Fast Bayesian Method for Practical Ambient Modal Identification

The modal properties of a structure are the interface between its physical properties (stiffness, mass, topology) and dynamic response. They primarily include the natural frequencies, damping ratios and mode shapes. Identifying modal properties based on measured vibration data is an important task often performed in vibration control, structural health monitoring or damage detection. Modal identification using ambient vibration data has aroused increasing attention in both theory development and industrial application due to its high economy in implementation. A Bayesian approach to modal identification has great promise for sustainable development because it provides a rigorous means for inferring information about modal parameters based on available data and assumed model, consistent with probability logic. Bayesian formulations of the ambient modal identification problem have existed in the literature. However, they require prohibitive computational effort that grows drastically with the number of measured degrees of freedom (dofs); the latter often being moderate to large in real applications. This severely undermines the power of the Bayesian approach.This project aims at developing a fast computational procedure for ambient modal identification following a Bayesian frequency domain approach formulated. It allows the user to make use of information on a selected frequency band for modal identification. The mathematical structure of the problem shall be analyzed with the aim to developing an efficient solution. The theoretical advance of this project lies in the discovery of a canonical reformulation of the governing equation in the original problem (namely, the log-likelihood function) that allows efficient determination of the mode shapes and effectively suppresses the growth of computational effort with the number of measured dofs. This project targets at providing a fast solution applicable to a large number of synchronous measured dofs that can be practically implemented even in the field. To fulfill this project mission, extensive field implementation and verification work are proposed.