Fast Bayesian FFT modal parameter identification under single-input impact load

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Journal of Vibration and Shock ›› 2025, Vol. 44 ›› Issue (10) : 1-9.

SHOCK AND EXPLOSION

Fast Bayesian FFT modal parameter identification under single-input impact load

LI Binbin1,2，LIU Yafei1，WANG Peixiang*2，GUO Shanzhi3

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Abstract

The impact vibration test is widely used in modal analysis, because of its convenience, low cost, and efficiency in identifying multiple modes with a single impact.To achieve efficient and accurate estimation and uncertainty quantification of modal parameters in the impact test, a fast Bayesian fast Fourier transform method was proposed.The likelihood function was first developed based on the equation of motion and the complex normal assumption of measurement error, and the Laplace approximation was then adopted to obtain the posterior distribution of modal parameters, i.e., fitting the posterior distribution with a Gaussian distribution, whose mean was computed by minimizing the negative log likelihood function (NLLF) while the covariance matrix was obtained by taking the inverse of the Hessian matrix of NLLF at the posterior mean.A coordinate descent algorithm was proposed to minimize the NLLF taking advantage of the analytical gradient of NLLF.The Hessian matrix was obtained via the calculus of complex matrix, allowing an efficient implementation.Finally, the performance of the proposed method was validated through synthetic and laboratory data.A comparison with the methods based on free and ambient vibration tests was also provided, respectively.

Key words

impact vibration test / Bayesian method / experimental modal analysis / modal identification / uncertainty quantification

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LI Binbin1, 2, LIU Yafei1, WANG Peixiang2, GUO Shanzhi3. Fast Bayesian FFT modal parameter identification under single-input impact load[J]. Journal of Vibration and Shock, 2025, 44(10): 1-9

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