Quasi-ARX Modeling and Identification

Neural networks (NNs) and neurofuzzy networks (NFs) have been proved to have universal approximation ability. They can learn any non linear mapping. Many non linear ARMAX models have been proposed based directly on NNs and NFs. However, system identification is always followed by certain applications such as system control and fault diagnosis. From a user's point of view, NNs and NFs are not user-friendly since they do not have structures favourable to the applications of system control and fault diagnosis. To solve this problem, it is natural to consider a modelling scheme to construct models consisting of two parts: macro-part and kernel-part. The macro-part is a user-friendly interface constructed using application specific knowledge and the nature of network structure; efforts in this part are made to introduce some properties favourable to certain applications, while to embed the resulted model complexity in the coefficients. The kernel-part is a flexible multi-input multi-output (MIMO) non linear model such as NN and NF, etc. which is used to represent the complicated coefficients of macro-parts. Non linear models constructed in this way are expected to be user-friendly and to have excellent presentation ability.


   It is obviously that the above modelling scheme is application oriented because application specific knowledge is used to construct the macro-part. For different application interests, different user-friendly models are to be developed. In this research, we proposed a class of quasi-ARX models for non linear systems. Similar to ordinary non linear ARX models, the quasi-ARX models are flexible black-box models, but they have various linearity properties similar to those of linear ARX model.


   It is shown that the proposed quasi-ARX models have both good approximation ability and some easy-to-use properties. The proposed models have been successfully applied to prediction, fault detection and adaptive control of non linear systems.