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

对于岩土和结构工程师，以及一般的无损评估来说，重要的是能够在不侵入介质的情况下分别估计土壤性质和结构性质。该项目涉及对穿过地球或结构的数据进行时间序列分析，以确定介质的物理性质。将使用系统识别技术对系统进行建模。主要的研究工作将是从系统辨识系数到比以前采用的更真实的物理模型的物理参数的映射。将采用考虑混凝土水平上的分布质量(而不仅仅是集中质量)和摩擦(而不仅仅是粘性阻尼)引起的阻尼的模型。将考虑平面波解，以确定从SI系数到物理参数的映射。在确定平面波解的存在性、这种平面波解的数值计算、由于分布质量的离散性质而引起的晶格诱导各向异性的影响以及用于系统辨识的ARMA模型的替代方案等方面，都存在一些有趣的数学问题。PI将在加州大学伯克利分校土木工程与环境工程系工作，与史蒂文·D·格拉瑟教授合作。这个IGMS项目由MPS多学科活动办公室(OMA)和数学科学部(DMS)联合支持。

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).