Estimation of the shear strength of UHPC beams via interpretable deep learning models: Comparison of different optimization techniques

In this article, optimized deep learning (DL) models with different algorithms are adopted to estimate the shear strength of rectangular ultra-high performance concrete beams (UHPC-Bs) in order to overcome the challenges in traditional mechanics-based approaches. Long short-term memory (LSTM) and gated recurrent unit (GRU) are chosen as the DL models, whereas the recent popular optimization algorithms are phasor particle swarm optimization (PPSO), dwarf mongoose optimization (DMO), mountain gazelle optimizer (MGO), and atom search optimization (ASO). A thorough and reliable dataset of 244 UHPC-Bs test results with ten input features has been used to construct the hybrid DL models. The performance of the optimized hybrid LSTM and GRU models with different algorithms is extensively assessed and compared based on various statistical metrics, error, and score analyses. Then, the model with the best estimation performance is determined and compared with the mechanics-based formulas in the current international design codes. Additionally, Shapley additive explanations (SHAP) analysis is used to assist in the interpretability of DL models and to reveal the effects of input features that contribute to the model's estimation. According to the results of the present work, all DL models successfully estimate the shear strength of UHPC-Bs. Among these models, the MGO-LSTM model stands out compared to the other models in terms of several performance measures for both the training and testing phases, like a higher R-2 value, lower RMSE, MAPE, and MAE values, as well as a smaller error ratio and a higher final score. The performance of the algorithms applied to optimize the hyper-parameters of the LSTM and GRU models can be ranked as follows: MGO > DMO > PPSO > ASO. Moreover, a graphical user interface (GUI) was constructed based on the best estimation model that was built so that the shear strength of UHPC-Bs could be estimated in real-world situations without the need for any extra software or tools. This enables more users to quickly and easily estimate the shear strength of UHPC-Bs, optimize design processes, and decrease experimental testing costs.