Abstract
Direct measurement of relevant system parameters often represents a problem due to different lim- itations. In geomechanics, measurement of geotechnical material constants which constitute a material model is usually a very difficult task even with modern test equipment. Back-analysis has proved to be a more effi- cient and more economic method for identifying material constants because it needs measurement data such as settlements, pore pressures, etc., which are directly measurable, as inputs. Among many model parameter iden- tification methods, the Kalman filter method has been applied very effectively in recent years. In this paper, the extended Kalman filter - local iteration procedure incorporated with finite element analysis (FEA) software has been implemented. In order to prove the efficiency of the method, parameter identification has been performed for a nonlinear geotechnical model.
Highlights
The back analysis procedures require reliable and sufficient measurement data, a robust numerical model and an efficient method for the solution of the inverse problem [1]
Some applications of the Kalman filter (KF) method have arisen in the field of geotechnical engineering for estimation of material parameters [3, 4, 6]
2 Extended Kalman filter (EKF) - local iteration procedure incorporated with finite element analysis
Summary
The back analysis procedures require reliable and sufficient measurement data, a robust numerical model and an efficient method for the solution of the inverse (optimization) problem [1]. Whenever observation data at time tk are available, a posteriori estimate and its covariance matrix can be calculated as follows: xk+ = E xk|y1, y2, · · · , yk ; P+k = E (xk − xk+)(xk − xk+)T. Before observation data of the model are available, the EKF propagates the mean and error covariance of the state through time. At time tk in the local iterative loop i of the EKF - local iteration procedure, the Kalman gain Kk,i, observation update of the state xk+,i+1 and estimation error covariance matrix P+k,i+1 are calculated according to the following equations: Hk,i. In order to begin the filter process, an initial value x0 for the state vector along with the corresponding estimation error covariance matrix P0 have to be assigned. The third stop criterion is selected since the number of iterations is usually small and it serves the purpose of examining the filter process at some later time after convergence has been reached
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