Process-Integrated Optimization and Symbolic Regression for Direct Prediction of CFRP Area in Masonry Wall Strengthening

Unreinforced masonry walls exhibit limited resistance to lateral loads and, therefore, frequently require strengthening interventions. Carbon fiber reinforced polymer (CFRP) systems provide an efficient retrofit solution; however, current design procedures defined in structural guidelines require repetitive trial calculations to determine the necessary reinforcement amount. This study introduces a hybrid computational process that integrates metaheuristic optimization with symbolic regression to generate direct analytical equations for the estimation of the required CFRP area. First, a comprehensive database containing 1300 optimal strengthening scenarios was generated using the Jaya optimization algorithm under the constraints specified in ACI 440.7R and ACI 530. The resulting dataset was subsequently processed through symbolic regression using the PySR platform to identify explicit mathematical relationships between structural parameters and the optimum CFRP area. Most traditional machine learning approaches operate as black-box predictors. In contrast, the proposed approach generates interpretable closed-form expressions that can be used directly in engineering calculations. Two models were derived from the Pareto-optimal solution set. The first model is a simplified equation emphasizing algebraic simplicity. The second model prioritizes prediction accuracy. The simplified formulation achieved a coefficient of determination of approximately 0.992. The accuracy-focused model achieved a value above 0.997 with very low prediction errors. Validation studies with independent test samples showed that the obtained equations are reliable. The average error for the simplified model is below 4%, and for the high-accuracy model, it is approximately 2%. The results demonstrate that combining the optimization-generated datasets with symbolic regression makes it possible to obtain transparent design equations. These equations eliminate iterative design processes and provide a fast and reliable estimation tool for CFRP strengthening of masonry walls.