An analytical investigation into the propagation properties of uncertainty in a two-stage fast Bayesian spectral density approach for ambient modal analysis

This paper investigates the uncertainty propagation properties of a two-stage fast Bayesian spectral density approach (two-stage fast BSDA) with separated modes proposed previously by the authors Yan and Katafygiotis (2015a,b) [1,2], deriving explicit formulas for the dependence of the posterior coefficients of variation (c.o.v.) of the identified modal parameters in terms of different parameters influencing the identification. For this, an approximation analysis strategy proposed in Au (2014a,b) [3,4] is adopted. Although the explicit closed-form approximation expressions are relatively complex, the expressions for the approximate dependence of uncertainty are simple and informative. The analysis reveals a strong correlation among the prediction error, the damping ratio and the power spectral density (PSD) of the modal excitation. While similar correlation trends have been observed in the posterior uncertainty analysis of the fast Bayesian FFT (fast BFFT) approach Au (2014a) [3], the present method shows that the identification results are more sensitive to modeling error. Note that this is not a contradicting result, as the uncertainty propagation properties of different methods may generally differ. Note that fast BFFT is a more fundamental method, in the sense that it processes FFT data directly, while the two-stage fast BSDA uses spectral density data in a manner that allows for decoupling of the mode shape data. Validation studies using synthetic data and field data measured from a laboratory model provide a practical verification of the rationality and accuracy of the theoretical findings.