The article is devoted to the methods of monitoring and control of vibration processes occurring in the structure and units of complex and unique electromechanical equipment. The monitoring object is considered as a dynamic multidimensional information object, for the study of which analytical and numerical methods of modeling and simulation of multidimensional chaotic systems are used in the context of the scientific direction of physics of open systems. The structure of research of signals of vibration activity of equipment, description of mathematical models and algorithms based on them are presented. Demonstrative results of experiments carried out to analyze and evaluate the possibilities of controlling the behavior of a complex system using methods of influencing signals of various nature are presented. Using the methodology of Visual Thinking will improve the quality and efficiency of monitoring the vibrational activity of a complex technical object. Such a technique will make it possible to reasonably interpret the decision made to control the vibration process. The calculated parameters and the constructed visual images of the processed signals are proposed for use in the Input Layer of the Recurrent Neural Network of the Deep Learning algorithm.