A software package for computer modeling of parametric identification processes for mathematical models of convection-diffusion transfer

The paper describes a software package for computer modeling of parameter identification processes of one-dimensional mathematical models of convection-diffusion transfer with constant coefficients under noisy measurement conditions. The parameter identification methods implemented in the software package are based on the transition from a mathematical model described by partial differential equations with initial and boundary conditions to a model described by a linear discrete stochastic system in the state space with noisy measurements followed by the application of optimal discrete filtering and parameter identification methods to this system. The software package is written in MATLAB and is a set of functions and scripts for construct-ing a finite-difference grid, discretizing the original problem, constructing a solution to the original problem by the finite difference method, modeling experimental data, numerical identification of boundary conditions, identification of the convection velocity and diffusion coefficient, as well as performing various auxiliary operations, such as: visualization of results, conducting numerical ex-periments, etc. The identification of boundary conditions is performed using the algorithm of S. Gillijns and B. Moore for simultaneous estimation of the state vector and the unknown control vector of a linear dynamic system. The identification of the convection velocity and the diffusion coefficient is per-formed by minimizing the identification criterion taken in the form of a logarithmic likelihood function based on the values calculated by the Kalman filter. The minimization of the identification criterion is performed using the functions of the MATLAB system for gradient-free and gradient optimization. The paper gives a detailed description of the software package and the results of computer mod-eling confirming the operability of the algorithms.