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

摘要/Abstract

摘要：

目的: 提出一个基于理论生长方程（Richards公式）的激活函数，解决神经网络算法在森林生长建模时输出可能不符合生物学规律的问题，为神经网络在森林生长建模方面的应用提供一个新的思路和方法。方法: 以吉林省汪清林业局臭冷杉为研究对象，利用96株解析木数据，分别建立传统非线性回归模型、基于普通激活函数的深度神经网络模型和新的基于Richards激活函数的深度神经网络树高-胸径模型。结果: 相较基于普通激活函数的深度神经网络模型，新的基于Richards激活函数的深度神经网络模型具有明显的树高渐近线，更符合生物学规律。与传统非线性回归模型（直接使用Richards公式拟合）相比，新的基于Richards激活函数的深度神经网络模型精度略有提高，R²提升0.175%，均方根误差（RMSE）与平均绝对误差（MAE）分别降低2.282%和4.011%。结论: 提出一个基于Richards方程的深度神经网络激活函数，具有如下优点：1）输出一定存在一个合理的最大值；2）配合合理的神经网络结构可使输出一定大于1.3；3）将传统回归方法拟合得到的参数作为神经网络模型输入，能使神经网络的训练得到先验知识。

关键词: 深度神经网络, 激活函数, 理论生长方程, 树高-胸径模型

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

中图分类号:

S757

徐奇刚,雷相东,郑宇,胡兴国,雷渊才,何潇. 基于Richards方程的冷杉树高曲线深度神经网络激活函数[J]. 林业科学, 2023, 59(10): 50-56.

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.

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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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