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ŠUMARSKI LIST 9-10/2019 str. 35     <-- 35 -->        PDF

In this study, Artificial Neural Network models were evaluated as an alternative method to predict the individual tree volume by using diameter at breast height and a total height of trees as explanatory variables. This neural network model building involved some training, verification and testing process by randomly total sample plots partitioning into training (75% of all data), verification (15% of all data) and test (the remaining 10% of all data) data. Various computer software applications have been developed to operate the ANN process and present estimations, the STATISTICA® software was selected to train the ANN models because this software provides multiple comparisons for different ANN structures, including various network architectures, a number of neurons and activation function in the input, hidden and output layers. When developing these network models, a total of 320 trained networks in the Multilayer Perceptron (MLP) and a total of 20 trained networks in the Radial Basis Function (RBF) architectures were trained and used to obtain the individual tree volume predictions. For those aiming, in ANNs training process with MLP, the number of neurons of the input layer ranged from 1 to 20 neurons options, four activation functions, e.g. identity, logistic, tan-sig, and exponential functions, in the hidden layer, correspondingly four activation functions in output layer were used (20X4X4=320 alternatives; 20: number of neurons, 4: number of transfer functions in the hidden layer and 4: number of transfer functions in the output layer). In RBF, the number of neurons of the input layer ranged from 1 to 20 neurons options, the hidden layer has the activation function as being on the isotropic Gaussian basis and identity function was used in the output layer. MLP includes a feedforward neural network architecture based on the input, hidden and output layers with a bias term. In MLP, the training algorithm is Broyden-Fletcher-Goldfarb-Shanno (BFGS), which is a robust training algorithm with very fast convergence with the Hessian matrix.
Comparison Criteria – Kriteriji za usporedbu
After the individual tree volume predictions were obtained by these three methods, including the single and double volume equations, the Fang et al. (2000)’s compatible volume equation and ANN models, these three volume prediction methods were compared by using some evaluation criteria based on the magnitudes and distributions of predictions’ residual. These evaluation criteria are some goodness-of-fit statistics including the sum of squared errors (SSE), Akaike’s information criterion (AIC), Schwarz Bayesian criterion (SBC), Root Mean Square Error (RMSE), Mean Squared Error (MSE) and Adjusted Coefficient of Determination (R2adj). In these criteria, it is desirable for the SSE, MSE, RMSE, AIC, and SBC to have a small value as possible, while the R2adj is expected as close as possible to 1. The formulae for these statistical values are provided below:
Mean squared errors (MSE) =          (8)
Root mean squared error (RMSE) =                (9)
The Sum of Squared error (SSE) =   (10)
Adjusted coefficient of determination                                 (11)
                AIC = n . ln + 2 . p (12)
                SBC = n . ln + p . ln (n)         (13)
In these formulae listed above; represents the calculated volume; represents the estimated volume, represents average volume, n represents the number of data and p represents the number of parameters within the model.
To further evaluate these network models, the independent data, including 54 sample trees were used in predicting the tree volume values that were not included in training neural networks. These evaluations were performed by analysis of the difference (residual values) between observed and predicted values for validation data set, 54 sample trees. The t-paired test was used to evaluate the null hypothesis of mean prediction residuals equal to zero. If the null hypothesis tested by t-paired test revealed that the null hypothesis could not be rejected and mean residuals statistically not significantly different from zero, these ANN models were applicable for predicting tree volume values based on the dbh and height variables in studied forest stands.
Results
Rezultati
In this study, the prediction methods including single and double entry volume equations, the Fang (2000)’s compatible volume equation and artificial neural network models were used to obtain the individual tree volume predictions. The parameter estimates with probability levels for the single and double volume equations and the segmented taper equation of Fang et al. (2000) are given in Table 2. All parameters of estimates for these nonlinear models were found to be significant at the 0.05 level (p<0.05). The predicted single and double-entry volume equations and Fang et al. (2000)’s volume equations are as follow:
The single-entry volume equation:
                V = 0.000203 . dbh2.2985       (14)
The double-entry volume equation:
                V = 0.000448 . (dbh2 . h)     (15)