Simultaneous Identification of Bidirectional Path Models Based on Process Data

In multivariate systems, the causality relationships between any two different data variables and the corresponding path models are often unknown. In this paper, the identification of bidirectional path models of a bivariate system is investigated by extending the augmented UD identification (AUDI) algorithm proposed by Niu (1992) which can simultaneously identify the order and parameters for open-loop systems with unclear physical meanings of the even columns in the data matrix. To extract more information than the AUDI algorithm for identification of bidirectional path models, we develop a novel approach based on construction of the interleave data vector and UD factorization of the data matrix. The odd and even columns of the resulting data matrix correspond to the parameters of the forward and backward path models, respectively. Moreover, the information contained in the data matrix can be evaluated to determine the causality between the two data variables. The ARMAX process with white noise is first considered. The results are then extended to the case with colored noise. Simulation results are presented to show the effectiveness of our proposed methods.