Artificial neural networks and non-linear regression for quantifying the wood volume in <i>Eucalyptus</i> species

Abstract

Wood volume is the variable that best represents the yield of planted forests, and several regression models are used in its estimation. Artificial neural networks (ANNs) are recognised for their accuracy and generalisation capacity associated with the quality and quantity of data in training and validation. Box–Müller transformation generates random variables from the original data and provides a consistent dataset. Given the above, the hypothesis of this research is that the expansion of data by the Box–Müller theorem provides more accurate estimates for predicting wood volume in eucalyptus species. The objectives were to (i) to evaluate the efficiency of the Box–Müller method for expanding the dataset of eucalyptus sample tree cubing, (ii) use different ANN topologies to predict the wood volume of different Eucalyptus species, and (iii) compare the estimates with those obtained by using the Schumacher and Hall model. The experimental design used randomised blocks with four replicates, composed of the following treatments: Corymbia citriodora and different Eucalyptus species. Sample trees were cubed at ages 2 years and 4.5 years. The estimated volume was obtained using the Schumacher and Hall non-linear regression model for each species and compared with the ANNs through Pearson’s correlation, and root mean square error at the steps training, validation, and utilisation. Two ANN architectures were tested, multilayer perceptron (MLP) and radial basis function (RBF). Dataset expansion of cut-down sample trees for cubing is efficient and can be used for ANNs training when there are cubing restrictions of sample size. The topology with seven neurons in the first hidden layer and 12 in the second with expanded data of RBF showed better performance for predicting wood volume. When evaluating all species, the accuracy of the estimates provided by ANNs was higher than that obtained with non-linear regression.

Keywords: Brazil; forest measurement; multilayer perceptron; radial basis function; volume equations