突变论尖角模型在树材积估算中的应用研究

doi:10.13209/j.0479-8023.2016.092

摘要/Abstract

摘要：

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

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 various species of spatial competition.

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

中图分类号:

S758

李伟, 陈秀万, 毛海颖, 李飞. 突变论尖角模型在树材积估算中的应用研究[J]. 北京大学学报自然科学版, 2017, 53(1): 189-196.

Wei LI, Xiuwan CHEN, Haiying MAO, Fei LI. Application and Researches for Trees Volume Estimation Based on Cusp Catastrophe Theory Model[J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2017, 53(1): 189-196.

图/表 7

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地区	年均气温/℃	年积温/℃	极端低温/℃	极端高温/℃	无霜期/d	年日照/h	年均风速/(m·s^-1)	年均降水/mm
赤峰市	0~7	2600~3800	-10	41	78~90	2700~3100	2.5	300~500
喀喇沁旗	3.5~7	2000~3200	-30.9	37.4	110~150	2913.3	2.8	591.2

地区	年均气温/℃	年积温/℃	极端低温/℃	极端高温/℃	无霜期/d	年日照/h	年均风速/(m·s^-1)	年均降水/mm
赤峰市	0~7	2600~3800	-10	41	78~90	2700~3100	2.5	300~500
喀喇沁旗	3.5~7	2000~3200	-30.9	37.4	110~150	2913.3	2.8	591.2

树种	模型	RMSE	SSE	R	R²	DC	C-S	F
油松 Pinus tabuliformis.	y=-40.671x₁⁴-2.975x₂² +2.742x₃+13.753	0.0200	0.0064	0.9969	0.9938	0.9938	0.00881	2232.1520
樟子松 Pinus sylvestnis var. mongolica Litv.	y=-5.048x₁⁴+9.821x₂² -0.0002x₃+0.0014	0.0044	0.0002	0.9995	0.9990	0.9990	0.0017	9134.0809
落叶松 Larix gmelinii (Ruprecht) Kuzeneva.	y=-1.927x₁⁴+9.067x₂² +2.754x₃-0.057	0.0520	0.0461	0.9919	0.9839	0.9839	0.1097	918.9520
红松 Pinus koraiensis Siebold et Zuccarini.	y=-7.958x₁⁴+0.0001x₂² +0.00032x₃-0.0429	0.0090	0.0007	0.9936	0.9873	0.9873	0.0041	467.1430
五角枫 Acer elegantulum Fang et P. L. Chiu.	y=-5.536x₁⁴+8.979x₂² -1.837x₃+4.467	0.0015	1.3536	0.9998	0.0006	0.9996	0.0002	9952.2379
榆树 Ulmus pumila L.	y=-4.199x₁⁴+0.0001x₂² -0.0001x₃+0.0003	0.0355	0.0151	0.9904	0.9809	0.9809	0.0289	514.8484
柞树 Xylosma racemosum.	y=-6.343x₁⁴+7.258x₂² +0.0005x₃-0.0421	0.0152	0.0032	0.9945	0.9891	0.9891	0.0400	1085.7894
黑桦 Betula dahurica Pall.	y=-3.544x₁⁴+9.346x₂² +2.177x₃-0.0183	0.0150	0.0033	0.9969	0.9939	0.9939	0.0135	1956.3780
白桦 Betula platyphylla Suk.	y=-5.166x₁⁴-9.459x₂² +0.0016x₃-0.1594	0.0498	0.0447	0.9829	0.9662	0.9662	0.1472	457.7420
山杨 Populus davidiana.	y=-2.507x₁⁴+7.583x₂² +0.00032x₃-0.0738	0.0700	0.0986	0.9913	0.9827	0.9827	-0.0509	1024.1950

树种	模型	RMSE	SSE	R	R²	DC	C-S	F
油松 Pinus tabuliformis.	y=-40.671x₁⁴-2.975x₂² +2.742x₃+13.753	0.0200	0.0064	0.9969	0.9938	0.9938	0.00881	2232.1520
樟子松 Pinus sylvestnis var. mongolica Litv.	y=-5.048x₁⁴+9.821x₂² -0.0002x₃+0.0014	0.0044	0.0002	0.9995	0.9990	0.9990	0.0017	9134.0809
落叶松 Larix gmelinii (Ruprecht) Kuzeneva.	y=-1.927x₁⁴+9.067x₂² +2.754x₃-0.057	0.0520	0.0461	0.9919	0.9839	0.9839	0.1097	918.9520
红松 Pinus koraiensis Siebold et Zuccarini.	y=-7.958x₁⁴+0.0001x₂² +0.00032x₃-0.0429	0.0090	0.0007	0.9936	0.9873	0.9873	0.0041	467.1430
五角枫 Acer elegantulum Fang et P. L. Chiu.	y=-5.536x₁⁴+8.979x₂² -1.837x₃+4.467	0.0015	1.3536	0.9998	0.0006	0.9996	0.0002	9952.2379
榆树 Ulmus pumila L.	y=-4.199x₁⁴+0.0001x₂² -0.0001x₃+0.0003	0.0355	0.0151	0.9904	0.9809	0.9809	0.0289	514.8484
柞树 Xylosma racemosum.	y=-6.343x₁⁴+7.258x₂² +0.0005x₃-0.0421	0.0152	0.0032	0.9945	0.9891	0.9891	0.0400	1085.7894
黑桦 Betula dahurica Pall.	y=-3.544x₁⁴+9.346x₂² +2.177x₃-0.0183	0.0150	0.0033	0.9969	0.9939	0.9939	0.0135	1956.3780
白桦 Betula platyphylla Suk.	y=-5.166x₁⁴-9.459x₂² +0.0016x₃-0.1594	0.0498	0.0447	0.9829	0.9662	0.9662	0.1472	457.7420
山杨 Populus davidiana.	y=-2.507x₁⁴+7.583x₂² +0.00032x₃-0.0738	0.0700	0.0986	0.9913	0.9827	0.9827	-0.0509	1024.1950

树种	迭代次数	RS	E	P/%
油松-Pinus tabuliformis.	317	0.0200	-0.027	90.13
樟子松- Pinus sylvestnis var. mongolica Litv.	309	0.0436	0.008	97.21
落叶松-Larix gmelinii (Ruprecht) Kuzeneva.	338	0.0520	0.015	89.10
红松-Pinus koraiensis Siebold et Zuccarini.	296	0.0092	-0.113	87.12
五角枫-Acer elegantulum Fang et P. L. Chiu.	314	0.0015	0.008	88.17
榆树-Ulmus pumila L.	314	0.0355	0.017	89.21
柞树-Xylosma racemosum.	246	0.0151	-0.021	90.97
黑桦-Betula dahurica Pall.	280	0.0154	0.001	93.26
白桦-Betula platyphylla Suk.	267	0.0498	0.019	94.55
山杨-Populus davidiana.	294	0.0702	-0.007	96.78