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

LI Wei1, CHEN Xiuwan1,†, MAO Haiying2, LI Fei1

1. School of Earth and Space Sciences, Peking University, Beijing 100871; 2. Specialized Forces College of CAPF, Beijing 102202; † Corresponding author, E- mail: xwchen@pku. edu. cn

Abstract 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