基于支持向量机优化粒子群算法的活立木材积测算

材积模型是编制立木材积表的关键，通常用经验材积方程来预测材积量。由于树木生长具有不确定性，传统的材积方程很难有效地对模型的复杂性和多样性做出测算，导致目前活立木材积测算的准确率较低。为了提高活立木材积的测算准确率，将粒子群（particle swarm optimization，PSO）算法引入到活立木材积模型中，并用支持向量回归机（support vector machine，SVM）优化参数。PSO-SVM将活立木胸径和树高数据输入到SVM中学习，将SVM参数作为PSO中的粒子，把活立木实测材积值作为PSO的目标函数，然后通过粒子之间相互协作得到 SVM 最优参数，对活立木测算材积值进行模型测算并采用实测材积值验证。论文应用电子经纬仪与人工量测立木地径、胸径相结合的方法，通过软件计算求得400组树高、树干材积值；然后对300组数据集以活立木胸径和树高作为输入数据，材积为输出数据，采用粒子群耦合支持向量机（PSO-SVM）算法训练得到模型，并用100组数据进行预测；最后引用经典Spurr材积模型算法、BP神经网络算法和PSO-SVM算法进行了对比，其结果表明，PSO-SVM算法预测准确率最高，预测值与实测值间复相关系数达0.91，平均误差率为0.58%。

Calculation of live tree timber volume based on particle swarm optimization and support vector regression

Abstract: Establishment of each tree species volume table is an important research subject in forest management. Accurate tree tables were used to determine the forest reserves. Moreover, these tree tables were applied to provide precise forest management decision making references for the forestry center and local forestry authorities. However, because of the difference of increment between different tree species, live tree tables must be revised every 10 years in China. Previously, to establish tree tables, sample trees were selected in the local area according the corresponding rules, and these sample trees were cut down and divided into several sections, and each section's volume were summed up as the total tree volume. Based the analytic data, the unary models between diameter at breast and volume were established, and also, to set diameter at breast and tree height as independent variables, tree volume as dependent variable, the binary models could be established, as well as a ternary model that describes the relationship between volume and 3 independent variables including diameter at breast, tree height, and tree step form. Nevertheless, these models mentioned above are sample linear models or nonlinear models. To estimate the forest stocks in the forest survey, former researchers usually cut down target trees and extracted samples based on the principle of sampling, and then made a corresponding volume table. This felled, destructive, and time-consuming method damaged many growth dominant trees. Tree volume modeling is the key step of volume table establishment, and volume usually was predicted by the volume equation that was derived from experience. However, because of the uncertainty of tree growth, it is difficult to effectively predict the complexity and diversity of the volume model through conventional volume equations. For this reason, the volume prediction accuracy rate is unsatisfactory. In order to promote the volume prediction accuracy rate, the algorithm of particle swarm optimization (PSO) was introduced into the standing tree volume prediction model. Moreover, the parameters were optimized by the support vector regression (SVM). The data of diameters at breast height and tree heights of standing trees were input into SVM, which were used to learn, parameters of SVM were used as the particle of PSO, standing trees volume value that were measured by authors were considered as objective function of PSO, then prediction values of standing trees volume were detected by the optimized parameters which were obtained through mutual co-ordination of particle, and the prediction values of standing trees' volume were verified by the measured value. This research first applied electronic theodolite and artificial measurement to get the stumpage diameter and breast diameter of 400 samples; and then considered stumpage diameter and breast diameter as input data, volumes as output data, trained with 300 samples by PSO-SVM; and finally, compared the results by PSO-SVM, Spurr volume model, and BP neural network by predicting 100 samples. The results showed that PSO-SVM, which showed the highest correlation coefficient between the predicted and measured values (0.91) and lowest average error rate (0.58%), was better than the others.