Identification of regularities in time series by the method of software engineering

Abstract

The subject of the study in the article are the processes of revealing hidden models of behavior of complex systems for solving applied problems of analysis and identification of anomalous events occurring in the process of functioning of the investigated object: the manifestation of the moment and localization the occurrence of an anomalous event, the length of stay in a certain numerical range and the causes of its occurrence. The purpose is to investigate the possibility of using nonlinear dynamics methods to identify and evaluate patterns of behavior of complex systems that generate indefinite time series. The tasks to be solved are: to develop a method for identifying hidden patterns of behavior of complex systems, based on temporal patterns of behavior, to develop an intelligent module of the diagnostic system in the form of software and algorithmic support; to develop an engineering technique for constructing a mathematical model of a signal, profiled for a given mask of a phase portrait; on the examples of the research of experimental data, to prove the viability of the proposed method and the ability of the engineering technique to establish the relationship between the type of process in the system and the phase trajectory. The method used is a combined approach based on methods of nonlinear dynamics (phase analysis), time patterns of behavior reflecting fragments of relationships in data and methods of classification analysis. The following results are obtained. Software is developed in the LabVIEW graphical programming environment of National Instruments, which provides maximum visualization of the process of analyzing and modeling time series based on the construction of phase portraits of correlation functions of time series. As a result of researching experimental data on dynamic behavior with the help of the developed software module, the main types of phase portraits corresponding to different stages of the system state were generated, generating non-definite time series. A preliminary grouping of phase portraits based on the topological identity of phase portraits at various time segments was carried out. The analysis and interpretation of grouping results are carried out, the diagram of transition from one ordered state to another is made. A mathematical model of a signal configured for a given mask of a phase portrait is constructed, by combining individual components "responsible" for individual features of the phase portrait, and its parameters are determined. On the examples of the research of experimental data, the viability of the proposed method and the ability of the engineering technique to establish the connection between the type of process in the system and the phase trajectory are proved. Conclusions. The scientific novelty of the results obtained is as follows: a method is proposed for revealing the hidden regularities in the behavior of complex systems using phase portraits of the correlation function, based on temporal patterns of behavior, and methods of classification analysis; an engineering technique for constructing a mathematical model of a signal, configured for a given mask of the phase portrait, was proposed.