Parameter identification algorithm for convection-diffusion transport model

Abstract

This paper considers an application of gradient-type optimization algorithm for solving the problem of convection velocity and diffusion coefficient identification in the convection-diffusion transport model. A solution is obtained by the means of numerical minimization of the parameter identification criterion for a discrete linear stochastic model in state space. The log-likelihood function is used as the identification criterion. Numerical experiments were conducted to confirm the efficiency of the proposed solution.

SVD-Based Parameter Identification of Discrete-Time Stochastic Systems with Unknown Exogenous Inputs

“…Let us prove that ( 6) and ( 17) are equivalent. Using the general SVD form (25), from (17) we obtain…”

“…Following [25], let us move from the original continuous model to a discrete-time model. This model is described by a linear dynamic system in state space.…”

“…Solving the parameter identification problem, we will apply two different numerical identification methods: the first is with known boundary conditions (41), (42), and the second with unknown boundary conditions. The first solution is based on the approach considered in [25] where the identification criterion has the form of the negative logarithmic likelihood function J LR with the associated conventional Kalman filter (KF) [35]. The second solution is based on the instrumental criterion J SVD and the novel SVD-GDM algorithm.…”

“…For example, it was used to solve the problem of identifying parameters for linear discrete-time stochastic systems [18], as well as the problems of Kalman filtering for inertial measurement unit readings [19], research of MIMU/GPS integrated navigation [20], adaptive KF filtering for some engineering applications [21], and an indoor positioning and tracking based on angle-of-arrival using a dual-channel array antenna [22]. It was also used to determine attitude and angle rate of gyroless spacecraft only using a star sensor [23], estimate GARCH-in-Mean(1,1) models [10], model epileptic seizures count time series with external inputs [24], and identify parameters of convection-diffusion transport models [25].…”

Investigation the Accuracy of Crank Nicolson Methods and their Modified Schemes for One-Dimensional Linear Convection-Reaction-Diffusion Equations

“…These model's problems contain parameters that must be specified to uniquely determine the result of boundary value problems. But in practice, situations frequently arise when some of these parameters are unknown or given roughly and they need to be determined or clarified [5,6]. Applications of ecology, geophysics, and seismology have also arisen in the form of advection-reaction-diffusion or convection-reaction-diffusion equations.…”