Cramer-Rao bounds for acoustic emission events localization in a flat plate

Alain Le Duff (1, 2, 3) , Seif Eddine Hamdi (1, 2, 3) , Guy Plantier (1, 2, 3) , Anthony Sourice (1, 2, 3) , Romain Feron (1, 2, 3)

1 ESEO-Tech
2 GSII - ESEO-GSII
3 LAUM - Laboratoire d'Acoustique de l'Université du Mans

This article addresses the problem of 2D localization of acoustics source in a plate. This localization is based on Time Difference of Arrival (TDOA) measurements thanks to an array of three sensors arbitrary distributed on the 2D plane. Some previous works proposed approximated solutions or maximum likelihood methods. In order to obtain a fast, but robust and accuracy, algorithm, allowing an online estimation of the location of hits or Acoustic Emission (AE) events in a composite plate for example, the authors propose an exact solution of the TDOA problem by solving a nonlinear system of coupled equations. The exact analytical Cramer-Rao Bounds (CRBs) on the variance of the estimations is then presented. Moreover, the statistical performances of the method are illustrated by means of Monte-Carlo simulations and are compared to the CRBs. These last expressions can be very useful in order to justify the accuracy of TDOA measurements and for guiding the choice of the sensors position.

Mots clés: Cramer Rao Bounds; TDOA; Acoustic Emission; Monte-Carlo simulation

Domaines: Acoustique [physics.class-ph]

Alain Le Duff, Seif Eddine Hamdi, Guy Plantier, Anthony Sourice, Romain Feron. Cramer-Rao bounds for acoustic emission events localization in a flat plate. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00810842⟩