Luan T. Nguyen

Nonlinear Kalman Filters for Model Calibration of Soil Parameters for Geomechanical Modeling in Mechanized Tunneling

AbstractThis work shows that nonlinear Kalman filters can be applied very effectively for the calibration of geomaterial parameters for geomechanical modeling in mechanized tunneling, using tunneling-induced settlements and horizontal displacements. The data curves measured along tunnel excavation steps, which exhibit a nonlinear relationship with respect to soil parameters and are prone to measurement inaccuracies, are utilized in combination with finite element modeling to estimate the underlying soil parameters, using a sequential inference framework: the nonlinear Kalman filtering. The paper shows the comparative performance of the two types of nonlinear Kalman filters that are effective for the identification of soil parameters in terms of convergence speed and accuracy: the extended Kalman filter (EKF) and the sigma-point Kalman filter (SPKF). The effectiveness of the two Kalman filters for inverse analysis is demonstrated through computer simulations for identifying a number of important constituti...

A Study of Misfit Topography towards Waveform Inversion for Prediction Ahead of Underground Tunnel

This work presents a synthetic study of misfit topography towards identification of geological structure ahead of the underground tunnel by waveform inversion. Simulation of viscoelastic waves is performed by the spectral element method implemented in SPECFEM2D package. By modeling a simple 2-dimensional underground tunnel model with a dip geological interface ahead of the tunnel face, we construct the misfit error landscapes with respect to geometric parameters defining the dip layer interface. As a result it is found that the misfit topography is very multimodal and therefore finding the true model by waveform inversion is likely to be very challenging. However, the choice of misfit definition, for example by using the envelope misfit, can help ease the toughness of misfit topography and facilitate the inversion task.

INVERSION METHODS BASED ON KALMAN FILTERING FOR IDENTIFICATION IN TUNNELING PROBLEMS

In this study we present an overview of the inversion methods based on the Kalman filtering technique, which was implemented for the identification of geological structure ahead of the underground tunnel. The methodology is particularly aimed at solving for model parameters even in the presence of noisy environment (measurements). One of the main goals of this investigation is related to the advance of the tunnel boring machine (TBM) during excavation in unknown environment in order to mitigate the excavation risks due to unpredicted obstacles and reduce costs caused by the TBM stoppage during tunneling under uncertain soil conditions. The inversion methods are implemented for the purpose of the reconnaissance in mechanized tunneling. Several inversion methods are investigated and implemented. The Kalman filter as parameter estimator, already having been successfully implemented in control systems, has been introduced here also for the purpose of geotechnical parameters estimation. Since the Kalman filter was originally developed for linear systems primarily represented in the state space form, the implementation with the geotechnical soil models was limited by the nonlinearities. Therefore modifications of the Kalman filter have been introduced and implemented, such as extended Kalman filter (EKF), sigma-point Kalman filter (SPKF) and unscented Kalman filter (UKF). The extended Kalman filter local iteration procedure incorporated with finite element analysis software has been used for identification of the soil parameters using tunneling induced deformations under assumptions of existing surface pressure load and an obstacle ahead of the tunnel face. The identification is performed based on the numerically generated noisy measurements. The inherent linearization in the extended Kalman filter makes it difficult to implement and it is reliable only for slightly nonlinear system models. Therefore the further improvement of the inversion method has been done by combining the EKF with the derivativeless deterministic sampling-based approximation where a set of deterministically sampled points, called sigma points, can be used to represent the mean and covariance of the estimated quantities. The update mechanisms are inherited from the linear Kalman filter. For the purpose of the full seismic waves inversion for predicting ahead of the underground tunnel a new hybridized global optimization method that combines the simulated annealing global search with unscented Kalman filter minimization has been proposed. The implementation of the inversion methods has been shown on several numerical examples.