The inverse problem of restoring the parameters of a mathematical model in the absence of information about the data error

Le Van-Huyen

Abstract


This paper examines the recovery of mathematical model parameter values in cases where the uncertainty of the initial data is unknown. The objective of the paper is to find approximate parameter values that should continuously depend on the uncertainty of the initial data. An inverse problem of recovering the mathematical model parameters is formulated. To solve the inverse problem, a two-criteria optimization problem is combined with a Tikhonov functional minimization problem. The Tikhonov regularization method is used to solve the Tikhonov functional minimization problem. A method for selecting quasi-optimal regularization parameter values is used to select the regularization parameter values. A set of Pareto-optimal solutions to the two-criteria optimization problem is found. To simplify the selection of a solution from the Pareto set, an algorithm developed based on the k-means method is used. A mathematical model of the kinetics of an oil refining process is considered as an example. The values of the mathematical model parameters are found.

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References


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