基于反向傳播神經(jīng)網(wǎng)絡(luò)的退化紅壤區(qū)杉木樹(shù)干液流模擬

涂潔， 劉琪璟， 危駿， 胡良

(1.南昌工程學(xué)院生態(tài)與環(huán)境科學(xué)研究所，南昌 330099；2.北京林業(yè)大學(xué)林學(xué)院，北京 100083)

基于反向傳播神經(jīng)網(wǎng)絡(luò)的退化紅壤區(qū)杉木樹(shù)干液流模擬

涂潔1*， 劉琪璟2， 危駿1， 胡良1

(1.南昌工程學(xué)院生態(tài)與環(huán)境科學(xué)研究所，南昌 330099；2.北京林業(yè)大學(xué)林學(xué)院，北京 100083)

以江西退化紅壤區(qū)杉木人工林為研究對(duì)象，采用MATLAB工具箱中的log-sigmoid型函數(shù)(tansig)為神經(jīng)元作用函數(shù)，以空氣溫度、空氣相對(duì)濕度、平均凈輻射、水汽壓虧缺為輸入變量，液流速率為輸出變量，運(yùn)用貝葉斯正則化算法和Levenberg-Marquardt算法對(duì)4 000組氣象數(shù)據(jù)和液流數(shù)據(jù)進(jìn)行網(wǎng)絡(luò)訓(xùn)練和檢驗(yàn)，構(gòu)建拓?fù)浣Y(jié)構(gòu)為4-10-1的杉木樹(shù)干液流反向傳播(back propagation, BP)神經(jīng)網(wǎng)絡(luò)模型。結(jié)果表明：在2種算法下訓(xùn)練樣本和檢驗(yàn)樣本模型輸出值與實(shí)測(cè)值之間線性回歸的擬合程度均較高，回歸方程的相關(guān)系數(shù)在0.93以上；訓(xùn)練樣本的擬合精度分別為83.57%和83.06%，檢驗(yàn)樣本的仿真精度分別為82.87%和82.15%。說(shuō)明該網(wǎng)絡(luò)模型能夠很好地反映液流速率與氣象因子之間的非線性函數(shù)關(guān)系，可為杉木人工林的可持續(xù)經(jīng)營(yíng)和林地水資源的科學(xué)管理提供有效手段。

杉木； 樹(shù)干液流； 貝葉斯正則化算法； Levenberg-Marquardt算法； 反向傳播神經(jīng)網(wǎng)絡(luò)

SummaryCunninghamialanceolatais commonly considered to be one of the most important tree species for forest restoration and reconstruction in subtropical area of China, owing to its advantages of rapid growth, good quality and high yield per unit area. However, they also consume certain amount of water during the course of growth and play roles of ecological benefits. Therefore, quantitative research on tree water consumption characteristics by transpiration has become a hot issue in the field of tree physiological ecology in recent years.

Taking theC.lanceolataplantation in degraded red soil of Jiangxi Province as the research object, the log-sigmoid type function (tansig) of MATLAB toolbox was selected as the transmission function for the role of neurons. Four main factors including air temperature, relative air humidity, average net radiation and vapor pressure deficit were chosen as the input variables, and the sap flow velocity was selected as the output variable, to train and examine the neural network model with Bayesian regularization algorithm and Levenberg-Marquardt algorithm. The optimum network model ofC.lanceolatasap flow velocity was built with the topological structure of 4-10-1.

Based on Bayesian regularization algorithm and Levenberg-Marquardt algorithm, good fitting results were obtained from the linear regression between predictive and measured values, with correlation coefficients both higher than 0.93. The fitting accuracies of training samples were 83.57% and 83.06%, and the simulation accuracies of testing samples were 82.87% and 82.15%, respectively.

In conclusion, the BP network model can well reflect the non-linear relationship between the meteorological factors and the sap flow velocity, thus may provide an effective tool for sustainable developing strategy ofC.lanceolataplantations and scientific management of the associated water resource in the future.

杉木(Cunninghamialanceolata)是我國(guó)南方亞熱帶地區(qū)重要的造林樹(shù)種，具有生長(zhǎng)快、材質(zhì)好、單產(chǎn)高等優(yōu)點(diǎn)，在該區(qū)植被恢復(fù)重建中占有十分重要的地位。長(zhǎng)期以來(lái)對(duì)杉木的研究主要集中在生物量及生產(chǎn)力[1-2]、凋落物分解及養(yǎng)分歸還[3-4]、土壤理化性質(zhì)[5-6]、土壤微生物[7-8]、土壤呼吸[9-10]以及水文生態(tài)效益[11]等方面，而對(duì)杉木液流速率與環(huán)境因子相關(guān)性的報(bào)道較少[12-13]。已有的對(duì)液流速率與環(huán)境因子二者之間關(guān)系的描述基本上以線性回歸方程為主[12,14-15]，這些模型通常假定生物與環(huán)境的關(guān)系都是平滑、連續(xù)的線性多項(xiàng)式關(guān)系，不能全面反映其非線性關(guān)系。反向傳播(back propagation, BP)神經(jīng)網(wǎng)絡(luò)是采用BP算法訓(xùn)練權(quán)值的多層前饋網(wǎng)絡(luò)，是迄今為止應(yīng)用最多的一種非線性函數(shù)逼近方法，可以很好地解決傳統(tǒng)概率函數(shù)模型適用范圍窄、模型實(shí)用性差等問(wèn)題，非常適合解決林業(yè)問(wèn)題。Foody等[16]、King等[17]通過(guò)對(duì)BP神經(jīng)網(wǎng)絡(luò)與其他方法模擬效果的比較發(fā)現(xiàn)，BP神經(jīng)網(wǎng)絡(luò)更具優(yōu)勢(shì)。目前，BP神經(jīng)網(wǎng)絡(luò)在林業(yè)領(lǐng)域的應(yīng)用研究大多圍繞林木生物量[18]、森林碳蓄積[19]、林分直徑分布[20]以及林分固碳釋氧效益[21]等方面展開(kāi)，但對(duì)于樹(shù)干液流的報(bào)道仍不多見(jiàn)。朱建剛等[22]成功利用BP神經(jīng)網(wǎng)絡(luò)建立了油松、側(cè)柏的液流預(yù)測(cè)網(wǎng)絡(luò)模型，預(yù)測(cè)精度較高，能夠用于實(shí)際預(yù)測(cè)。

本研究選擇退化紅壤區(qū)優(yōu)勢(shì)樹(shù)種杉木為研究對(duì)象，以熱擴(kuò)散探針?lè)▽?duì)樹(shù)干液流的測(cè)定結(jié)果為目標(biāo)向量，以其主要影響因子——空氣溫度(air temperature, Ta)、空氣相對(duì)濕度(relative air humidity, RH)、平均凈輻射(average net radiation, ANR)、水汽壓虧缺(vapor pressure deficit, VPD)為輸入變量，不依賴任何現(xiàn)有數(shù)學(xué)函數(shù)式進(jìn)行模擬，在MATLAB 7.0軟件平臺(tái)上利用嵌套的貝葉斯正則化和Levenberg-Marquardt(L-M)2種算法進(jìn)行網(wǎng)絡(luò)訓(xùn)練，構(gòu)建杉木樹(shù)干液流BP神經(jīng)網(wǎng)絡(luò)模型，以期實(shí)現(xiàn)從多特征氣象要素到樹(shù)干液流速率之間的非線性函數(shù)關(guān)系映射，為退化紅壤區(qū)杉木人工林的科學(xué)經(jīng)營(yíng)和林地水資源的有效管理提供更為有效的技術(shù)方法。

1 材料與方法

1.1 試驗(yàn)地概況

試驗(yàn)地位于江西省泰和縣中國(guó)科學(xué)院千煙洲試驗(yàn)站區(qū)內(nèi)(26°44′48″ N，115°04′01″ E)，樣地設(shè)在站區(qū)1985年前后營(yíng)造的針闊混交風(fēng)景林內(nèi)，具體情況參見(jiàn)文獻(xiàn)[23]。

1.2 樣本數(shù)據(jù)采集

根據(jù)TDP探頭的長(zhǎng)度和被測(cè)木具有代表性的原則，選取生長(zhǎng)良好、樹(shù)干通直、沒(méi)有被擠壓的3株杉木[胸徑(22.9±0.8) cm]安裝液流計(jì)。在被測(cè)木樹(shù)干1.3 m處安裝TDP探針(型號(hào)TDP-30，Dynamax公司，美國(guó))，另一端與數(shù)據(jù)采集器(型號(hào)DT-50，Data Taker公司，澳大利亞)連接。采用自動(dòng)氣象站記錄空氣溫度、風(fēng)速、風(fēng)向、降水、土壤含水量和土壤溫度(土層深度分別為10 cm、20 cm和50 cm)、空氣相對(duì)濕度、平均凈輻射等環(huán)境因子，數(shù)據(jù)采集與液流計(jì)同步(數(shù)據(jù)采集間隔為5 min，每30 min記錄1次)。此外，采用水汽壓虧缺綜合表達(dá)空氣溫度與空氣相對(duì)濕度的協(xié)同效應(yīng)[24]。

樹(shù)干液流速率(v)由Granier經(jīng)驗(yàn)公式計(jì)算得到。

(1)

式中：ΔT為2個(gè)探針間的溫差；ΔTmax為連續(xù)7～10 d所測(cè)液流數(shù)據(jù)中的最大值[25]。

2 網(wǎng)絡(luò)模型的構(gòu)建

2.1 樣本數(shù)據(jù)的預(yù)處理

為了得到最優(yōu)的預(yù)測(cè)結(jié)果，選取2007年4—12月的液流數(shù)據(jù)和氣象數(shù)據(jù)，利用SPSS 16.0軟件中的皮爾遜(Pearson)雙尾相關(guān)分析法對(duì)氣象因子與液流速率進(jìn)行偏相關(guān)分析。結(jié)果發(fā)現(xiàn)，液流速率與平均凈輻射(ANR)、空氣溫度(Ta)、水汽壓虧缺(VPD)呈顯著正相關(guān)，與空氣相對(duì)濕度(RH)呈顯著負(fù)相關(guān)(表1)。說(shuō)明液流速率與這4個(gè)氣象因子具有較好的生態(tài)學(xué)同步性。因此，本文將空氣溫度、空氣相對(duì)濕度、平均凈輻射、水汽壓虧缺作為輸入變量，液流速率作為輸出變量，組建BP神經(jīng)網(wǎng)絡(luò)液流模型的初始樣本數(shù)據(jù)集，具體數(shù)據(jù)統(tǒng)計(jì)格式見(jiàn)表2。在數(shù)據(jù)采集過(guò)程中，由于設(shè)備有時(shí)會(huì)受到外界干擾或人為操作失誤等因素的影響，因此文中參照文獻(xiàn)[26]中提到的無(wú)量綱判別參數(shù)P來(lái)判斷試驗(yàn)監(jiān)測(cè)數(shù)據(jù)中的異常值，實(shí)現(xiàn)對(duì)原始數(shù)據(jù)的篩選。將經(jīng)預(yù)處理后得到的4 000組有效數(shù)據(jù)隨機(jī)均分成2組，其中2 000組數(shù)據(jù)作為訓(xùn)練樣本，余下的2 000組作為檢驗(yàn)樣本。

表 1 杉木液流速率與氣象因子的偏相關(guān)分析

Table 1 Partial correlation analysis between sap flow velocity ofC.lanceolataand meteorological factors

控制變量Controlvariables分析變量Analysisvariables偏相關(guān)系數(shù)Partialcorrelationcoefficient4月April7月July10月OctoberTa,RH,VPDANR0.487**0.775**0.512**RH,VPD,ANRTa0.872**0.830**0.747**Ta,ANR,VPDRH-0.977**-0.781**-0.928**Ta,ANR,RHVPD0.901**0.702**0.926**

Ta：空氣溫度；RH：空氣相對(duì)濕度；VPD：水汽壓虧缺；ANR：平均凈輻射。**表示在P<0.01水平顯著相關(guān)。

Ta: Air temperature; RH: Air relative humidity; VPD: Vapor pressure deficit; ANR: Average net radiation. Double asterisks (**) indicate significant correlation at the 0.01 probability level (Duncan’s multiple range test).

表2 杉木液流預(yù)測(cè)初始樣本數(shù)據(jù)集

由于數(shù)據(jù)采集中各因素、各指標(biāo)的量綱或數(shù)量級(jí)不同，為了更好地反映各因素間的相互關(guān)系，充分發(fā)揮BP神經(jīng)網(wǎng)絡(luò)的預(yù)測(cè)功能，提高其輸出精度，模型訓(xùn)練之前需對(duì)具體對(duì)象的實(shí)測(cè)數(shù)據(jù)進(jìn)行標(biāo)準(zhǔn)化處理，以提高模型的泛化能力。BP神經(jīng)網(wǎng)絡(luò)通常采用的神經(jīng)元作用函數(shù)是S形函數(shù)，以雙曲正切函數(shù)tansig為例，tansig函數(shù)在[-1,1]這一區(qū)間具有最大斜率，因此需要將表2中的數(shù)據(jù)都?xì)w一化到[-1,1]范圍內(nèi)，其計(jì)算公式為

(2)

式中：X、X′分別為變量歸一化前、后的數(shù)值；Xmax為某一變量中的最大值；Xmin為某一變量中的最小值。

2.2 網(wǎng)絡(luò)結(jié)構(gòu)參數(shù)的確定

網(wǎng)絡(luò)結(jié)構(gòu)參數(shù)包括網(wǎng)絡(luò)層數(shù)、每層節(jié)點(diǎn)數(shù)、每層神經(jīng)元的作用函數(shù)、網(wǎng)絡(luò)訓(xùn)練方法和學(xué)習(xí)速率等。當(dāng)隱含層的神經(jīng)元激活函數(shù)采用S形函數(shù)，且神經(jīng)元個(gè)數(shù)足夠多時(shí)，BP神經(jīng)網(wǎng)絡(luò)能映射出任意復(fù)雜的非線性函數(shù)關(guān)系。文中輸入層節(jié)點(diǎn)數(shù)為4，輸出層節(jié)點(diǎn)數(shù)為1。隱含層節(jié)點(diǎn)數(shù)一般通過(guò)設(shè)置較少的節(jié)點(diǎn)數(shù)進(jìn)行網(wǎng)絡(luò)訓(xùn)練確定，測(cè)試網(wǎng)絡(luò)的逼近誤差，然后逐漸增加節(jié)點(diǎn)數(shù)，直到測(cè)試誤差不再有明顯的減小為止?！霸囧e(cuò)法”訓(xùn)練結(jié)果表明，當(dāng)隱含層節(jié)點(diǎn)數(shù)為10時(shí)，網(wǎng)絡(luò)的逼近效果最好。因此，樹(shù)干液流BP神經(jīng)網(wǎng)絡(luò)模型的拓?fù)浣Y(jié)構(gòu)為4-10-1。網(wǎng)絡(luò)的學(xué)習(xí)速率設(shè)置為0.1，最小誤差0.000 1，迭代次數(shù)1 000。前期采用SPSS 16.0軟件對(duì)數(shù)據(jù)的預(yù)處理發(fā)現(xiàn)，采用線性模型對(duì)數(shù)據(jù)擬合無(wú)法得到理想的收斂結(jié)果，因此，本文神經(jīng)網(wǎng)絡(luò)模型中每層神經(jīng)元作用函數(shù)均采用tansig函數(shù)。

貝葉斯正則化算法和L-M算法是神經(jīng)網(wǎng)絡(luò)訓(xùn)練中2種常用的方法。貝葉斯正則化法通過(guò)修正神經(jīng)網(wǎng)絡(luò)的訓(xùn)練性能函數(shù)來(lái)提高其推廣能力，對(duì)內(nèi)存量的需求不大，但訓(xùn)練速度較慢。L-M法由于避免了直接計(jì)算赫賽矩陣，對(duì)于中等規(guī)模的BP神經(jīng)網(wǎng)絡(luò)有最快的收斂速度，但需要較大的內(nèi)存量。本文對(duì)2種算法都進(jìn)行了分析與測(cè)試。

在貝葉斯正則化算法中，網(wǎng)絡(luò)性能函數(shù)經(jīng)改進(jìn)變?yōu)槿缦滦问剑?/p>

MSEREG=γ·MSE+(1-γ)·MSW，

(3)

(4)

式中：MSEREG為改進(jìn)后的函數(shù)；γ為比例系數(shù)；MSE為均方差；MSW為網(wǎng)絡(luò)連接權(quán)值的均方誤差；N為樣本數(shù)；ti為期望輸出誤差；ai為網(wǎng)絡(luò)實(shí)際輸出誤差。

由式(4)可知，貝葉斯正則化算法不僅能保證網(wǎng)絡(luò)訓(xùn)練誤差盡可能小，而且使網(wǎng)絡(luò)的有效權(quán)值盡可能少，大大減少了發(fā)生過(guò)度訓(xùn)練的機(jī)會(huì)。而且貝葉斯正則化算法可以在網(wǎng)絡(luò)訓(xùn)練過(guò)程中自適應(yīng)地調(diào)節(jié)γ的大小，并使其達(dá)到最優(yōu)。

L-M算法是高斯-牛頓法的改進(jìn)形式，既有高斯牛頓法的局部收斂性，又有梯度下降法的全局特性，在收斂速度和訓(xùn)練精度方面明顯優(yōu)越于共軛梯度法、動(dòng)量梯度法和變學(xué)習(xí)率法。

設(shè)W(k)為第k次迭代的網(wǎng)絡(luò)權(quán)值向量，維數(shù)為M，新的權(quán)值向量W(k+1)可根據(jù)下面的規(guī)則求得：

W(k+1)=W(k)+ΔW(k)。

(5)

設(shè)誤差指標(biāo)函數(shù)為

(6)

設(shè)e(W)=[e1(W)，e2(W)，…，ei(W)]T，

ΔW=-[JT(W)J(W)+μI]-1J(W)e(W)。

(7)

式中：N為輸出向量維數(shù)；ei(W)為誤差；ti為期望的網(wǎng)絡(luò)輸出向量；ai為實(shí)際的網(wǎng)絡(luò)輸出向量；W為網(wǎng)絡(luò)權(quán)值和閥值組成的向量；ΔW為權(quán)值增量；J(W)為Jacobian矩陣；μ為比例系數(shù)(>0)；I為單位矩陣。

在實(shí)際操作中，μ是一個(gè)試探性的參數(shù)，對(duì)于給定的μ，如果求得的ΔW能使誤差指標(biāo)函數(shù)E(W)降低，則μ降低；反之，則μ增加。用式(7)修改一次權(quán)值需要求M階的代數(shù)方程，L-M算法的復(fù)雜度計(jì)算公式為O=M3/6(M為網(wǎng)絡(luò)中權(quán)值數(shù)目)，若M很大，則計(jì)算量和存儲(chǔ)量都非常大。然而，每次迭代效率顯著提高，可大大改善其整體性能，特別是在精度要求高時(shí)。

3 模型檢驗(yàn)與分析

3.1 模型預(yù)測(cè)精度

對(duì)于模型預(yù)測(cè)精度的檢驗(yàn)，通常采用模型輸出值與實(shí)測(cè)值之間線性回歸的擬合程度來(lái)表征。將實(shí)測(cè)值作為被解釋變量，預(yù)測(cè)值作為解釋變量，建立一元線性回歸方程y=ax+b。如果模型預(yù)測(cè)值與實(shí)測(cè)值線性關(guān)系顯著、回歸方程合理，則a越接近1，b值越接近0，說(shuō)明預(yù)測(cè)值與實(shí)測(cè)值之間吻合度越高。圖1為液流速率實(shí)測(cè)值與預(yù)測(cè)值之間的線性回歸分布情況。從圖1中不難看出，液流速率BP神經(jīng)網(wǎng)絡(luò)模型的輸出結(jié)果與實(shí)測(cè)結(jié)果在上述4種情況下都較好地符合了y=x的分布。

對(duì)BP神經(jīng)網(wǎng)絡(luò)模型總體訓(xùn)練結(jié)果進(jìn)行分析，其中，線性回歸方程的參數(shù)估計(jì)按照公式(8)計(jì)算得到，相關(guān)系數(shù)(r)由公式(9)計(jì)算得到。

(8)

(9)

從表3中可以看出，當(dāng)隱含層節(jié)點(diǎn)數(shù)選擇為10左右時(shí)，無(wú)論是訓(xùn)練樣本還是測(cè)試樣本，采用貝葉斯正則化算法和L-M法都能得到較好的線性回歸結(jié)果，回歸方程的相關(guān)系數(shù)均在0.93以上。運(yùn)用2種算法對(duì)訓(xùn)練樣本進(jìn)行網(wǎng)絡(luò)訓(xùn)練，擬合精度分別為83.57%和83.06%，將檢驗(yàn)樣本代入液流BP神經(jīng)網(wǎng)絡(luò)模型進(jìn)行檢驗(yàn)，仿真精度分別為82.87%和82.15%。由此可以證明，該BP網(wǎng)絡(luò)模型符合精度檢驗(yàn)要求，能夠較準(zhǔn)確地反映實(shí)際液流速率變化規(guī)律。

A：訓(xùn)練樣本用貝葉斯正則化算法訓(xùn)練得到的結(jié)果；B：訓(xùn)練樣本用L-M方法訓(xùn)練得到的結(jié)果；C：檢驗(yàn)樣本用貝葉斯正則化算法訓(xùn)練得到的結(jié)果；D：檢驗(yàn)樣本用L-M方法訓(xùn)練得到的結(jié)果。A: Training results of training samples by Bayesian regularization algorithm; B: Training results of training samples by Levenberg-Marquardt algorithm; C: Training results of testing samples by Bayesian regularization algorithm; D: Training results of testing samples by Levenberg-Marquardt algorithm.

表3 BP神經(jīng)網(wǎng)絡(luò)模型訓(xùn)練結(jié)果統(tǒng)計(jì)

3.2 模型泛化能力

模型泛化能力檢驗(yàn)一般通過(guò)比較訓(xùn)練樣本與測(cè)試樣本的回歸檢驗(yàn)實(shí)現(xiàn)。當(dāng)訓(xùn)練樣本與測(cè)試樣本的模型輸出與實(shí)測(cè)結(jié)果的線性回歸擬合程度相當(dāng)或稍大時(shí)，表明該網(wǎng)絡(luò)模型具有較好的泛化能力。圖2為樣本數(shù)據(jù)集中隨機(jī)24 h液流速率的模型輸出結(jié)果與實(shí)測(cè)結(jié)果。從中可以看出，運(yùn)用2種算法進(jìn)行網(wǎng)絡(luò)訓(xùn)練得出的擬合值、仿真值均能很好地逼近實(shí)測(cè)值。因此，該BP神經(jīng)網(wǎng)絡(luò)模型具有較好的泛化能力。

A:訓(xùn)練樣本模型輸出與實(shí)測(cè)結(jié)果擬合情況；B:測(cè)試樣本模型輸出與實(shí)測(cè)結(jié)果擬合情況。A: Fitting results between predictive output of training samples and measured values; B: Fitting results between predictive output of testing samples and measured values.

4 討論與結(jié)論

4.1 本文將BP神經(jīng)網(wǎng)絡(luò)模型與SPSS相關(guān)性法相結(jié)合，確定了4個(gè)主要影響因子(平均凈輻射、空氣溫度、水汽壓虧缺、空氣相對(duì)濕度)為輸入變量，液流速率為輸出變量，在模型訓(xùn)練前對(duì)所有樣本數(shù)據(jù)進(jìn)行標(biāo)準(zhǔn)化處理，每層神經(jīng)元的作用函數(shù)均采用tansig函數(shù)，采用MATLAB工具箱中提供的貝葉斯正則化算法和L-M法反向傳播2種算法進(jìn)行網(wǎng)絡(luò)訓(xùn)練，構(gòu)建了拓?fù)浣Y(jié)構(gòu)為4-10-1的樹(shù)干液流BP神經(jīng)網(wǎng)絡(luò)模型。從模型的檢驗(yàn)結(jié)果可以看出，訓(xùn)練樣本與測(cè)試樣本的模型輸出與實(shí)測(cè)結(jié)果的線性回歸擬合程度相當(dāng)，回歸方程的相關(guān)系數(shù)在0.93以上。訓(xùn)練樣本的擬合精度達(dá)83%以上，檢驗(yàn)樣本的仿真精度達(dá)82%以上。因此，在2種算法下建立的BP神經(jīng)網(wǎng)絡(luò)模型均表現(xiàn)出較高的預(yù)測(cè)精度和網(wǎng)絡(luò)泛化能力，實(shí)現(xiàn)了從多特征氣象要素到液流速率之間的非線性函數(shù)關(guān)系映射，可以作為對(duì)傳統(tǒng)樹(shù)干液流模型建模方法的一種補(bǔ)充。

4.2 該樹(shù)干液流BP神經(jīng)網(wǎng)絡(luò)模型是根據(jù)一定自然條件下的試驗(yàn)結(jié)果建立的，有其相應(yīng)的適用范圍，對(duì)于不同地區(qū)、不同樹(shù)種、不同結(jié)構(gòu)林分的研究以及更多因素的考慮是今后探討的方向。雖然神經(jīng)網(wǎng)絡(luò)非線性映射能力很好，但其固有的缺點(diǎn)需要不斷改進(jìn)，目前已有一些新的算法用來(lái)改進(jìn)網(wǎng)絡(luò)的訓(xùn)練過(guò)程，如泛化改進(jìn)算法[27-28]、遺傳算法[29]。此外，朱建剛等[22]研究認(rèn)為雖然應(yīng)用BP神經(jīng)網(wǎng)絡(luò)建立的植物液流預(yù)測(cè)模型具有較好的預(yù)測(cè)性能，但神經(jīng)網(wǎng)絡(luò)為黑箱模型，不能解釋液流傳輸?shù)臋C(jī)制。

致謝 感謝中國(guó)科學(xué)院地理科學(xué)與資源研究所生態(tài)系統(tǒng)網(wǎng)絡(luò)觀測(cè)與模擬重點(diǎn)實(shí)驗(yàn)室千煙洲生態(tài)站工作人員為本文基礎(chǔ)數(shù)據(jù)收集提供的幫助。

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Sap flow simulation ofCunninghamialanceolatain degraded red soil region based on back propagation neural network. Journal of Zhejiang University (Agric. & Life Sci.), 2015,41(2):205-212

Tu Jie1*, Liu Qijing2, Wei Jun1, Hu Liang1

(1.ResearchInstituteofEcology&EnvironmentalSciences,NanchangInstituteofTechnology,Nanchang330099,China; 2.DepartmentofForestSciences,BeijingForestryUniversity,Beijing100083,China)

Cunninghamialanceolata; sap flow; Bayesian regularization algorithm; Levenberg-Marquardt algorithm; back propagation neural network

國(guó)家自然科學(xué)基金(31260172)；江西省高等學(xué)校大學(xué)生創(chuàng)新創(chuàng)業(yè)計(jì)劃項(xiàng)目(201311319039).

2014-05-19；接受日期(Accepted)：2014-09-29；網(wǎng)絡(luò)出版日期(Published online)：2015-03-20

S 718

A

*通信作者(Corresponding author)：涂潔,E-mail:tujie8058@163.com

URL:http://www.cnki.net/kcms/detail/33.1247.S.20150320.1937.005.html