Optimal field reconstruction of distributed process systems from partial measurements

In this article, we develop a systematic approach for efficient field reconstruction in distributed process systems from a limited number of measurements. The approach generalizes previous methods for sensor placement so as to be able to handle field reconstruction problems in arbitrary spatial domains where complex nonlinear phenomena take place. Pattern formation in fluid dynamics or diffusion-reaction systems are examples exhibiting complex nonlinear distributed behaviors, especially when taking place in arbitrary 2D or 3D domains. Our approach exploits the dissipative nature of the diffusion-convection process and the underlying algebraic structure of the finite element method to efficiently construct field representations in terms of globally defined basis functions and to optimally select the placement of sensors. The results will be illustrated on a fluid dynamic process: the Rayleigh-Benard problem.