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基于多层感知机的长白落叶松人工林林分生物量模型

徐奇刚 雷相东 国红 李海奎 李玉堂

徐奇刚, 雷相东, 国红, 李海奎, 李玉堂. 基于多层感知机的长白落叶松人工林林分生物量模型[J]. 北京林业大学学报, 2019, 41(5): 97-107. doi: 10.13332/j.1000-1522.20190035
引用本文: 徐奇刚, 雷相东, 国红, 李海奎, 李玉堂. 基于多层感知机的长白落叶松人工林林分生物量模型[J]. 北京林业大学学报, 2019, 41(5): 97-107. doi: 10.13332/j.1000-1522.20190035
Xu Qigang, Lei Xiangdong, Guo Hong, Li Haikui, Li Yutang. Stand biomass model of Larix olgensis plantations based on multi-layer perceptron networks[J]. Journal of Beijing Forestry University, 2019, 41(5): 97-107. doi: 10.13332/j.1000-1522.20190035
Citation: Xu Qigang, Lei Xiangdong, Guo Hong, Li Haikui, Li Yutang. Stand biomass model of Larix olgensis plantations based on multi-layer perceptron networks[J]. Journal of Beijing Forestry University, 2019, 41(5): 97-107. doi: 10.13332/j.1000-1522.20190035

基于多层感知机的长白落叶松人工林林分生物量模型

doi: 10.13332/j.1000-1522.20190035
基金项目: 林业行业公益性科研项目“我国主要林区林地立地质量和生产力评价研究”(201504303)
详细信息
    作者简介:

    徐奇刚,博士生。主要研究方向:森林生长收获模型。Email:adslxqg@126.com 地址:100091 北京市海淀区香山路东小府1号中国林业科学研究院资源信息研究所

    责任作者:

    雷相东,研究员,博士生导师。主要研究方向:森林生长模型与模拟。Email:xdlei@caf.ac.cn 地址:同上

Stand biomass model of Larix olgensis plantations based on multi-layer perceptron networks

  • 摘要: 目的神经网络模型能避免林分生物量模型建模时自变量共线性与异方差问题,研究多层感知机在林分生物量模型中的应用,为森林经营单位、区域生物量和碳储量的估算提供方法和依据。方法以长白落叶松人工林为研究对象,利用吉林省一类清查固定样地的917组数据,分别建立了基于传统的对数转化后线性模型和神经网络多层感知机的地上生物量和总生物量模型。使用AIC、决定系数(R2)、均方根误差(RMSE)、相对均方根误差(RMSEr)和平均绝对误差(MAE)来评价模型。结果估计精度最高的模型是输入单元为林分平均胸径(D)−平均高(H)−林分密度指数(S)−海拔(HB)−坡向(PX)−坡位(PW)、2个隐藏层、隐单元数为40−20的神经网络模型,与传统对数转换线性回归模型相比,地上生物量和总生物量模型的调整决定系数(Adj.R2)分别从0.902 1提高到了0.914 1,从0.897 9提高到了0.908 9;RMSEr分别从6.330 5%降低到了5.992 2%,从6.490 1%降低到了6.153 6%。包含立地因子的神经网络模型比未包含立地因子的神经网络模型估计精度略有提升,地上生物量与总生物量的Adj.R2分别提高了0.88%和0.99%,RMSEr分别降低了5.33%和5.46%。结论多层感知机生物量模型的估计精度比传统回归模型略有提高,但它可以避免模型选型和违背传统统计假设的处理等问题,且能够一次性计算地上生物量和总生物量模型,有一定优势。

     

  • 图  1  各个林分变量与地上生物量和总生物量的散点图

    Figure  1.  Scatter plots of stand variables and aboveground and total biomass

    图  2  对数转换线性回归模型残差图(n = 917)

    Figure  2.  Residual plot of predictions and observations based on the logarithmic transformation linear regression model (n = 917)

    图  3  人工神经网络模型(模型25)残差图(n = 184)

    Figure  3.  Scatter plots of predictions and observations based on artificial neural network model (model 25) (n = 184)

    图  4  人工神经网络模型(模型25)训练集与验证集预测结果对比图

    Figure  4.  Artificial neural network model (model 25) prediction comparison of training set and validation set

    图  5  人工神经网络模型(模型34)残差图(n = 184)

    Figure  5.  Residual plot of predictions and observations based on artificial neural network model (model 34) (n = 184)

    图  6  人工神经网络模型(模型34)训练集与验证集预测结果对比图

    Figure  6.  Artificial neural network model (model 34) prediction comparison of training set and validation set

    图  7  人工神经网络模型(模型34)残差图(n = 917)

    Figure  7.  Residual plot of predictions and observations based on artificial neural network model (model 34) (n = 917)

    表  1  样地基本因子与生物量统计量

    Table  1.   Summary statistics of sample plot basic variables and biomass

    林分因子   
    Stand factor   
    最大值
    Max.
    最小值
    Min.
    平均值
    Mean
    标准差
    Standard deviation
    变异系数
    Coefficient of variation/%
    年龄/a Age/year57 5 27 11 40.10
    郁闭度 Crown density 1.00 0.20 0.67 0.2030.09
    株数密度/(株·hm− 2) Stand density/(tree·ha− 1)4 033 267 1 257 675 53.64
    林分断面积/(m2·hm− 2) Stand basal area/(m2·ha− 1) 34.63 3.2513.46 6.6749.55
    蓄积量/(m3·hm− 2) Stand volume/(m3·ha− 1)284.3112.9286.2051.1659.35
    平均胸径 Quadratic mean diameter (D)/cm27.75.812.2 3.629.38
    平均树高 Mean tree height (H)/m23.08.415.9 2.717.16
    海拔 Altitude (HB)/m1 190 10 525 209 39.88
    坡度 Slope (PD)/(°)36 0 11 7 68.93
    地上生物量/(t·hm− 2) Aboveground biomass/(t·ha− 1)174.62 9.9060.0033.4055.67
    总生物量/(t·hm− 2) Total biomass/(t·ha− 1)213.2712.0373.6340.9655.63
    下载: 导出CSV

    表  2  地上生物量对数转换线性回归模型参数估计值

    Table  2.   Estimated parameters of aboveground biomass based on log-linear regression model

    编号 No.异速方程 Allometric equationb0b1b2b3
    1lnY = b0 + b1lnD 0.319 8**1.463 8***
    2lnY = b0 + b1ln(D2 × H− 0.676 8***0.599 2***
    3lnY = b0 + b1lnD + b2lnH− 3.188 2***0.148 2ns 2.450 3***
    4lnY =b0 + b1ln(D2 × H × S− 2.989 5***0.502 7***
    5lnY = b0 + b1lnD + b2lnH + b3lnS− 3.865 1***0.404 9***0.750 0***0.778 1***
    6lnY = b0 + b1ln(D2 × S− 2.554 1***0.589 0***
    7lnY = b0 + b1lnD + b2lnS− 2.993 9***0.764 8***0.828 7***
    8lnY =b0 + b1ln(D2 × H) + b2lnS− 3.372 0***0.314 4***0.803 6***
    9lnY =b0 +b1ln(D2 × S) + b3lnH− 2.307 6***0.628 8***− 0.248 5**
    注:D为平均胸径;H为平均树高;S为林分密度指数; b0b1b2b3为模型参数;ns代表参数在0.05水平上不显著;**代表在0.01水平上显著;***代表在0.001水平上显著。下同。Y为地上生物量;Notes: D represents quadratic mean diameter; H represents mean tree height; S represents stand density index; b0, b1, b2, b3 are parameters of models; ns represents no significant difference at 0.05 level; ** represents significant difference at 0.01 level; *** represents significant difference at 0.001 level. The same below. Y represents aboveground biomass.
    下载: 导出CSV

    表  3  地上生物量对数线性回归模型拟合优度与精度检验

    Table  3.   Fitting statistics of aboveground biomass based on log-linear regression model

    编号
    No.
    AIC决定系数
    R2
    调整决定系数
    Adj.R2
    均方根误差/(t·hm− 2)
    RMSE/(t·ha− 1)
    相对均方根误差
    RMSEr/%
    平均绝对误差/(t·hm− 2)
    MAE/(t·ha− 1)
    18 303.537 90.448 60.448 024.790 415.049 9 19.134 8
    28 219.147 20.500 90.500 423.584 114.317 6 18.190 9
    38 091.547 90.572 60.571 621.825 613.250 0 16.851 1
    47 301.056 00.826 20.826 013.918 38.449 610.278 4
    56 888.135 90.902 40.902 110.427 76.330 56.850 3
    67 240.699 10.835 90.835 713.525 08.210 89.940 4
    76 955.132 70.894 20.894 010.859 06.592 37.358 0
    86 910.318 90.900 30.900 110.542 26.400 07.005 9
    97 235.057 20.836 70.836 413.489 48.189 29.888 6
    下载: 导出CSV

    表  4  总生物量对数转换线性回归模型参数估计值

    Table  4.   Estimated parameters of total biomass based on log-linear regression model

    编号 No.异速方程 Allometric equationb0b1b2b3
    10lnY = b0 + b1lnD 0.534 8***1.459 6***
    11lnY = b0 + b1ln(D2 × H− 0.460 4** 0.597 7**
    12lnY = b0 + b1lnD + b2lnH− 2.986 0***0.139 2ns 2.459 3***
    13lnY = b0 + b1ln(D2 × H × S− 2.770 5***0.501 7***
    14lnY = b0 + b1lnD + b2lnH + b4lnS− 3.661 8***0.395 4***0.762 0***0.776 7***
    15lnY = b0 + b1ln(D2 × S− 2.335 5***0.587 7***
    16lnY = b0 + b1lnD + b2lnS− 2.776 5***0.761 1***0.828 2***
    17lnY = b0 + b1ln(D2 × H) + b2lnS− 3.153 5***0.313 1***0.803 0***
    18lnY = b0 + b1ln(D2 × S) + b3lnH− 2.095 2***0.626 5***− 0.242 3**
    注:Y为总生物量。Note: Y represents total biomass.
    下载: 导出CSV

    表  5  总生物量对数转换线性回归拟合优度与精度检验

    Table  5.   Fitting statistics of total biomass based on log-linear regression model

    编号 No.AICR2Adj.R2RMSE/(t·hm− 2)
    RMSE/(t·ha− 1)
    RMSEr/%MAE/(t·hm− 2)
    MAE/(t·ha− 1)
    108 684.928 00.444 50.443 930.510 515.161 023.547 6
    118 600.925 10.497 00.496 429.033 914.427 322.397 4
    128 472.676 50.569 70.568 726.853 213.343 720.732 3
    137 696.929 90.821 50.821 417.292 88.593 012.781 9
    147 292.576 70.898 20.897 913.060 86.490 18.778 7
    157 638.875 60.831 10.830 916.825 88.360 912.362 3
    167 359.598 60.889 70.889 513.594 16.755 09.369 3
    177 315.456 50.895 90.895 713.207 46.562 98.973 9
    187 633.789 10.831 90.831 516.785 28.340 812.309 4
    下载: 导出CSV

    表  6  未加入立地因子的人工神经网络模型结果与拟合优度检验(基于测试集,n = 184)

    Table  6.   Results and goodness of fitting statistics based on artificial neural network models without site factors (based on test set, n = 184)

    编号
    No.
    输入单元
    Input unit
    隐藏层数
    Number of hidden layers
    隐单元数
    Number of hidden units
    训练轮数
    Epoch
    R2Adj.R2
    AGBTotal BAGBTotal B
    19D2H240−202040.523 60.505 80.521 00.503 1
    20D2HS240−20960.721 80.712 40.720 30.710 8
    21D2HS340−40−201120.793 60.782 30.792 50.781 1
    22D2HS440−40−40−201310.790 40.780 70.789 20.779 5
    23D-H240−20920.626 30.617 20.622 20.612 9
    24D-S240−203500.900 90.896 60.899 80.895 4
    25D-H-S240−202910.910 90.907 20.909 40.905 6
    26D-H-S340−40−202590.909 90.906 40.908 40.904 9
    27D-H-S440−40−40−201780.895 50.892 60.893 70.890 8
    28D2HS-D-H-S240−203750.909 30.904 90.907 30.902 8
    29D2HS-D-H-S340−40−202620.908 30.903 60.906 20.901 4
    30D2HS-D-H-S440−40−40−201380.899 80.895 40.897 50.893 1
    注:AGB代表地上生物量(t/hm2),Total B代表总生物量(t/hm2)。下同。Notes: AGB stands for aboveground biomass (t/ha) and Total B stands for total biomass (t/ha). The same below.
    下载: 导出CSV

    表  7  未加入立地因子的人工神经网络模型精度检验(基于测试集,n = 184)

    Table  7.   Accuracy test statistics based on artificial neural network models without site factors (based on test set, n = 184)

    编号 No.RMSE/(t·hm− 2)
    RMSE/(t·ha− 1)
    RMSEr/%MAE/(t·hm− 2)
    MAE/(t·ha− 1)
    AGBTotal BAGBTotal BAGBTotal B
    1924.874 530.791 015.458 815.735 59.559 111.827 7
    2019.006 923.491 811.812 312.004 16.946 6 8.630 2
    2114.785 218.412 3 9.832 6 9.870 25.236 9 6.507 1
    2216.501 120.514 310.255 010.482 75.998 0 7.459 6
    2322.029 727.102 013.690 813.848 98.709 110.745 9
    2411.345 514.087 4 7.050 9 7.198 53.999 8 5.012 9
    2510.758 913.345 2 6.686 4 6.819 33.692 8 4.736 1
    2610.815 713.400 0 6.721 6 6.847 33.719 4 4.710 5
    2711.650 414.353 8 7.240 4 7.334 73.746 1 4.744 5
    2810.851 413.508 8 6.743 8 6.902 93.668 1 4.687 1
    2910.912 613.601 0 6.781 9 6.950 03.855 4 4.887 5
    3011.409 914.166 4 7.091 0 7.238 94.286 3 5.376 1
    下载: 导出CSV

    表  8  加入立地因子的人工神经网络模型结果与拟合优度检验(基于测试集,n = 184)

    Table  8.   Results and goodness of fit statistics based on artificial neural network models with site factors (based on test set, n = 184)

    编号
    No.
    输入单元
    Input unit
    隐藏层数
    Number of hidden layer
    隐单元数
    Number of hidden units
    训练轮数
    Epoch
    R2Adj.R2
    AGBTotal BAGBTotal B
    31D-H-S-HB-PD-PX-PW240−201130.905 90.901 40.893 00.887 8
    32D-H-S-HB-PD-PX-PW340−40−201600.898 40.895 10.884 50.880 7
    33D-H-S-HB-PD-PX-PW440−40−40−201280.881 50.880 30.865 20.863 9
    34D-H-S-HB-PX-PW240−201260.910 90.906 60.909 40.905 1
    35D-H-S-HB-PX-PW340−40−201790.898 30.895 60.885 10.882 0
    36D-H-S-HB-PX-PW440−40−40−201360.907 10.903 20.894 90.890 6
    37D-H-S-PX-PW240−201080.908 00.904 40.896 70.892 6
    38D-H-S-PX-PW340−40−20650.901 70.897 30.889 60.884 6
    39D-H-S-PX-PW440−40−40−201260.900 70.897 90.888 40.885 3
    注:HB代表海拔(m),PD代表坡度(°),PX代表坡向,PW代表坡位。Notes: HB stands for altitude, PD stands for slope (°), PX stands for slope aspect, and PW stands for slope position.
    下载: 导出CSV

    表  9  加入立地因子的人工神经网络模型精度检验(基于测试集,n = 184)

    Table  9.   Accuracy test statistics based on artificial neural network models with site factors (based on test set, n = 184)

    编号 No.RMSE/(t·hm− 2)
    RMSE/(t·ha− 1)
    RMSEr/%MAE/(t·hm− 2)
    MAE/(t·ha− 1)
    AGBTotal BAGBTotal BAGBTotal B
    3111.053 313.758 06.870 67.030 23.760 54.818 1
    3211.484 914.185 07.137 67.248 43.883 24.943 2
    3312.406 315.153 97.710 27.743 54.216 15.212 7
    3410.758 013.385 16.685 86.839 73.611 94.662 4
    3511.491 614.152 07.141 77.231 53.731 34.704 2
    3610.987 313.625 36.828 36.962 43.903 24.921 7
    3710.929 913.541 26.792 66.919 43.707 04.742 8
    3811.298 614.039 97.021 87.174 33.756 44.809 0
    3911.358 613.998 27.059 17.152 93.846 94.933 7
    注:AGB代表地上生物量(t/hm2),Total B代表总生物量(t/hm2)。Notes: AGB stands for aboveground biomass (t/ha) and Total B stands for total biomass (t/ha).
    下载: 导出CSV

    表  10  各组最优模型的比较(n = 917)

    Table  10.   Comparison of the 4 best models for each group (n = 917)

    模型 Model地上生物量 Aboveground biomass总生物量 Total biomass
    R2Adj.R2RMSE/(t·hm− 2)
    RMSE/(t·ha− 1)
    RMSEr/%MAE/(t·hm− 2)
    MAE/(t·ha− 1)
    R2Adj.R2RMSE/(t·hm− 2)
    RMSE/(t·ha− 1)
    RMSEr/%MAE/(t·hm− 2)
    MAE/(t·ha− 1)
    50.902 40.902 110.427 76.330 56.850 3
    140.898 20.897 913.060 86.490 18.778 7
    250.906 40.906 110.426 06.329 56.985 10.900 40.900 013.099 06.509 08.990 2
    340.916 10.914 1 9.870 55.992 26.737 70.911 00.908 912.383 76.153 68.625 0
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-01-15
  • 修回日期:  2019-03-13
  • 网络出版日期:  2019-04-30
  • 刊出日期:  2019-05-01

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