On the estimation process of a particular class of global transmissibility functions: the R-FRFs

The importance and the role of a specific class of transmissibility functions (i.e. R-FRFs - Response-based Frequency-Response-Functions), within the realm of modal identification and continuous monitoring of structures, have been highlighted in previous works of the research group. The ability of the R-FRFs to incorporate modal data essentially related to subparts of a system, when thought subjected to certain virtual boundary conditions, makes these functions deserving of being measured through suitable estimators, whose definition and performance analysis comprise the main objective of this paper. The specific formal representation of the R-FRFs generally requires a simultaneous measurement of groups of these functions arranged in response-based transfer matrices. In this sense, we perform the assessment of R-FRFs by investigating the estimators for MIMO linear systems, extending known concepts and introducing new ideas. Specifically, we propose the definition of output-only and input-output estimators, including, in the latter case, the advantage of using the measured exciting forces, when available. Therefore, in this work, we present a detailed performance comparison of the proposed estimators by making usage of data from simulated and experimental case studies. The analysis carried out leads to conclusions aimed at identifying the best estimators for measuring R-FRFs.