Bayesian Ambient Modal Identification: Theory and Practice

Abstract eng:
Modal identification involves primarily the determination of natural frequencies, damping ratios and mode shapes of a constructed structure using measured data. It is often among the first few tasks to be performed in structural vibration control, retrofitting or health monitoring projects, providing a factual basis for further decision making. Ambient vibration tests have attracted increasing attention in both field applications and identification theory development because they can be performed economically with the structure under working condition and without artificial loading that can be too large to be practical. Ambient modal identification techniques do not require specific knowledge of loading but they assume that the loading is statistically random instead of being organized in some characteristic manner. Since the signal-to-noise ratio under ambient vibration cannot be actively controlled, quantifying and managing the uncertainties of the identified modal parameters is a primary concern. A Bayesian approach provides a rational framework for this purpose, yielding conclusions that are consistent with modeling assumptions and probability logic. This paper presents an overview of a Bayesian frequency-domain approach for modal identification and discusses the issues associated with its practical implementation. Working in the frequency domain allows one to make inference based only on relevant information in a resonance band and legitimately ignore frequency bands that are difficult to model, thereby reducing modeling error risk. On the implementation side, determining the posterior statistics of modal parameters requires solving a multi-dimensional numerical optimization problem, which is computationally prohibitive because the number of parameters grows with the number of measured dofs. A recently developed fast algorithm yields the Bayesian solution in a matter of seconds and hence can be practically implemented even in the field. Issues of theoretical, computational and practical nature are discussed, drawing experience from a number of field applications.

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