Acta Scientiarum Naturalium Universitatis Pekinensis ›› 2017, Vol. 53 ›› Issue (1): 189-196.DOI: 10.13209/j.0479-8023.2016.092

• Orginal Article • Previous Articles    

Application and Researches for Trees Volume Estimation Based on Cusp Catastrophe Theory Model

Wei LI1, Xiuwan CHEN1,(), Haiying MAO2, Fei LI1   

  1. 1. School of Earth and Space Sciences, Peking University, Beijing 100871
    2. Specialized Forces College of CAPF, Beijing 102202
  • Received:2015-08-25 Revised:2015-12-26 Online:2017-01-20 Published:2017-01-20
  • Contact: Xiuwan CHEN


李伟1, 陈秀万1,(), 毛海颖2, 李飞1   

  1. 1. 北京大学地球与空间科学学院, 北京 100871
    2. 中国人民武装警察部队警种学院, 北京 102202
  • 通讯作者: 陈秀万
  • 基金资助:


In order to study whether the growth of trees existence mutations problems, measurement and calculation of the mutation based on the cusp model theory is applied to 10 common species single tree volume in Wang Ye Dian forest farm which is located in Chifeng City, Inner Mongolia, China. 10 northern common tree species were selected to carry out the experiment, the tree height (H), DBH (D), volume (V), diameter (D0) were measured which as the true value. To test the Internal and external accord accuracy of the “V-H-D” model by using the improved differential evolution algorithm and edge species and then compare the difference between model calculation value and instrument measuring. After a certain iteration, the results showed that the overall relative error (RS) of the model is in the range of [0.001, 0.05], the average relative error (E) is in the range of [-0.11, 0.02], and the overall prediction accuracy (P) is greater than 80%. The outcome had shown the good fitness of the model, namely the cusp catastrophe theory model applies to northern China 10 single species tree volume. With the growing of trees, when the height of the tree reaches a certain height, the volume will follow the theory model of cusp catastrophe theory. This is the cusp catastrophe theory model was first applied to the determination of single tree volume and got a better fitting result. Meanwhile, a low-dimensional model of mutation was established in the discontinuous measurement, which provides a theoretical and practical basis for the study of tree volume and various species of spatial competition.

Key words: catastrophe theory, northern tree species, cusp model, improved differential evolution algorithm, trees volume


为了研究树木的生长是否也存在突变的问题, 将突变论的尖角模型理论应用于我国北方——内蒙古赤峰市旺业甸林场 10 个常见树种单木材积的测定和计算。选取 10 个北方常见树种, 对其树高(H)、胸径(D)、材积(V)、地径(D0)等参数进行测定, 并以此作为真值, 利用改进差分进化算法对建立的“材积-树高-胸径”模型进行内符合精度检验, 利用边缘树种对模型进行外符合精度检验, 比较模型计算值与仪器测量值之间的差异。在经过一定的迭代之后, 结果表明: 模型的总体相对误差 RS 在[0.001, 0.05]范围, 平均相对误差 E 在 [-0.11, 0.02]范围, 总体预估精度 P 大于 80%, 说明模型拟合较好, 即突变论中的尖角模型理论适用于我国北方 10 个树种单木材积模型的建立, 同时说明随着树木的不断生长, 当树高达到一定高度时, 材积将遵循突变论的尖角模型理论。这是突变论的尖角模型理论首次应用到单木材积的测定, 并得到较好的拟合结果。同时, 在不连续的测量状态下建立的突变低维模型为树木材积的研究和各树种间的空间竞争研究提供了一定的理论和实践依据。

关键词: 突变论, 北方树种, 尖角模型, 改进差分进化算法, 树材积

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