DIGITALNA ARHIVA ŠUMARSKOG LISTA

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ŠUMARSKI LIST 9-10/2019 str. 37 <-- 37 --> PDF |

variables, the neural network architecture of MLP with 15 neurons in hidden layer with the exponential activation function in both input layer and output layer resulted in best predictive volume values. The best satisfactory results in RBF including dbh and total height as input variables were obtained by the neural network architectures, including 9 neurons in hidden layer with Gaussian activation function and identity activation function in the output layer. Table 3 presented the comparative results for prediction methods, including the single and double entry volume equations, the Fang (2000)’s compatible volume equation and best predictive artificial neural network models based on the values of goodness-of-fit statistics such as SSE, AIC, SBC, RMSE, MSE and . From these fitting statistics, SSE was 2.7763 and 3.8539 for single entry volume predictions and 0.8354 and 3.4715 for double entry volume predictions; was 0.9082 and 0.9339 for single entry volume predictions and 0.9173 and 0.9801 for double entry volume predictions; MSE was 0.00910 and 0.01264 for single entry volume predictions and 0.00274 and 0.01138 for double entry volume predictions; RMSE was 0.0954 and 0.1124 for single entry volume predictions and 0.0523 and 0.1067 for double entry volume predictions; AIC was -823.25 and -723.23 for single entry volume predictions and -918.85 and -229.26 for double entry volume predictions: SBC was -1421.81 and -1327.51 for single entry volume predictions and -1788.11 and -1359.38 for double entry volume predictions. On the basis of the goodness-of-fit statistics, the ANN-based on MLP 1-9-1 including dbh as an input variable for single entry volume predictions showed better fitting ability with SSE (2.7763), (0.9339), MSE (0.00910), RMSE (0.0954), AIC (-823.25) and SBC (-1421.81) than that by the other studied volume methods including dbh as an explanatory variable. For double entry volume predictions including dbh and total height as input variables, ANN based on MLP 2-15-1 resulted in better fitting statistics with SSE (0.8354), (0.9801), MSE (0.00274), RMSE (0.0523), AIC (-579.55) and SBC (-1788.11).In figure 2, the residuals against predicted volume obtained by single entry volume equation (a), ANN based on MLP 1-9-1 (b) and ANN based on RBF 1-7-1 (c) were presented. In figure 3, it was showed that the residuals against predicted volume obtained by double entry volume equation (a), Fang (2000)’s compatible volume equation (b), ANN based on MLP 2-15-1 (c) and ANN based on RBF 2-9-1 (d). It is seen that ANN based on MLP 1-9-1 (Fig. 2b) and ANN based on MLP 2-15-1 (Fig. 3c) presented better predictive results than others and there are no serious failure of homoscedasticity, violations of the assumption of the constant variance in predictions obtained by the ANN based on the MLP. Further, analyze were performed to evaluate the best predictive ANN based on MLP 1-9-1 for single-entry volume predictions and ANN based on MLP 2-15-1 for double-entry volume predictions. These validation processes were realized with the analysis of the difference between observed and predicted tree volume values (residual values) based on |