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活立木年龄微损测量是解决很多林业问题的关键,对森林经营、生长模拟以及古树保护等都具有重要的意义[1-4]。传统的确定活立木年龄是通过识别树木的年轮数量[5-6],这种方法虽然比较准确,但是需要用生长锥取树木生长芯,或者伐倒树木截取圆盘,对树木具有侵入性和破坏性;无损的确定活立木年龄的方法有查数轮生枝法和建立非线性数学模型[7-11]等,由于树木有时一年形成二层轮枝,查数轮生枝法确定树木年龄精度不高;通过建立数学模型来估算树木的年龄方法不具有普遍性,并且准确性较低[12],实际生产中并不能得到广泛的应用。
树木针刺仪是微损的测定树木年龄的工具,将其应用于活立木,可以获得相对阻力折线图[13],折线图中峰谷的趋势反映树木年轮内早材和晚材边界引起的变化[14],可以估计树木的年龄和树木生长率[15-16]。树木针刺仪自带DECOM软件可以对抗钻阻力折线图进行分析,通过人工干预半自动检测年轮边界,估计树木年龄[17],由于针刺仪的钻针轴直径只有1.5 mm,对树干的损伤很小,使用针刺仪确定树木年龄的方法对活立木伤害小,是微损的设备,但是DECOM软件自动识别结果很不准确,很多真实年轮边界不能正确识别,误差很大,无法在林业生产中投入使用。
本研究以德国RINNTECH公司生产的树木针刺仪(Resistograph 4450P/S)钻入活立木获取的抗钻阻力值序列折线图为研究对象,给出峰谷分析算法,根据确定阈值Det,记录关键点值和关键点序号,来分析利用峰谷分析算法估计活立木年龄的可行性,为针刺仪自带DECOM软件改进提供理论支撑,推进微损测定树木年龄方法的研究进程。
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德国RINNTECH公司开发的树木针刺仪(Resistograph 4452P/S)是通过电脑控制电子传感器的钻刺针,测量树木的钻入阻抗,获取抗钻阻力折线图,横坐标轴刻度代表针头钻入的深度(单位:mm),纵坐标轴刻度为阻力值(单位:resi)。根据阻力和密度之间的线性关系,可以利用折线图中波峰波谷的趋势来确定活立木早材和晚材边界[18]。使用针刺仪自身携带的DECOM软件可以自动分析折线图,识别年轮边界,估计树木的年龄。
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由于树木春材和秋材的密度不同,相应抗钻阻力值总会有差异,在抗钻阻力折线图中可以很直观的看到很多波峰和波谷出现,其中有很多跃度较小的峰谷,并不代表年轮变化。峰谷分析算法可以根据实测树芯年轮数,确定跃度的阈值Det,去掉伪年轮,留下真年轮,并将有效的年轮峰值和谷值记录下来,确定最终有效的峰谷数来估计树木的年龄。
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首先对获取的抗钻阻力剖面进行去首尾处理,去掉两端无效数据,保留木质部的数据,处理后的针刺仪获取树木的相对阻力记录为整数序列
$x = \{ {x_1},{x_2},\cdots,{x_n}\} $ ,$n$ 为针刺仪测量点的序列号。峰谷分析算法是从抗钻阻力序列$x$ 起始点${k_0}$ 开始,设定阈值Det,允许误差$e = 0.2$ ,确定峰值点和峰谷点序号,以及相应的极值。各项初始值如下:极值点进入点:
$K\max = {k_0},K\min = {k_0},$
极大值点起始进入点和退出点分别记为:
$K\max sta = K\max ,K\max end = K\max ,$
极小值点起始进入点和退出点分别记为:
$K\min sta = K\min ,K\min end = K\min ,$
极值点
$X\max = X({k_0}),X\min = X({k_0})$ ,极值点起始点$Ksta = 0$ 。分成3种情况进行分析:从起始点
$X({k_0})$ 以后未知升降段、升段、降段。输入为:
$x$ ,Det,e,${k_0}$ ,升降段表示islor2,取值为0,1,2,其中islor2=1表示升段,islor2=2表示降段,islor2=0表示未知升降;输出为:极值点起点序号
$Ksta$ ,极值点最后一点序号$Kend$ ,极值点值$Vmid$ ;升降段表示$is12 = YZ$ 两位数,$Y$ 是本段代码,$Z$ 是下段代码,$is12 = - 1$ 表示出错;其中,$Y = 1$ 表示本段升,$Y = 2$ 表示本段降,$Y = 3$ 表示本段是头(不完整段);$Z = 1$ 表示下段升,$Z = 2$ 表示下段降,$Z = 3$ 表示下段是尾(不完整段);流程图见图1:
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根据2.2.1节得到的极值点起点和退出序号,以及升降段表示,记录峰点和谷点的数量,以及关键点值和关键点号。参数说明如下:
根据2.2.1节输出极值点起点序号
$Ksta$ ,极值点最后一点序号$Kend$ ,极值点值$Vmid$ ;升降段表示$is12 = YZ$ 两位数,将参数$is12 = YZ$ 拆分成两个参数$id1$ 和$id2$ ,令
$is12 = YZ = 10id1 + id2$ ,记$id1$ 是$\dfrac{{is12}}{{10}}$ 向零方向取的整数,$id2 = is12 - 10id1$
则有:
$id1 = 1$ 表示本段升,$id1 = 2$ 表示本段降,$id1 = 3$ 表示本段是头(不完整段);$id2 = 1$ 表示下段升,$id2 = 2$ 表示下段降,$id2 = 3$ 表示下段是尾(不完整段);用
$id1 = 1$ 表示波峰,$id1 = 2$ 表示波谷,$id1 = 3$ 表示端点;矩阵P为
$m$ 行3列矩阵,第一列记录关键点号,第二列记录关键点值,第三列记录$id$ ;矩阵
$N$ 为1行2列的矩阵,$N = (No1,No2)$ ,其中$No1$ 统计峰点的个数,$No2$ 统计谷点个数。 -
输入:针刺仪测量数据去首尾得到的列向量
$X = \{ {x_1},{x_2}, \cdots ,{x_n}\} $ 和阈值Det;step1. 将原来针刺仪数据去首尾,得到的数据
$X = \{ {x_1},{x_2}, \cdots ,{x_n}\} $ ,加上一列序号${X_1} = \{ 1,2, \cdots ,n\} $ , 分别以${X_1}$ 作为第一列,$X$ 作为第二列,构造矩阵的$DX$ ,则矩阵DX表示带序号的观测值,可以表示为:$DX = ({X_1},X)$
step2. 分析初始段
此时取参数islor2=0,
${k_0} = 1$ ,$e = 0.2$ ,根据2.2.1得到相应的输出Ksta,Kend,Vmid,is12。若
$id2 = 3$ ,记录矩阵P为$m$ 行3列矩阵,第一列记录关键点号,第二列记录关键点值,第三列记录$id$ 。$P = \left( {\begin{array}{*{20}{c}} 1&{DX(1,2)}&3 \\ n&{DX(n,2)}&3 \end{array}} \right)$
若
$id2 = 1$ ,分成两种情况讨论:若
$id1 = 3$ ,此时有不完整前段,记录$P = \left( \!\!\!\!{{array}{*{20}{c}} 1\!\!&\!\!{DX(1,2)}\!\!&\!\!3 \\ {DX(Kend,1)}\!\!&\!\!{DX(Kend,2)}\!\!&\!\!2 {array}}\!\!\!\! \right)$ ,$No2 = No2 + 1$ 若
$id1 = 1$ ,此时没有前段,记录$P = \left(\!\!\!\! {{array}{*{20}{c}} {DX(Kend,1)}\!\!&\!\!{DX(Kend,2)}\!\!&\!\!2 {array}} \!\!\!\! \right)$ ,$No2 = No2 + 1$ 若
$id2 = 2$ ,此时后段是完整段,分成两种情况讨论:若
$id1 = 3$ ,记录$P = \left(\!\!\!\! {{array}{*{20}{c}} 1\!\!&\!\!{DX(1,2)}\!\!&\!\!3 \\ {DX(Kend,1)}\!\!&\!\!{DX(Kend,2)}\!\!&\!\!1 {array}}\!\!\!\! \right)$ ,$No1 = No1 + 1$ 若
$id1 = 2$ ,记录$P = \left(\!\!\!\! {{array}{*{20}{c}} {DX(Kend,1)}\!\!&\!\!{DX(Kend,2)}\!\!&\!\!1 {array}}\!\!\!\! \right)$ ,$No1 = No1 + 1$ step3. 初始段之后,各段轮流升降
当
$Kend < n$ 时,取参数islor2=id2,${k_0} = Kend$ ,$e = 0.2$ ,根据2.1.1节得到相应的输出Ksta,Kend,Vmid,is12。记录$P$ 为分块矩阵,将所有的关键点序号和关键点值依次循环写入,即$P = \left(\frac {P}{{DX(Ksta)}\quad{Vmid}\quad{id1} } \right)$
若
$id1 = 1$ ,则记录$No1 = No1 + 1$ ;若
$id1 = 2$ ,则记录$No2 = No2 + 1$ ;若
$Kend > Ksta$ ,则记录$P = \left( \frac{P}{{DX(K{\rm{end}})}\quad{Vmid}\quad{id1}} \right);$
输出:矩阵
$P$ ,矩阵$No = [No1,No2]$ 。峰谷分析算法的估计年龄
$A$ 可以由峰谷数的均值的二分之一取整数得到,即$A = (No1 + No2)/4$ 取整数。 -
根据2.3节输出的结果矩阵
$P$ ,$P$ 中的第一列是关键点序号,即峰点起点序号和结束点序号以及谷点起点序号和结束点序号,第二列是关键点值,第三列表示关键点序号是峰点或者谷点。由于针刺仪的取样规律是每1 mm取100个点,说明抗钻阻力两个相邻的序号之间的距离就为0.01 mm,假设矩阵$P$ 每个波峰的第一个波峰点所在的行号为${l_i},i = 1,2, \cdots ,No1,$
提取
$P$ 所有的${l_i},i = 1,2, \cdots ,No1$ 行,重新组成新的矩阵,记为$Q = (\begin{array}{*{20}{c}} {P({l_i})}&{Vmid}&1 \end{array})$
将矩阵
$Q$ 中的第一列相邻两个元素做差分,得到相邻两个峰点之间序号之差,因针刺仪抗钻阻力数据采取间隔是每1 mm取100个点,则相邻序号差值的百分之一可以是对应年度树木的估计年轮宽度,年轮宽度单位为mm。
基于峰谷分析算法用针刺仪测定树木年龄的可行性分析
Feasibility Analysis of Tree Age Estimation Algorithm Using Resistograph Based on Peak-valley Analysis
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摘要:
目的 介绍峰谷分析算法在树木针刺仪抗钻阻力数据中的应用,推进微损测定树木年龄方法的研究进程。 方法 以吉林省汪清县林业局金沟岭林场天然林中红松、冷杉为研究对象,钻取树木生长芯,同时使用针刺仪获取104组抗钻阻力数据。利用峰谷分析算法,根据树芯的实测年龄选定恰当的阈值Det,记录抗钻阻力的峰和谷的个数为估算的树木年轮数。 结果 根据树芯的实测年龄选定阈值后,利用峰谷分析算法估计树木年龄与实际年龄很接近。该算法估计年龄平均绝对误差是−2,范围在−5年至5年之间,平均相对误差为−2.69%,范围在−6.73%至6.73%之间。经过成对数据t检验得到t值为1.31,说明该算法估计树木年龄均值与真实年龄均值之间无显著差异。 结论 峰谷分析算法应用于针刺仪抗钻阻力序列来估计树木年龄是可行的,确定存在恰当的阈值使针刺仪估计树木年龄精度很高,阈值的选择依据是下一步研究的重点内容。 Abstract:Objective To study the application of Peak-valley analysis algorithm in the Resistograph drilling resistance sequence so as to promote the research on quasi-nondistructive tree age estimation. Method The increment cores and 104 groups Resistograph drilling resistance data were collected from Pinus koraiensis and Abies fabri in Jingouling Forest Farm, Wangqing Forestry Bureau, Jilin Province of northeastern China. The appropriate threshold value was selected according to the tree real age and the Peak-valley analysis algorithm was used to record the number of peaks and valleys of drilling resistance data as the estimation of tree age. Result The tree ages were estimated by the peak-valley analysis with the selected threshold value (Det), and the results showed that the data are close to the real tree age, with mean absolute error as −2 years, ranging from −5 to 5 years, and the mean relative error as −2.69%, ranging from −6.73% to 6.73%. Paired data t-test was carried out with t-value of 1.31, indicating that there is no significant difference between estimated tree age estimated by the method of peak-valley analysis and the real mean tree age. Conclusion The application of the drill resistance sequence on the tree age with peak-valley analysis algorithm is proved to be feasible. The appropriate threshold value is the key to guarantee the accuracy of tree age estimation by Resistograph, therefore it is the main part for further research. -
Key words:
- tree age
- / resistograph
- / drilling resistance data
- / peak-valley analysis
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