Analysis and data processing systems最新文献

{"title":"A parabolic model in the form of space states of the dynamics of savings","authors":"G. Abdenova, K. Bazikova, Zhangul Kenzhegalym","doi":"10.17212/2782-2001-2021-2-7-18","DOIUrl":"https://doi.org/10.17212/2782-2001-2021-2-7-18","url":null,"abstract":"An important place in the theory of partial differential equations and its applications is occupied by the heat equation, a representative of the class of the so-called parabolic equations. It is known that to check the correctness of a mathematical model based on a parabolic equation, the existence of its solution is very important since a mathematical model is not always adequate to a specific phenomenon and the existence of a solution to a corresponding mathematical problem does not follow from the existence of a solution to a real applied problem. Therefore, methods for solving partial differential equations, both analytical and numerical, are always relevant. Nowadays, a computational experiment has become a powerful tool for theoretical research. It is carried out over a mathematical model of the object under study, but at the same time, other parameters are calculated using one of the parameters of the model and conclusions are drawn about the properties of the object or phenomenon under study. The problem of passive parametric identification of systems with distributed parameters for resource accumulation dynamics of many households using a stochastic distributed model in the form of a state space with regard to the white noise of the dynamics model of the object under study and the white noise of the model of a linear-type measuring system is considered in the paper. The use of the finite difference method allowed us to reduce the solution of partial differential equations of a parabolic type to the solution of a system of linear finite difference and algebraic equations represented by models in the form of a state space. It was also proposed to use a filtering algorithm based on the Kalman scheme for reliable estimation of the object behavior. Calculations were carried out using the Matlab mathematical system based on statistical data for five years, taken from the site “Agency for Strategic Planning and Reforms of the Republic of Kazakhstan Bureau of National Statistics”. Estimation of the coefficients of the equations for the household resource accumulation in the form of a state space using this technique is sufficiently universal and can be applied in other fields of science and technology.","PeriodicalId":292298,"journal":{"name":"Analysis and data processing systems","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115826869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Building robust neural networks using different loss functions","authors":"M. Sivak, V. Timofeev","doi":"10.17212/2782-2001-2021-2-67-82","DOIUrl":"https://doi.org/10.17212/2782-2001-2021-2-67-82","url":null,"abstract":"The paper considers the problem of building robust neural networks using different robust loss functions. Applying such neural networks is reasonably when working with noisy data, and it can serve as an alternative to data preprocessing and to making neural network architecture more complex. In order to work adequately, the error back-propagation algorithm requires a loss function to be continuously or two-times differentiable. According to this requirement, two five robust loss functions were chosen (Andrews, Welsch, Huber, Ramsey and Fair). Using the above-mentioned functions in the error back-propagation algorithm instead of the quadratic one allows obtaining an entirely new class of neural networks. For investigating the properties of the built networks a number of computational experiments were carried out. Different values of outliers’ fraction and various numbers of epochs were considered. The first step included adjusting the obtained neural networks, which lead to choosing such values of internal loss function parameters that resulted in achieving the highest accuracy of a neural network. To determine the ranges of parameter values, a preliminary study was pursued. The results of the first stage allowed giving recommendations on choosing the best parameter values for each of the loss functions under study. The second stage dealt with comparing the investigated robust networks with each other and with the classical one. The analysis of the results shows that using the robust technique leads to a significant increase in neural network accuracy and in a learning rate.","PeriodicalId":292298,"journal":{"name":"Analysis and data processing systems","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125824381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Implementation of the adaptive quantization method in digitally controlled measuring generators","authors":"M. Babichev","doi":"10.17212/2782-2001-2021-2-121-134","DOIUrl":"https://doi.org/10.17212/2782-2001-2021-2-121-134","url":null,"abstract":"Measuring generators with digital control, in particular power calibrators, used to calibrate electricity meters, contain a digital-to-analog converter (DAC) that converts codes of the generated signal into voltage. Signal codes are stored in the generator memory. A truncation discreteness error (quantization noise) arises caused by sampling (quantization) in time and by the level of signal samples in the DAC. A relative value of the quantization noise depends on the amplitude of the generated signal (relative to the reference voltage of the DAC): the larger the amplitude, the more significant bits of the DAC are involved in the conversion process, and the less the relative value of the noise. In generators, where the amplitude of the output signal changes over a wide range (high dynamic range) by changing the digital samples of the signal, the quantization noise at low signal amplitudes can become unacceptably large. This situation occurs in power calibrators where the output current changes hundreds of times since the error of the verified electricity meter is normalized in a wide range of current flowing through it. A new algorithm for generating samples of a sinusoidal signal in measuring generators with digital control called adaptive quantization is proposed. Adaptive quantization can significantly improve one of the selected signal parameters (the so-called optimality criterion), for example, reduce the error in reproduction of the first harmonic, or reduce the value of higher harmonic components. In addition, the proposed algorithm reduces the dependence of the selected parameter on the sampling frequency and on the number of DAC bits used, which makes it possible to expand the dynamic range of the generator (in the current channel) without using additional amplifiers with programmable gain (PGA). Studies carried out using computer simulation have confirmed the efficiency of the adaptive quantization algorithm.","PeriodicalId":292298,"journal":{"name":"Analysis and data processing systems","volume":"425 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115251168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}