分段削度方程2种估计方法比较

Comparison of Two Parameters Estimation Methods for Segmented Taper Equations

【目的】分段削度方程广泛用于模拟树木干形变化,其通常采用最小二乘回归法估计参数,但是最小二乘回归法估计分段削度方程时,拐点参数a_1和a_2(相对树高,值域在0和1之间)经常不能保证落在(0,1)区间内,从而限制了模型的应用。基于以上问题,本文采用双因素自动优选法和最小二乘回归法进行比较,找出分段削度方程最优拟合方法,为构建树木曲线模型和精细化合理造材提供技术支撑。【方法】以Max等(1976)分段削度方程为基础模型,以热带3个主要珍贵树种红椎、格木、柚木共120株解析木为例,分别采用最小二乘回归法和双因素自动优选法构建各树种干形曲线模型,并以决定系数、残差平方和、平均残差、残差方差和均方误差等统计量指标进行比较分析。【结果】最小二乘回归法和双因素自动优选法的拟合精度都高达95%以上,格木、红椎、柚木都满足决定系数相同、残差平方和相同;对于残差方差和均方误差,格木、红椎、柚木都满足双因素自动优选法最小;对于平均残差,格木满足最小二乘回归法最小,而红椎和柚木则满足双因素自动优选法最小,但是2种方法对应的平均残差差距很小;树干曲线预测效果也很相似;双因素自动优选法可保证所估计出的拐点参数在(0,1)区间内,计算简单,拟合结果稳定。【结论】双因素自动优选法能从理论上说明分段削度方程参数a_1和a_2的最优值,因此建议选择双因素自动优选法拟合分段削度方程。

[ Objective] Taper equation is a key tool to describe stem form variations. By far, different taper equations have been proposed in the world. Among them, the segmented taper equation is one of the most commonly used equation. The method of ordinary least squares regression （OLS） is commonly used to estimate the parameters in the model. However, in practical terms, the application of the segmented taper equation was restricted because the estimated parameters of inflection points a~ and a2 （ the relative tree height with numerical region of 0 to 1 ） obtained by OLS regression do not ensure to fall into the region of 0 to 1. Based on the above issue, the aim of this research is to find out the optimal fitting method by using TS（ the two-factor automatic selection algorithm）and OLS, which provides technical supports for the construction of tree curve model and fine material. [ Method ] The three rare species such as Erythrophleum fordii, Castanopsis hystrix and Tectona grandis were developed using 120 individual data （40 for each species）, the segmented taper equation was constructed for each species using OLS and TS, respectively. They were evaluated and compared based on the indexes of the coefficient of determination, the residual sum of squares, the mean prediction error, the variance of prediction errors and the root mean square error. [ Result ] The results show that both the OLS regression and TS fitting accuracy are preferred more than 95% and their coefficient of determination, residual sum of squares are the same. For the variance of prediction errors and the root mean square error TS is the best for E. fordii, C. hystrix and T.grandis; for the mean prediction error OLS method is the best for E. fordii, but TS is the best for C. hystrix and T. grandis, however, the difference between the two methods corresponding the mean prediction error is small; stem profiles prediction results are also very similar; TS can ensure that the inflection point of the estimated parameters is in the （0,1） ,and it is simple, fitting result is stable. [ Conclusion ]TS could explained theoretically the optimal value of segmented taper equation parameters a1 and a2. Therefore, it was recommended to fit the segmented taper equations with TS.