Estimation of the temporal coefficients for an empirical approximator. New approach based on the Proper Orthogonal Decomposition modes

A new approach to identify the temporal coefficients of an empirical approximator of a process without any knowledge of the mathematical model of the system is introduced. This approach is based on the Proper Orthogonal Decomposition method, and only a few experimental values are required to determine the empirical eigenfunction, and the temporal coefficients. The scheme studied is verified by a numerical example regarding the chemical reaction in a tubular reactor. The approach consists of the minimisation of an objective function, which is based on the sum of the square errors between the original snapshots and the values predicted from the linear combination of the empirical eigenfunctions and the time coefficients. This method is easy and fast to implement, produces the lowest deviation from the original experimental data, and is very useful when the theoretical model of the system is unknown or difficult to determine.