# Computational Vibro-Acoustic Time Reversal for Source and Novelty Localization
## 1 Introduction  
Two decades ago, time reversal was introduced in the scientific community as a physical process that refocuses the waves back to the original source that created them [1]. Since then, the technique has been utilized as a computational tool for solving inverse wave propagation problems [2]. There are two main distinct steps in the time reversal technique, namely, the forward and backward steps. During the forward step, a source excitation is used to generate the propagating field and the response of the medium is acquired using recorders. The signals acquired during the forward step are then time reversed and re-emited. This is the backward step, during which the field re-focuses at the location of the forward's step excitation source. One of these steps or even both of them might be performed numerically, giving birth to a computational approach. As two typical examples, we refer to the problem of source localization, where the backward step is usually realized numerically, while for some energy focusing applications, the forward step could be the design step and the backward step could be the one to be performed physically in order to succeed the energy focusing. In some previous studies [3], a detailed Signal-to-Noise ratio (SNR) analysis for the time reversal process on bounded acoustic domains was presented for both source and defect localization. The SNR definition used, which is retained here, is the value of the image at the true source or defect (here novelty) location, divided by the maximal value of the image outside a small region around the true source (or novelty) location. A study of the time reversal approach in an elastodynamic bounded domain has been presented in [4],where a singular value decomposition of the array response matrix was used in order to detect multiple scatterers. In another work [5], some initial effort on the application of the time reversal process on structures has been presented and further developed in [6], where some theoretical links with classical reciprocity theorems have also been attempted. Furthermore, a study of the sensor's placement together with a variety of applications are given in that latter work. In the current work, we extend previous efforts in the framework of coupled structural-acoustic systems, which we will call vibro-acoustic environments. A first attempt for an experimental evidence of time reversal in an elasto-acoustic medium is given in [7], while a numerical reproduction for the case where ultrasound elastic waves are time reversed back to their source with a time reversal mirror in a fluid adjacent to the solid is given in [8]. The combination of microphone-acquired data together with a kinematic response (i.e., displacements, velocities or accelerations) was presented in [9], where a methodology was designed for fault detection following the previous published approaches [10]. In this work, the authors considered the acquisition of acoustic data via microphones in combination with a numerical vibro-acoustic model and suggested that this could be a viable way to achieve non-intrusive sensing with a high accuracy. They further exploited this feature for fault detection in a plate. Later, this setup was extended, considering also the Time-Reversal MUltiple SIgnal Classification (TR-MUSIC) algorithm in order to successfully localize extended defects [11]. A study on the improvement of the sensor's placement has been presented [12] in regard to the latter TR-MUSIC approach on vibro-acoustic systems. The main difference with the framework introduced in our work is that the time reversal approach for fault detection presented in the aforementioned references is based on a costly and difficult minimization approach using a set of reference trial models with different fault locations, while here we use the difference between the response of the vibro-acoustic system that contains the novelty and the original vibro-acoustic system (i.e., before the novelty was introduced).