Foundation Pit Support Deformation Prediction Based on Deep Echo State Network Optimized by Empirical Balance Particle Swarm Optimization

The deformation of foundation pit excavation is influenced by various factors, exhibiting high nonlinearity and instability. To achieve more accurate prediction of foundation pit deformation, the Variational Mode Decomposition (VMD) algorithm is introduced to perform multi-modal decomposition on the deformation of foundation pit support structures, thereby reducing the non-stationarity of the data. A Deep Echo State Network (DESN) model is established to train and predict each modal sequence, with the parameters of the DESN optimized during the training process using the Empirical Balance Particle Swarm Optimization (EBPSO) algorithm. The preliminary results are obtained by summing the predicted results of each mode. To further improve the accuracy of deformation prediction, the EBPSO-DESN model is employed to predict and compensate for prediction errors. Finally, the final prediction results are obtained by superposition. Simulation results demonstrate that the VMD-EBPSO-DESN model with error correction achieves higher accuracy compared to several other models.