Uniqueness of Damping and Stiffness Distributions in the Identification of Soil and Structural Systems

Abstract

As the interest in the seismic design of structures has increased considerably over the past few years, accurate predictions of the dynamic responses of soil and structural systems has become necessary. Such predictions require a knowledge of the dynamic properties of the systems under consideration. This paper is concerned with the uniqueness of the results in the identification of such properties. More specifically, the damping and stiffness distributions, which are of importance in the linear range of response, have been investigated. An N-storied structure or an N-layered soil medium is modeled as a coupled, N-degree-of-freedom, lumped system consisting of masses, springs, and dampers. Then, assuming the mass distribution to be known, the problem of identification consists of determining the stiffness and damping distributions from the knowledge of the base excitation and the resulting response at any one mass level. It is shown that if the response of the mass immediately above the base is known, the stiffness and damping distributions can be uniquely determined. Following this, some nonuniqueness problems have been discussed in relation to the commonly used ideas of system reduction in the study of layered soil media. A numerical example is provided to verify some of these concepts and the nature of nonuniqueness of identification is indicated by showing how two very different (yet physically reasonable) systems could yield identical excitation-response pairs. Errors in the calculation of the dynamic forces, due to erroneous identification have also been illustrated thus making the results of the present study useful from the practical standpoint of the safe design of structures to ground shaking.

On the identification of continuous vibrating systems modelled by hyperbolic partial differential equations

“…The stiffness distribution, a(x) of such a structure (for which a0 = 1 and b0 = 0) can thus be uniquely identified, if the stress induced at the base of the structure by a ground shaking g0(t) can be determined, provided the stiffness a(0) (assuming ax(0) = ax( 1) = 0) is known a priori. This result is a natural extension of the results on discrete structural models wherein unique identification of the interstory stiffness is obtained through measurement of the displacement response of the first story level and that of the base motion [5].…”

“…Introduction. The identification of spatially varying parameters in systems that can be described by hyperbolic equations has attracted a considerable amount of interest in recent years [1][2][3][4][5], The main interest in this area is to make improved predictions of the response of continuous mechanical and structural systems subjected to various types of dynamic loads. Such predictions naturally require an adequate knowledge of the parameters which are involved in the system model.…”

Noise-bias compensation in physical-parameter system identification under microtremor input

“…Although the cost of sensors is getting cheaper recently, this instrumentation and data management may not be cost-effective in multi-storied buildings, especially in high-rise buildings. To avoid this, Udwadia et al [25] proposed a unique SI theory for a shear building model. They clarified that unique identification of story stiffnesses and viscous damping coefficients is possible theoretically when acceleration records at the floors just above and below a specific story are available.…”

“…The mathematical limit manipulation toward an infinite frequency [25] has been avoided by introducing a limit manipulation toward zero frequency together with an interpolation technique. In that method, both the material and viscous damping properties together with the story stiffness can be identified simultaneously in a unified manner and only an FFT technique is needed.…”

Frequency-Domain Physical-Parameter System Identification of Building Structures with Stiffness Eccentricity

“…This is also quite useful for the damage detection. Nevertheless that the physical SI is preferred in SHM, its development is quite limited and slow due to the strict requirement on multiple measurements or the necessity of complicated mathematical manipulation (Hart and Yao, 1977;Udwadia et al, 1978;Shinozuka and Ghanem, 1995;Nakamura, 2000, 2005;Brownjohn, 2003;Nagarajaiah and Basu, 2009;Takewaki et al, 2011;Zhang and Johnson, 2013;Johnson and Wojtkiewicz, 2014;Wojtkiewicz and Johnson, 2014).…”