Bayesian identification of soil-foundation stiffness of building structures

Abstract

Summary A probabilistic method is presented for identifying the dynamic soil‐foundation stiffnesses of building structures. It is based on model updating of a Timoshenko beam resting on sway and rocking springs, which respectively represent the superstructure and the soil‐foundation system. Unlike those previously employed for this particular problem, the proposed method is a Bayesian one, which accounts for the prevailing uncertainties due to modeling and measurement errors. As such, it yields the probability distribution of the system parameters as opposed to average/deterministic values. In this approach, the joint probability density function of the parameters that control the flexible‐base Timoshenko beam model, together with the fundamental natural frequency and mode shape of the system, forms the prior distribution. Using Bayes' theorem, a posterior distribution is obtained by updating the prior distribution with a sparsely measured mode shape and frequency. The most probable realizations of the system parameters are then determined by maximizing the posterior distribution. For this purpose, first‐ and second‐order derivatives of the objective function are analytically computed via direct differentiation. The proposed method is verified using a synthetic example. Additionally, sensitivity analyses are carried out on both the system parameters and standard deviations of the sources of error. Subsequently, the proposed method is applied to real‐life data recorded at the Millikan Library building, which is located at the California Institute of Technology campus in Pasadena, California, and the results are compared with a previous deterministic study.

Transfer function‐based Bayesian damage detection under seismic excitation

“…For detecting damage based on model updating by Bayesian method, it is often reasonable to assume no correlation between the estimating parameters and the covariance matrix Σ would be a diagonal matrix . In this study, equal variances and stochastic independence are assumed for the noise in the TF measurement and error in the natural frequency identification. Hence, the covariance matrices could be assumed as Where σ 2 denotes the variance of the related parameters.…”

Estimation of Soil-Structure Model Parameters for the Millikan Library Building Using a Sequential Bayesian Finite Element Model Updating Technique

“…The Millikan Library is a reinforced concrete shear wall building, with a basement and nine stories above the ground, located on the California Institute of Technology (Caltech) campus (Figure 1). The Millikan Library has been the subject of many studies, especially in the fields of soil-structure system identification, due to its unique structural and soil properties, and its relatively old and dense instrumentation, which recorded its seismic responses during numerous earthquakes ( [24], [25], [26], [27], [28], [29], [30]). The Millikan Library building is 43.9 m tall above ground including the roof level.…”

Quantifying modeling uncertainty in simplified beam models for building response prediction

“…Therefore, at least in theory, their seismic responses can be accurately approximated by using simple beam models. Since the pioneering work of Biot 13 and several key studies that followed, 14–17 there have been quite a few efforts wherein various beam models are devised or used to represent building structures—for relatively recent examples, see literature 18–25 …”

“…Since the pioneering work of Biot 13 and several key studies that followed, [14][15][16][17] there have been quite a few efforts wherein various beam models are devised or used to represent building structures-for relatively recent examples, see literature. [18][19][20][21][22][23][24][25] As lateral systems of buildings are usually combinations of various types of structural elements/subsystems-such as frames, walls, and braces-researchers realized that a single shear or Bernoulli beam might not be adequate to capture the overall seismic response. In 1965, Osawa 26 introduced the concept of the coupling beam in which uniform shear and uniform flexure (Bernoulli) beams are connected with rigid lateral elements to have similar displacements.…”