Dynamic Identification of a Lightly Damped Slender Structure Using Compressive Sensing

Abstract

A great deal of signals coming from structural monitoring scenarios are sparse in the frequency domain, suggesting the application of Compressive Sensing (CS) techniques in order to reduce the quantity of transmitted information. CS can recover data vectors starting from a subset of the original vector entries, thus allowing to recover a previously sampled signal with much less samples than those suggested by the Nyquist-Shannon theorem, and much less than what is commonly used in dynamic identification of structures. A CS technique, specifically Basis Pursuit, is applied for the dynamic identification study of a 30-meter-high lightning rod, consisting of a steel monotubular pole, where possible issues had been raised concerning fatigue damage due to resonant response with the first and second modes of vibration. An experimental measurement campaign was carried out to estimate damping coefficients useful for structural verifications. The ambient response was collected using triaxial accelerometers positioned at the top and at an intermediate height, which transmit data via WiFi to a nearby workstation. Different sampling frequencies for the compressed records are utilized for the dynamic identification of the structure, comparing modal frequencies and damping ratios with values obtained from the original records to find the best trade-off between data reduction and accuracy of modal parameters. Despite the usual challenges inherent in identification problems, further complicated by the low damping levels of the structure under consideration, the comparisons demonstrate a very good approximation. Fundamental frequencies are accurately estimated, while the slight discrepancies in the damping coefficients are associated with the intrinsic uncertainties of this parameter. Regarding the structural aspect of the case study, the outcomes of the analysis indicate very low damping values, pointing to potential criticality, particularly in the second mode of vibration. Moreover, the solid approximation achieved with the CS technique marks a significant advancement in applying IoT solutions for structural monitoring, emphasizing a significant reduction in data flow without affecting data quality. This may lead to several benefits, including simpler installation and maintenance, lower costs, and decreased energy consumption.

Keywords

• Compressive sensing
• modal parameters
• operational modal analysis
• structural monitoring
• vertical slender structures