System identification of structures using their measured earthquake response can play a key role in structural health monitoring, structural control and improving performance-based design. Implementation using data from strong seismic shaking is complicated by the nonlinear hysteretic response of structures. Furthermore, this inverse problem is ill-conditioned1 for example, even if some components in the structure show substantial yielding, others will exhibit nearly elastic response, producing no information about their yielding behavior. Classical least-squares or maximum likelihood estimation will not work with a realistic class of hysteretic models because it will be unidentifiable based on the data. It is shown here that Bayesian updating and model class selection provide a powerful and rigorous approach to tackle this problem when implemented using a recently developed stochastic simulation algorithm called Transitional Markov Chain Monte Carlo. The updating and model class selection is performed on a previously-developed class of Masing hysteretic structural models that are relatively simple yet can give realistic responses to seismic loading. The theory for the Masing hysteretic models, and the theory used to perform the updating and model class selection, are presented and discussed. An illustrative example is given that uses simulated dynamic response data and shows the ability of the algorithm to identify hysteretic systems even when the class of models is unidentifiable based on the data.

A new Bayesian model updating approach is presented for linear structural models. It is based on the Gibbs sampler, a stochastic simulation method that decomposes the uncertain model parameters into three groups, so that the direct sampling from any one group is possible when conditional on the other groups and the incomplete modal data. This means that even if the number of uncertain parameters is large, the effective dimension for the Gibbs sampler is always three and so high-dimensional parameter spaces that are fatal to most sampling techniques are handled by the method, making it more practical for health monitoring of real structures. The approach also inherits the advantages of Bayesian techniques: it not only updates the optimal estimate of the structural parameters but also updates the associated uncertainties. The approach is illustrated by applying it to two examples of structural health monitoring problems, in which the goal is to detect and quantify any damage using incomplete modal data obtained from small-amplitude vibrations measured before and after a severe loading event, such as an earthquake or explosion.

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We expound on the nature of collapse of one class of tall buildings (steel moment frame buildings) under earthquake excitation. Using a parametric analysis of a couple of index buildings subjected to idealized ground motion histories, we establish the ground motion features that cause collapse in these structures. Systematically mapping damage localization patterns, we track the evolution of the collapse mechanism. We demonstrate the existence of a select few preferred mechanisms of collapse in these buildings and describe the associated physics using wave propagation through a shear beam. A simple theory based on work-energy principles can identify these mechanisms. Figure 1. (a) Existing building (1982 UBC design) FRAME3D model; (b) Existing building typical floor plan; (c) Redesigned building (1997 UBC design) typical floor plan.