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作 者 ：刘恩斌,李永夫,周国模*,施拥军,莫路锋

期 刊 ：生态学报 2010年 30卷 10期 页码：2549~2561

关键词：生物量估算统一模型；偏最小二乘改进算法；生物量；

Keywords:unified model for biomass estimation, the improved partial Least-Squares Algorithm, biomass,

摘 要 ：从生物量模型的构建与参数辨识方法的改进对生物量进行精确估算。用Chebyshev多项式系的组合构建了p维连续函数空间的一组乘积型基，进而建立了生物量估算统一模型，它具有如下特点：(1）可以克服常用生物量估算模型的经验性、不稳定性、不通用性及对生物量影响因素适应性差的特点，(2）它适合于影响生物量的任何因素，故适应范围非常广且很稳定，(3）可根据实际需要及估算精度确定影响生物量的因素及其阶数大小，(4）模型对生物量的估算相当于在区间

$$-1,1$$ 上进行的数值插值，变量阶数越高，所插入的点就越多，估算结果越符合实际，整个估算的插值过程与树木的树干解析与树木生长原理是相一致的。对所建模型的参数辨识方法做了探讨，经典最小二乘算法是生物量估算的最常用参数辨识方法，由于它本身固有的一些缺陷使常用最小二乘的估算精度与使用范围受到很大的限制，现代多元统计分析的偏最小二乘算法可以克服常用最小二乘的缺陷，但在提取成分时仍具有不足，针对偏最小二乘的缺陷本文对它做了改进，改进算法即能克服偏最小二乘的不足还能使估算精度大大提高。用2个案例对3种生物量估算方法做了对比分析，结果表明生物量估算统一模型与偏最小二乘改进算法精度最高，其生物量估计误差在零附近排成一条直线。

Abstract:This paper explores further the precision estimate of biomass by making improvement on the way biomass models are constructed and parameters identified. To that end, a unified model is set up to estimate the biomass by constructing a group of product-type base of p-dimensional continuous function space through Chebyshev polynomial combination. This model has the following characteristics: (1) It can overcome the experientialism, instability, limited applicability and poor adaptability to biomass-affecting factors ridden in conventional models in biomass estimate. (2）It has wider and more stable applicability given that this model is applicable to any of the biomass-influencing factors. (3）It can determine on the factors that affect the biomass and the size of the order according to actual needs and required accuracy of estimate in different cases. (4）This model works in a way similar to number interpolation between the interval

$$-1,1$$ , the higher order the variables go, the more points should be inserted, the more realistic the estimate becomes. The above interpolation process in estimation abides by the same principle by which tree growth are measured based on the tree trunk analysis. Moreover, it constitutes an equally important task to find best method in identifying parameters for each estimate model. So far, the most commonly used method in parameter identification in term of biomass estimate is classic least squares algorithm. However, because of its inherent defects, classic least squares algorithm is bounded in accuracy and application. Though the partial least-squares algorithm of modern multivariate statistical analysis can somewhat overcome the shortcomings of traditional least-square, it is still not perfect in abstracting constituents. In view of that problem, this thesis has made improvement on modern multivariate statistical analysis to increase the accuracy of calculation. As a result, not only are the shortcomings of the partial least-square overcome, but the accuracy in estimate is raised substantially. By comparing three methods in calculating biomass in two cases, it proved that the unified model in biomass estimate, together with improved partial least square algorithm can render the most accurate result so much so that the biomass-estimate error formed a straight line closely along the zero axis.

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