Generalized multiple-regression techniques with interaction and nonlinearity for system identification in biological...

A class of multiple regression models, called "generalized multiple-regression" (GMR) is proposed. GMR has the advantages of being easy and rapid to fit, and uses standard multilinear regression software. It has an advantage over ARIMA models in modeling nonlinearity and linear and nonlinear interactions among variables. Its main disadvantage is that, if there are many independent variables, the reduction of degrees of freedom may be important. It is less parsimonious than other models, but availability of increased computational power makes this not a serious disadvantage. The GMR models are compared to autoregressive transfer function models and feedforward back propagation neural network models. In the case of modeling effluent volatile suspended solids, GMR models were superior to both linear autoregressive models and neural network models. The neural network models did, however, outperform the linear models. In the case of modeling sludge volume index, both GMR and the neural network model were unable to improve upon ARIMA models. It was concluded that ARIMA models may, in some cases, produce the most parsimonious model, but in other cases they may miss important process behaviors. The GMR models showed robust capability to describe complex data.