This paper has induced the algorithm of Multi-dimension Cyclic Subspace Regression (MCSR)

an approach as linear regression which can deal with multi-dimension dependent variables. By combining the Radial Basis Functions (RBF) with MCSR

it provides a better approach of modeling non-linear systems in chemical engineering process in which its dependent variables are multi-dimensional. It adopts the frame of the RBFN

which can express a complicated non-linear relationship

and combines with the MCSR to avoid a variety of troubles of the design and training of the network. Thus

it can search the optimal model in an extensive solution space and the model has a briefly analytic form. Its good performance is demonstrated by an example of modeling the equipment of isomerization of xylene to paraxylene as compared with the RBF-PLSR.