Analysis of Errors in the Estimation of Impact Positions in Plate-Like Structure through the Triangulation Formula by Piezoelectric Sensors Monitoring

The structural health monitoring (SHM) of critical structures is a complex task that involves the use of different sensors that are also aimed at the identification of the location of the impact point using ultrasonic sensors. For the evaluation of the impact position, reference is often made to the well-known triangulation method. This method requires the estimation of the differential time of arrival (DToA) and the group velocity of the Lamb waves propagating into a plate-like structure: the uncertainty of these two parameters is taken into consideration as main cause of localization error. The work proposes a simple laboratory procedure based on a set-up with a pair of sensors that are symmetrically placed with respect to the impact point, to estimate the uncertainty of the DToA and the propagation velocity estimates. According to a theoretical analysis of the error for the impact position, the experimental uncertainties of DToA and the propagation velocity are used to estimate the overall limit of the SHM system for the impact positioning. Because the error for the DToA estimate depends also on the adopted signal processing, three common methods are selected and compared: the threshold, the correlation method, and a likelihood algorithm. Finally, the analysis of the positioning error using multisensory configuration is reported as useful for the design of the SHM system.