Of importance to geotechnical and structural engineers, and for nondestructive evaluation in general, is the ability to estimate soil properties and structural properties, respectively, without intruding into the medium. This project involves using time series analysis on data that has traveled through the earth or through a structure to determine physical properties of the medium. System identification techniques will be used to model the system. The main research effort will be the mapping from the system identification coefficients to the physical parameters of a more realistic physical model than has been previously employed. A model that takes into account distributed mass on a discrete level (not just lumped mass) and damping due to friction (not just viscous damping) will be employed. Plane wave solutions will be considered to determine the mapping from the SI coefficients to the physical parameters. There are interesting mathematical questions in determining the existence of plane wave solutions, the numerical computation of such plane wave solutions, the effects of lattice induced anisotropy due to the discrete nature of the distributed mass, and alternatives to the ARMA model for system identification. The PI will work at the Department of Civil and Environmental Engineering at the University of California, Berkeley, collaborating with Professor Steven D. Glaser.
This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).
