Interpretable Constrained Monotonic Neural Network Model for Fiber-Reinforced Polymer (FRP) Shear Contribution in Strengthened Reinforced Concrete (RC) Beams

Abstract

This study includes an interpretable machine learning (ML) framework for predicting the shear contribution of externally bonded fiber-reinforced polymer (FRP) composites in reinforced concrete beams. A database including total 313 experimental specimens was collected from previous experimental research. The data screening process has been conducted using the Isolation Forest algorithm, resulting in 268 cleaned specimens. The cleaned database was divided into a training subset containing 214 specimens and an independent test set containing 54 specimens. The trained subset was enlarged into 5204 synthetic data using two advanced generative models including Wasserstein generative adversarial network and conditional Variational autoencoder (CVAE). Separate constrained monotonic neural network (CMNN) models were then trained on both datasets and WGAN-based CMNN achieved R2=0.9524 for the synthetic training dataset and R2=0.9120 for the independent test set, whereas the CVAE-based CMNN achieved corresponding values of 0.9632 and 0.9011. To improve practical applicability, response functions were extracted from WGAN-based CMNN and fitted with analytical expressions to derive a closed-form prediction equation. The proposed equation was independently validated using separate unseen test specimens, which were not used in CMNN training and achieved R2 = 0.79, RMSE = 24.98 kN, MAE = 19.65 kN, MAPE = 21.72%, VAF = 79.35%, U95 = ±54.94 kN, SI = 3.04, and PI = 0.11. Compared with ACI 440.2R-17, CSA-S806.12, CNR-DT200 R1.2013, TR-55, and JSCE, the proposed equation showed superior accuracy while maintaining a transparent and design-oriented format.