Soft Computing in Water Engineering

Soft Computing in Water Engineering

Model Uncertainty, Study-Grouped Validation and Reliability-Based Resistance Factors for the Ultimate Conditions of FRP-Confined Concrete

Document Type : Original Article

Authors
School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
10.22034/scwe.2026.603655.1030
Abstract
Design-oriented equations for the ultimate strength and strain of fibre-reinforced polymer (FRP) confined concrete are usually compared through error statistics obtained from a single random split of a test database. Such statistics say little about the safety margin that a designer needs, and they ignore the fact that specimens from the same laboratory are not independent. This study re-analysed a database of 780 circular FRP-confined concrete specimens (530 carbon, 162 glass and 88 aramid FRP, 63 test programmes) compiled for a recent hybrid machine-learning study. Eight strength models and seven strain models were treated as resistance models and their model uncertainty θ = experiment/prediction was characterised. For the strength models the coefficient of variation of θ was 0.177–0.251, while for the strain models it was 0.36–0.82, an order-of-magnitude difference in the information available for design. A random-effects decomposition showed that 53–67% (strength) and 49–62% (strain) of the variance of ln θ lies between test programmes rather than within them. Gradient-boosting models were then validated both with random 10-fold cross-validation and with study-grouped cross-validation. The random split reproduced the large accuracy gains reported in the literature (RMSE 0.252 for the strength ratio), but under study-grouped validation the same model gave 0.366, which is no better than the best closed-form equation (0.349); for the strain ratio the machine-learning model was worse than the closed-form equation. Grouped cross-conformal intervals achieved their nominal 90% coverage on average but failed for individual test programmes. Finally, resistance factors were calibrated with EN 1990 Annex D and with the first-order reliability method for an axially loaded confined column. A factor φ ≈ 0.53 is needed to reach βT = 4.0 with the best strength model, whereas φ = 0.65 gives β ≈ 3.18. Data-driven refinement of the mean prediction does not remove the scatter that controls design, and reporting model uncertainty with study-grouped validation should become standard practice.
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