Papers by Vairis Shtrauss
Inverse problems of performing integral transforms with kernels depending on the division or prod... more Inverse problems of performing integral transforms with kernels depending on the division or product of arguments are considered in the study of linear viscoelastic behaviour of solid materials. Mechanism of arising instability of the solution is disclosed. An approach of solving the inverse problems is proposed by combining the logarithmic transformation of signal scale with digital filtering and utilizing sampling as a regularization tool to minimize output error. As an example, inherently ill-conditioned problem of the relaxation analysis is considered.
WIT transactions on engineering sciences, 1970
Inverse problems of performing integral transforms with kernels depending on the
division or pro... more Inverse problems of performing integral transforms with kernels depending on the
division or product of arguments are considered in the study of linear viscoelastic
behaviour of solid materials. Mechanism of arising instability of the solution is
disclosed. An approach of solving the inverse problems is proposed by combining the
logarithmic transformation of signal scale with digital filtering and utilizing
sampling as a regularization tool to minimize output error. As an example,
inherently ill-conditioned problem of the relaxation analysis is considered.
WSEAS Transactions on Signal Processing archive, Feb 1, 2008
Decomposition of multi-exponential and related signals is generalized as an inverse filtering pro... more Decomposition of multi-exponential and related signals is generalized as an inverse filtering problem on a logarithmic time or frequency scale, and discrete-time filters operating with equally spaced data on a logarithmic scale (geometrically spaced on linear scale) are proposed for its implementation. Ideal prototypes, algorithms and types of filters are found for various time-and frequency-domain mono-components. It is disclosed that the ill-posedness in the decomposition originates as high sampling-rate dependent noise amplification coefficients arising from the large areas under the increasing frequency responses. A novel regularization method is developed based on the noise transformation regulation by filter bandwidth control, which is implemented by adaptation of the appropriate sampling rate. Algorithm design of decomposition filters is suggested joining together signal acquisition, regularization and discrete-time filter implementation. As an example, decomposition of a frequency-domain multi-component signal is considered by a designed filter.
Journal of Non-crystalline Solids, Dec 1, 2007
Determination of the distribution of relaxation times (DRT) from a wide variety of the time-and t... more Determination of the distribution of relaxation times (DRT) from a wide variety of the time-and the frequency-domain material functions, such as polarization current and charge, real and imaginary parts of complex dielectric permittivity and complex dielectric modulus, the appropriate mechanical and magnetic counterparts is generalized as a filtering problem on a logarithmic time or frequency scale. Algorithms of the appropriate digital DRT estimators are derived. A novel regularization strategy is proposed based on choosing sampling rate for the input data, which ensures acceptably low random error of the recovered spectra. Optimum frequency ranges and sampling rates are found for determination of the relaxation spectrum from the real part of complex permittivity and complex modulus. A multi-filter DRT recovery strategy is suggested by a bank of filters with different smoothing abilities.
Signal Processing, Oct 1, 2006
It is shown that relaxation data conversion by the Kramers-Kronig (KK) relations can be treated a... more It is shown that relaxation data conversion by the Kramers-Kronig (KK) relations can be treated as a filtering problem of band-unlimited relaxation signals in the Mellin transform domain. Based on this concept, KK relations are implemented in the form of FIR filters with the logarithmic sampling. It is demonstrated that KK transformers have sampling rate dependent impulse and frequency responses and only calculation of the imaginary part from the real part can be implemented by a computationally realisable filter. The performance of different types of transformers is studied. Approximately inversely proportional relationship is established between the error and the frequency range of input signal used for computing an output sample. It is found that transformers with even number of coefficients provide better performance than those having an odd number if input data are available within a frequency range wider than four decades. Usage of additional transformers with the shifted or shortened impulse responses is investigated for eliminating shortening of usable output sequence due to filter delay. The simulation results are provided for an elementary relaxation system (a single Debye relaxation) and systems described by the Havriliak-Negami dispersion relation. Some known numerical KK transform techniques are analysed in the functional filtering context.
Structural evaluation of materials by artificial neural networks
Mechanics of Composite Materials, 1999
It is shown that due to the complexity of interaction of the excitation field with a material in ... more It is shown that due to the complexity of interaction of the excitation field with a material in determining its physical characteristics, as well as sophisticated correlation relationships between the physical characteristics and structure of a real material, in many cases, relization of the structural evaluation of materials on the basis of idealized mathematical models of the underlying physical processes is of limited use. As an alternative, it is proposed to use an artificial neural network for the extraction of quantitative information of interest from measurements of the physical characteristics. A general overview of artificial neural networks is given. A methodology of the use of a multilayer perceptron for determining various structural parameters from the dielectric spectra is described. As an example, determination of the moisture content and density of sawdust from the dielectric modulusis considered by the neural-network technique. The noise performance of the neural network is analyzed by applying an additive and multiplicative noise to the input data.
Journal of Non-newtonian Fluid Mechanics, May 1, 2010
The article is devoted for the determination of the relaxation and retardation spectrum (RRS) fro... more The article is devoted for the determination of the relaxation and retardation spectrum (RRS) from monotonic time-and frequency-domain material functions by the inverse functional filters executing discrete convolution algorithms for geometrically spaced data. It is shown that the problem of RRS determination from a wide variety of material functions leads to the three inverse filtering tasks on a logarithmic time or frequency scale with the three specific frequency responses concerning: (i) the time-domain functions, (ii) the real parts and (iii) the imaginary parts of the frequency-domain functions, and three algorithms (having the versions with even and odd number of coefficients) are to be applied to: (i) timedomain compliance and modulus functions, (ii) their derivatives, and (iii) frequency-domain functions. It is demonstrated that ill-posedness of an inverse filter manifests as large sampling-rate-dependent noise amplification coefficients. A novel regularization strategy allowing to ensure the desired noise immunity is proposed based on choosing sampling rate for geometrically spaced data. The performance of the algorithms is investigated. Optimal sampling rates are disclosed for specific material functions. The frequency range of 2-3 decades is established to be optimal for the recovery of a single RRS point estimate ensuring maximum accuracy with reasonable noise immunity. Practical algorithms are proposed for recovering RRS from the real and imaginary parts of frequency-domain functions. Some known non-parametric methods are compared with the suggested functional filters.
Abstract:- The article is devoted to improving quality of decomposition of monotonic multi-compon... more Abstract:- The article is devoted to improving quality of decomposition of monotonic multi-component timeand frequency-domain signals. Decomposition filters operating with data sampled at geometrically spaced times or frequencies (at equally spaced times or frequencies on a logarithmic scale) are combined with artificial neural networks. A nonlinear processing unit, which can be considered as a deconvolution network or a nonlinear decomposition filter, is proposed to be composed from several linear decomposition filters with common inputs, which outputs are nonlinearly transformed, multiplied by weights and summed. One of the fundamental findings of this study is a square activation function, which provides some useful features for the decomposition problem under consideration. First, contrary to conventional activation functions (sigmoid, radial basis functions) the square activation function allows to recover sharper peaks of distributions of time constants (DTC). Second, it ensur...
Abstract-Decomposition of multi-exponential and related signals is generalized as a filtering pro... more Abstract-Decomposition of multi-exponential and related signals is generalized as a filtering problem on a logarithmic time or frequency scale and finite impulse response (FIR) filters operating with logarithmically sampled data are proposed to use for its implementation. The filter types and algorithms are found for various time-domain and frequency-domain mono-components. It is established that the ill-posedness of the multi-component decomposition manifests as high sampling-rate dependent noise amplification coefficients. A regularization method is proposed based on noise transformation control by choosing an optimum sampling rate. Algorithm design is suggested integrating together the signal acquisition, the regularization and the discrete-time filter implementation. As an example, the decomposition of a frequencydomain multi-component signal is considered by a designed discretetime filter.
Abstract:- Decomposition of multi-exponential and related signals is generalized as an inverse fi... more Abstract:- Decomposition of multi-exponential and related signals is generalized as an inverse filtering problem on a logarithmic time or frequency scale, and discrete-time filters operating with equally spaced data on a logarithmic scale (geometrically spaced on linear scale) are proposed for its implementation. Ideal prototypes, algorithms and types of filters are found for various time- and frequency-domain mono-components. It is disclosed that the ill-posedness in the decomposition originates as high sampling-rate dependent noise amplification coefficients arising from the large areas under the increasing frequency responses. A novel regularization method is developed based on the noise transformation regulation by filter bandwidth control, which is implemented by adaptation of the appropriate sampling rate. Algorithm design of decomposition filters is suggested joining together signal acquisition, regularization and discrete-time filter implementation. As an example, decomposit...
Decomposition of multi-exponential and related signals is generalized as a filtering problem on a... more Decomposition of multi-exponential and related signals is generalized as a filtering problem on a logarithmic time or frequency scale and FIR filters operating with logarithmically sampled data are proposed to use for its implementation. The filter algorithms and types are found for various time-domain and frequency-domain mono-components. It is demonstrated that the ill-posedness in the multi-component decomposition manifests as high sampling-rate dependent noise amplification coefficients. The noise transformation control of a filter is provided by algorithm design, which integrates together the signal acquisition, the discrete-time filter design and the regularization based on choosing an optimum sampling rate. As an example, an algorithm is designed for the decomposition in the frequency-domain.
WSEAS Transactions on Signal Processing archive, 2017
The paper is devoted to the determination of the real and imaginary parts from the magnitude resp... more The paper is devoted to the determination of the real and imaginary parts from the magnitude responses for causal linear time-invariant systems having monotonic impulse responses. We demonstrate that the problem can be considered as a special filtering task in the Mellin transform domain having a diffuse magnitude response. The theoretical background is given for the separating the magnitude response into the real and imaginary parts by discrete-time Mellin convolution filters processing geometrically sampled magnitude responses and the appropriate finite impulse response (FIR) filters are designed. To compensate exponential shortening frequency ranges of the real and imaginary parts due to the end-effects of FIR filters processing geometrically sampled magnitude responses, the multiple filtering mode is used, where the sets of the first and last input samples are repeatedly processed by the filters having impulse responses with the shifted origins, which gradually vary the number o...
It is shown that the conventional sampling schemes are of limited use for conversion of monotonic... more It is shown that the conventional sampling schemes are of limited use for conversion of monotonic long-time-interval and wide-frequency-band data of relaxation experiments, which can be measured over many decades of time or frequency. The problem of sampling is considered in combination with designing the discrete-time algorithms for relaxation data conversion has been generalized as a convolution on a logarithmic scale, for which implementation discrete-time filters with the logarithmic sampling are proposed. It is demonstrated that the sampling rate has a direct influence on the performance of the discrete-time filters to govern the potential accuracy and noise behaviour. A pragmatic approach is proposed for choosing sampling rate based on ensuring the maximum accurate output signal with the acceptable random error (noise). The optimum sampling is searched for an inverse filter executing the ill-posed inversion of an integral transform for determination of relaxation spectrum wher...
The paper is devoted to improving and simplifying determination of the relaxation and retardation... more The paper is devoted to improving and simplifying determination of the relaxation and retardation spectrum (RRS). A concept is postulated that determination of RRS from some specially selected material responses differing from the explicitly defined material functions, such as the real or imaginary parts of complex compliance and complex modulus, may improve the recovery performance at the price of better measurability of these specific material responses. As one of possible implementations of the postulated concept, we propose to recover RRS from the modulus (absolute value) of a complex frequency-domain (dynamic) material function, which, compared to the real or imaginary part, can be more accurately and easy acquired by measuring the amplitudes of harmonic responses of a material. It is demonstrated that RRS recovery problem from the modulus of a complex frequency-domain material function may be interpreted as a filtering task with a diffuse magnitude response bounded by the resp...
Inversion of convolution transforms is considered by FIR filters for aperiodic bandand time-unlim... more Inversion of convolution transforms is considered by FIR filters for aperiodic bandand time-unlimited signals from the perspective attaining maximum accurate inverted waveforms with controllable noise amplification of the filter . The difficulties hampering to gain this goal, such as a lack of knowledge how the digital filter shall deviate from ideal one to produce waveforms as accurately as possible, complexity to choose optimal sampling rate, necessity to sacrifice the accuracy for suppressing noise, etc. are analysed. Based on learning in the input-output signal domain and controlling noise amplification by varying sampling rate, an approach is developed for designing maximum accurate filters, which are specified only by two user’s relevant parameters: (i) the desired noise gain and (ii) the continuous time support. Implementation of the approach is ill ustrated by designing a digital differentiator for the logarithmic derivative and a digital estimator of the distribution of rel...
Dielectric Permittivity of Rigid Rapeseed Oil Polyol Polyurethane Biofoams and Petrochemical Foams at Low Frequencies
Journal of Renewable Materials, 2020
Asymmetric filtering algorithms with the shifted origins (zero points) of impulse responses are p... more Asymmetric filtering algorithms with the shifted origins (zero points) of impulse responses are proposed to use for expanding time intervals of the relaxation and retardation spectra (RRS) and increasing density of spectrum points. A filter bank is presented recovering RRS from the real part of complex compliance recorded at frequencies spaced geometrically with progression ratio 2, which produces the spectrum points with doubled density over the retardation time interval 4 times exceeding the reciprocal frequency range. Key-Words: Relaxation and Retardation Spectrum (RRS), Geometric Sampling, Symmetric and Asymmetric RRS Recovery Filters, Filter Bank
The paper is devoted to finding ways for improving resolution and accuracy for decomposition of m... more The paper is devoted to finding ways for improving resolution and accuracy for decomposition of monotonic time- and frequency-domain multi-component signals. For solving the problem, a nonlinear decomposition filter is proposed operating with equally spaced data on a logarithmic time or frequency scale (geometrically spaced on linear scale), which is implemented as a parallel connection of several linear filters, which output signals are transformed by a nonlinear activation function, multiplied by weights and summed. One of the fundamental findings of this study is a square activation function, which ensures physically justified nonnegativity for the recovered distributions of time constants (DTC). It is found that the nonlinear decomposition filter under consideration transforms the Gaussian input noise into the nonnegative output noise with a specific probability distribution having the standard deviation and the mean proportional to the variance of input noise. For most practica...
The article is devoted to improving quality of decomposition of monotonic multi-component time-an... more The article is devoted to improving quality of decomposition of monotonic multi-component time-and frequency-domain signals. Decomposition filters operating with data sampled at geometrically spaced times or frequencies (at equally spaced times or frequencies on a logarithmic scale) are combined with artificial neural networks. A nonlinear processing unit, which can be considered as a deconvolution network or a nonlinear decomposition filter, is proposed to be composed from several linear decomposition filters with common inputs, which outputs are nonlinearly transformed, multiplied by weights and summed. One of the fundamental findings of this study is a square activation function, which provides some useful features for the decomposition problem under consideration. First, contrary to conventional activation functions (sigmoid, radial basis functions) the square activation function allows to recover sharper peaks of distributions of time constants (DTC). Second, it ensures physica...
The paper is addressed to increasing the accuracy of discrete-time computation of linear rheologi... more The paper is addressed to increasing the accuracy of discrete-time computation of linear rheological and viscoelastic material functions belonging to the class of smooth non-bandlimited (NBL) signals. It is demonstrated that the ideology of classical discrete-time processing, which is based on preserving accurate spectrum over the Nyquist frequency band, ignores the anti-aliasing distortion caused by removal of a signal portion above the Nyquist frequency needed for preserving accurate spectrum and, so, gives the inadequate accuracy evaluation of computed material functions. To ensure the adequate accuracy evaluation of NBL material functions, we propose to waive the criterion of preserving accurate spectrum over the Nyquist frequency band, but instead to use the criterion of maintaining accurate shape of a material function in the time-domain. Both the criteria are compared and the appropriate error models are developed and investigated. Increase of accuracy of filtering algorithms...
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Papers by Vairis Shtrauss
division or product of arguments are considered in the study of linear viscoelastic
behaviour of solid materials. Mechanism of arising instability of the solution is
disclosed. An approach of solving the inverse problems is proposed by combining the
logarithmic transformation of signal scale with digital filtering and utilizing
sampling as a regularization tool to minimize output error. As an example,
inherently ill-conditioned problem of the relaxation analysis is considered.