A new probabilistic frequency-domain approach for influence line extraction from static transmissibility measurements under unknown moving loads. (1st August 2020) - Yan, Wang-Ji; Yuen, Ka-Veng
Highlights: Static transmissibility under moving loads are equal to the ratio of Fourier transform of influence lines; Influence lines can be extracted directly by using the static transmissibility subjected to moving loads; A fast Bayesian inference scheme is developed to accommodate uncertainties; The analytical solutions of the MPVs and variances of influence lines in frequency domain are derived; The closed-form transformation between the MPVs (or variances) of FFT and those of inverse FFT are established. Abstract: On the basis of the amazing theoretical finding that there is equivalence between the static transmissibility subjected to moving loads and the ratio of two influence lines in the frequency domain, a new approach is proposed to extract the influence lines for a beam-like structure under moving loads. To accommodate the uncertainties involved in the measurements as well as modelling error, the relationship between response measurements and the Fourier transform of influence lines is embedded in the framework of Bayesian inference with the aid of complex-valued probabilistic model of prediction error. The formulas are presented for closed-form transformation between the solutions of FFT coefficients and those of inverse FFT coefficients. Analytical solutions of the Most Probable Values (MPVs) as well as posterior uncertainties of the influence lines in both frequency domain and spatial domain are derived. Two applications are conducted to verify the efficiency and accuracy of the fast Bayesian scheme. It is shown that the new approach can be realized by avoiding the ill-poseness nature of inverse problem. Due to the introduction of the concept of static transmissibility, given that the reference influence line is known in advance, this method possesses an obvious advantage in avoiding using the knowledge of the moving loads. As a frequency-domain approach, it can reduce the computational complexity of influence line extraction by avoiding complicated matrix manipulation.