Hybrid soft computing-based predictive models for shear strength of exterior reinforced concrete beam-column joints

The existing empirical equations for predicting the shear strength (SSP) of reinforced concrete (RC) beam-column joints (BCJs) have been developed by considering a limited number of governing variables, primarily the concrete compressive strength (CCS) and effective joint area. However, due to uncertainties in experimental data and the neglect of direct impact of other influential parameters, the predictions made by the codes' formulas may be unreliable and erroneous. In this study, the Kriging, Bayesian artificial neural network (BANN), Bayesian multi-kernel relevance vector machine (BMRVM), and the Long short-term memory (LSTM) recurrent neural network are employed for SSP of exterior RCBCJs. Bayesian algorithm was utilized to automatically tune the hyperparameters of both the ANN and multi-kernel RVM models. A comprehensive database with 270 specimens and 13 input parameters was used to develop models. A statistical analysis comparing the developed models to common empirical equations showed that the forecasts generated by these codes not only differed for identical samples, but also significantly overestimated the shear strength of RCBCJs. Kriging and the proposed BMRVM ( \({R}_{train}^{2}\) $R_{\mathit{train}}^2$ = 0.98) showed superior training performance. In contrast, the LSTM model ( \({R}^{2}\) $R^2$ =0.977, RMSE = 55.31 kN, MAPE = 9.55%, SDPO = 41.86%, and U₉₅ = 149.2) demonstrated exceptional generalization capability, achieving the best rank during testing. The proposed Bayesian ANN closely followed LSTM and outperformed all other models in the evaluation. Additionally, a game theory-based SHapley Additive exPlanations (SHAP) model interpretation analysis revealed that the top and bottom longitudinal reinforcement of the beam, CCS, longitudinal reinforcement, and width of the column, as well as the beam depth, are the most significant factors influencing the shear strength of RCBCJs. Conversely, the beam width and axial load have a comparatively lower influence on the model's output compared to the other variables.