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Nonlinear Grey Bernoulli Model for Long-Term Marine Corrosion Forecasting of Steel Pipe under Sparse-data Conditions Cover

Nonlinear Grey Bernoulli Model for Long-Term Marine Corrosion Forecasting of Steel Pipe under Sparse-data Conditions

Open Access
|Aug 2026

Figures & Tables

Table 1:

Chemical composition of the SKK490 steel coupons (Nguyen & Le Trung, 2025)

CompositionSKK490 bare steel
Carbon [C]0.17%
Silicon [Si]0.30%
Manganese [Mn]1.40%
Phosphorus [P]0.035%
Sulfur [S]0.03%
Niobium [Nb]-
Vanadium [V]-
Titanium [Ti]-
Table 2:

Initial mechanical properties of the SKK490 steel coupons (Nguyen & Le Trung, 2025)

PropertySKK490 bare steel
Yield strength [MPa]325
Tensile strength [MPa]510
Elongation [%]17
Table 3:

Geometry and exposed area of the SKK490 steel coupons (Nguyen & Le Trung, 2025)

SampleLength, l [cm]Cross-section, a [cm]Cross-section, b [cm]Immersed length [cm]Exposed area [cm2]
Bare steel SKK490201.621075.2
Table 4:

Composition of the simulated seawater solution (Nguyen & Le Trung, 2025)

ComponentAmount / VolumeUnit
Deionized water1L
NaCl32.48g
NaHCO311.87g
Figure 1:

Accelerated corrosion test setup for the SKK490 steel coupons under simulated Vietnamese marine conditions (Nguyen & Le Trung, 2025)

Table 5:

Laboratory test duration and adopted equivalent exposure duration (Nguyen & Le Trung, 2025)

Test stageTest duration [hours]Equivalent exposure duration [years]Number of specimensApplied current [mA]
01724.530160
021207.530
032401530
04320203
05480303
06800503
071200753
0816001003
Table 6:

Statistical summary of pre-processed corrosion data

YearsTrimmed Mean [%]SD [%]COV [%]95% CI Lower [%]95% CI Upper [%]
4.53.780.266.99333.683.88
7.55.770.396.73395.625.91
1514.181.047.311613.8014.57
2015.720.171.105515.2916.15
3022.210.170.774521.7822.64
Figure 2:

Experimental corrosion mass-loss ratio with trimmed mean and 95% confidence interval

Figure 3:

Experimental corrosion mass-loss ratio over equivalent exposure time

Figure 4:

Smoothed corrosion sequence generated by the non-equidistant accumulated generation operation (AGO)

Figure 5:

Sensitivity of the long-term NGBM response to prescribed values of the nonlinear exponent n; the optimized value n = 0.419 is reported separately and used for forecasting

Figure 6:

Parametric-bootstrap ensemble, mean NGBM forecast, and 95% uncertainty interval

Figure 7:

Comparison of the NGBM forecast and 95% uncertainty interval with experimental observations and the calibrated Weibull and power-law benchmarks

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

© 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.