Linear regression is often used as a diagnostic tool to understand the relative contributions of operational variables to some key performance indicator or response variable. However, owing to the nature of plant operations, predictor variables tend to be correlated, often highly so, and this can lead to significant complications in assessing the importance of these variables. Shapley regression is seen as the only axiomatic approach to deal with this problem but has almost exclusively been used with linear models to date. In this paper, the approach is extended to random forests, and the results are compared with some of the empirical variable importance measures widely used with these models, i.e., permutation and Gini variable importance measures. Four case studies are considered, of which two are based on simulated data and two on real world data from the mineral process industries. These case studies suggest that the random forest Shapley variable importance measure may be a more reliable indicator of the influence of predictor variables than the other measures that were considered. Moreover, the results obtained with the Gini variable importance measure was as reliable or better than that obtained with the permutation measure of the random forest.

Texture analysis is key to better understanding of the relationships between the microstructures of the materials and their properties, as well as the use of models in process systems using raw signals or images as input. Recently, new methods based on transfer learning with deep neural networks have become established as highly competitive approaches to classical texture analysis. In this study, three traditional approaches, based on the use of grey level co-occurrence matrices, local binary patterns and textons are compared with five transfer learning approaches, based on the use of AlexNet, VGG19, ResNet50, GoogLeNet and MobileNetV2. This is done based on two simulated and one real-world case study. In the simulated case studies, material microstructures were simulated with Voronoi graphic representations and in the real-world case study, the appearance of ultrahigh carbon steel is cast as a textural pattern recognition pattern. The ability of random forest models, as well as the convolutional neural networks themselves, to discriminate between different textures with the image features as input was used as the basis for comparison. The texton algorithm performed better than the LBP and GLCM algorithms and similar to the deep learning approaches when these were used directly, without any retraining. Partial or full retraining of the convolutional neural networks yielded considerably better results, with GoogLeNet and MobileNetV2 yielding the best results.