Parameter Identification Problems in Structural and Geotechnical Engineering

Abstract

This paper investigates some problems related to the ill‐posedness of parameter identification problems which are commonly met with in structural and geotechnical engineering. Viewing the identification problem within a suitable framework, two basic types of ill‐posedness are introduced. The first is inherent to the system (the governing differential equations), while the second is related to the type of data that is acquired at a given location (e.g., velocity, acceleration, etc.) and the basic algorithms used in the identification process. Examples of each type of ill‐posedness are analyzed. Particular attention is given to the recurrent problem of identification of a nonconstant coefficient of a linear differential equation. Such coefficients often model the spatial variation of material properties in media. A method of handling spatially varying parameters for geotechnical applications is proposed. A general stochastic model for the parameter variation is used and it is shown that the identification problem using the Bayesian approach then leads to stable estimates, circumventing the instability problems of the direct inverse approach. Sensitivity studies are included to indicate the robust nature of the estimator. Simultaneous estimation of the “scatter” in the material property variation, and the material property parameter values themselves is next undertaken and it is shown that the method yields good estimates though the estimator now becomes a nonlinear function of the measurement. Simultaneous estimation of the measurement noise characteristics is also shown to be possible.