Carreau's Rheological Model and A.N. Tikhonov’s Regularization Method: Parametric Identification Based on a CFD model

Introduction. Carreau's rheological model can describe the three-dimensional flows of non-Newtonian media. However, it requires modeling parameters for the viscosity of the medium at the limiting values of shear rates, which cannot be achieved by instrumental methods. The present article introduces a novel method that can identify the parameters of Carreau’s model using a regularization algorithm. Study objects and methods. The study featured fondant mass produced according to the traditional formulation for Creamy Fondant unglazed candies. Standard methods were used to describe the properties of the raw materials and semi-finished products, as well as methods of mathematical processing, modeling, and optimization. Results and its discussion. The research produced an algorithm based on A.N. Tikhonov’s regularization method of the parametric identification of Carreau's rheological model. The calculation residual was minimized by the viscometric measurements and the CFD model, which provided the calculation of the hydrodynamic flow regime at the limiting values of shear rates. The CFD model of a steady non-isothermal flow of a nonlinear viscous medium through a cylindrical capillary was based on the equations of conservation of mass, energy, and momentum. The rheological parameters of Carreau’s model were illustrated by the case of fondant mass. The error for the viscosity prediction did not exceed 14.07%. Conclusion. The parametric identification algorithm made it possible to evaluate the rheological parameters of structured liquid media with Carreau's rheological law in cases that lack experimental information on the behavior of the medium at limiting shear rates. The algorithm eliminated the computational problems typical of Ostwald and de Ville’s rheological model, which usually arise when solving practical problems of three-dimensional flows of non-Newtonian media with limiting viscosity values.

Scale experimental measurement of impulse response UWB emitters.

This work presents the results of experimental measurements of the impulse response of ultra-wideband emitters: a biconical antenna and a symmetrical dipole. A measurement technique was presented. The channel impulse response is calculated using Tikhonov’s regularization. It is shown that the measured signal corresponds to calculated.

On the Method of Determining Onboard Ephemeris Data L1OC and L3OC GLONASS Aimed at Testing Positioning Algorithms in the GNSS Receiver

The paper considers a method of determining GLONASS ephemeris data in the L1OC and L3OC digital form aimed at testing the algorithms of accurate navigation determinations in consumer navigation equipment. The task of determining long-term motion model parameters of a navigation spacecraft is set as nonlinear problem of designing a matching model. This task is unstable and according to the analysis is categorized as incorrect. The application of a traditional least squares method to determine the long-term motion model parameters of a navigation spacecraft does not allow to obtain equally accurate solutions of condition equations system when initial conditions and/ or iterations amount have been changed. In this respect, Tikhonov’s regularization method has been carried out. It is based on the application of additional prior information. The obtained results have been tested by the comparison of estimated navigation spacecraft position according to the adjusted (speed and acceleration) ephemeris data, long-term motion model parameters and SP3 final reference ephemeris published on the SVOEVP website. The long-term motion model parameters of GLONASS navigation spacecraft that were defined by regularizing algorithms, have allowed to calculate the position of navigation spacecraft orbital grouping in terms of four-hours fitting intervals within 0,2 m tolerance (maximum deviations according to module of estimated navigation spacecraft position from SVOEVP SP3 reference ephemeris)

Сравнительный анализ методов решения некорректных обратных задач для многоканальной гиперспектрометрии

A comparative analysis of various implementations of multichannel recording using optical filters is performed to improve the spectral resolution of multichannel hyperspectrometers at maintaining the high spatial resolution. The computing power of different means of multichannel data processing is considered as well. The recovery of spectral brightness density using multichannel recording data is shown to be an incorrect task. The methods proposed to solve it are wavelet transformation, Tikhonov’s regularization approach, and Godunov method. The spectral brightness density is simulated using the multichannel recording results taking into account the measurement error. The applicability limits are established for each method. It is supposed that the Tikhonov method is more resistant to measurement errors. Various approaches for selecting optical filters that participate in the multichannel recording are compared with respect to the final accuracy of spectral brightness density reconstruction using the recording data, which evidences the benefits of the classical method. The optimal combination of the amount of optical filters and the number of recording channels is found as well. The wide application necessitates three channels with four optical filters and eight channels with two optical filters.

Inverse problems of sounding pulse formation in ultrasound tomography: mathematical modeling and experiments

Статья посвящена разработке методов формирования акустических зондирующих импульсов в задачах ультразвуковой томографии. Обратная задача формирования акустических зондирующих импульсов рассматривается в рамках линейной модели. Эта задача является некорректной и требует использования регуляризирующих алгоритмов. Для численного решения использована тихоновская схема регуляризации. Разработанные алгоритмы протестированы на решении модельных задач и с помощью специально поставленного эксперимента, в котором акустический тракт включает в себя цифровой генератор импульсов, усилитель, источник акустического излучения, акустический детектор, предусилитель и аналого-цифровой преобразователь. Экспериментально подтверждены как адекватность линейной модели, так и высокая эффективность предложенных алгоритмов. This paper is concerned with developing the methods of forming acoustic sounding pulses in ultrasound tomography applications. The inverse problem of forming acoustic sounding pulses is considered in the framework of linear models. This problem is ill-posed and requires the use of regularizing algorithms. Tikhonov's regularization scheme is used to solve the problem numerically. The developed algorithms are tested on model problems as well as on experimental data. In the experimental setup, the acoustic path includes a digital waveform generator, an amplifier, an ultrasound emitter, a hydrophone with a preamplifier, and an analog-digital converter. The applicability of the linear model and the efficiency of the proposed algorithms are substantiated experimentally.

Existence of variational source conditions for nonlinear inverse problems in Banach spaces

Variational source conditions proved to be useful for deriving convergence rates for Tikhonov’s regularization method and also for other methods. Up to now, such conditions have been verified only for few examples or for situations which can be also handled by classical range-type source conditions. Here we show that for almost every ill-posed inverse problem variational source conditions are satisfied. Whether linear or nonlinear, whether Hilbert or Banach spaces, whether one or multiple solutions, variational source conditions are a universal tool for proving convergence rates.

Preliminary Results of Integrating Tikhonov’s Regularization in Forward-Backward Time-Stepping Technique for Object Detection

The inverse scattering in time domain known as Forward-Backward Time-Stepping (FBTS) technique is applied to determine the sizes, shape and location of the embedded objects. Tikhonov’s regularization method has been proposed in order to improve or solve the ill-posed of FBTS inverse scattering problem. The reconstructed results showed that FBTS technique can detect the presence of embedded objects. The reconstructed results of FBTS technique utilizing with the Tikhonov’s regularization method shown better results than the results only applied FBTS technique. Tikhonov’s regularization combined with FBTS technique to improve the quality of image reconstruction.