Solution of the Inverse Incorrectly Posed Problem by the Library Method

Abstract

The presented study considers a range of problems to be interpreted as inverse problems. The complexity of solving incorrectly posed inverse problems due to their unique features and the lack of a universal method for their solution is highlighted. In this regard, the importance of considering the application of different methods on the example of specific problems is emphasised. The research analyses a method of solving the problem of determining the composition of gaseous hydrocarbon fuel in the process of its combustion in real time. It is emphasised that the way of measuring technological parameters allows to consider this problem as a complex problem of interpretation. The method of "library" (selection) as the most universal one is chosen. For its implementation the method of library formation in the form of a three-dimensional array is proposed, where the initial data for each solution of the direct problem are presented in the form of a single number, using the positional principle of recording decimal numbers. In the process of forming the working array, the method of comparing the oxidant excess ratio and the ratio of oxidant and fuel volume flow rates was used. This made it possible to use the results of the solution of the direct problem to determine the composition of fuel by the measured temperature of combustion products within the framework of the inverse problem. A method of searching for a solution among the elements of the working array based on the results of technological measurements of the combustion product temperature and the ratio of oxidant and fuel volume flow rates was developed.