A New Theorem on Multivariate Complex Statistics Towards Uncertainty Quantification for Transmissibility Function

摘要

Transmissibility function is now considered to be a good candidate for structural health monitoring.Due to the inherent randomness of measurement and variability of environmental conditions, uncertainty affects the behavior of its application significantly.Few algorithms utilizing transmissibility functions available so far are able to accommodate various uncertainties successfully.Therefore, the assessment and presentation of the uncertainty behavior of dynamic transmissibility are recognized as a critical issue in the field of structural health monitoring.To address this issue, the most serious difficulty in accomplishing the goal raised above is how to characterize the exact probability density distribution for dynamic transmissibility.By exploiting a result on the distribution of complex multivariate statistics, a new theorem on circularly-symmetric complex normal ratio distribution was proved mathematically recently.Based on the new theorem, an explicit closed-form formula for the probability density function (pdf) of dynamic transmissibility vector was derived, which turns out to be very compact and concise.Numerical study shows that the proposed probabilistic models provide substantial accuracy for uncertainty quantification.