Application of unsupervised learning algorithms for analysis the vibrations of an oscillator forced by a random series of impulses

Paper discusses a mathematical model describing the vibrations of a linear oscillator forced by a random series of impulses. The study aims at checking how precisely the distributions of values of the impulses forcing the vibrations of an oscillator can be differentiated. The analysis was carried out in the MatLab environment with the use of hierarchical clustering algorithms of unsupervised machine learning, for samples generated from computer simulation. The time series are non-stationary. The studies showed that high precision could be achieved in distinguishing two very similar distributions forcing the vibrations, on the basis of an analysis of the two first moments calculated from the movement.