REDES NEURAIS ARTIFICIAIS E MODELAGEM DE EFEITOS MISTOS NA DESCRIÇÃO DO PERFIL DO FUSTE DE Pinus taeda L.

Abstract

This research aimed to compare the performance of Artificial Neural Networks (ANNs) in relation to taper functions, applying the multilevel mixed effect modeling, to describe the profile of stems of Pinus taeda L. For that, 246 trees were sampled in the Telêmaco Borba region, Paraná State, Brazil, from which 80% were randomly selected to adjust and train the neural networks, and 20% randomly selected to validate the equations and generalize the networks. Were adjusted 15 taper functions, being five non-segmented models (NS), two segmented models (S), and eight models of variable form (FV). To adjust the models was applied the technique of nonlinear regression (nls) with fixed effect, selecting then the equation with better performance to estimate the diameters along the stem, to which was applied the nonlinear modeling with mixed effects (nlme). The nlme was applied in two levels, using the age class (ci) and DBH class (cd) factors, to estimate the diameters along the stem, as well the diameters with stratification of the stem in three sections (basal, medium and apical) and partial volume estimations for the same stratifications. For the volume estimations, the numeric integration process was applied. The adjustment were performed using the nls and nlme functions of the R software. The selected equations, of fixed and of mixed effect, were compared with the ANNs, generate with the software Neuro 4.0, in two scenarios, one for comparison with the fixed effect equation, and another, for comparison with the mixed effect equations selected. The models were ranked according to statistical criteria and graphical analysis of residuals. The methodologies tested showed efficiency to reach the proposed aims. The taper equations of variable form adjusted by the nls were more accurate than the non-segmented and segmented equations, and of the taper equations of variable form, the equation of Bi (2000) showed better performance to estimate diameters without stem stratification. The application of the nlme technique to the equation of Bi improved the accuracy of the diameter and partial volume estimations of Pinus taeda, in comparison to the adjustment performed with the nls technique. The ANNs showed adequate results, indicating to be adequate and accurate for the proposed estimations. When the ANNs and the equation of Bi with fixed effects are compared, the neural networks showed better performance for all the proposed estimations, for diameters and volume. In the comparison of the ANNs with the variations of the equation of Bi with mixed effects, for the diameter estimations, the neural networks showed a similar performance to estimate the diameter variable for all the tree stem and the basal section, however, for the medium and apical sections, the neural networks showed superior statistical criteria in comparison to the nlme regression. The neural networks were more efficient and adequate for the estimations of the partial volume, and for the three sections of the stem, especially for the medium and apical sections of the stem, for which they showed better accuracy than the variations of the equation of Bi with mixed effects adjusted by the nlme.