A time series prediction model of foundation pit deformation based on empirical wavelet transform and NARX network

Abstract

Large deep foundation pits are usually in a complex environment, so their surface deformation tends to show a stable rising trend with a small range of fluctuation, which brings certain difficulty to the prediction work. Therefore, in this study we proposed a nonlinear autoregressive exogenous (NARX) prediction method based on empirical wavelet transform (EWT) pretreatment is proposed for this feature. Firstly, EWT is used to conduct adaptive decomposition of the measured deformation data and extract the modal signal components with characteristic differences. Secondly, the main components affecting the deformation of the foundation pit are analyzed as a part of the external input. Then, we established a NARX prediction model for different components. Finally, all predicted values are superpositioned to obtain a total value, and the result is compared with the predicted results of the nonlinear autoregressive (NAR) model, empirical mode decomposition-nonlinear autoregressive (EMD-NAR) model, EWT-NAR model, NARX model, EMD-NARX model and EWT-NARX model. The results showed that, compared with the EWT-NAR and EWT-NARX models, the EWT-NARX model reduced the mean square error of KD25 by 91.35%, indicating that the feature of introducing external input makes NARX more suitable for combining with the EWT method. Meanwhile, compared with the EMD-NAR and EWT-NAR models, the introduction of the NARX model reduced the mean square error of KD25 by 78.58% and 95.71%, indicating that EWT had better modal decomposition capability than EMD.