Identification of parameters of convection–diffusion–reaction model and unknown boundary conditions in the presence of random noise in measurements

The study considers mathematical models described by partial differential equations, namely, convection-diffusion-reaction models, which are related to heat and mass transfer models and are used in the study of natural and technogenic processes. For this class of models, the actual problem is to identify both the model parameters itself and the boundary conditions included in it based on the results of measuring the values of the desired function at certain points of the area under consideration. The problem is complicated by the presence of incomplete measurements distorted by random noise.
The solution is to develop a combined two-stage identification method based on the sequential application of a gradient-free identification criterion minimization method and a recurrent method for estimating unknown input signals. To apply the above methods, a transition is made from the original model described by partial differential equations to a discrete linear stochastic state-space model in which unknown boundary conditions are treated as unknown input signals.
In this paper, new discrete linear stochastic models of convection–diffusion–reaction are constructed for three different types of boundary conditions. A general scheme of the parameter identification process is proposed, including two-stage identification of unknown parameters of a mathematical model and identification of unknown boundary conditions.
To test the efficiency of the proposed method, computer models of convection–diffusion–reaction were built and all algorithms were implemented in MATLAB. A series of computational experiments was carried out, the results of which showed that the developed two-stage combined scheme allows one to identify the parameters of the original model, the values of the functions included in the boundary conditions, and also to calculate estimates of the function, which describes the process of convection–diffusion–reaction given incomplete noisy measurements.
The results obtained can be used not only in the study of heat and mass transfer processes, but also in solving problems of identifying the model parameters of discrete-time stochastic systems with unknown input signals and in the presence of random noise.