Abstract
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.
Highlights
Acoustic source (AS) localization from the measurements of passive sensors is a widely-investigated problem in structural health monitoring (SHM) [1,2]
In order to validate the design procedure and the directivity properties of the Directive Complex sensor (DCS), in the following subsections, the beampatterns obtained from the Finite Element Method (FEM) are shown and compared with the theoretical ones
Since it is sufficient to shape just one metalization of the DCS to achieve the desired directive behavior, the DCS was modeled using the geometry obtained in the design procedure, below which a small disk of piezoelectric material with a radius of 12 [mm] was defined
Summary
Acoustic source (AS) localization from the measurements of passive sensors is a widely-investigated problem in structural health monitoring (SHM) [1,2]. Minimal monitoring system weight, including cabling and circuitry; Minimal power consumption, to be compatible with wireless systems This means reducing the computational cost for the signals local processing and/or the amount of data to be wirelessly transferred; Inverse methods [4,5]; Hyperbolic positioning [6]; Methods which use Directions of Arrival (DoAs) estimation [7,8,9]; The first typology requires very accurate modeling of ultrasonic propagation. The cluster design procedure is based on the computation of the CRB of DoA in case of the unknown velocity of propagation (CRBu−v ), and on the usage of its Bayesian average (assuming that the DoA is a random variable with a known probability distribution) as a cost function for the optimal design This allows us to minimize both the DoA lower bound and the DoA accuracy loss due to the unknown wave velocity. The details of the cluster design strategy, the adopted DoA estimator, the novel directional transducer concept and, the numerical validations are thoroughly illustrated
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