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

Abstract

Reliable long-term forecasts of marine corrosion are difficult because observations are usually sparse, irregularly spaced, and uncertain. This study evaluates a constrained Nonlinear Grey Bernoulli Model (NGBM) using corrosion mass-loss data from SKK490 steel coupons representative of steel pipe material in a simulated Vietnamese marine environment. Measurements corresponding to 4.5–30 years of equivalent exposure were used for calibration, and those at 50, 75, and 100 years were withheld for comparison. The procedure combines non-equidistant grey-sequence processing, numerical and physical admissibility checks, and a 300-realization parametric bootstrap. Forecasts were required to remain nonnegative, monotonic in cumulative mass loss, and below 100%. The fitted NGBM produced a bounded, decelerating trajectory, and its uncertainty interval widened beyond the calibration range. Weibull and power-law benchmarks rose more steeply and were closer to some late experimental means, whereas the deterministic NGBM underestimated the 75- and 100-year values; those observations nevertheless fell within the bootstrap interval. At 100 years, the Weibull and power-law forecasts were approximately 78% and 76%, compared with about 50% for the deterministic NGBM. For this dataset, the constrained model provides a controlled way to extrapolate cumulative mass loss and to report the associated uncertainty. The equivalent-exposure scale and fitted parameters remain specific to the present accelerated test program and require validation with other steels, environments, and natural-exposure data.