The extended Kalman Filter and the unscented Kalman Filter for Material Parameter Identification with Application in Tunneling

We present in this work the use of the extended Kalman filter (EKF) and unscented Kalman filter (UKF) for identification of constitutive material parameters with application in mechanized tunneling. Although both filters are based on the principle of recursive least squares estimation, one differs from another in terms of where approximation is made. Whereas in the EKF first-order Taylor series expansion is used to approximate the nonlinear modeling equation, in the UKF approximation of the probability density of the state is made using a small number of well defined points. To validate the methods, we performed parameter identification of the Hardening Soil constitutive model used for describing the soil behavior in an tunnel excavation model. Both methods showed fast and stable convergence of the considered soil parameters - the four parameters of the Hardening Soil model. Although the EKF requires less number of forward calculations of the numerical model, the UKF is favored since it does not require calculation of the derivatives of the observables with respect to the identifying parameters. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)