Fast Bayesian FFT Method for Ambient Modal Identification with Separated Modes

• Published in: Journal of engineering mechanics Vol. 137; no. 3; pp. 214 - 226
• Main Author: Au, Siu-Kui
• Format: Journal Article
• Language: English
• Published: Reston, VA American Society of Civil Engineers 01.03.2011
• Subjects: Asymptotic properties; Bayesian analysis; Channels; Covariance matrix; Exact sciences and technology; Focusing; Fundamental areas of phenomenology (including applications); Mathematical models; Measurement and testing methods; Modal identification; Physics; Signal to noise ratio; Solid mechanics; Structural and continuum mechanics; TECHNICAL PAPERS; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Bayes estimation; Measurement; Vibration; Modal analysis; Fast Fourier transformation; Frequency domain method; Covariance matrix; Modeling; Spectral analysis; Optimization; Uncertain system; Field tests; Asymptotic approximation; System identification; Bayesian analysis; Signal to noise ratio
• ISSN: 0733-9399; 1943-7889
• DOI: 10.1061/(ASCE)EM.1943-7889.0000213

Previously a Bayesian theory for modal identification using the fast Fourier transform (FFT) of ambient data was formulated. That method provides a rigorous way for obtaining modal properties as well as their uncertainties by operating in the frequency domain. This allows a natural partition of information according to frequencies so that well-separated modes can be identified independently. Determining the posterior most probable modal parameters and their covariance matrix, however, requires solving a numerical optimization problem. The dimension of this problem grows with the number of measured channels; and its objective function involves the inverse of an ill-conditioned matrix, which makes the approach impractical for realistic applications. This paper analyzes the mathematical structure of the problem and develops efficient methods for computations, focusing on well-separated modes. A method is developed that allows fast computation of the posterior most probable values and covariance matrix. The analysis reveals a scientific definition of signal-to-noise ratio that governs the behavior of the solution in a characteristic manner. Asymptotic behavior of the modal identification problem is investigated for high signal-to-noise ratios. The proposed method is applied to modal identification of two field buildings. Using the proposed algorithm, Bayesian modal identification can now be performed in a few seconds even for a moderate to large number of measurement channels.