Signal processing and recognition of true kinetic equations containing non-integer derivatives from raw dielectric data

Signal processing in dielectric spectroscopy implies that it is necessary to find a 'true' fitting function (having a certain physical meaning), which describes well the complex permittivity and impedance data. In dielectric spectroscopy for description of complex permittivity/impedance data researches usually use the empirical Cole-Davidson (CD) and Havriliak-Negami (HN) equations that contains one relaxation time. But the parameters figuring in CD and HN equations do not have clear physical meaning as well as fitting parameters entering into linear combination of several CD or HN equations. For description of dielectric (especially asymmetric) spectra we suggest the complex permittivity functions containing two or more characteristic relaxation times. These complex susceptibility functions correspond in time domain to new type of kinetic equation containing non-integer (fractional) integrals and derivatives. We suppose that these kinetic equations describe a wide class of dielectric relaxation phenomena taking place in heterogeneous substances. To support and justify this statement the special recognition procedure has been developed that helps to identify this new kinetic equation from raw dielectric data. It incorporates the ratio presentation (or RP) format and separation procedure. Separation procedure was turned out to be helpful in detection of number of relaxation processes (each process is described by a characteristic relaxation time) taking place in the dielectric material under consideration. We suppose that this procedure can be applicable also for identification of fractal noises. © 2003 Elsevier B.V. All rights reserved

Application of fractional-moments statistics to data for two-phase dielectric mixtures

A new method for quantitative "reading" of dielectric data of two-phase dielectric mixtures is suggested. This method is based on ideas related to the application of the generalized mean value (GMV) function to random data series (statistics of fractional moments). The GMV function allows transformation of arbitrary random data series to smooth curves that in turn can be fitted by an analytical function with a limited number of parameters. These fitting parameters are sensitive to the influence of an external factor, so the dependence of these parameters on the external factor can be used as calibration curves. In this instance we analyzed dielectric data measured for ground hard red winter wheat with 12.5%, 17.9% and 21.2% moisture contents in the temperature range from 2°C to 76°C. This system is a complex system from the viewpoint of the complexity of the dielectric data interpretation. The common treatment of these dielectric spectra does not provide a monotonic calibration curve. We treated these spectra as random data series by the use of the GMV function. As a result of this treatment, we obtained the monotonic temperature dependence of several fitting parameters for the given moisture contents, and these relationships can be fitted by an analytical function for calibration use. We hope that this new method will find application for analysis of other complex systems. © 2008 IEEE

New approach in the description of dielectric relaxation phenomenon: Correct deduction and interpretation of the Vogel-Fulcher-Tamman equation

An empirical Vogel-Fulcher-Tamman (VFT) equation, connecting the maximum of the loss peak with temperature, was described. In order to establish the loss peak VFT dependence, a complex permittivity function should contain at least two relaxation times obeying the Arrhenius formula with two different set of parameters. It was shown that at a certain combination of initial parameters the parameter TVF can be negative or even accept complex value

NAFASS: Discrete spectroscopy of random signals

In this paper we suggest a new discrete spectroscopy for analysis of random signals and fluctuations. This discrete spectroscopy is based on successful solution of the modified Prony's problem for the strongly-correlated random sequences. As opposed to the general Prony's problem where the set of frequencies is supposed to be unknown in the new approach suggested the distribution of the unknown frequencies can be found for the strongly-correlated random sequences. Preliminary information about the frequency distribution facilitates the calculations and attaches an additional stability in the presence of a noise. This spectroscopy uses only the informative-significant frequency band that helps to fit the given signal with high accuracy. It means that any random signal measured in t-domain can be "read" in terms of its amplitude-frequency response (AFR) without model assumptions related to the behavior of this signal in the frequency region. The method overcomes some essential drawbacks of the conventional Prony's method and can be determined as the non-orthogonal amplitude frequency analysis of the smoothed sequences (NAFASS). In this paper we outline the basic principles of the NAFASS procedure and show its high potential possibilities based on analysis of some actual NIR data. The AFR obtained serves as a specific fingerprint and contains all necessary information which is sufficient for calibration and classification of the informative-significant band frequencies that the complex or nanoscopic system studied might have. © 2011 Elsevier Ltd. All rights reserved

The justified data-curve fitting approach: Recognition of the new type of kinetic equations in fractional derivatives from analysis of raw dielectric data

Usually, for the description of dielectric spectra one uses the empirical Cole-Davidson (CD) and Havriliak-Negami (HN) equations each of which contains one relaxation time. However, the parameters figuring in the CD and HN equations (or the linear combination of several CD or HN equations) do not have any clear physical meaning. For the description of such asymmetric dielectric spectra, we suggest complex permittivity functions containing two or more characteristic relaxation times. These complex susceptibility functions correspond, in the time-domain, to a new type of kinetic equation, which contains non-integer (fractional) integrals and derivatives. The physical meaning of these operators is discussed in [1]. We suppose that these kinetic equations describe a wide class of dielectric relaxation phenomena taking place in heterogeneous substances. To support and justify this statement, a special recognition procedure has been developed that helps to identify this new kinetic equation from real dielectric data. This recognition procedure can be considered as the justified data-curve fitting (JDCF) approach, in contrast to the conventional 'imposed' data-curve fitting (IDCF) treatment invariably used in modern dielectric spectroscopy. The JDCF approach incorporates the ratio presentation (RP) format and a separation procedure. It is shown how this separation procedure can be helpful in the detection of the many relaxation processes (each process is described by a characteristic relaxation time), which are taking place in the dielectric material under consideration

Theory and practice of unit creation for technogenic material compacting

No Abstrac

Application of Fractional Moments for Comparing Random Variables with Varying Probability Distributions

New methods are being presented for statistical treatment of different random variables with unknown probability distributions. These include analysis based on the probability circles, probability ellipses, generalized mean values, generalized Pearson correlation coefficient and the beta-function analysis. Unlike other conventional statistical procedures, the main distinctive feature of these new methods is that no assumptions are made about the nature of the probability distribution of the random series being evaluated. Furthermore, the suggested procedures do not introduce uncontrollable errors during their application. The effectiveness of these methods is demonstrated on simulated data with extended and reduced sample sizes having different probability distributions

Application of the generalized Prony spectrum for extraction of information hidden in chaotic trajectories of triple pendulum

In this paper we apply a new method of analysis of random behavior of chaotic systems based on the Prony decomposition. The generalized Prony spectrum (GPS) is used for quantitative description of a wide class of random functions when information about their probability distribution function is absent. The scaling properties of the random functions that keep their invariant properties on some range of scales help to fit the compressed function based on the Prony's decomposition. In paper [1] the first author (RRN) found the physical interpretation of this decomposition that includes the conventional Fourier decomposition as a partial case. It has been proved also that the GPS can be used for detection of quasi-periodic processes that are appeared usually in the repeated or similar measurements. A triple physical pendulum is used as a chaotic system to obtain a chaotic behavior of displacement angles with one, two and three positive Lyapunov's exponents (LEs). The chaotic behavior of these angles can be expressed in the form of amplitude-frequency response (AFR) that is extracted from the corresponding GPS and can serve as a specific "fingerprint" characterizing the random behavior of the triple-pendulum system studied. This new quantitative presentation of random data opens additional possibilities in classification of chaotic responses and random behaviors of different complex systems. © 2014 Versita Warsaw and Springer-Verlag Wien

Extraction of reliable information from hme-domain pressure and flow signals measured by means of forced oscillation techniques

This paper aims to give a proof-of-concept for the possible application of the forced oscillation lung function test to assess the viscoelastic properties of the airways and tissue. In particular, a novel signal processing algorithm is employed on non-stationary, noisy, (relatively) short time series of respiratory pressure and flow signals. This novel technique is employed to filter the useful information from the signals acquired under two measurement conditions: pseudo-functional residual capacity (PFRC) and pseudo-total lung capacity (PTLC). The PFRC is the measurement performed at lowest lung volume with maximum deflation, and the PTLC is measurement performed at the maximum lung volume under maximum inflation. The results suggest that the proposed technique is able to extract information on the viscoelastic properties of the lung tissue at a macroscopic level. The conclusion of this preliminary study is that the proposed combination of signal processing method and lung function test is suited to be employed on a large database in order to deliver reference values and perform further statistical analysis