Abstract
A method has been constructed for the threshold semi-adaptive scaling transformation. The method provides calculation of recurrent plots, which adequately map the dynamics of real complex dynamic systems in natural and technical spheres. A new scientific result implies the development of theoretical basis for the method of semi-adaptive scaling transformation of the threshold during calculation of recurrent plots by improvement of linear normalized spaces due to introduction of a scalar product of vectors. The proposed method of threshold transformation provides computation of recurrent plots with increased information content, invariance to parameters of measured state vectors, and irregularity of measurements. We performed tests of operability of the proposed method of semi-adaptive scaling transformation of the threshold based on experimental measurements of concentrations of formaldehyde, ammonia, and carbon monoxide in atmospheric air in a typical industrial city with conventional stationary and mobile sources of pollution. Taking into account the proposed method of semi-adaptive scaling transformation, the obtained results of the calculation of recurrent plots confirmed its operability in general. It was found that the calculation of RP during the semi-adaptive transformation of the threshold for various α angular dimensions of a recurrence cone, equal to 1°, 5°, 10°, and 20°, indicates that accuracy of recurrent plots in detection of dangerous states in dynamic systems increases with a decrease in angular dimensions of a cone. It was established experimentally that the values of angular dimensions of the recurrence cone should be 1–5° for adequate mapping of recurrent states of real dynamic systems with the use of calculated recurrent plots
Highlights
Most of real natural, technical, and social systems exhibit recurrent behavior, which means that certain states of systems repeat over time often [1]
Accuracy of mapping of recurrent states of systems in recurrent plots (RP) calculation depends on specific measurement conditions and methods of processing of measurement information implemented in the case
We can state that an important and unresolved part of the problem of improvement of the well-known methods of RP calculation is a lack of threshold transformation methods, which provide a reflection of recurrence of states adequate to real systems
Summary
Technical, and social systems exhibit recurrent behavior, which means that certain states of systems repeat over time often [1]. Capabilities of RQA methods depend on adequacy of RP mapping of the recurrent behavior of real systems substantially. Accuracy of mapping of recurrent states of systems in RP calculation depends on specific measurement conditions and methods of processing of measurement information implemented in the case. One of the limitations of the known methods of RP calculation for a given norm functional [7] is the dependence of accuracy of mapping of recurrent states on the threshold used, that is the threshold uncertainty of methods of RP calculation. Under various and changing conditions, which are characteristic for most of applications, the threshold uncertainty of methods reduces accuracy in displaying the recurrent states of real systems. An existing variety of types of real systems, conditions for measurement of their states, and presence of threshold uncertainty of known methods for RP calculation, which reduce accuracy of displaying of recurrent states.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Eastern-European Journal of Enterprise Technologies
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
