Experimental modal analysis of structural systems by using the Vector Fitting method

The increasingly required maintenance and redevelopment of the architectural and infrastructural heritage have led to the use of structural monitoring and system identification, as useful tools for assessing the state of conservation of the structures and their behaviour, both in operating conditions and in specific conditions, such as in presence of an earthquake. This is fundamental to increase the knowledge of the overall response of the structure and to identify any structural problems. Therefore, the use of monitoring in the study of civil structures is increasing and it involves both existing and new buildings. Thanks to this approach, it is possible to assess the structural reliability allowing higher durability and resistance. Unnecessary periodical inspections can be avoided leading to a reduction of maintenance costs. For this reason, in the last years the research of new methods, also used in other engineering research environments, has become very important. This dissertation focuses on testing of new dynamic identification strategies, especially on experimental modal analysis techniques. It concerns, in particular, the implementation of an algorithm in frequency domain, called Vector Fitting (VF), commonly used in many engineering societies, from high-voltage power systems to microwave systems and high-speed electronics. Since its introduction, Vector Fitting has gained much popularity due to its simplicity, robustness and higher performance. The Vector Fitting scheme computes poles and residues of a rational function providing a fit to the raw data points. The optimization process is relaxed to a weighted linear least squares system, which is reformulated and solved iteratively until convergence. This work shows the implementation of this algorithm under the influence of parameters typical of civil and mechanical structures. In particular, modal analysis and estimation of experimental parameters by using Vector Fitting are described. Firstly, Vector Fitting method is applied on numerical tests in order to validate the new implementation. The effectiveness of the proposed method is verified on numerically-simulated noisy data. Subsequently, it is applied on experimental data sets related to different cases studies, in which the influence of high level of noise on the Vector Fitting results is discussed. The confidence of the results has been estimated by using modal criteria, such as Modal Assurance Criterion (MAC), and statistical relations.