The present study provides the mathematical description of changing metals characteristics during exploitation, as well as identifies behaviors and features during plastic deformation. Modern experimental facilities allow conducting a full-scale experiment, recording the effects observed, determining the patterns of materials behavior of and their alloys to predict the occurrence of unstable plastic flow. The arrays of experimental data obtained in the format of discrete values were processed with the wave-record method for the data interpolation and normalization. The results' comparison enabled to determine the class of materials with similar patterns of deformational plastic behavior. That allowed us to describe the patterns of irreversible deformations and their nature to formulate the postulates for the theory of plasticity, materials science, and prediction of complex systems' behavior. The paper presents the results of experimental studies of plastic deformation of aluminum alloy samples to determine the characteristics of unstable plastic flow in the material. The analysis of the obtained data for the samples confirmed the presence of the Portevin-Le Chatelier effect. Based on the experimental results, deformation diagrams and time series were developed, and the data correlation for the samples was also confirmed. The wave process that occurs in the material during stretching correlates hydrodynamic with the occurrence of rogue waves. It is important to note that when analyzing the time series of experimental data for aluminum alloys, a pattern of correspondence with time series in the analysis of rogue waves was noted.