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3rd International Conference on Chemical Engineering and Advanced Materials (CEAM 2013)

作者： Liu, Wenbo Lu, Laijun Jilin Univ Coll Earth Sci Changchun 130023 Peoples R China

ISBN: (纸本)9783037858141

In mineral resources prediction and other research of geological variables, stability exactness of quantitative models concern modeling conditions, geological variables from model and the status of the variable. In traditional geological modeling process, variable support is measured under some contrains weight and this kind of weight is characterized by constant coefficients. Constant weight([1]) has some limitations due to structuredness and dependency of variable. For overcoming the inflexibility of constant weight, this paper proposes geological variable mathematics model basedd state variable vector. We revise existing form of state variable weight and provide logarithm state variable vector as measurement level of geological variable weight coefficients. According to 1:200000 scale geochemistry measured data from Baishan area, we calculate the samples unit connection degree based on exponent and logarithm state variable vector and compare the connection degree based on constant weight. The connection degree sorting has the similarity as a whole among them, but there is the obvious difference locally. We can conclude that geological variable weight function based on state variable vector is more flexible and fine.

关键词： geological modeling state variable vector sample connection degree variable weight function

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The Chebyshev Approximation by the Logarithm of a Rational Expression

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CYBERNETICS AND SYSTEMS ANALYSIS 2025年第1期61卷 77-85页

作者： Malachivskyy, P. S. Melnychok, L. S. NAS Ukraine Pidstryhach Inst Appl Problems Mech & Math Lvov Ukraine

The authors propose a method for constructing the Chebyshev approximation with an absolute error by the logarithm of a rational expression. It intends to build the intermediate Chebyshev approximation with a relative error of the exponent of the approximated function by a rational expression. The approximation by the rational expression is calculated as the boundary of mean-power approximation using an iterative scheme based on the least squares method with two variable weight functions. The results of solving the test examples confirm the fast convergence of the method.

关键词： Chebyshev approximation by logarithmic expression approximation by rational expression mean-power approximation least squares method variable weight function

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Chebyshev Approximation of functions of Several variables

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CYBERNETICS AND SYSTEMS ANALYSIS 2020年第1期56卷 118-125页

作者： Malachivskyy, P. S. Pizyur, Ya. V. Malachivskyi, R. P. Ukhanska, O. M. Natl Acad Sci Ukraine Pidstryhach Inst Appl Problems Mech & Math Lvov Ukraine Natl Univ Lviv Polytech Lvov Ukraine Lohika Syst Lvov Ukraine

The authors propose an algorithm to construct Chebyshev approximation for functions of several variables by a generalized polynomial as a limiting approximation in the norm of space L-p as p -> infinity. It is based on serial construction of power-average approximations using the least squares method with variable weight function. The convergence of the method provides an original way to consistently refine the values of the weight function, which takes into account the results of approximation at all previous iterations. The authors describe the methods of calculating the Chebyshev approximation with absolute and relative errors. The results of test examples confirm the efficiency of using the method to obtain Chebyshev approximation of tabular continuous functions of one, two, and three variables.

关键词： functions of several variables Chebyshev (uniform) approximation power-mean approximation least squares method variable weight function

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Chebyshev Approximation of Multivariable functions by the Exponential Expression

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CYBERNETICS AND SYSTEMS ANALYSIS 2021年第3期57卷 429-435页

作者： Malachivskyy, P. S. Melnychok, L. S. Pizyur, Ya. V. Natl Acad Sci Ukraine Pidstryhach Inst Appl Problems Mech & Math Lvov Ukraine Lviv Polytech Natl Univ Lvov Ukraine

A method for constructing the Chebyshev approximation of multivariable functions by an exponential expression with a relative error is proposed. It generates an intermediate Chebyshev approximation of the values of the logarithm of a function by a polynomial with the absolute error. An iterative scheme based on the least squares method with a variable weight function is used to construct the Chebyshev approximation of the multivariable functions by a generalized polynomial. The results of solution of the test examples confirm the fast convergence of the method in calculating the parameters of the Chebyshev approximation of the tabular continuous functions of one, two, and three variables.

关键词： Chebyshev approximation by an exponential expression multivariable functions mean-power approximation least squares method variable weight function

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Chebyshev Approximation of a Multivariable function with Reproducing the Values of the function and Its Partial Derivatives

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CYBERNETICS AND SYSTEMS ANALYSIS 2023年第4期59卷 660-671页

作者： Malachivskyy, P. S. Melnychok, L. S. Pizyur, Ya. V. Natl Acad Sci Ukraine Pidstryhach Inst Appl Problems Mech & Math Lvov Ukraine Lviv Polytech Natl Univ Lvov Ukraine

The method for constructing the Chebyshev approximation of a discrete multivariable function with reproducing the values of the function and its partial derivatives at given points is proposed. The method is based on constructing a boundary mean-power approximation with appropriate interpolation conditions. The authors use an iterative scheme based on the least squares method with a variable weight function for constructing the mean-power approximation. The results of approximating the one-variable function confirm the fulfillment of the characteristic feature of the Chebyshev approximation with the reproduction of the function and its derivative values at given points. The test examples instantiate the fast convergence of the proposed method.

关键词： Chebyshev approximation Chebyshev approximation with the condition multivariable functions mean-power approximation least squares method variable weight function partial derivatives

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Chebyshev Approximation of Multivariable functions by a Logarithmic Expression

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CYBERNETICS AND SYSTEMS ANALYSIS 2023年第2期59卷 317-324页

作者： Malachivskyy, P. S. Melnychok, L. S. Pizyur, Ya. V. Natl Acad Sci Ukraine Pidstryhach Inst Appl Problems Mech & Math Lvov Ukraine Lviv Polytech Natl Univ Lvov Ukraine

The method for constructing the Chebyshev approximation of multivariable functions by a logarithmic expression with an absolute error is proposed. It implies constructing an intermediate Chebyshev approximation of the values of the exponent of an approximated function by a polynomial with the relative error. The construction of the Chebyshev approximation by a polynomial is based on calculating the boundary mean-power approximation by an iterative scheme based on the least squares method with properly formed values of variable weight function. The presented results of test examples' solving confirm the fast convergence of the method in calculating the parameters of the Chebyshev approximation of the functions of one, two, and three variables by the logarithmic expression.

关键词： Chebyshev approximation of the multivariable functions logarithmic expression mean-power approximation least squares method variable weight function

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Chebyshev Approximation of Multivariable functions by a Power Expression

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CYBERNETICS AND SYSTEMS ANALYSIS 2024年第4期60卷 571-578页

作者： Malachivskyy, P. S. Melnychok, L. S. Pizyur, Ya. V. Natl Acad Sci Ukraine Pidstryhach Inst Appl Problems Mech & Math Lvov Ukraine Lviv Polytech Natl Univ Lvov Ukraine

The paper proposes the method for constructing Chebyshev approximation of multivariable functions with a relative error using a power expression. It involves building an intermediate Chebyshev approximation of values rooted to the corresponding degree of the approximated function by a polynomial with a relative error. Parameters for the polynomial approximation are computed as the boundary mean-power approximation through an iterative scheme using the least squares method with a variable weight function. The authors provide test examples, confirming the fast convergence of the method for constructing the Chebyshev approximation for the functions of one, two, and three variables using power expression.

关键词： Chebyshev approximation of multivariable functions power expression mean-power approximation least squares method variable weight function

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Chebyshev Approximation of Multivariable functions by a Constrained Rational Expression

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CYBERNETICS AND SYSTEMS ANALYSIS 2023年第1期59卷 146-155页

作者： Malachivskyy, P. S. Melnychok, L. S. Pizyur, Ya. V. Natl Acad Sci Ukraine Pidstryhach Inst Appl Problems Mech & Math Lvov Ukraine Lviv Polytech Natl Univ Lvov Ukraine

The authors propose a method for constructing the Chebyshev approximation of multivariable functions by the rational expression with the interpolation condition. The idea of the method is based on constructing the limiting power mean approximation by a rational expression with an interpolation condition in the norm of space L-p as p -> infinity. To construct such an approximation, an iterative scheme based on the least squares method with two variable weight functions is used. One weight function ensures the construction of a power mean approximation with the interpolation condition, and the second one specifies the parameters of the rational expression according to its linearization scheme. The convergence of the method is provided by the original method of sequential specification of the values of weight functions, which takes into account the approximation results at previous iterations. The results of test examples confirm the fast convergence of the proposed method of constructing the Chebyshev approximation by a rational expression with a condition.

关键词： Chebyshev approximation by a rational expression constrained Chebyshev approximation multivariable functions power mean approximation least squares method variable weight function

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Health status perception of oil-immersed power transformers considering wind power uncertainty

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ELECTRIC POWER SYSTEMS RESEARCH 2024年 234卷

作者： Yi, Lingzhi Su, Xingren Wang, Yahui Xu, Xunjian Liu, Jiangyong She, Haixiang Xiangtan Univ Coll Automat & Elect Informat Xiangtan 411105 Hunan Peoples R China Hunan Engn Res Ctr Multienergy Cooperat Control Te Xiangtan 411105 Hunan Peoples R China Key Lab Open Project Fund Disaster Prevent & Mitig Changsha 410000 Hunan Peoples R China Puer infrastructure Sect China Railway Kunming Grp Kunming 665000 Yunnan Peoples R China

The power transformer is the most important and critical component in the power grid of the electrical system. Its safe and stable operation is of great significance for the reliable transmission of renewable energy generation and the reliable power supply to end users. With the continuous development of new types of power systems, the load of the power system undergoes drastic changes, resulting in increased volatility and instability, which leads to issues such as overload, harmonics, and short circuits in transformers. Therefore, in order to accurately assess the operating status of transformers and promptly identify any existing conditions, a method is proposed in this paper. This method uses an optimal cloud entropy parameter calculation method and a variable weighting method to optimize the gray-cloud evidence model. Through a novel multi-source information fusion method, the results of various test items are fused to obtain the state awareness results. Meanwhile, different evaluation indicators are selected for different levels of renewable energy penetration and compared with other methods. The results are validated through examples, demonstrating that the method proposed in this paper can accurately reflect the operating status of transformers and has good scalability.

关键词： Power transformer State perception New power system Modeling of ash cloud evidence variable weight function

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