Non-linear modelling with a coupled neural network — PLS regression system

In this work a methodology is presented for the transformation of non-linear response data via a neural network and subsequent standard linear PLS regression. The superb transparency of linear PLS is retained with respect to the diagnostic capabilities via residual analysis and leverage, thus making this method an excellent candidate for process modelling and control. The approach developed performs an initial linear PLS to elucidate the relationship between predicted and observed values, to determine the initial parameters for the neural network and to determine the optimal number of PLS components. The parameters of the neural network are optimized via a modified simplex optimization, with a linear PLS regression at the predetermined number of components being the objective function, minimizing the mean squared error of cross-validation. The optimal neural network was defined as the one giving the lowest mean squared error of cross-validation. The applicability of this approach was demonstrated using three real-life industrial data sets, which gave reductions in the estimates of mean squared error in the range of 64%–98% of the original error.