Construction of methods for computing recurrence plots in space with a scalar product

Поспелов, Борис; Andronov, Vladimir; Meleshchenko, Ruslan; Danchenko, Yuliya; Artemenko, Igor; Romaniak, Mikhailo; Khmyrova, Anastasiia; Butenko, Tetiana

doi:10.15587/1729-4061.2019.169887

Cited by 4 publications

(11 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The results of the experimental verification, shown in Fig. 1-3 of the proposed method generally indicate greater information content, accuracy and adequacy of the mapping of recurrence states for real systems in comparison with the known method (1), (2). An important feature of the developed method for calculating RP is the ability to clearly display the presence of dangerous states in dynamic systems in the form of vertical and horizontal lines of black dots.…”

Section: Discussion Of the Results Of Experimental Verification Of Thmentioning

confidence: 74%

“…Verification shows that the proposed method for calculating RP has an important applied property related to overcoming the existing metric-threshold uncertainty of the known methods considered (1) together with (2). In addition, the method ensures the invariance of the structure of the calculated RPs to the nature of the measured data, irregularity and the absence of measurements.…”

Section: Computer Sciencesmentioning

confidence: 91%

“…Within the framework of the development of the developed paradigm, it is advisable to move from considering the norms and generating metrics that define the corresponding spaces traditional for the methods of computing RP functionals to the corresponding improved space [2,3]. Such an improvement in [3] is proposed to be implemented by introducing an additional geometric characteristic in the form of a scalar product of two vectors.…”

Section: The Theoretical Basis Of the Proposed Methods For Calculatingmentioning

confidence: 99%

“…where ε θ is the maximum angle (in degrees) between the vectors at which state vectors are still considered recurrent in the sense of the selected threshold value ɛ. In this case, the characteristic function (2) in the improved space can be represented as…”

Section: The Theoretical Basis Of the Proposed Methods For Calculatingmentioning

confidence: 99%

“…When testing the method, the results of measurements of the concentrations of these atmospheric pollutants during May 2018 were considered, starting from 480 counts and ending with 604 counts. However, in order to compare the results of [2], the same interval was chosen as a test interval for testing, starting from 13:00 on May 3, 2018 (i=490) to 01:00 on May 11, 2018 (i=520). During this interval, the results of measuring the excess of the maximum permissible concentrations (MPC) were analyzed.…”

Section: Experimental Verification Of the Methods For Calculating Recumentioning

confidence: 99%

See 4 more Smart Citations

Development of a Self-Adjusting Method for Calculating Recurrent Diagrams in a Space With a Scalar Product

Поспелов

Meleshchenko

Asotskyi³

et al. 2019

EUREKA: Physics and Engineering

Self Cite

View full text Add to dashboard Cite

A self-adjusting method for calculating recurrence diagrams has been developed. The proposed method is aimed at overcoming the metric-threshold uncertainty inherent in the known methods for calculating recurrence diagrams. The method provides invariance to the nature of the measured data, and also allows to display the recurrence of states, adequate to real systems of various fields. A new scientific result consists in the theoretical justification of the method for calculating recurrence diagrams, which is capable of overcoming the existing metric-threshold uncertainty of known methods on the basis of self-adjusting by measurements by improving the topology of the metric space. The topology is improved due to the additional introduction of the scalar product of state vectors into the operation space. This allowed to develop a self-adjusting method for calculating recurrence diagrams with increased accuracy and adequacy of the display of recurrence states of real systems. Moreover, the method has a relatively low computational complexity, providing invariance with respect to the nature of the irregularity of measurements. Verification of the proposed method was carried out on the basis of experimental measurements of concentrations of gas pollutants of atmospheric air for a typical industrial city. The main gas pollutants of the atmosphere are formaldehyde, ammonia and nitrogen dioxide, caused by stationary and mobile sources of urban pollution. The obtained experimental verification results confirm the increased accuracy and adequacy of the display of the recurrence of atmospheric pollution states, as well as the invariance of the method with respect to the nature of the irregularity of measurements. It has been established that the accuracy of the method is influenced by the a priori boundary angular dimensions of the recurrence cone. It was shown that with a decrease in the boundary angular dimensions of the recurrence cone, the accuracy of the recurrence mapping of the real states of dynamical systems in the calculated diagrams increases. It was experimentally established that the accuracy and adequacy of the mapping of the recurrence states of real dynamical systems acceptable for applications is provided for a boundary angular size of the recurrence cone of 10° or less.

show abstract

Section: Discussion Of the Results Of Experimental Verification Of Thmentioning

confidence: 74%

Section: Computer Sciencesmentioning

confidence: 91%

Section: The Theoretical Basis Of the Proposed Methods For Calculatingmentioning

confidence: 99%

Section: The Theoretical Basis Of the Proposed Methods For Calculatingmentioning

confidence: 99%

Section: Experimental Verification Of the Methods For Calculating Recumentioning

confidence: 99%

See 3 more Smart Citations

Development of a Self-Adjusting Method for Calculating Recurrent Diagrams in a Space With a Scalar Product

Поспелов

Meleshchenko

Asotskyi³

et al. 2019

EUREKA: Physics and Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

Construction of the method for semi-adaptive threshold scaling transformation when computing recurrent plots

Поспелов

Rybka

Togobytska

et al. 2019

EEJET

Self Cite

View full text Add to dashboard Cite

Розроблено метод напiвадаптивної масштабної трансформацiї порогу, що забезпечує обчислення рекурентних дiаграм, якi адекватно вiдображають особливостi динамiки реальних складних динамiчних систем природної i технiчної сфери. Новий науковий результат полягає в розвитку теоретичної основи методу напiвадаптивної масштабної трансформацiї порогу при обчисленнi рекурентних дiаграм шляхом удосконалення лiнiйних нормованих просторiв за рахунок введення скалярного добутку векторiв. Пропонований метод трансформацiї порога забезпечує обчислення рекурентних дiаграм, якi мають пiдвищену iнформативнiстю, iнварiантнiстю щодо параметрiв вимiрюваних векторiв станiв, а також нерегулярностi вимiрювань. Перевiрка працездатностi запропонованого методу напiвадаптивної масштабної трансформацiї порогу проведена на основi експериментальних вимiрювань концентрацiй формальдегiду, амiаку та оксиду вуглецю в атмосферному повiтрi типового промислового мiста при традицiйних стацiонарних та рухомих джерелах забруднень. Отриманi результати обчислення рекурентних дiаграм з урахуванням запропонованого методу напiвадаптивної масштабної трансформацiї порогу в цiлому пiдтверджують його працездатнiсть. Встановлено, що обчислення RP при напiвадаптивнiй трансформацiї порогу для рiзних кутових розмiрiв α конуса рекурентностi, рiвних 1°, 5°, 10° i 20° свiдчить про те, що зi зменшенням кутових розмiрiв конуса точнiсть рекурентних дiаграм виявляти небезпечнi стани в динамiчних системах зростає. Експериментально встановлено, що для адекватного вiдображення рекурентних станiв реальних динамiчних систем, за допомогою обчислюваних рекурентних дiаграм, значення величини кутових розмiрiв конуса рекурентностi повиннi складати 1-5°К лючовi слова: рекурентная дiаграма, складнi динамiчнi системи, напiвадаптивна трансформацiя порога, забруднення атмосфери UDC 004.

show abstract

Development of the method operative calculation the recurrent diagrams for non-regular measurements

Поспелов¹,

Krainiukov

Savchenko

et al. 2019

EEJET

Self Cite

View full text Add to dashboard Cite

Construction of methods for computing recurrence plots in space with a scalar product

Cited by 4 publications

References 28 publications

Development of a Self-Adjusting Method for Calculating Recurrent Diagrams in a Space With a Scalar Product

Development of a Self-Adjusting Method for Calculating Recurrent Diagrams in a Space With a Scalar Product

Construction of the method for semi-adaptive threshold scaling transformation when computing recurrent plots

Development of the method operative calculation the recurrent diagrams for non-regular measurements

Contact Info

Product

Resources

About