Identification of Low Order Tensorial Models for Tubular Reactors

In this paper we propose a novel procedure for obtaining a low order model of a large scale, non-linear process. The method is of generic nature. The efficiency of the proposed approach is illustrated on a benchmark example depicting industrial tubular reactor which are often used in petrochemical industries. The results show good performance of the proposed method. Our approach is based on the combinations of the methods of Proper Orthogonal Decomposition (POD), and non-linear System Identification techniques. It is showed here that the modal coefficient corresponding to the spectral decomposition of the system solutions can be viewed as the states of the reduced model. This has paved a way to propose a novel model reduction strategy for large scale systems. In the first step the spectral decomposition of system solutions is used to separate the spatial and temporal patterns (time varying modal coefficients) and in the second step a reduced model structure and it's parameters; linear and of non-linear tensorial (multivariable polynomial) type are identified for approximating the temporal patterns obtained by the spectral decomposition. The state space matrices which happens to be the parameters of a black-box to be identified, appears linearly in the identification process. For the same reason, Ordinary Least Square method is used to identify the model parameters. The simplicity and reliability of proposed method gives computationally very efficient linear and non-linear low order models for large scale processes. The novel method also allows the way to compensate the mismatch between real plant and the reduced model outputs.