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Technology of Cut-Glue Approximation Method for Modeling Strongly Nonlinear Multivariable Objects. Theoretical Bases and Prospects of Practical Application
Technical Paper
2016-01-2035
ISSN: 0148-7191, e-ISSN: 2688-3627
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English
Abstract
The main difficulties of the mathematical models vehicles creation are defined by strongly nonlinearity of dependences which connect various variables their states and conditions of the movement environment. Most it belongs to aircrafts as aerodynamic interactions are characterized by essential nonlinearity up to discontinuity of variables and their derivatives. Creation process of these models is complicated by high-dimensionality, characteristic for the mechanical movement laws. Experimental creation of the mathematical models (MM) of such dependences is carried out by various mathematical methods of approximation of data. Universal remedies of the solution of the formulated task don't exist. Each of it possesses both benefits, and considerable shortcomings.
In this regard the possibilities of a method creation of high-precision analytical approximations of the strongly nonlinear dependences using the analytical functions have been investigated. The Cut-Glue approximation (CGA) method for one-dimensional dependences is justified, and then this method is developed for approximation by functions of two arguments. In this method approximation is carried out by splitting of data into fragments similarly as in the method of piecewise approximation. Each data fragment is approximated by suitable function from which along its borders is cut out a fragment of this function. Cutting out of the function fragment is carried by multiplication its on the other nonlinear function with special characteristics. Properties of a nonlinear multiplier are such that in borders of a fragment of its value coincide with the approximating function, but are almost equal to zero in other range of definition. The received fragments are glued together in the united function which is model of the overall approximated dependence. The advantage of the Cut-Glue approximation method is differentiability of the mathematical models. It gives the chance to investigate functions analytically and to use their in MM of dynamics.
In the offered article the possibility of application of a method for creation of nonlinear models of any dimension is proved and the ideology of accomplishment of all stages of "Cut-Glue" approximation is formulated. Tasks of optimum splitting experimental data into fragments, approximations of these fragments by analytical functions and their effective pasting in single in MM are formalized. The received result significantly expands a application area of a method and its opportunity in problems of mathematical modeling of dynamics of aircrafts and vehicles in general. Possibilities of optimal multidimensional "Cut-Glue" of approximation are illustrated by an example.
Authors
Citation
Neydorf, R. and Neydorf, A., "Technology of Cut-Glue Approximation Method for Modeling Strongly Nonlinear Multivariable Objects. Theoretical Bases and Prospects of Practical Application," SAE Technical Paper 2016-01-2035, 2016, https://doi.org/10.4271/2016-01-2035.Also In
References
- Rawlings John O. , Pantula Sastry G. , Dickey David A. Applied Regression Analysis: A Research Tool Second 1998
- Bates , Douglas M. Nonlinear regression analysis and its applications Bates Douglas M. , Watts Donald G. John Wiley & Sons New York 1988 365
- Drapper , N.R. Applied regression analysis 1 Drapper N.R. , Smith H. John Wiley & Sons New York 1981 366
- Drapper , N.R. Applied regression analysis 2 Drapper N.R. , Smith H. John Wiley & Sons New York 1981 351
- Vilmos Totik Orthogonal Polynomials Surveys in Approximation Theory 1 2005 70 125
- Sergey Khrushchev Orthogonal Polynomials and Continued Fractions From Euler’s Point of View Atilim University, Turkey Cambridge University Press 2008 www.cambridge.org/9780521854191
- Recent Developments In Generalized Analytic Functions And Their Applications Giorgadze G. 2011
- Loran P.-J. Approximation and optimization 1975 496
- Лоран П.-Ж. Аппроксимация и оптимизация: Пер 1975 496
- Alberg J. Splines theory and its applications 1972 318
- Альберг Дж. Теория сплайнов и ее приложения/ Дж 1972 318
- De Boor , C. A practical guide to splines Springer 1978
- Multiquadric Radial Basis Function Approximation Methods for the Numerical Solution of Partial Differential Equations Sarra Scott A. , Marshall University and Kansa Edward J. University of California Davis June 30 2009 220 www.ScottSarra.org/math/math.html
- Buhmann , M.D. Radial Basis Functions: Theory and Implementations Cambridge University Press 2003
- Neydorf R.A. Approximating creation of mathematical models on dot experimental data by cut-glue method DSTU bulletin 2014 14 1 45 58
- Нейдорф Р.А. Аппроксимационное построение математи-ческих моделей по точечным экспериментальным данным методом "cut-glue" Вестник ДГТУ 2014 14 1 45 58
- Neydorf R.A. Proceedings of the ASME-IMECE 2014-37236 November 14-20, 2014 Montreal, Quebec, Canada
- Neydorf , R. Bivariate “Cut-Glue” Approximation of Strongly Nonlinear Mathematical Models Based on Experimental Data SAE Int. J. Aerosp. 8 1 47 54 2015 10.4271/2015-01-2394
- Neydorf , R. and Sigida , Y. Identification of Traction and Power Characteristics of Air-Screw Propulsors in Mathematical Description of Airship SAE Technical Paper 2014-01-2134 2014 10.4271/2014-01-2134
- Neydorf , R. , Sigida , Y. , Voloshin , V. , and Chen , Y. Stability Analysis of the MAAT Feeder Airship During Ascent and Descent with Wind Disturbances SAE Technical Paper 2013-01-2111 2013 10.4271/2013-01-2111
- Voloshin , V. , Chen , Y. , Neydorf , R. , and Boldyreva , A. Aerodynamic Characteristics Study and Possible Improvements of MAAT Feeder Airships SAE Technical Paper 2013-01-2112 2013 10.4271/2013-01-2112
- Pshikhopov , V. , Medvedev , M. , Neydorf , R. , Krukhmalev , V. et al. Impact of the Feeder Aerodynamics Characteristics on the Power of Control Actions in Steady and Transient Regimes SAE Technical Paper 2012-01-2112 2012 10.4271/2012-01-2112
- Pshikhopov , V. , Medvedev , M. , Gaiduk , A. , Neydorf R. , Fe-dorenko , R. , and Krukhmalev , V. Mathematical Model of Robot on Base of Airship 2013 Proceedings of the IEEE Conference on Decision and Control
- Neydorf , R. , Krukhmalev , V. , Kudinov , N. , and Pshikhopov , V. Methods of Statistical Processing of Meteorological Data for the Tasks of Trajectory Planning of MAAT Feeders SAE Technical Paper 2013-01-2266 2013 10.4271/2013-01-2266
- Neydorf , R. , Sigida , Y. , Kudinov , N. , and Portnova , E. Aerostatic Aircraft Flight Environment Modeling and Investigation SAE Technical Paper 2014-01-2147 2014 10.4271/2014-01-2147
- Neydorf , R.A. Algorithms of statistical processing of the mete-odata for problems of the aircraft simulated test Neydorf R.A. , Sigida Ju.L. Actual problems of humanitarian and natural sciences 12 2013 109 114
- Нейдорф Р.А. Алгоритмы статистической обработки метеоданных для задач имитационного испытания летательных аппаратов Нейдорф Р.А. , Сигида Ю.Л. Актуальные проблемы гуманитарных и естественных наук 12 2013 109 114
- Neydorf , R. , Novikov , S. , and Fedorenko , R. Continuous-Positional Automatic Ballonet Control System for Airship 2013 SAE International Journal of Aerospace 1946-3855 6 2 2013
- Neydorf , R. , Novikov , S. , and Kudinov , N. Airship Positioning Fuzzy Multi-Ballonet Control Study SAE Technical Paper 2014-01-2146 2014 10.4271/2014-01-2146
- Pshikhopov , V. , Krukhmalev , V. , Medvedev , M. , and Neydorf , R. Estimation of Energy Potential for Control of Feeder of Novel Cruiser/Feeder MAAT System SAE Technical Paper 2012-01-2099 2012 10.4271/2012-01-2099