Estimation of the activity of lead in the binary Pb-Sb and Pb-Bi systems

The activity of lead in its alloys with bismuth and antimony is estimated by the least squares method and interval analysis. The interval method of processing the experimental results is shown to calculate the reliable ranges of the estimated parameters in the dependences of thermodynamic functions and the actual level of the total measurement errors. © 2013 Pleiades Publishing, Ltd

In system identification, interval (and fuzzy) estimates can lead to much better accuracy than the traditional statistical ones: General algorithm and case study

In many real-life situations, we know the upper bound of the measurement errors, and we also know that the measurement error is the joint result of several independent small effects. In such cases, due to the Central Limit Theorem, the corresponding probability distribution is close to Gaussian, so it seems reasonable to apply the standard Gaussian-based statistical techniques to process this data - in particular, when we need to identify a system. Yes, in doing this, we ignore the information about the bounds, but since the probability of exceeding them is small, we do not expect this to make a big difference on the result. Surprisingly, it turns out that in some practical situations, we get a much more accurate estimates if we, vice versa, take into account the bounds - and ignore all the information about the probabilities. In this paper, we explain the corresponding algorithms. and we show, on a practical example, that using this algorithm can indeed lead to a drastic improvement in estimation accuracy. © 2017 IEEE

Criteria for analysis and comparison of experimental data under conditions of uncertainty

The paper deals with investigation of the important problem of processing the ophthalmic data on the post-operation status of patients. The groups of patients differ by the type (technology) of fixing the intraocular lenses (IOL). Validity of each type of technology is estimated by computation of criteria for distinction of data between groups. The initial information comprises measurements of several ophthalmic indices. The samples on each index are very short; in each index, as a rule, the samples of patients' groups overlap each other; any probabilistic characteristics of the measuring indices are unknown; any probabilistic characteristics of the measuring errors are also unknown. So, the standard methods of mathematical statistics can be applied only in the formal way and have shown to be inefficient. In contrast, the Hausdorff distance (from the set theory) as the criterion of distinction between two samples (both for one- and, especially, for two-dimensional indices) demonstrated to be reliable to distinct the patient's status. Computations of the Hausdorff distance are valid for any relative location of point sets under comparison. © 2020 American Institute of Physics Inc.. All rights reserved.The work was supported by the RFBR grant, project no. 18-01-00410

Application of interval analysis to digital procession of data from ship magnetic compass

Поступила: 01.12.2018. Принята в печать: 28.12.2018.Received: 01.12.2018. Accepted: 28.12.2018.В статье описываются результаты применения методов интервального анализа к цифровой обработке реальной зашумленной информации магнитного курса от корабельного цифрового магнитного компаса. Функционирование алгоритмов оценивалось как при постоянном курсе корабля, так и при выполнении им разворота. Показано, что в условиях неопределенности вероятностных характеристик шумовой компоненты в измерении сигнала, интервальный подход обеспечивает существенно лучшую точность обработки по сравнению со стандартным статистическим подходом.The paper presents results of application of interval analysis methods to digital processing of noised data from the ship digital magnetic compass. Noises and chaotic corruptions of the data are stipulated by influence of the ship electric mechanisms and power nets. The problem of processing the noised data is formulated as follows: to filtrate off the noised components and to obtain enhanced estimations of the current magnetic course and its accuracy. Data for processing is presented as a short sample of measurements of the magnetic course and any probability characteristics of the summary noise components are unknown. Actually, only reasonable interval constraints on maximal modulus (bounds) onto these components can be shown. Under such uncertainty conditions, the standard mathematical statistics methods can be applied only in a formal way. As the alternative, methods of Interval Analysis can by used, since they do not need information on the probability characteristics of the noising components. In contrast to the statistical approaches, the interval procedures give the guaranteed information set of the process admissible parameters and the guaranteed interval of values of the current magnetic course. For the user the following information is provided. The central point of such interval is given out as a pointwise estimate of the current course, the half of the interval presents the accuracy of this estimate, and the tube of admissible values of the process under observation is also calculated. Investigations of the elaborated interval algorithms were performed both under the constant course of the ship and under performing the turn maneuver. The real primary data of the ship digital magnetic compass were used. For comparison, estimations were calculated on the basis of formal application of the standard least squares method. It was shown that under mentioned uncertainty conditions the interval approach gives crucially better estimates.Работа выполнена при частичной поддержке РФФИ, проект № 18-01-00410.The work is partly accomplished with the assistance of RFBR, the project № 18-01-00410

Determination of the Growth Time Period of Loose Zinc Deposit Using Interval Analysis Methods

Abstract: A characteristic of obtaining metal powders by direct current electrolysis is changes in the morphology of particles over the loose deposit layer thickness up to the formation of large spherulites. Deposits should be periodically removed from the cathode in order to obtain a powder with homogeneous composition. This paper justifies the choice of the parameter describing the change in loose deposit properties and proposes a method for determining the periodicity of its removal from the cathode. Loose zinc deposits were obtained at 25°C from zincate electrolyte containing 0.3 mol L–1 of ZnO and 4 mol L–1 of NaOH at a current setpoint exceeding six times the limiting diffusion current calculated using the smooth electrode. Electrode potential, deposit thickness and evolved hydrogen volume were measured directly in the process of electrolysis. Current redistribution between the metal reduction and hydrogen evolution leads to a change in the structure of loose deposit particles. It is shown that the differential current efficiency of zinc is the parameter describing the change in the loose zinc deposit density. Its value should not exceed 0.96, in order to ensure deposition of loose deposit with homogeneous properties. A further increase in current efficiency will lead to the formation of aggregates at the deposit growth front. It is proposed to determine the periodicity of loose deposit removal from the cathode using the empirical equation for the time dependency of differential current efficiency of zinc. The mathematical and statistical analysis of the data obtained in six replicates was carried out. The interval approach made it possible to significantly narrow the range of permissible differential current efficiency values and, as a consequence, to determine empirical equation coefficients with acceptable accuracy and calculate the growth time period of a deposit with homogeneous structure. The obtained approach can be used to estimate the time period of loose metal deposition accompanied by hydrogen evolution. © 2020, Allerton Press, Inc.This study was supported by the Government of the Russian Federation, regulation no. 211, state assignment no. 0836-2020-003

Interval approach to processing the noised thermophysical data

The paper deals with application of numerical methods to processing the experimental data on the thermophysical properties of several chemical substances and their compounds (cryolites, rare earth compounds, and alkali halides). The main aim of investigations is in estimating the parameters of dependencies between the heat of fusion and the melting temperature of these chemical substances. The data are corrupted by the measuring errors. Procession is implemented under conditions of uncertainty: there is no any information on probabilistic properties of the corrupting factors, samples of measurements are short, and only approximate functions are known that describes mentioned dependencies. Under such conditions, the standard statistical methods can be applied formally. To obtain guarantied results in parameters estimation, the interval analysis methods and procedures are used. © 2020 American Institute of Physics Inc.. All rights reserved.The work was supported by the RFBR grants, projects nos. 18-01-00410 and 18-03-00785 А

Interval analysis methods in lecture course of digital procession of information

In addition to study of the standard statistical methods, ones of the interval analysis have been introduced into engineering lecture courses joined with digital processing information, parameter and state estimation of corrupted data. The paper introduces materials of the lecture course devoted to robust parameter and state estimation techniques in a bounded-error context in the presence of outliers. Several examples illustrating the course content are given. © 2012 IFAC