Time series prediction of tunnel surrounding rock deformation using CPO-CLA integrated model

Tunnel surrounding rock (TSR) deformation exhibits time- and space-dependent behavior, making it challenging for a single prediction model to capture these characteristics over extended periods. Utilizing 8 years of TSR deformation data from the Beishan exploration tunnel (BET) test platform, the metaheuristic algorithm crested porcupine optimizer (CPO) was applied for the first time to optimize the time series of TSR deformation, and an integrated model incorporating convolutional neural network (CNN), long short-term memory network (LSTM), and attention mechanism (ATT) was proposed. This model integrates the strong feature extraction capabilities of CNN, the superior sequence prediction performance of LSTM, and the effective attention mechanism of ATT. The results show that during blasting excavation, the internal displacement of TSR exhibits a stepwise change pattern. After excavation, the internal displacement enters a phase of gradual increase, ultimately reaching a stable convergence stage. The CPO-CNN-LSTM-ATT (CPO-CLA) integrated model demonstrated excellent predictive accuracy and stability across various evaluation metrics, achieving a determination coefficient ( R 2 ) of 0.985. Compared to the CNN-LSTM-ATT (CLA) model, the CPO-CLA model showed a 14.1% increase in R 2 , a 61.5% decrease in root mean square error (RMSE), and a 72.9% decrease in mean absolute error (MAE). In comparison with current mainstream metaheuristic integrated models, the CPO-CLA model is better suited for predicting long-term TSR deformation. It offers high computational efficiency, accurate predictions, and expertise in optimizing large datasets.