Multivariate regression (MVR) and different artificial neural network (ANN) models developed for optical transparency of conductive polymer nanocomposite films

Abstract

The present study addresses a comparative performance assessment of multivariate regression (MVR) and well-optimized feed-forward, generalized regression and radial basis function neural network models which aimed to predict transmitted light intensity (Itr) of carbon nanotube (CNT)-loaded polymer nanocomposite films by employing a large set of spectroscopic data collected from photon transmission measurements. To assess prediction performance of each developed model, universally accepted statistical error indices, regression, residual and Taylor diagram analyses were performed. As a novel performance evaluation criterion, 2D kernel density mapping was applied to predicted and experimental Itr data to visually map out where the correlations are stronger and which data points can be more precisely estimated using the studied models. Employing MVR analysis, empirical equation of Itr was acquired as a function of only four input elements due to sparseness and repetitive nature of the remaining input variables. Relative importance of each input variable was calculated separately through implementing Garson’s algorithm for the best ANN model and mass fraction of CNT nanofillers was found as the most significant input variable. Using interconnection weights and bias values obtained for feed-forward neural network (FFNN) model, a neural predictive formula was derived to model Itr in terms of all input variables. 2D kernel density maps computed for each ANN model have shown that correlations between measured data and ANN predicted values are stronger for a specific Itr range between 0% and 18%. To measure the stability of the ANN models, as a final analysis, 5-fold cross-validation method was applied to whole measurement data and 5 different iterations were additionally performed on each ANN model for 5 different training and test data splits. Statistical results found from 5-fold cross-validation analysis have reaffirmed that FFNN model exhibited outperformed prediction ability over all other ANN models and all FFNN predicted Itr values agreed well with experimental Itr data. Taken all computational results together, one can adapt our proposed FFNN model and neural predictive formula to predict Itr of polymer nanocomposite films, which can be made from different polymers and nanofillers, by considering specific data range as presented in this study with statistical details.