基于Richards方程的冷杉树高曲线深度神经网络激活函数

doi:10.11707/j.1001-7488.LYKX20220076

Abstract

Abstract:

Objective: An activation function based on theoretical growth equation (Richards formula) is proposed to solve the problem that the output of neural network algorithm does not accord with biological laws in forest growth modeling, in order to provide a new idea and method for the application of neural network in forest growth modeling. Method: Using the stem analysis data of 96 Abies nephrolepis trees in Wangqing Forestry Bureau of Jilin Province, the traditional nonlinear regression model, the deep neural network tree height-DBH model based on ordinary activation function and the new deep neural network tree height DBH model based on Richards activation function were established respectively. Result: Compared with the traditional nonlinear regression model, R² of the deep neural network model increased by 0.175%, root mean squared error (RMSE) and mean absolute error (MAE) decreased by 2.282% and 4.011%, respectively. Compared with the deep neural network model of ordinary activation function, the new model has obvious tree height asymptote, which is more fitted with the biological law. Conclusion: A neural network activation function based on Richards formula is proposed, which has the following advantages: 1) There must be a maximum value for the output. 2) The output must be greater than 1.3 with a reasonable ANN structure. 3) The new method can take the parameters fitted by the traditional regression method as the input of the neural network model, so that the neural network training can obtain a priori knowledge.

Key words: deep neural network, activation function, theoretical growth equation, height-diameter model

CLC Number:

S757

Qigang Xu,Xiangdong Lei,Yu Zheng,Xingguo Hu,Yuancai Lei,xiao He. A New Activation Function Based on Richards Equation for Tree Height-Diameter Deep Neural Network Model of Abies nephrolepis[J]. Scientia Silvae Sinicae, 2023, 59(10): 50-56.

Figures/Tables 5

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References 0

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测树因子 Tree variable	建模数据 Calibration data				检验数据 Validation data
测树因子 Tree variable	最小值 Min.	最大值 Max.	平均值 Mean	标准差 SD	最小值 Min.	最大值 Max.	平均值 Mean	标准差 SD
胸径 DBH/cm	1.18	29.38	11.26	6.56	1.18	27.45	10.98	7.24
树高 Tree height/m	1.60	20.00	9.43	4.68	1.80	18.20	8.99	4.97

层数 Number of layer	模型1：Richards激活函数深度神经网络 Model 1: a deep neural networks with Richards activation function		模型2：普通激活函数深度神经网络 Model 2: a deep neural networks with normal activation function		模型3：普通激活函数深度神经网络-Tanh Model 3: a deep neural networks with normal activation function-Tanh
层数 Number of layer	神经元个数 Number of neurons	激活函数 Activation function	神经元个数 Number of neurons	激活函数 Activation function	神经元个数 Number of neurons	激活函数 Activation function
1	64	ReLu	64	ReLu	64	ReLu
2	128	ReLu	128	ReLu	128	ReLu
3	256	Softplus	256	Softplus	256	Softplus
4	128	ReLu	128	ReLu	128	Sigmoid
5	64	Softplus	64	ReLu	64	Tanh
6	1	Richards	1	Linear	1	Linear

数据 Dataset	统计量 Model statistics	传统模型 Traditional method	模型1 Model 1	模型2 Model 2	模型3 Model 3
训练集 Calibration set	R²	0.926	0.927	0.925	0.930
	RMSE/m	1.272	1.268	1.283	1.238
	MAE/m	0.954	0.953	0.954	0.933
测试集 Validation set	R²	0.948	0.950	0.942	0.943
	RMSE/m	1.134	1.109	1.186	1.174
	MAE/m	0.896	0.860	0.917	0.898

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A New Activation Function Based on Richards Equation for Tree Height-Diameter Deep Neural Network Model of Abies nephrolepis

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