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Analysis of recordings in structural engineering; adaptive filtering, prediction, and control

Analyses of recordings include processing of data, determining analytical models that match the record, and identification of the system from which the record is obtained. Current methods that are used to analyze recordings in structural engineering are based on the classical filtering and Fourier analysis approach. These methods assume that: (a) either the signal and noise spectra are nonoverlapping, or there is a frequency band where the signal to noise ratio is high (i.e., noise can be neglected), and (b) the properties of the signal within the selected time window are time-invariant. Recently, new methods for record analysis have been developed based on the concepts of adaptive filtering and stochastic approximation. These methods are commonly known as the stochastic-adaptive methods. Stochastic-adaptive methods make use of the statistical properties of the record, and integrate filtering, modeling, and identification into a single algorithm. The advantages of stochastic-adaptive methods over the classical methods are: (a) they can remove the noise from the signal over the whole frequency band, (b) they can track time-varying characteristics of the signal, and (c) they make it possible to apply adaptive control on unknown systems. In this report, a concise theory of stochastic-adaptive methods, and their applications in structural engineering are presented. The theoretical part includes the following topics: discrete models for dynamic systems, one-step-ahead prediction, stochastic approximation, recursive prediction error method, model selection, model validation, spectral estimation, and adaptive control. The application part presents ten examples by using earthquake, ambient vibration, and simulated data. The examples include identification of time-invariant and time varying simulated systems; identifications of buildings with soil-structure interaction, nonlinear behavior, and ambient vibrations; modeling of spectral shape, site amplification, and source scaling of earthquake ground motions; and adaptive minimum variance control of a simulated system and a building with ambient vibrations.