A reduced order parameter estimation technique using orthonormal wavelets
In this work we introduce methods for model order reduction using orthonormal wavelets. Specifically, we propose techniques and algorithms for wavelet-based reduced order parameter estimation using orthonormal wavelets for solving nonlinear least squares problems. Approaches for parameter reduction using the one dimensional and two dimensional wavelet transforms are presented using multiple levels of decomposition. The performance of wavelet-based reduced order parameter estimation is tested using a suite of orthonormal wavelets on a groundwater hydraulics model provided by the U.S. Army Corps of Engineers. Using the hydraulics model, the goal is to find a least-squares solution of the permeability field given the pressure field observations such that the discrepancy between the model and the observed behavior of the system is minimized. The results show that in terms of the number of iterations, time, and error, there exist reduced order parameter estimation models obtained with orthonormal wavelets that can be used in lieu of the full order model. By incorporating these wavelet-based reduced order parameter estimation techniques into nonlinear least squares parameter estimation problems, a faster characterization can be achieved.
Hernandez, Miguel, "A reduced order parameter estimation technique using orthonormal wavelets" (2011). ETD Collection for University of Texas, El Paso. AAI1503727.