Integral Equations Related to Volterra Series and Inverse Problems: Elements of Theory and Applications in Heat Power Engineering
The paper considers two types of Volterra integral equations of the first kind, arising in the study of inverse problems of the dynamics of controlled heat power systems. The main focus of the work is aimed at studying the specifics of the classes of Volterra equations of the first kind that arise w...
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| Published in | Mathematics (Basel) Vol. 9; no. 16; p. 1905 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Basel
MDPI AG
01.08.2021
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| Subjects | |
| Online Access | Get full text |
| ISSN | 2227-7390 2227-7390 |
| DOI | 10.3390/math9161905 |
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| Abstract | The paper considers two types of Volterra integral equations of the first kind, arising in the study of inverse problems of the dynamics of controlled heat power systems. The main focus of the work is aimed at studying the specifics of the classes of Volterra equations of the first kind that arise when describing nonlinear dynamics using the apparatus of Volterra integro-power series. The subject area of the research is represented by a simulation model of a heat exchange unit element, which describes the change in enthalpy with arbitrary changes in fluid flow and heat supply. The numerical results of solving the problem of identification of transient characteristics are presented. They illustrate the fundamental importance of practical recommendations based on sufficient conditions for the solvability of linear multidimensional Volterra equations of the first kind. A new class of nonlinear systems of integro-algebraic equations of the first kind, related to the problem of automatic control of technical objects with vector inputs and outputs, is distinguished. For such systems, sufficient conditions are given for the existence of a unique, sufficiently smooth solution. A review of the literature on these problem types is given. |
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| AbstractList | The paper considers two types of Volterra integral equations of the first kind, arising in the study of inverse problems of the dynamics of controlled heat power systems. The main focus of the work is aimed at studying the specifics of the classes of Volterra equations of the first kind that arise when describing nonlinear dynamics using the apparatus of Volterra integro-power series. The subject area of the research is represented by a simulation model of a heat exchange unit element, which describes the change in enthalpy with arbitrary changes in fluid flow and heat supply. The numerical results of solving the problem of identification of transient characteristics are presented. They illustrate the fundamental importance of practical recommendations based on sufficient conditions for the solvability of linear multidimensional Volterra equations of the first kind. A new class of nonlinear systems of integro-algebraic equations of the first kind, related to the problem of automatic control of technical objects with vector inputs and outputs, is distinguished. For such systems, sufficient conditions are given for the existence of a unique, sufficiently smooth solution. A review of the literature on these problem types is given. |
| Author | Bulatov, Mikhail Solodusha, Svetlana |
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| Cites_doi | 10.1109/ICAIIC48513.2020.9065214 10.1023/B:AURC.0000014723.06564.f4 10.1109/ENERGYCON.2010.5771706 10.1016/j.energy.2018.04.061 10.1016/j.ymssp.2016.10.029 10.1109/PTC.2015.7232462 10.1109/ICIEAM.2018.8728575 10.1017/CBO9780511543234 10.1016/j.ifacol.2015.09.320 10.1023/B:AURC.0000019379.43119.d0 10.1137/0727089 10.1080/00207160.2015.1121247 10.1049/icp.2021.1027 10.1134/S1995423918010093 10.1002/mma.4884 10.1134/S0005117909040122 10.15276/eltecs.19.95.2015.65 10.1109/IDAACS.2017.8095251 10.1109/TSP.2017.2777391 10.1134/S0965542513030044 10.24294/tse.v1i1.357 10.1134/S0005117911060099 10.1134/S0005117908040012 10.1109/TPEC48276.2020.9042550 10.1016/j.apnum.2019.06.014 10.1109/SLED-PRECEDE.2013.6684497 10.1134/S0965542507080106 10.1093/imamci/1.3.243 10.3390/en6031385 10.1134/S0005117914010068 10.1016/j.egypro.2017.03.233 10.1051/e3sconf/201913901029 10.1134/S0005117911060142 10.1134/S0965542512050041 |
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| References | ref_50 Shcherbinin (ref_25) 2010; 3 Hadizadeh (ref_65) 2018; 5 ref_14 Apartsyn (ref_24) 1994; 3 ref_57 Filimonova (ref_7) 2017; 111 ref_12 ref_11 Gear (ref_64) 1990; 27 Zadeh (ref_17) 1964; Volume 3 Apartsyn (ref_46) 2004; 65 ref_19 Solodusha (ref_36) 2018; 14 ref_18 ref_15 Sit (ref_6) 2019; 1 Fedorova (ref_37) 2015; 19 Solodusha (ref_41) 2015; 48 Licheng (ref_22) 1996; 7 ref_61 ref_60 Tairov (ref_35) 2011; 3 Solodusha (ref_56) 2014; 75 Zhou (ref_2) 2018; 153 Budnikova (ref_67) 2012; 52 ref_69 ref_68 ref_23 Solodusha (ref_44) 2011; 72 ref_63 ref_62 Magid (ref_34) 1985; 5 Belbas (ref_49) 2011; 217 ref_29 ref_28 Bulatov (ref_74) 2018; 41 ref_26 Solodusha (ref_53) 2009; 70 Apartsyn (ref_39) 2004; 65 Cheng (ref_20) 2017; 87 ref_71 ref_70 Apartsyn (ref_42) 2013; 2 ref_32 ref_30 Solodusha (ref_54) 2018; 11 Bulatov (ref_58) 2001; 6 Shnayder (ref_4) 2011; 32 Bulatov (ref_73) 2013; 53 ref_38 Pishbin (ref_66) 2017; 94 Stegmayer (ref_21) 2004; 3 Boyd (ref_31) 1984; 1 Solodusha (ref_55) 2019; 30 Juravliov (ref_8) 2005; 1 Apartsyn (ref_51) 2008; 69 Apartsyn (ref_52) 2011; 72 Bulatov (ref_72) 2010; 15 ref_45 Fomin (ref_27) 2016; 10 Apartsyn (ref_47) 2007; 47 ref_43 Zhang (ref_5) 2018; 199 Hernandez (ref_10) 2013; 6 Osak (ref_13) 2019; 139 ref_40 Bulatov (ref_75) 2020; 149 ref_1 ref_3 Tairov (ref_33) 1989; 1 Bulatov (ref_59) 1998; 38 ref_9 Burt (ref_48) 2018; 66 Ayalew (ref_16) 2018; 3 |
| References_xml | – ident: ref_11 doi: 10.1109/ICAIIC48513.2020.9065214 – volume: 30 start-page: 73 year: 2019 ident: ref_55 article-title: Identification of input signals in integral models of one class of nonlinear dynamic systems publication-title: Bull. Irkutsk State Univ. Ser. Math. – ident: ref_32 – volume: 199 start-page: 154 year: 2018 ident: ref_5 article-title: A new method for boiler combustion calculation publication-title: Earth Environ. Sci. – volume: 65 start-page: 263 year: 2004 ident: ref_46 article-title: Multilinear Volterra equations of the first kind publication-title: Autom. Remote Control doi: 10.1023/B:AURC.0000014723.06564.f4 – ident: ref_9 doi: 10.1109/ENERGYCON.2010.5771706 – volume: 153 start-page: 638 year: 2018 ident: ref_2 article-title: Affine nonlinear control for an ultra-supercritical coal fired once-through boiler-turbine unit publication-title: Energy doi: 10.1016/j.energy.2018.04.061 – ident: ref_68 – volume: 15 start-page: 3 year: 2010 ident: ref_72 article-title: Variational approaches to numerical solution of differential algebraic equations publication-title: Comput. Technol. – volume: 2 start-page: 16 year: 2013 ident: ref_42 article-title: Modeling of Nonlinear Dynamic Systems with Volterra Polynomials: Elements of Theory and Applications publication-title: Int. J. Energy Optim. Eng. – volume: 87 start-page: 364 year: 2017 ident: ref_20 article-title: Volterra-series-based nonlinear system modeling and its engineering applications: A state-of-the-art review publication-title: Mech. Syst. Signal Process. doi: 10.1016/j.ymssp.2016.10.029 – ident: ref_26 doi: 10.1109/PTC.2015.7232462 – ident: ref_61 – ident: ref_1 – ident: ref_23 – ident: ref_71 – ident: ref_43 doi: 10.1109/ICIEAM.2018.8728575 – ident: ref_69 doi: 10.1017/CBO9780511543234 – volume: 48 start-page: 982 year: 2015 ident: ref_41 article-title: A New Algorithm for Construction of Quadratic Volterra Model for a Non-Stationary Dynamic System publication-title: IFAC Pap. OnLine doi: 10.1016/j.ifacol.2015.09.320 – volume: 3 start-page: 117 year: 2011 ident: ref_35 article-title: Development of methods to simulate the dynamics of heat power engineering plants publication-title: Bull. ISTU – volume: 3 start-page: 28 year: 1994 ident: ref_24 article-title: Application of the Volterra integro-power series to modelling the heat-exchange dynamics publication-title: Proc. RAS Energy – volume: 3 start-page: 36 year: 2010 ident: ref_25 article-title: Optimization of Consumption of Power Resources of Turbo Compressor M-1 Ep-300 Using Programming and Computing Suite publication-title: Sci. Tech. Bull. OJSC NK Rosneft – volume: 3 start-page: 8 year: 2018 ident: ref_16 article-title: Optimization Techniques in Power System: Review publication-title: Int. J. Eng. Appl. Sci. Tech. – volume: 7 start-page: 1 year: 1996 ident: ref_22 article-title: Volterra Feedforward Neural Networks: Theory and Algorithms publication-title: J. Syst. Eng. Electr. – volume: 65 start-page: 464 year: 2004 ident: ref_39 article-title: Test signal amplitude optimization for identification of the Volterra kernels publication-title: Autom. Remote Control doi: 10.1023/B:AURC.0000019379.43119.d0 – volume: 38 start-page: 585 year: 1998 ident: ref_59 article-title: Numerical solution of a system of Volterra equations of the first kind publication-title: Comput. Math. Math. Phys. – volume: 3 start-page: 432 year: 2004 ident: ref_21 article-title: Towards a Volterra Series Representation from a Neural Network Model publication-title: WSEAS Trans. Syst. – volume: 27 start-page: 1527 year: 1990 ident: ref_64 article-title: Differential-Algebraic Equations, Indices, and Integral Algebraic Equations publication-title: SIAM J. Numer. Anal. doi: 10.1137/0727089 – volume: 1 start-page: 43 year: 2005 ident: ref_8 article-title: Design of the control law of the steam drum boiler level taking into consideration energy economy publication-title: Probl. Energ. Reg. – ident: ref_62 – ident: ref_38 – ident: ref_45 – volume: 94 start-page: 650 year: 2017 ident: ref_66 article-title: Error analysis of the ultraspherical spectral-collocation method for high-index IAEs publication-title: Int. J. Comp. Math. doi: 10.1080/00207160.2015.1121247 – ident: ref_12 doi: 10.1049/icp.2021.1027 – ident: ref_30 – volume: 11 start-page: 89 year: 2018 ident: ref_54 article-title: To the numerical solution of one class of systems of the Volterra polynomial equations of the first kind publication-title: Num. Anal. Appl. doi: 10.1134/S1995423918010093 – volume: 5 start-page: 34 year: 1985 ident: ref_34 article-title: Mathematical model of transient processes of a once-through boiler for a simulator for an operator of a 250 MW cogeneration power unit publication-title: Therm. Eng. – volume: 41 start-page: 9048 year: 2018 ident: ref_74 article-title: Collocation-variation difference schemes for differential-algebraic equations publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.4884 – volume: 1 start-page: 90 year: 2019 ident: ref_6 article-title: Control of Heat Exchanger with Variable Heat Transfer Surface Area publication-title: Probl. Energ. Reg. – volume: 70 start-page: 663 year: 2009 ident: ref_53 article-title: A class of systems of bilinear integral Volterra equations of the first kind of the second order publication-title: Autom. Remote Control doi: 10.1134/S0005117909040122 – volume: 10 start-page: 158 year: 2016 ident: ref_27 article-title: Intelligent technology of nonlinear dynamics diagnostics using Volterra kernels moments publication-title: Int. J. Math. Models Methods Appl. Sci. – volume: 19 start-page: 296 year: 2015 ident: ref_37 article-title: The method of constructing multidimensional Volterra model of the oculo-motor apparatus publication-title: Electr. Comput. Syst. doi: 10.15276/eltecs.19.95.2015.65 – ident: ref_40 – volume: Volume 3 start-page: 338 year: 1964 ident: ref_17 article-title: Fuzzy Sets publication-title: Fuzzy Sets – ident: ref_63 – ident: ref_18 – ident: ref_28 doi: 10.1109/IDAACS.2017.8095251 – volume: 66 start-page: 804 year: 2018 ident: ref_48 article-title: Efficient Computation of Bilinear Approximations and Volterra Models of Nonlinear Systems publication-title: IEEE T Signal Process. doi: 10.1109/TSP.2017.2777391 – volume: 53 start-page: 284 year: 2013 ident: ref_73 article-title: Numerical solution of differential-algebraic equations using the spline collocation-variation method publication-title: Comput. Math. Math. Phys. doi: 10.1134/S0965542513030044 – ident: ref_3 doi: 10.24294/tse.v1i1.357 – volume: 72 start-page: 1229 year: 2011 ident: ref_52 article-title: Studying the polynomial Volterra equation of the first kind for solution stability publication-title: Autom. Remote Control doi: 10.1134/S0005117911060099 – volume: 69 start-page: 545 year: 2008 ident: ref_51 article-title: Multilinear Volterra equations of the first kind and some problems of control publication-title: Autom. Remote Control doi: 10.1134/S0005117908040012 – ident: ref_14 doi: 10.1109/TPEC48276.2020.9042550 – volume: 6 start-page: 3 year: 2001 ident: ref_58 article-title: Numerical solution of systems of integral equations of the first kind publication-title: Comput. Technol. – volume: 5 start-page: 728 year: 2018 ident: ref_65 article-title: Direct Regularization for System of Integral-Algebraic Equations of index-1 publication-title: Inverse Probl. Sci. Eng. – volume: 149 start-page: 153 year: 2020 ident: ref_75 article-title: Collocation-variation difference schemes with several collocation points for differential-algebraic equations publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2019.06.014 – ident: ref_29 doi: 10.1109/SLED-PRECEDE.2013.6684497 – ident: ref_50 – volume: 47 start-page: 1323 year: 2007 ident: ref_47 article-title: On the convergence of numerical methods for solving a Volterra bilinear equations of the first kind publication-title: Comput. Math. Math. Phys. doi: 10.1134/S0965542507080106 – volume: 1 start-page: 243 year: 1984 ident: ref_31 article-title: Analytical Foundations of Volterra Series publication-title: IMA J. Math. Control Inf. doi: 10.1093/imamci/1.3.243 – volume: 1 start-page: 150 year: 1989 ident: ref_33 article-title: Nonlinear modeling of the dynamics of heat transfer in a channel with single phase coolant publication-title: Proc. RAS Power Eng. Transp. – volume: 32 start-page: 221 year: 2011 ident: ref_4 article-title: Energy efficient predictive control of complex manufacturing processes publication-title: Upr. Bol’shimi Sist. – volume: 6 start-page: 1385 year: 2013 ident: ref_10 article-title: Short-Term Load Forecasting for Microgrids Based on Artificial Neural Networks publication-title: Energies doi: 10.3390/en6031385 – volume: 14 start-page: 131 year: 2018 ident: ref_36 article-title: Quadratic and cubic Volterra polynomials: Identification and application publication-title: Vestn. SPb Univ. Appl. Math. Comput. Sci. Control. Process. – ident: ref_15 – volume: 75 start-page: 87 year: 2014 ident: ref_56 article-title: Modeling heat exchangers by quadratic Volterra polynomials publication-title: Autom. Remote Control doi: 10.1134/S0005117914010068 – volume: 111 start-page: 710 year: 2017 ident: ref_7 article-title: Heat Supply Modes Optimization Based on Macromodeling Technology publication-title: Energy Procedia doi: 10.1016/j.egypro.2017.03.233 – volume: 217 start-page: 4791 year: 2011 ident: ref_49 article-title: Numerical solution of multiple nonlinear Volterra integral equations publication-title: Appl. Math. Comput. – ident: ref_70 – ident: ref_19 – ident: ref_60 – ident: ref_57 – volume: 139 start-page: 01029 year: 2019 ident: ref_13 article-title: Analysis of the emergency control and relay protection structures approached from the point of view of EPS reliability and survivability by taking into account cybersecurity threats publication-title: E3S Web Conf. doi: 10.1051/e3sconf/201913901029 – volume: 72 start-page: 1264 year: 2011 ident: ref_44 article-title: Applications of nonlinear Volterra equations of the first kind to the control problem for heat exchange dynamics publication-title: Autom. Remote Control doi: 10.1134/S0005117911060142 – volume: 52 start-page: 691 year: 2012 ident: ref_67 article-title: Numerical solution of integral-algebraic equations for multistep methods publication-title: Comput. Math. Math. Phys. doi: 10.1134/S0965542512050041 |
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| SubjectTerms | Algorithms Automatic control Computational fluid dynamics Dynamical systems Energy Enthalpy Fluid flow Fuzzy sets Heat exchange Heat exchangers Integral equations integro-algebraic equations Inverse problems Literature reviews mathematical modeling Neural networks Nonlinear dynamics Nonlinear systems Numerical analysis Optimization Polynomials Power plants Power series Radiation Simulation Volterra integral equations Volterra series |
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| Title | Integral Equations Related to Volterra Series and Inverse Problems: Elements of Theory and Applications in Heat Power Engineering |
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