The interpretation of unlabeled acoustic emission (AE) data classically relies on general-purpose clustering methods. While several external criteria have been used in the past to select the hyperparameters of those algorithms, few studies have paid attention to the development of dedicated objective functions in clustering methods able to cope with the specificities of AE data. We investigate how to explicitly represent clusters onsets in mixture models in general, and in Gaussian Mixture Models (GMM) in particular. By modifying the internal criterion of such models, we propose the first clustering method able to provide, through parameters estimated by an expectation-maximization procedure, information about when clusters occur (onsets), how they grow (kinetics) and their level of activation through time. This new objective function accommodates continuous timestamps of AE signals and, thus, their order of occurrence. The method, called GMMSEQ, is experimentally validated to characterize the loosening phenomenon in bolted structure under vibrations. A comparison with three standard clustering methods on raw streaming data from five experimental campaigns shows that GMMSEQ not only provides useful qualitative information about the timeline of clusters, but also shows better performance in terms of cluster characterization. In view of developing an open acoustic emission initiative and according to the FAIR principles, the datasets and the codes are made available to reproduce the research of this paper.