Predicting long-term displacements of deep tunnels using an artificial neural network optimized by sand cat swarm optimization with Chebyshev map

Abstract

Long-term tunnel displacement prediction is of great engineering significance to tunnel maintenance and hazard warning. To that end, this paper provides a novel combination idea that uses the analytical solution considering the rheological properties of the rock masses and the poor blasting for excavation of a deep tunnel to establish a long-term tunnel displacement database. In the analytical solution, 12 parameters are considered to predict the deep tunnel displacements (${u}_{r}$) in different periods, i.e., instantaneous displacement (${u}_{r} at {T}_{C}^{0}$), the first year (${{u}_{r} at T}_{C}^{1}$), and, the fifth year (${{u}_{r} at T}_{C}^{5}$), and the tenth year (${{u}_{r} at T}_{C}^{10}$). An artificial neural network (ANN) is optimized by the Sand Cat swarm optimization (SCSO) with the Chebyshev (Che) map (i.e., CheSCSO-ANN model) to predict the tunnel displacement and compared to the other five prediction models. The coefficient of determination (R²), the variance accounted for (VAF), the root mean squared error (RMSE), and the weighted average percentage error (WAPE) are utilized to evaluate the model performance. The outcomes of this research indicate that the CheSCSO-ANN model obtains the most satisfactory accuracy for predicting the long-term tunnel displacement (${{u}_{r}\mathrm{ at }T}_{C}^{1}$: 0.9997, 99.9685%, 2.2105, 0.0116; ${{u}_{r}\mathrm{ at }T}_{C}^{5}$: 0.9997, 99.9704%, 2.5387, 0.0093 and ${{u}_{r}\mathrm{ at }T}_{C}^{10}$: 0.9994, 99.9426%, 3.3365, 0.0115). The CheSCSO-ANN model performance is verified using two independent published cases. The verification results show that the calculation accuracy of the proposed model is slightly lower than that of the analytical solution, but the model is still reliable considering the calculation efficiency and the allowable error range. Besides, the effect of the geological strength index (GSI) and damaged zone radius (${R}_{D}$) on the long-term tunnel convergence prediction is far greater than the other parameters one.

Appendix A

The comparison results of all proposed models for predicting the ${{u}_{r} at T}_{C}^{1}$, ${{u}_{r} at T}_{C}^{5}$, and ${{u}_{r} at T}_{C}^{10}$ are illustrated in Figs. 11, 12 and 13. 

Compared with the prediction of short-term displacement, SCSO-ANN and CheSCSO-ANN models had slight difference in the prediction performance of long-term displacement, although they were far ahead of other models. Therefore, it is impossible to fully assess the model performance only by the performance indices and regression analysis.

Noted that the prediction accuracy of CSO-ANN and CheSCSO-ANN models for small displacement is almost the same, and higher than that for large displacement. But for the large displacement prediction, the slight difference in the prediction performance will cause obvious errors, which provides the necessary data conditions for further evaluation of model performance.

Fig. 11

Predicted versus simulated ${{u}_{r} at T}_{C}^{1}$ by the proposed models (test set)

Fig. 12

Predicted versus simulated ${{u}_{r} at T}_{C}^{5}$ by the proposed models (test set)

Fig. 13

Predicted versus simulated ${{u}_{r} at T}_{C}^{10}$ by the proposed models (test set)