## 1 Introduction  
Acoustic Emission (AE) is the transient elastic sound waves when a material undergoes stress. It is used as a Non-Destructive Testing technique to monitor damage in composites materials and structures [1; 2; 3; 4]. Usually, piezoelectric sensors applied directly on the samples surface capture these elastic waves. The analysis of the collected data can be used to discriminate the sources of damage (matrix cracks, fibre breaks, fibre/matrix decohesion, delamination) and to determine the kinetics of the various degradation mechanisms during the lifetime. Indeed, the shape and the characteristics of the AE signals are directly dependent on the local damage mechanisms such as delamination, matrix cracking, fibre matrix debonding, fibre break and fibre pull-out. Therefore, it is realistic to consider that this signal contains some features representative of the source in such a manner that direct correlation exists between the damage mechanisms and the AE parameters. In this type of studies, a main assumption is done: signals are affected by propagation but they remain images of sources. Therefore, acoustic emission events can be classified using multivariable statistical analysis techniques and then attributed to a damage mechanism in the material [5; 6; 7; 8; 9; 10; 11; 12]. The main assumption is: the acoustic signatures are unchanged during propagation and damage evolution. AE signals that have similar characteristics are grouped using a clustering method, based on similarity measures, in order to reveal the natural structure of data. This procedure is based on the representation of AE signals by relevant descriptors. The descriptors selection is an important step [13; 14; 15]. For the unsupervised pattern recognition, the descriptors should be relevant and limited in number. The possibility to identify AE signatures of damage mechanisms is an established field [5; 6; 7; 8; 9; 10; 11; 12]. In most studies, the attribution of each class to a specific damage mechanism is based mainly on empirical approach and the validation of this labelling remains difficult and is still a challenge. In most works, the assignment of a signal to a damage mechanism is very difficult, if not impossible, to validate without any modelling [16; 17; 18; 19]. [PERSON] [16] models AE sources in a specimen for different damage mechanisms, as well as the signal propagation and the different elements of the acquisition chain by a finite element method. For each cluster and for each mechanism, he compares the experimental values of the signal descriptors with the theoretical values generated by the damage mechanism, which is affiliated to it. It can thus judge the relevance of its labelling. Moreover, several authors use acoustic emission in the aim of prognostics, in order to make remaining useful lifetime previsions [8; 20; 21; 22; 23; 24; 25; 26]. An estimate of the composite materials remaining lifetime can be considered based on a real-time tracking of the damage recorded by EA. In the context of the failure of the prediction of composite, [PERSON] [23] predicted residual tensile strength of impacted carbon/epoxy laminates using an artificial neural network with AE data collected up to 50% of failure loads. The chosen descriptors are the cumulative counts and the amplitude. Several authors [24] used AE peak amplitude and energy parameter into neural network for predicting the tensile strength of carbon epoxy composites. For the specific study of CMCs (ceramic matrix composites) in fatigue, [PERSON] et al. [25] introduced an indicator, denoted R\({}_{\text{AE}}\), the coefficient of emission, which is shown to go through a minimum value of around 50-60% of the total test duration. Therefore, beyond 50% of the total test duration, a power law can model the criticality in order to evaluate time to failure. Study of the damage indices based on acoustic energy or parameters enlightens the damage evolution, enabling predictions of the remaining life [8; 25; 26].