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

Demirbay B., Bayram Kara D., Uğur Ş.

EXPERT SYSTEMS WITH APPLICATIONS, vol.207, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 207
  • Publication Date: 2022
  • Doi Number: 10.1016/j.eswa.2022.117937
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, PASCAL, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, Metadex, Public Affairs Index, Civil Engineering Abstracts
  • Keywords: Feed-forward neural network, Generalized regression neural network, Radial basis function neural network, Multivariate regression, Kernel density mapping, Polymer nanocomposites, SURFACTANT-FREE, PREDICTION, GRAPHENE, TEMPERATURE, OPTIMIZATION, PERFORMANCE, SETTLEMENT, SELECTION, MWCNTS, SENSOR
  • Istanbul Technical University Affiliated: Yes


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 (I-tr) 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 I-tr 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 I-tr 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 I-tr. 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 I-tr 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 It,. values agreed well with experimental I-tr data. Taken all computational results together, one can adapt our proposed FFNN model and neural predictive formula to predict I-tr 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.