Uncertainty Quantification Working Group
January 8, 11:30 AM, CNLS Conf. Room, TA-3, Bldg. 1690

Use of the extended Kalman filter in quantification of margin and uncertainty, Part II: Parameter identification

Jim Kao, X-4


The current LANL methodology for the nuclear weapon certification, termed Quantification of Margin and Uncertainty (QMU), has three major capability requirements: (1) determination of performance gates at crucial points in the time span of a nuclear weapon operation, (2) prediction of the final performance without underground testing, and (3) utilization of highly processed, and yet sparse data. The extended Kalman filter (EKF) technique has the capabilities to fulfill all of the three requirements. Data assimilation strives to determine optimally the state of an evolving physical system from a limited number of observations. The EKF method solves the full nonlinear state evolution in time. It also estimates the system's time-dependent error-covariance matrix (i.e., uncertainties) through a first-order approximation, which measures the sensitivities of the model dynamics to all the state variables. The state variables are updated by the blending of the model's prediction with currently available data, along with their associated minimized errors. These variables are then used as initial conditions for further prediction till the next time at which data becomes available, or if data is no longer available, till any desired future time. Most importantly, EKF estimates uncertainties requiring the full assessment of the errors built in computer codes and available data. This is one essential element that many of the existing estimation methods have not or cannot address.

We have recently tested EKF for its capability in the optimal estimation of a model's physical parameters used. This is accomplished by expanding the state variable vector to include the model parameters, where they are only subject to the stochastic forcing which serves as the sole source for their uncertainties. This modification provides us a unique opportunity to optimize the model parameters with the available data. The assimilated fields are improved over the case where only state variables were assimilated. The pure prediction with the optimized parameters performs much better than the counterpart with the original parameters. This test verifies that the model parameter space does play a dominant role in the model performance of the hydrodynamic code at hand.