Tunnel displacement prediction under spatial effect based on Gaussian process regression optimized by differential evolution

Abstract

The prediction and analysis of surrounding rock deformation is a primary risk assessment method in tunnel engineering. However, the accurate prediction result is not easy to achieve due to the influence of multiple factors such as rock mass properties, support structure, and the spatial effect of tunnel construction. In this paper, a multivariate time-series model (MTSM) for tunnel displacement prediction is studied based on Gaussian process regression (GPR) optimized by differential evolutionary (DE) strategy, where the spatial effect is intuitively expressed through an extended time-series model. First, building learning samples for GPR, in which the inputs is the displacement data of the previous n days and the output is the data of the day (n + 1). Then, for each sample, an input item is added successively to form an expanded learning sample, which is the “distance between the construction face and monitoring section” on the day (n+ 1). Taking the root mean square error between the regression and measured data as the control index, the GPR model is trained to express the nonlinear mapping relationship between input and output, and the optimal parameters of this model are searched by DE. The displacement multivariate time-series model represented by DE-GPR is known as MTSM. On this basis, the applicability of GPR for tunnel displacement prediction and the necessity of DE optimization are illustrated by comparing the prediction results of several commonly used machine learning models. At the same time, the influence of GPR and DE parameters on the regression result and the computational efficiency of the MTSM model is analyzed, the recommendation for parameter values are given considering both calculation efficiency and accuracy. This method is successfully applied to the Leshanting tunnel of Puyan expressway in Fujian province, China, and the results show that the MTSM based on DE-GPR has a good ability in the deformation prediction of the surrounding rock, which provides a new method for tunnel engineering safety control.