On the problem of stochastic experimental modal analysis based on multiple-excitation multiple-response data, part I: Dispersion analysis of continuous-time structural systems

Abstract

Despite its importance and the undisputable significance of stochastic effects, the problem of multiple-excitation multiple-response experimental modal analysis has thus far been almost exclusively considered within a deterministic framework. In this paper a novel, comprehensive and effective stochastic approach, that, unlike alternative schemes, can operate on vibration displacement, velocity or acceleration data, is introduced. The proposed approach is capable of effectively dealing with noise-corrupted vibration data, while also being characterized by unique features that enable it to overcome major drawbacks of current modal analysis methods and achieve high performance characteristics by employing: (a) proper and mutually compatible force excitation signal type and stochastic model forms, (b) an estimation scheme that circumvents problems such as algorithmic instability, wrong convergence, and high computational complexity, while requiring no initial guess parameter values, (c) effective model structure estimation and model validation procedures, and, (d) appropriate model transformation, reduction and analysis procedures based on a novel dispersion analysis methodology.This dispersion analysis methodology is a physically meaningful way of assessing the relative importance of the estimated vibrational modes based on their contributions ("dispersions") to the vibration signal energy. The effects of modal cross-correlations are fully accounted for, physical interpretations are provided in both the correlation and spectral domains, and the phenomenon of negative dispersion modes is investigated and physically interpreted. The effectiveness of the proposed approach is finally verified via numerical and laboratory experiments, as well as comparisons with the classical frequency domain method and the deterministic eigensystem realization algorithm (ERA).The paper is divided into two parts: the proposed dispersion analysis methodology is introduced in the first one; whereas the complete stochastic experimental modal analysis approach is presented in the second [23].