Modeling of stem form and volume through machine learning

Abstract Taper functions and volume equations are essential for estimation of the individual volume, which have consolidated theory. On the other hand, mathematical innovation is dynamic, and may improve the forestry modeling. The objective was analyzing the accuracy of machine learning (ML) techniques in relation to a volumetric model and a taper function for acácia negra. We used cubing data, and fit equations with Schumacher and Hall volumetric model and with Hradetzky taper function, compared to the algorithms: k nearest neighbor (k-NN), Random Forest (RF) and Artificial Neural Networks (ANN) for estimation of total volume and diameter to the relative height. Models were ranked according to error statistics, as well as their dispersion was verified. Schumacher and Hall model and ANN showed the best results for volume estimation as function of dap and height. Machine learning methods were more accurate than the Hradetzky polynomial for tree form estimations. ML models have proven to be appropriate as an alternative to traditional modeling applications in forestry measurement, however, its application must be careful because fit-based overtraining is likely.

摘要 削度函数与材积方程是单木材积估算的核心工具，其理论体系已臻完善。与此同时，数学领域的创新始终处于动态演进之中，可为林业建模带来新的优化思路。本研究以黑荆树（acácia negra）为研究对象，旨在对比机器学习（machine learning, ML）技术与传统材积模型、削度函数的估算精度。研究采用伐倒实测材积数据，分别拟合舒马赫-霍尔（Schumacher and Hall）材积模型与赫拉德茨基（Hradetzky）削度函数，并选取k近邻（k nearest neighbor, k-NN）、随机森林（Random Forest, RF）与人工神经网络（Artificial Neural Networks, ANN）三种算法开展总材积与相对高度处直径的估算对比。研究基于误差统计指标对各模型进行排序，并验证了其预测离散程度。结果显示，舒马赫-霍尔材积模型与人工神经网络在以胸径（diameter at breast height, dap）与树高为自变量的材积估算中表现最优；在树木形态估算方面，机器学习方法的精度优于赫拉德茨基多项式模型。本研究证实，机器学习模型可作为林业测树传统建模方法的有效替代方案，但需谨慎应用，因为基于拟合的过拟合风险较高。