Integral Equations Related to Volterra Series and Inverse Problems: Elements of Theory and Applications in Heat Power Engineering

Svetlana Solodusha,Mikhail Bulatov

doi:10.3390/math9161905

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.

Highlights

Present power plants belong to the category of complex technical systems, the study of the functioning dynamics of which is based on the formalization of the physical nature of the object, on carrying out natural experiments, as well as on the use of simulation models that describe processes in actual time
Kernels were identified on the discrete mesh with the step h = 1 using responses ∆i (t) to test signals of
This paper presents mathematical tools for solving problems, associated with the application of the Volterra integro-power series

Summary

Introduction

Present power plants belong to the category of complex technical systems, the study of the functioning dynamics of which is based on the formalization of the physical nature of the object (obtaining an analytical model), on carrying out natural experiments (using a real model), as well as on the use of simulation models that describe processes in actual time. Problems with statistical or dynamic technological criteria (optimization of the basic parameters of the boiler unit [2], temperature control [3], maximum efficiency of combustion processes [4,5], changes in design parameters [6], etc.); Problems with statistical or dynamic technical and economic criteria (energy-saving of thermal energy [7], minimization of operating costs [8], maximum profit [9], etc.); Forecasting problems for the technical state of heat and power equipment (shortterm and long-term forecasts of the mode parameters [10,11], planning of repair and maintenance work, development of a strategy for equipment service [12], etc.); Multicriteria control problems, including emergency control from the point of view of reliability [13], optimization of technical indicators of energy sources depending on 4.0/).

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