Modeling Height–Diameter Relationship for Poplar Plantations Using Combined-Optimization Multiple Hidden Layer Back Propagation Neural Network

Jianbo Shen,Ram P Sharma,Qiulai Wang,Xiang Meng,Gongming Wang,Mengxi Wang,Zongda Hu,Liyong Fu

doi:10.3390/f11040442

Abstract

Relationship of total height and diameter at breast height (hereafter diameter) of the trees is generally nonlinear, and therefore has complex characteristics, which can be accurately described by the height-diameter model developed using the back propagation (BP) neural network approach. The multiple hidden layered-BP neural network has several hidden layers and neurons, and is therefore considered more appropriate modeling approach compared to the single hidden layered-BP neural network approach. However, the former approach is not widely applied for tree height prediction due to absence of the effective optimization method, but it can be done using the BP neural network modeling approach. The poplar (Populus spp. L.) plantation data acquired from Guangdong province of China were used for evaluating the BP neural network modeling approach and compared its results with those obtained from the traditional regression modeling and mixed-effects modeling approaches. We determined the best BP neural network structure with two hidden layers and five neurons in each layer, and logistic sigmoid transfer functions. Relative to the Mitscherlich height-diameter model that had the highest fitting precision among the six traditional height-diameter models evaluated, coefficient of determination (R2) of the neural network height-diameter model increased by 10.3%, root mean squares error (RMSE) and mean absolute error (MAE) decreased by 12% and 13.5%, respectively. The BP neural network height-diameter model also appeared more accurate than the mixed-effects height-diameter model. Our study proposes the method of determining the optimal numbers of hidden layers, neurons of each layer, and transfer functions in the BP neural network structure. This method can be useful for other modeling studies of similar or different types, such as tree crown modeling, height, and diameter increments modeling, and so on.

Highlights

Tree height is one of the most important tree characteristics and measurement of which is used as a fundamental basis for evaluating forest growth and biomass, site quality, and classifying the vertical structures of a forest [1,2]
Due to a strong relationship between tree height and diameter at breast height (DBH), height can be predicted using DBH as a predictor in the height-diameter model [3,4,5,6,7,8,9,10,11,12]. This method uses the measurements of tree height and DBH to fit the mathematical functions with different forms and number of parameters, and the optimal one is determined based on the standard statistical indices
We proposed the modeling method which can generate several back propagation (BP) neural network models based on the combinatorics mathematics, and among them, the model with the best structure was selected through comparison of the fitting and prediction precisions, and convergence rate

Summary

Introduction

Tree height is one of the most important tree characteristics and measurement of which is used as a fundamental basis for evaluating forest growth and biomass, site quality, and classifying the vertical structures of a forest [1,2]. Due to a strong relationship between tree height and diameter at breast height (DBH), height can be predicted using DBH as a predictor in the height-diameter model [3,4,5,6,7,8,9,10,11,12] This method uses the measurements of tree height and DBH to fit the mathematical functions with different forms and number of parameters, and the optimal one is determined based on the standard statistical indices. Tree height growth is substantially affected by various factors whose relationships may be in the nonlinear forms, which may pose the difficulty in describing wider variations of the tree height with a single height-diameter equation

Methods

Results

Discussion

Conclusion