Simultaneous structure and parameter identification of multivariate systems by matrix decomposition

Abstract

Structure determination and parameter identification of multivariate systems are crucial but rather difficult issues in system identification. Due to the explosive growth of process data along with the scale increase of industrial processes, directional links between variables of such complex processes are often undistinguishable, which is indispensable to model structure determination but is often assumed to be known beforehand in most identification methods. In this article, a new modelling approach is developed to simultaneously estimate the model parameters and structures (including model orders as well as the directional links between different process variables) of multivariate systems. A vector auto-regressive (VAR) form is utilized as the model formulation in this algorithm. The key technique lies in constructing an interleaved information matrix with respect to a multiple model structure formulated for the VAR representation. Then by utilizing the upper diagonal factorization, all the parameter estimates of all path models with orders from zero to m, as well as the corresponding cost function values, can be obtained simultaneously. The effectiveness of the proposed method is demonstrated via a numerical example and a distillation column system.