A Numerical and Experimental Investigation of the Most Fundamental Time-Domain Input–Output System Identification Methods for the Normal Modal Analysis of Flexible Structures

This paper deals with developing a comparative study of the principal time-domain system identification methods suitable for performing an experimental modal analysis of structural systems. To this end, this work focuses first on analyzing and reviewing the mathematical background concerning the analytical methods and the computational algorithms of interest for this study. The methods considered in the paper are referred to as the AutoRegressive eXogenous (ARX) method, the State-Space ESTimation (SSEST) method, the Numerical Algorithm for Subspace State-Space System Identification (N4SID), the Eigensystem Realization Algorithm (ERA) combined with the Observer/Kalman Filter Identification (OKID) method, and the Transfer Function ESTimation (TFEST) method. Starting from the identified models estimated through the methodologies reported in the paper, a set of second-order configuration-space dynamical models of the structural system of interest can also be determined by employing an estimation method for the Mass, Stiffness, and Damping (MSD) matrices. Furthermore, in practical applications, the correct estimation of the damping matrix is severely hampered by noise that corrupts the input and output measurements. To address this problem, in this paper, the identification of the damping matrix is improved by employing the Proportional Damping Coefficient (PDC) identification method, which is based on the use of the identified set of natural frequencies and damping ratios found for the case study analyzed in the paper. This work also revisits the critical aspects and pitfalls related to using the Model Order Reduction (MOR) approach combined with the Balanced Truncation Method (BTM) to reduce the dimensions of the identified state-space models. Finally, this work analyzes the performance of all the fundamental system identification methods mentioned before when applied to the experimental modal analysis of flexible structures. This is achieved by carrying out an experimental campaign based on the use of a vibrating test rig, which serves as a demonstrative example of a typical structural system. The complete set of experimental results found in this investigation is reported in the appendix of the paper.