System Identification and Nonlinear Wave Equations for the Modeling of Soil Properties

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Of importance to geotechnical and structural engineers, and fornondestructive evaluation in general, is the ability to estimatesoil properties and structural properties, respectively, withoutintruding into the medium. This project involves using timeseries analysis on data that has traveled through the earth orthrough a structure to determine physical properties of themedium. System identification techniques will be used to modelthe system. The main research effort will be the mapping from thesystem identification coefficients to the physical parameters ofa more realistic physical model than has been previouslyemployed. A model that takes into account distributed mass on adiscrete level (not just lumped mass) and damping due to friction(not just viscous damping) will be employed. Plane wave solutionswill be considered to determine the mapping from the SIcoefficients to the physical parameters. There are interestingmathematical questions in determining the existence of plane wavesolutions, the numerical computation of such plane wavesolutions, the effects of lattice induced anisotropy due to thediscrete nature of the distributed mass, and alternatives to theARMA model for system identification. The PI will work at theDepartment of Civil and Environmental Engineering at theUniversity of California, Berkeley, collaborating with ProfessorSteven D. Glaser.This IGMS project is jointly supported by the MPS Office ofMultidisciplinary Activities (OMA) and the Division ofMathematical Sciences (DMS).