Optimal Array Design and Directive Sensors for Guided Waves DoA Estimation

The estimation of Direction of Arrival (DoA) of guided ultrasonic waves is an important task in many Structural Health Monitoring (SHM) applications. The aim is to locate sources of elastic waves which can be generated by impacts or defects in the inspected structures. In this paper, the array geometry and the shape of the piezo-sensors are designed to optimize the DoA estimation on a pre-defined angular sector, from acquisitions affected by noise and interference. In the proposed approach, the DoA of a wave generated by a single source is considered as a random variable that is uniformly distributed in a given range. The wave velocity is assumed to be unknown and the DoA estimation is performed by measuring the Differences in Time of Arrival (DToAs) of wavefronts impinging on the sensors. The optimization procedure of sensors positioning is based on the computation of the DoA and wave velocity parameters Cramér-Rao Matrix Bound (CRMB) with a Bayesian approach. An efficient DoA estimator is found based on the DToAs Gauss-Markov estimator for a three sensors array. Moreover, a novel directive sensor for guided waves is introduced to cancel out undesired Acoustic Sources impinging from DoAs out of the given angles range. Numerical results show the capability to filter directional interference of the novel sensor and a considerably improved DoA estimation performance provided by the optimized sensor cluster in the pre-defined angular sector, as compared to conventional approaches.