Moment–Curvature Relationship Prediction of Reinforced Concrete Beams by Adaptive Neuro-Fuzzy Inference System (ANFIS) Modelling

Abstract Estimation of the moment–curvature (MC) relationship of reinforced concrete (RC) beam cross sections presents challenges due to the quite complex mixture of their composition. It is known that traditional MC calculation methods are time-consuming, require high computer power, and have a scarcity of data. The modern soft-computing models offer a reliable solution for precise estimation. This research proposes a new modified version of the adaptive neuro-fuzzy inference system (ANFIS) model that takes quite uncertainty source reduction in the estimation of the MC relationship that is valid for RC beam cross sections. The new approach provides an automatic deep-learning procedure to form a nonlinear MC relationship in the light of ANFIS software that accounts for uncertainty source reductions through fuzzy sets. For the application of this method, six input parameters are considered: cross-section width and height, concrete compressive and rebar yield strengths, total rebar area, and curvature. A normalization procedure is applied to transform each parameter into dimensionless amounts for comparison with existing models in the literature. The ANFIS model is prepared in such a way that training and test data percentages are taken as 75% and 25%, respectively. Finally, the comparison of the actual and proposed model output curves shows a ± 5% difference, which is a practically acceptable limit in practical applications. The best ANFIS computation results are achieved with three Gaussian fuzzy sets for each parameter and five fuzzy sets for curvature. It is recommended that this model can be improved by larger datasets also for different materials such as steel, timber, and prestressed concrete beam types to identify valid MC relationships of each material. Apart from the structural setup of methodological approaches, the innovative nature of this article is to eliminate the number of rule bases by taking into account expert opinions and obtaining the most meaningful outputs with the least percentage of errors.