Optimized functional linked neural network for predicting diaphragm wall deflection induced by braced excavations in clays

Deep excavation during the construction of underground systems can cause movement on the ground, especially in soft clay layers. At high levels, excessive ground movements can lead to severe damage to adjacent structures. In this study, finite element analyses (FEM) and the hardening small strain (HSS) model were performed to investigate the deflection of the diaphragm wall in the soft clay layer induced by braced excavations. Different geometric and mechanical properties of the wall were investigated to study the deflection behavior of the wall in soft clays. Accordingly, 1090 hypothetical cases were surveyed and simulated based on the HSS model and FEM to evaluate the wall deflection behavior. The results were then used to develop an intelligent model for predicting wall deflection using the functional linked neural network (FLNN) with different functional expansions and activation functions. Although the FLNN is a novel approach to predict wall deflection; however, in order to improve the accuracy of the FLNN model in predicting wall deflection, three swarm-based optimization algorithms, such as artificial bee colony (ABC), Harris’s hawk’s optimization (HHO), and hunger games search (HGS), were hybridized to the FLNN model to generate three novel intelligent models, namely ABC-FLNN, HHO-FLNN, HGS-FLNN. The results of the hybrid models were then compared with the basic FLNN and MLP models. They revealed that FLNN is a good solution for predicting wall deflection, and the application of different functional expansions and activation functions has a significant effect on the outcome predictions of the wall deflection. It is remarkably interesting that the performance of the FLNN model was better than the MLP model with a mean absolute error (MAE) of 19.971, root-mean-squared error (RMSE) of 24.574, and determination coefficient (R²) of 0.878. Meanwhile, the performance of the MLP model only obtained an MAE of 20.321, RMSE of 27.091, and R² of 0.851. Furthermore, the results also indicated that the proposed hybrid models, i.e., ABC-FLNN, HHO-FLNN, HGS-FLNN, yielded more superior performances than those of the FLNN and MLP models in terms of the prediction of deflection behavior of diaphragm walls with an MAE in the range of 11.877 to 12.239, RMSE in the range of 15.821 to 16.045, and R² in the range of 0.949 to 0.951. They can be used as an alternative tool to simulate diaphragm wall deflections under different conditions with a high degree of accuracy.