Data assimilation with an extended Kalman filter for impact-produced shock-wave dynamics

Model assimilation of data strives to determine optimally the state of an evolving physical system from a limited number of observations. The present study represents the first attempt of applying the extended Kalman filter (EKF) method of data assimilation to shock-wave dynamics induced by a high-speed impact. EKF solves the full nonlinear state evolution and estimates its associated error-covariance matrix in time. The state variables obtained by the blending of past model evolution with currently available data, along with their associated minimized errors (or uncertainties), are then used as initial conditions for further prediction until the next time at which data becomes available. s study, a one-dimensional (1D) finite-difference code is used along with data measured from a 1D flyer plate experiment. An ensemble simulation suggests that the nonlinearity of the modeled system can be reasonably tracked by EKF. The results demonstrate that the EKF assimilation of a limited amount of pressure data, measured at the middle of the target plate alone, helps track the evolution of all the state variables. The fidelity of EKF is further investigated with numerically generated synthetic data from so-called “identical-twin experiments”, in which the true state is known and various measurement techniques and strategies can be made easily simulated. We find that the EKF method can effectively assimilate the density fields, which are distributed sparsely in time to mimic radiographic data, into the modeled system.