Tree-Bole Volume Estimation on Standing Pine Trees Using Cascade Correlation Artificial Neural Network Models

Total tree volume estimation is an integral part of forest growth and yield forecasting. Complex formulae are used to estimate bole volume by section, based on relationships proposed by Huber, Smalian and Newton. All these relationships require many measurements of bole diameters at certain heights that are difficult to obtain on standing trees especially when diameter measurements have to be taken several meters above ground. The common practice used till now days to face the problem is the application of regression analysis for tree-bole estimation, but there are many problems to be solved and assumptions to be carefully selected etc. In this paper an attempt was made to overcome the above difficulties by indirect tree volume estimation using the necessary values of the diameters at certain heights and the Cascade Correlation Artificial Neural Network models (CCANNs). The cascade correlation algorithm accomplished the training of the ANNs, which is a feedforward and supervised learning algorithm. Adaptive gradient and Kalman’s learning rules were used to modify the artificial neural networks weights. Kalman’s learning rule was found superior for the estimation of diameter values at certain heights of the tree-bole. The networks are designed to adapt weights of the synapses, by using the hyperbolic-tangent function of training. The reliability of the developed CCANNs is assessed by validation on independent testing data set. Paired t-test and 45-degree line test were also used for validation of the selected CCANNs. The system proposed in this paper, can be applied in forest inventory calculations producing an accurate estimate of any bole section volume. For example, total tree-bole volume estimation resulted to a root mean square error value of 0.0054 m (9.2%). This tree-bole volume estimation is based only on two diameter measurements (stump diameter, d0.3 and diameter at breast height, d1.3) and an estimate of total tree height (h), and is accurate enough to replace many standard forestry measurement procedures.