exchange rates of Taiwan’s major trading partners by novel nonlinear Grey Bernoulli model NGBM (1, 1). Communications in Nonlinear Science and Numerical Simulation, 13(6), 1194–1204.
https://doi.org/10.1016/j.cnsns.2006.08.008 . - Coelho, L. B., Zhang, D., Van Ingelgem, Y., Steckelmacher, D., Nowé, A., & Terryn, H. (2022). Reviewing machine learning of corrosion prediction in a data-oriented perspective. Npj Materials Degradation, 6(1), 8.
https://doi.org/10.1038/s41529-022-00218-4 . - Dong, Z., Ding, L., Meng, Z., Xu, K., Mao, Y., Chen, X., Ye, H., & Poursaee, A. (2024). Machine learning-based corrosion rate prediction of steel embedded in soil. Scientific Reports, 14(1), 18194.
- Hacıefendioğlu, K., Özgan, K., Mostofi, S., & Altunışık, A. C. (2025). Rapid Detection of Corrosion on Steel Bridges Using a Deep Learning Method. Applied Sciences, 15(22), 11929.
https://doi.org/10.3390/app152211929 . - Julong, D. (1989). Introduction to grey system theory. The Journal of Grey System, 1(1), 1–24.
- Jung, K.-H., & Kim, S.-J. (2025). Statistical and ANN Modeling of Corrosion Behavior of Austenitic Stainless Steels in Aqueous Environments. Materials, 18(18), 4390.
- Khadom, A. A., Mahdi, M. S., & Mahood, H. B. (2020). Mathematical Regression and Artificial Neural Network for Prediction of Corrosion Inhibition Process of Steel in Acidic Media. Journal of Bio- and Tribo-Corrosion, 6(3), 92.
https://doi.org/10.1007/s40735-020-00390-7 . - Le, T. H., Nguyen, T. T. T., & Ngo, Q. T. (2026). Experimental Calibration of a Weibull Model for Corrosion Mass Loss in Steel Pipe Specimens Under Simulated Vietnamese Marine Conditions. Coatings, 16(5), 529.
https://doi.org/10.3390/coatings16050529 . - Liu, S., & Forrest, J. Y. L. (2010). Grey systems: Theory and applications. Springer Science & Business Media.
- Lu, J., Xie, W., Zhou, H., & Zhang, A. (2016). An optimized nonlinear grey Bernoulli model and its applications. Neurocomputing, 177, 206–214.
- Melchers, R. E. (2003a). Modeling of Marine Immersion Corrosion for Mild and Low-Alloy Steels—Part 1: Phenomenological Model. Corrosion, 59(4), 319–334.
https://doi.org/10.5006/1.3277564 . - Melchers, R. E. (2003b). Modeling of Marine Immersion Corrosion for Mild and Low-Alloy Steels—Part 2: Uncertainty Estimation. Corrosion, 59(4), 335–344.
https://doi.org/10.5006/1.3277565 . - Melchers, R. E., & Jeffrey, R. J. (2008). Probabilistic models for steel corrosion loss and pitting of marine infrastructure. Reliability Engineering & System Safety, 93(3), 423–432.
https://doi.org/https://doi.org/10.1016/j.ress.2006.12.006 . - Narayana, P. L., Tiwari, S., Maurya, A. K., Ishtiaq, M., Park, N., & Reddy, N. G. S. (2025). Quantitative and Qualitative Analysis of Atmospheric Effects on Carbon Steel Corrosion Using an ANN Model. Metals, 15(6), 607.
- Nguyen, T. T. T., & Le Trung, H. (2025). Accelerated corrosion effects on steel pipe pile materials in simulated Nhatrang seawater, Vietnam. Transport and Communications Science Journal, 76(1), 89–101.
https://doi.org/10.47869/tcsj.76.1.8 . - Noor, N. M., Smith, G. H., & Yahaya, N. (2007). The Weibull time-dependent growth model of marine corrosion in seawater ballast tank. Malaysian Journal of Civil Engineering, 19(2), 52–65.
- Noor, N. M., Yahaya, N., & Smith, G. H. (2013). A Probabilistic Time-Variant Corrosion Wastage Model for Seawater Ballast Tank. Arabian Journal for Science and Engineering, 38(6), 1333–1346.
https://doi.org/10.1007/s13369-013-0608-z . - Qin, S., & Cui, W. (2003). Effect of corrosion models on the time-dependent reliability of steel plated elements. Marine Structures, 16(1), 15–34.
https://doi.org/10.1016/S0951-8339(02)00028-X . - Shen, Y., He, B., & Qin, P. (2016). Fractional-order grey prediction method for non-equidistant sequences. Entropy, 18(6), 227.
https://doi.org/10.3390/e18060227 . - Wei, M., Yao, J., Chen, Y., Yang, B., Chen, D., & Cai, Y. (2024). Optimization and Evaluation of Accelerated Corrosion Tests Based on Mechanism Equivalence Principles. Materials, 17(16), 4042.
https://doi.org/10.3390/ma17164042 . - Weibull, W. (1951). A statistical distribution function of wide applicability. Journal of Applied Mechanics.
https://doi.org/10.1115/1.4010337 . - Xiao, X., & Peng, K. (2011). Research on generalized non-equidistance GM (1, 1) model based on matrix analysis. Grey Systems: Theory and Application, 1(1), 87–96.
https://doi.org/10.1108/20439371111106759 . - Yang, J., Zou, D., Zhang, M., Que, Z., Liu, T., Zhou, A., & Li, Y. (2024). Marine steel corrosion prediction and zonation using feature extraction and machine learning in the seas around China. Ocean Engineering, 314, 119649.
DOI: https://doi.org/10.2478/cee-2027-0014 | Journal eISSN: 2199-6512 (formerly 1336-5835) | Journal ISSN: 1336-5835
Language: English
Submitted on: May 28, 2026
Accepted on: Jun 28, 2026
Published on: Aug 19, 2026
Published by: University of Žilina
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
Related subjects:
© 2026 Thi Tuyet Trinh Nguyen, Trung Hieu Le, Nguyen Thanh Trung, Quoc Trinh Ngo, published by University of Žilina
This work is licensed under the Creative Commons Attribution 4.0 License.