The present paper reviews recent activities on inverse analysis strategies in geotechnical engineering using Kalman filters, nonlinear Kalman filters, and Markov chain Monte Carlo (MCMC)/Hamiltonian Monte Carlo (HMC) methods. Nonlinear Kalman filters with finite element method (FEM) broaden the choices of unknowns to be determined for not only parameters but also initial and/or boundary conditions, and the use of the posterior probability of the state variables can be widely applied to, for example, the decision making for design changes. The relevance of the unknowns and the observed values and the selection of the best sensor locations are some of the considerations made while using the Kalman filter FEM. This paper demonstrates several real-world geotechnical applications of the nonlinear Kalman filter and the MCMC with FEM. Future studies should focus on the following areas: attaining excellent performance for long-term forecasts using short-term observation and developing a viable method for selecting equations that describe physical phenomena and constitutive models.
Keywords: Hamiltonian Monte Carlo; Kalman filter; data assimilation; finite element method; geotechnical engineering; inverse problems.