Circularly-symmetric complex normal ratio distribution for scalar transmissibility functions. Part III: Application to statistical modal analysis

- Probabilistic model for transmissibility function in the vicinity of resonant frequency is formulated in modal domain.
- The statistical characteristics of transmissibility function in modal domain are investigated in detail.
- The process of transmissibility-based modal identification is posed in the context of Bayesian framework.
- 'Noise-to-environment' ratio is identified directly as a separate parameter.
- The possibility of distinguishing harmonic components and structural ones using uncertainty information is explored.

This study applies the theoretical findings of circularly-symmetric complex normal ratio distribution Yan and Ren (2016) [1,2] to transmissibility-based modal analysis from a statistical viewpoint. A probabilistic model of transmissibility function in the vicinity of the resonant frequency is formulated in modal domain, while some insightful comments are offered. It theoretically reveals that the statistics of transmissibility function around the resonant frequency is solely dependent on 'noise-to-signal' ratio and mode shapes. As a sequel to the development of the probabilistic model of transmissibility function in modal domain, this study poses the process of modal identification in the context of Bayesian framework by borrowing a novel paradigm. Implementation issues unique to the proposed approach are resolved by Lagrange multiplier approach. Also, this study explores the possibility of applying Bayesian analysis in distinguishing harmonic components and structural ones. The approaches are verified through simulated data and experimentally testing data. The uncertainty behavior due to variation of different factors is also discussed in detail.