scholarly journals Evaluating Noise Sensitivity on the Time Series Determination of Lyapunov Exponents Applied to the Nonlinear Pendulum

2003 ◽  
Vol 10 (1) ◽  
pp. 37-50 ◽  
Author(s):  
L.F.P. Franca ◽  
M.A. Savi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Time Series ◽  
Lyapunov Exponents ◽  
Random Noise ◽  
Noise Sensitivity ◽  
Correct Identification ◽  
Chaotic Motions ◽  
Nonlinear Pendulum

This contribution presents an investigation on noise sensitivity of some of the most disseminated techniques employed to estimate Lyapunov exponents from time series. Since noise contamination is unavoidable in cases of data acquisition, it is important to recognize techniques that could be employed for a correct identification of chaos. State space reconstruction and the determination of Lyapunov exponents are carried out to investigate the response of a nonlinear pendulum. Signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the signal. Basically, the analyses of periodic and chaotic motions are carried out. Results obtained from mathematical model are compared with the one obtained from time series analysis, evaluating noise sensitivity. This procedure allows the identification of the best techniques to be employed in the analysis of experimental data.

scholarly journals Determination of technological parameters of soil compacting process

2020 ◽  
pp. 3-15
Author(s):  
V. A. Basarab
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Differential Equations ◽  
Fourier Analysis ◽  
Soil Properties ◽  
Soil Compaction ◽  
Technological Parameters ◽  
Compaction Process ◽  
Properties Of Soil

The article is devoted to determine the technological parameters of soil compaction by rollers according to soil properties in construction. The compaction of the soil occurs due to certain force loads on the soil. Nowadays, there are enough methods to determine the technological parameters of soil compaction process, however, there are few research methods that consider the system of soil-machine-technological parameters. The urgency of the soil compaction process, which ultimately determines the quality of construction products, was emphasized. The basic physical and mechanical properties of soil and technological parameters of the compaction process were given. Analysis of discrete mathematical model of interaction between roller and soil was carried out in order to determine the technological parameters of soil compaction process in the field of construction technologies. A rheological model to describe the soil properties was used. The differential equations of the interaction between roller and soil have been made. A numerical calculation method to solve the differential equations has been proposed. The basic technological parameters of soil compaction process by rollers have been determined - the thickness of soil layer to be compacted, the number of the roller passes, and the speed of the roller movement. The methodology of theoretical and experimental researches of interaction between roller and soil has been proposed in order to clarify the mathematical model and to find the technological parameters of the compaction process. Experimental research methods are based on the determination of the stress-strain state of soil and on the Fourier analysis of the experimental data. Fourier analysis of the experimental data makes it possible to analyze the qualitative energy spectrum of the interaction between roller and soil to determine the rational amplitude-frequency characteristics of the compaction process. Experimental studies allow obtaining such rheological properties of soil as elasticity, viscosity, coefficient of elastic resistance, etc. The main recommendations for the choice of compaction method depending on the type of soil have been proposed.

REDUCTION ENTROPY

1995 ◽  
Vol 05 (02) ◽  
pp. 585-593 ◽  
Author(s):  
FLORIS TAKENS
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Numerical Determination ◽  
Sensitive Dependence ◽  
Noisy Time Series

In this paper we study the numerical determination of the different reduction entropies (or α-entropies) of dynamical systems from time series. This method is advocated as a more suitable way to investigate the different aspects of sensitive dependence on initial positions than the determination of Lyapunov exponents, especially in the case of “noisy” time series.

scholarly journals Calculation of erosion scour of cohesive soil

2021 ◽  
pp. 187-195
Author(s):  
А.Ю. Виноградов ◽  
О.В. Зубова ◽  
Е.А. Парфенов
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Shear Stress ◽  
Cohesive Soil ◽  
Cohesive Soils ◽  
Large Specific Surface Area ◽  
Empirical Relationships ◽  
Clay Particles ◽  
Angle Of Internal Friction

Проведен анализ существующих способов оценки размыва грунтов в гидротехнических и водопропускных сооружениях, показывающий, что определение глубины и скорости размыва проводится без учета физических свойств связных грунтов. Таким образом, данные параметры оцениваются по эмпирическим зависимостям и с существенными погрешностями. Опытные данные по размыву связных грунтов доказывают, что большая удельная поверхность и гидрофильность глинистых частиц приводят к разуплотнению и выносу микроагрегатов грунта в поток. Предложена математическая модель расчета глубины размыва связных грунтов в зависимости от касательного напряжения в грунте. Учет показателей сцепления и угла внутреннего трения в данной модели позволит избежать погрешностей в расчетах. The analysis of existing methods for assessing soil erosion in hydraulic engineering and culverts, showing that the determination of the depth and rate of erosion is carried out without taking into account the physical properties of cohesive soils. Thus, these parameters are estimated using empirical relationships and with significant errors. Experimental data on erosion of cohesive soils prove that the large specific surface area and hydrophilicity of clay particles lead to decompaction and the removal of soil microaggregates into the flow. A mathematical model is proposed for calculating the depth of erosion of cohesive soils depending on the shear stress in the soil. Taking into account the adhesion indicators and the angle of internal friction in this model will avoid errors in the calculations.

scholarly journals Determination of Temperature of Components of Cotton-Raw Material in a Drum Dryer with a Constant

2021 ◽  
Vol 939 (1) ◽  
pp. 012052
Author(s):  
A Z Mamatov ◽  
A K Usmankulov ◽  
I Z Abbazov ◽  
U A Norboyev ◽  
E T Mukhametshina
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Comparative Analysis ◽  
Boundary Value Problem ◽  
Parabolic Type ◽  
Raw Material ◽  
Drying Process ◽  
Moisture State ◽  
Type Boundary

Abstract This article solves one parabolic-type boundary value problem for determining the heat-moisture state of raw cotton in drum dryers at a constant air temperature. Numerical results are obtained by the Bubnov – Galerkin method of the problem under consideration, a comparative analysis is carried out with experimental data. It is shown that the proposed mathematical model and its numerical algorithm adequately describe the drying process of raw cotton.

Determination of the intensity of polychromatic radiation in the reaction compartment as a function of wavenumber

1991 ◽  
Vol 56 (6) ◽  
pp. 1173-1179 ◽  
Author(s):  
Radim Hrdina ◽  
Igor Čepčiansky ◽  
Hana Bittová
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
High Pressure ◽  
Emission Spectrum ◽  
Photochemical Reactions ◽  
Tabular Form ◽  
Mercury Lamp ◽  
Kinetics Of ◽  
Polychromatic Radiation

A procedure is suggested for studying the kinetics of photochemical reactions using excitation with polychromatic radiation, where the wavenumber dependence of the intensity of the polychromatic radiation entering the reaction compartment must be known. The observed relative intensities of the polychromatic source are calibrated by ferrioxalate actinometry, selected parts of the emission spectrum being eliminated by insertion of filters. The relative intensities of an HBO 200 high-pressure mercury lamp were measured. For the sake of brevity, the experimental data were fitted by a mathematical model (a polynominal), and only the parameters of the polynomial are presented in a tabular form.

A SIMPLE TEST FOR HIDDEN PERIODICITY IN TIME SERIES DATA

1995 ◽  
Vol 05 (01) ◽  
pp. 265-269 ◽  
Author(s):  
MICHAEL ROSENBLUM ◽  
JÜRGEN KURTHS
Keyword(s):  
Experimental Data ◽  
Time Series ◽  
Spectral Analysis ◽  
Additive Noise ◽  
Time Series Data ◽  
Series Data ◽  
Simple Test ◽  
Data Set ◽  
Dynamical Characteristics

We would like to draw the attention of specialists in time series analysis to a simple but efficient algorithm for the determination of hidden periodic regimes in complex time series. The algorithm is stable towards additive noise and allows one to detect periodicity even if the examined data set contains only a few periods. In such cases it is more suitable than other techniques, such as spectral analysis or recurrence map. We recommend the use of this test prior to the evaluation of attractor dimensions and other dynamical characteristics from experimental data.

scholarly journals The Mathematical Modeling of Ca And Fe Distribution In Peat Layers

2015 ◽  
Vol 2 ◽  
pp. 40
Author(s):  
Ērika Teirumnieka ◽  
Ilmārs Kangro ◽  
Edmunds Teirumnieks ◽  
Harijs Kalis ◽  
Aigars Gedroics
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Mathematical Model ◽  
Trace Elements ◽  
Mathematical Models ◽  
Organic Material ◽  
Low Concentrations ◽  
The Mathematical Model ◽  
Research Show

Bogs have been formed by an accumulation of peat - a light brown-to-black organic material, built up from partial decomposition of mosses and other bryophytes, sedges, grasses, shrubs, or trees under waterlogged conditions. The total peatlands area in Latvia covers 698 918 ha or 10.7% of the entire territory. Knowledge’s of peat metals content are important for any kind of peat using. Experimental determination of metals in peat is very long and expensive work. Using experimental data mathematical model for calculation of concentrations of metals in different points for different layers can help to very easy and fast to find approximately concentration of metals or trace elements. The results of the research show that concentrations of trace elements in peat are generally low. Concentrations differ between the superficial, middle and bottom peat layers, but the significance decreases depending on the type of mire. The mathematical model for calculation of concentration of metals in different points for different 3 layers in peat blocks is developed. As an example, mathematical models for calculation of Ca and Fe concentrations have been analyzed.

LYAPUNOV EXPONENTS FROM CHUA'S CIRCUIT

1993 ◽  
Vol 03 (02) ◽  
pp. 507-523 ◽  
Author(s):  
U. PARLITZ
Keyword(s):  
Experimental Data ◽  
Time Series ◽  
Lyapunov Exponents ◽  
Time Reversal ◽  
Chaotic Time Series ◽  
Lyapunov Spectrum ◽  
Diagnostic Tools ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Approximation Errors

The estimation of Lyapunov exponents from experimental data is demonstrated by means of a chaotic time series from Chua's circuit. The changes in the Lyapunov spectrum upon time reversal, the local thickness of the attractor, and the approximation errors of the locally linear fits are used as diagnostic tools to identify spurious Lyapunov exponents and to monitor the reliability of the results.

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