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

Abstract

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.In this study, a one-dimensional (1-D) finite-difference code is used along with data measured from a 1-D 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. 2

Estimating model parameters for an impact-produced shock-wave simulation: Optimal use of partial data with the extended Kalman filter

“…The underlying physical problem stems from a flyer plate experiment [16]. Our results [20] successfully demonstrated that: (1) EKF propagates information through the modelÕs governing equations from observed to unobserved variables as well as locations; (2) EKF should not be considered a curve fitting procedure; carefully assessing both the model and observation errors is crucial in obtaining meaningful results with this method; and (3) a single scalar observation can noticeably reduce the error in estimating the state of the 1-D system with its total number of over 200 discrete variables.…”

“…The extended Kalman filter (EKF) method of data assimilation [10,11,15,20] designed to optimize predictions of, as well as reduce uncertainties in, the modeled state variables, provided that the errors in the observations and model performance can be estimated. The EKF algorithm tracks the nonlinear state evolution and its associated error-covariance matrix in time.…”

“…We have recently applied the EKF method of data assimilation [20] to a one-dimensional (1-D) hydrodynamic shock-wave code [4] with a limited amount of pressure data measured at a single location. The underlying physical problem stems from a flyer plate experiment [16].…”

Graphical models for statistical inference and data assimilation

“…Methods to overcome the computational difficulties arising from large covariance matrices involve low-rank and partitioning approximations [19,20], as well as parallelization techniques [21,22]; reviews include [23,24]. At the same time, data assimilation is perceived more and more as a powerful strategy in advancing understanding, simulation and prediction in the earth sciences as a whole [25] and beyond [26].…”

Kalman filter finite element method applied to dynamic ground motion

“…Kalman Filter was frequently used in the field of meteorology and oceanography (e.g. [9][10][11][12][13][14]). Although a lot of applications are presented in the engineering fields, there are no previous studies of the Kalman Filter based on blasting vibrations.…”