This paper proposes an identification for a class of MIMO system. Taking "A simulation of the western basin of Lake Erie" as an example, quality characteristics of water system is analyzed and mathematical models of Lake Erie is made in this paper. An optimized BP ANN model is used for this MIMO system and the MATLAB's NNT is used to carry on data processing. The effectiveness of system identification is inspected by the curves between models' output and actual results. The comparison between traditional and optimized BP ANN is given at the end of this paper. In this paper data collected under different noises is compared to study on the effect of white noises on ANN.