Algoritmi di ricostruzione di segnali sotto-campionati per la misura di vibrazioni con sistemi di visione

Complex mechanical products in automotive, aerospace and other mechanical industries are validated using vibration measurements and experimental modal analysis. These tests are mainly performed using pointwise sensors connected to the structure. A limited number of transducers might not be able to comprehensively measure the dynamic response, especially when dealing with large-size or very small structures. This is one of the reasons behind the development of image processing techniques, like Digital Image Correlation (DIC), to perform modal analysis. A particular field of interest in using DIC for vibration analysis is in using cheap, light and low speed camera to detect structure’s high frequency behavior. To overcome the low sampling rate, techniques such as under-sampling and remapping the time histories, random sampling and smart aliasing to measure above the camera Nyquist frequency limit can be employed. Particularly, this thesis focuses on the use of signal reconstruction algorithms for bandlimited signals. It is possible, indeed, to go beyond the Nyquist Shannon frequency limit even without the use of high-speed cameras by exciting a structure using a bandlimited signal, reconstructing the output and perform modal analysis. The two main studied algorithms are one in time domain and one in the frequency domain. Additional procedures for Frequency response function (FRF) branches assembly in bandlimited regions have been performed. The case study involves both numerical and experimental validations also with the use of affordable sensors such as accelerometers. An appendix on a numerical study over Compressed Sensing, another signal reconstruction algorithm, is provided.