基于水氮互作的烟草高光谱特性及估测模型研究
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摘要
水氮是影响作物生长的最主要的限制因子之一。作物的叶片颜色、长势、品质以及其形态结构均会随着水分和氮素的多少发生一系列变化,光谱反射率则会与之相对应的发生变化。因此,可以根据作物的光谱反射特征来实现对作物水分和氮素的实时监控和诊断,从而为作物的大田管理提供一定的参考依据。传统的作物水氮监测手段费时费力,而通过借助遥感技术则可以方便快速的获取作物生长信息。本文通过野外手持光谱仪在地面遥感下研究了水氮互作条件下烟草的高光谱特征以及各种生理生化指标的估测模型,通过对所建立的模型进行检验,实测值与预测值的相关关系达到显著水平,模型的精度和预测能力较好。主要研究结果如下:
1.同一氮素水平不同水分下的烤烟冠层和叶片光谱反射率变化基本一致,可见光内,烤烟冠层的光谱反射率随着土壤水分含量的增加而呈下降状态。在近红外光区内,烤烟冠层的光谱反射率随着土壤水分含量的增加而随之变高。烤烟不同生育时期其光谱反射率也在不断变化,可见光区内随着烟草的生长发育,其冠层的高光谱反射率基本表现为在伸根期最低,旺长期升高,成熟期降低,近红外光区内冠层的高光谱反射率表现为伸根期至旺长期急剧升高,随后下降。旺长期是烟草生长发育最快的时期,生长中心从地下转移到地上,茎迅速伸长加粗,可见叶数迅速增加,叶片充实,光在叶片复杂的内部组织结构下进行了多次的反射散射致使反射率升高。旺长期到成熟期,由于叶片的成熟和开始采摘导致叶绿素总量减少,叶片内部海绵组织和栅栏组织结构发生变化,影响了光谱的反射率。
同一水分不同氮素下,在可见光区内,随着施氮量的增加,烤烟冠层和叶片的光谱反射率呈降低趋势,这主要是因为叶片色素含量的增加导致了烤烟叶片对光的强烈吸收。在近红外光区内,随着施氮量的增加,烤烟冠层和叶片的光谱反射率呈增加趋势。在可见光区,随着烟草的生长发育,冠层的高光谱反射率基本上为伸根期最低,旺长期变高,成熟期又降低的趋势。云烟87的反射率在各个时期均比K326高一些,可能是品种差异造成的。
不同水分和氮素组合条件下,烤烟光谱随土壤水分变化趋势一致。同一水分条件下,高氮处理的烟草冠层光谱反射率在可见光处低于低氮处理,在近红外波段高于低氮处理。
2.本文通过地面光谱仪在水氮互作下对烤烟的冠层、叶片及烤后叶片进行了高光谱的信息采集,采用相关分析方法分析多种生理生化指标与烟草冠层和鲜叶片的高光谱参数的关系,筛选出与各种生理生化指标关系最为密切的光谱特征变量,采用多元逐步回归方法,建立这些指标的估测模型,最后进行检验样本检验。
通过分析冠层光谱参数可知叶面积指数、地上鲜生物重、地上干生物重回归方程的第一自变量均为绿峰幅值,且其相关系数均达到极显著水平,以绿峰幅值为第一自变量的逐步回归方程亦达到显著水平,可作为叶面积指数、地上鲜生物重、地上干生物重的特征变量;土壤调整植被指数经分析与叶绿素a、叶绿素b、叶绿素总量、类胡萝卜素相关性最强,与总氮和烟碱相关性最强的特征变量是绿峰幅值,与叶片含水率和淀粉相关性最强的特征变量均是黄边幅值,黄边面积经分析与总糖和还原糖相关性最强;根据与烤烟生理生化指标关系最密切的光谱变量所建立的回归方程能够找出与这些生理生化指标相对应的特征变量。基于高光谱参数所建立的烤烟生理生化指标冠层逐步回归方程的决定系R2均达到了显著的水平,其对应的回归系数相伴概率也都达到了显著水平,通过随机选取一定数量的样本进行检测,发现基于烤烟生理生化指标的冠层逐步回归方程的估测值与实测值的相关系数均达到了显著水平,说明所建立的冠层逐步回归方程估测效果良好。
通过分析叶片光谱参数可知红边位置与叶绿素a、叶绿素b、叶绿素总量、类胡萝卜素相关性最强,与总糖和淀粉相关性最强的特征变量均是蓝边幅值,与还原糖和总氮相关性最强的特征变量均是绿峰幅值,与叶片含水率相关性最强的特征变量是红边面积与蓝边面积归一化值,与烟碱相关性最强的特征变量是红边面积;根据高光谱参数建立的叶片逐步回归方程,其决定系数R2都达到了显著的水平,通过随机选择一定数量的样本进行检测,发现基于烤烟生理生化指标的叶片逐步回归方程的估测值与实测值的相关系数均达到了极显著水平,说明所建立的叶片逐步回归方程估测效果良好。
3.化学品质、矿质元素以及中性致香物质都是烟叶质量的重要评价指标,通过分析烤烟的冠层、叶片及烤后烟叶的高光谱参数与这些质量指标的相关关系,建立基于高光谱参数的逐步回归估测模型,通过随机选择一定数量的样本进行检测,表明水氮互作下烟草的各种高光谱参数与烤后叶片的质量指标都具有不同程度的相关性,并且根据所相应的逐步回归模型可以进行相对精确地估测。表明通过高光谱估测模型对烟草这些质量指标进行预测是可行的,从而为烟草生长状况监控和烟田管理提供参考。
4.关于光谱分析方法的研究与应用已有很多,目前常用的主要是通过根据光谱反射率提取出的植被指数进行建模。植被指数方法在估算烟草各种生理生化指标时虽然也能取得较好的效果,但由于其一般仅利用几个波长的信息,模型预测能力及稳定性难以保证。主成分分析方法能够有效降维且尽量保持原有光谱重要信息,充分挖掘高光谱各波段信息,实现各波段之间信息互补,较好地降低了波段数少而带来的随机干扰,因此主成分分析的可靠性和普适性较好。神经网络具有很强的非线性映射能力,而且不要求数据呈正态分布,神经网络模型具有较强的线性和非线性拟合能力,在数据拟合与模拟中有着无比的优越性,但很难全面解释神经网络作出决策或者产生输出的过程。
Abstract: The levels of water and nitrogen are the most important limiting factors of crop growth. The shortage of water and nitrogen can cause a series of changes, such as leaf color, thickness, moisture content and morphological change, consequently causing the changes in spectral reflectance characteristic. The real-time monitoring and rapid diagnosis of the crop water and nitrogen is possible by remote sensing base on spectral reflectance characteristics to recognize the object. Compared with the traditional means, the more information can be obtained quickly by remote sensing. The remote sensing is indispensable basic technology for variable rate of water and fertilizer in Precision agriculture. The relationships between the physiological and biochemical of flue-cured tobacco canopy, fresh leaf, cured tobacco leaf and their hyperspectral reflectance characteristics were analyzed by remote sensing platform in different levels of water and nitrogen. The predictive models were established by stepwise regression, and the prediction results were good by comparing the measured values and model estimation values. The main results are as follows:
(1) The spectral reflectance of flue-cured tobacco canopy and leaf was almost consistent in the same levels of nitrogen with different levels of the soil moisture content. In visible light region, the spectral reflectance of flue-cured tobacco was tended to decrease with the soil moisture content increasing, because of the decreasing of chlorophyll content in tobacco due to drought. In the near-infrared light region, the spectral reflectance was tended to increase with the increase of water, the main reason is that the aboveground tobacco growth was effected by the sufficient water, and resulting in the increase of leaf area, enhanced the ability of metabolism and increased the biomass of plant groups. In different growth stage, the spectral reflectance have exhibit the variation, which the lowest in root extension period, increasing in vigorous period, and then decreasing in maturity period in visible light region. The spectral reflectance have exhibit the variation In the near-infrared light region, which the rapid increasing phase from root extension period to vigorous period, and then decreasing in maturity period. This is because the rapid growth of flue-cured tobacco from root extension period to vigorous period and resulting in increase of leaves, increased thickness, and the cell structure of leaf become complicated. Those change will cause the increasing of reflectance rate after several reflections and scattering within the leaf. From the vigorous period to mature period, the spectral reflectance have begun to weak, because of the leaf senescence, less chlorophyll, the changes of leaf internal structure.
in the same levels of soil moisture content with different levels of nitrogen content, the canopy and leaf of tobacco spectral reflectance were decreased with the amount of nitrogen increases in visible light region, the mainly reason due to the increase content of leaf pigment by increasing nitrogen. In the near-infrared light region, the canopy and leaf of tobacco spectral reflectance were increased with the increasing of nitrogen, which mainly relates to the differences in leaf structure. The reason is that the high content of nitrogen will result in enlarging of the gap of leaf cells, increasing the hydration degree of cell wall. In the visible range, the canopy spectral reflectance have exhibit the variation, which the lowest in root extension period, increasing in vigorous period, and then decreasing in maturity period. However, the trends of change were inconspicuous. The reflectance rate of Yunyan87 was higher than K326 at different stage, which caused by the variety maybe.
The canopy reflectance has the same trends of change with soil moisture content in different water and nitrogen treatment. In the same soil moisture treatment, the tobacco canopy spectral reflectance of high nitrogen treatment was lower than the low nitrogen treatment’s in visible light region. However, the tobacco canopy spectral reflectance of high nitrogen treatment was higher than the low nitrogen treatment’s in near-infrared light region.
(2) In this study, the ASD FieldSpec HandHeld spectroradiometer was used to measure the hyperspectral reflectance of canopy and leaf of tobacco. The relationship between several indexes of biophysical and biochemical and hyperspectral parameters of canopy and leaf was analyzed by correlation analysis, the closest relates of hyperspectral parameters with biophysical and biochemical indexes were filtrate and the predictive models of those indexes were established by stepwise regression.
The first independent variables of regression equations of LAI, AFW, ADW were Rg by analyzing the spectral parameters of canopy without exception, and the correlation coefficient reached a significant level, the regression equations of first independent variable as Rg also were significant. It can be used as characteristic variable for LAI, AFW, ADW. the most relevant characteristic variables of Chlorophyll a, Chlorophyll b, carotenoid, total Chlorophyll content are SAVI; the most relevant characteristic variables of total nitrogen and nicotine are the Rg; the most relevant characteristic variables of Leaf moisture content and starch are the Db; the most relevant characteristic variables of total sugar and reducing sugar are the SDb; There are the direct and effective method for finding the characteristic variable of hyperspectral parameters with indexes of biophysical and biochemical of tobacco by the predictive models. useing 25 spectral parameters as independent variables, multiple stepwise regression analysis was performed. all the estimating models of biophysical and biochemical indexes were obtained the significance level. By randomly selected test samples to test, the relationship between the measured values and estimation values were significant in the indexes of biophysical and biochemical of tobacco canopy, indicating the more accurate and the better effect of estimation.
By analyzing the spectral parameters of tobacco leaf shows that the most relevant characteristic variables of Chlorophyll a, Chlorophyll b, carotenoid, total Chlorophyll content areλr, the most relevant characteristic variables of total sugar and starch are Db, the most relevant characteristic variables of reducing sugar and total nitrogen are Rg, and the most relevant characteristic variables of leaf moisture content are (SDr-SDb)/(SDr+SDb). the most relevant characteristic variables of nicotine are SDr, The coefficient of determination of estimating models of tobacco biophysical and biochemical indexes were significant. The test show that the good predictive effect can be obtained by the estimating models by the sample randomly selected.
(3) The relationships between Mineral elements、neutral aroma components、quality indexes of flue-cured tobacco and the hyperspectral parameters of canopy、leaf、cured tobacco leaf were analyzed, and the estimating models of those indexes were established by stepwise regression. The test indicating that the correlation relationship was exist between the hyperspectral parameters of tobacco and the mineral elements、neutral aroma components、quality indexes in different levels of water and nitrogen, and those parameters can be predicted accurately by the stepwise regression model. Consequently, it is feasible to predict the indexes of physiological and biochemical by the hyperspectral estimating models and the results can be used as the reference for monitoring the growth of tobacco and tobacco field management.
(4) Although, most techniques of spectrum analysis have been studied and applied for precision agriculture. Currently, the models were established through extracting vegetation indexes by the hyperspectral reflectance. Estimation of vegetation index esmethod can achieve good results in predicting a variety of physiological and biochemical indexes of tobacco, but because of its general information using only a few wavelengths, the model predictive ability and stability cannot be guaranteed. The PCA method can effectively reduce dimension, and keeping the original important spectrum information. The information of each wave band can be excavated to achieve complementarities of information between each band, and to reduce the random interference from the little band. Therefore, the PCA method is dependable and universal fit. The neural network method has a strong nonlinear mapping ability, and it does not require normal distribution of data. The neural network model has strong ability of linear and nonlinear fitting, Has the incomparable superiority in the data fitting and simulation,but it is difficult to explain the decision by neural networks and the process of producing output.
1.同一氮素水平不同水分下的烤烟冠层和叶片光谱反射率变化基本一致,可见光内,烤烟冠层的光谱反射率随着土壤水分含量的增加而呈下降状态。在近红外光区内,烤烟冠层的光谱反射率随着土壤水分含量的增加而随之变高。烤烟不同生育时期其光谱反射率也在不断变化,可见光区内随着烟草的生长发育,其冠层的高光谱反射率基本表现为在伸根期最低,旺长期升高,成熟期降低,近红外光区内冠层的高光谱反射率表现为伸根期至旺长期急剧升高,随后下降。旺长期是烟草生长发育最快的时期,生长中心从地下转移到地上,茎迅速伸长加粗,可见叶数迅速增加,叶片充实,光在叶片复杂的内部组织结构下进行了多次的反射散射致使反射率升高。旺长期到成熟期,由于叶片的成熟和开始采摘导致叶绿素总量减少,叶片内部海绵组织和栅栏组织结构发生变化,影响了光谱的反射率。
同一水分不同氮素下,在可见光区内,随着施氮量的增加,烤烟冠层和叶片的光谱反射率呈降低趋势,这主要是因为叶片色素含量的增加导致了烤烟叶片对光的强烈吸收。在近红外光区内,随着施氮量的增加,烤烟冠层和叶片的光谱反射率呈增加趋势。在可见光区,随着烟草的生长发育,冠层的高光谱反射率基本上为伸根期最低,旺长期变高,成熟期又降低的趋势。云烟87的反射率在各个时期均比K326高一些,可能是品种差异造成的。
不同水分和氮素组合条件下,烤烟光谱随土壤水分变化趋势一致。同一水分条件下,高氮处理的烟草冠层光谱反射率在可见光处低于低氮处理,在近红外波段高于低氮处理。
2.本文通过地面光谱仪在水氮互作下对烤烟的冠层、叶片及烤后叶片进行了高光谱的信息采集,采用相关分析方法分析多种生理生化指标与烟草冠层和鲜叶片的高光谱参数的关系,筛选出与各种生理生化指标关系最为密切的光谱特征变量,采用多元逐步回归方法,建立这些指标的估测模型,最后进行检验样本检验。
通过分析冠层光谱参数可知叶面积指数、地上鲜生物重、地上干生物重回归方程的第一自变量均为绿峰幅值,且其相关系数均达到极显著水平,以绿峰幅值为第一自变量的逐步回归方程亦达到显著水平,可作为叶面积指数、地上鲜生物重、地上干生物重的特征变量;土壤调整植被指数经分析与叶绿素a、叶绿素b、叶绿素总量、类胡萝卜素相关性最强,与总氮和烟碱相关性最强的特征变量是绿峰幅值,与叶片含水率和淀粉相关性最强的特征变量均是黄边幅值,黄边面积经分析与总糖和还原糖相关性最强;根据与烤烟生理生化指标关系最密切的光谱变量所建立的回归方程能够找出与这些生理生化指标相对应的特征变量。基于高光谱参数所建立的烤烟生理生化指标冠层逐步回归方程的决定系R2均达到了显著的水平,其对应的回归系数相伴概率也都达到了显著水平,通过随机选取一定数量的样本进行检测,发现基于烤烟生理生化指标的冠层逐步回归方程的估测值与实测值的相关系数均达到了显著水平,说明所建立的冠层逐步回归方程估测效果良好。
通过分析叶片光谱参数可知红边位置与叶绿素a、叶绿素b、叶绿素总量、类胡萝卜素相关性最强,与总糖和淀粉相关性最强的特征变量均是蓝边幅值,与还原糖和总氮相关性最强的特征变量均是绿峰幅值,与叶片含水率相关性最强的特征变量是红边面积与蓝边面积归一化值,与烟碱相关性最强的特征变量是红边面积;根据高光谱参数建立的叶片逐步回归方程,其决定系数R2都达到了显著的水平,通过随机选择一定数量的样本进行检测,发现基于烤烟生理生化指标的叶片逐步回归方程的估测值与实测值的相关系数均达到了极显著水平,说明所建立的叶片逐步回归方程估测效果良好。
3.化学品质、矿质元素以及中性致香物质都是烟叶质量的重要评价指标,通过分析烤烟的冠层、叶片及烤后烟叶的高光谱参数与这些质量指标的相关关系,建立基于高光谱参数的逐步回归估测模型,通过随机选择一定数量的样本进行检测,表明水氮互作下烟草的各种高光谱参数与烤后叶片的质量指标都具有不同程度的相关性,并且根据所相应的逐步回归模型可以进行相对精确地估测。表明通过高光谱估测模型对烟草这些质量指标进行预测是可行的,从而为烟草生长状况监控和烟田管理提供参考。
4.关于光谱分析方法的研究与应用已有很多,目前常用的主要是通过根据光谱反射率提取出的植被指数进行建模。植被指数方法在估算烟草各种生理生化指标时虽然也能取得较好的效果,但由于其一般仅利用几个波长的信息,模型预测能力及稳定性难以保证。主成分分析方法能够有效降维且尽量保持原有光谱重要信息,充分挖掘高光谱各波段信息,实现各波段之间信息互补,较好地降低了波段数少而带来的随机干扰,因此主成分分析的可靠性和普适性较好。神经网络具有很强的非线性映射能力,而且不要求数据呈正态分布,神经网络模型具有较强的线性和非线性拟合能力,在数据拟合与模拟中有着无比的优越性,但很难全面解释神经网络作出决策或者产生输出的过程。
Abstract: The levels of water and nitrogen are the most important limiting factors of crop growth. The shortage of water and nitrogen can cause a series of changes, such as leaf color, thickness, moisture content and morphological change, consequently causing the changes in spectral reflectance characteristic. The real-time monitoring and rapid diagnosis of the crop water and nitrogen is possible by remote sensing base on spectral reflectance characteristics to recognize the object. Compared with the traditional means, the more information can be obtained quickly by remote sensing. The remote sensing is indispensable basic technology for variable rate of water and fertilizer in Precision agriculture. The relationships between the physiological and biochemical of flue-cured tobacco canopy, fresh leaf, cured tobacco leaf and their hyperspectral reflectance characteristics were analyzed by remote sensing platform in different levels of water and nitrogen. The predictive models were established by stepwise regression, and the prediction results were good by comparing the measured values and model estimation values. The main results are as follows:
(1) The spectral reflectance of flue-cured tobacco canopy and leaf was almost consistent in the same levels of nitrogen with different levels of the soil moisture content. In visible light region, the spectral reflectance of flue-cured tobacco was tended to decrease with the soil moisture content increasing, because of the decreasing of chlorophyll content in tobacco due to drought. In the near-infrared light region, the spectral reflectance was tended to increase with the increase of water, the main reason is that the aboveground tobacco growth was effected by the sufficient water, and resulting in the increase of leaf area, enhanced the ability of metabolism and increased the biomass of plant groups. In different growth stage, the spectral reflectance have exhibit the variation, which the lowest in root extension period, increasing in vigorous period, and then decreasing in maturity period in visible light region. The spectral reflectance have exhibit the variation In the near-infrared light region, which the rapid increasing phase from root extension period to vigorous period, and then decreasing in maturity period. This is because the rapid growth of flue-cured tobacco from root extension period to vigorous period and resulting in increase of leaves, increased thickness, and the cell structure of leaf become complicated. Those change will cause the increasing of reflectance rate after several reflections and scattering within the leaf. From the vigorous period to mature period, the spectral reflectance have begun to weak, because of the leaf senescence, less chlorophyll, the changes of leaf internal structure.
in the same levels of soil moisture content with different levels of nitrogen content, the canopy and leaf of tobacco spectral reflectance were decreased with the amount of nitrogen increases in visible light region, the mainly reason due to the increase content of leaf pigment by increasing nitrogen. In the near-infrared light region, the canopy and leaf of tobacco spectral reflectance were increased with the increasing of nitrogen, which mainly relates to the differences in leaf structure. The reason is that the high content of nitrogen will result in enlarging of the gap of leaf cells, increasing the hydration degree of cell wall. In the visible range, the canopy spectral reflectance have exhibit the variation, which the lowest in root extension period, increasing in vigorous period, and then decreasing in maturity period. However, the trends of change were inconspicuous. The reflectance rate of Yunyan87 was higher than K326 at different stage, which caused by the variety maybe.
The canopy reflectance has the same trends of change with soil moisture content in different water and nitrogen treatment. In the same soil moisture treatment, the tobacco canopy spectral reflectance of high nitrogen treatment was lower than the low nitrogen treatment’s in visible light region. However, the tobacco canopy spectral reflectance of high nitrogen treatment was higher than the low nitrogen treatment’s in near-infrared light region.
(2) In this study, the ASD FieldSpec HandHeld spectroradiometer was used to measure the hyperspectral reflectance of canopy and leaf of tobacco. The relationship between several indexes of biophysical and biochemical and hyperspectral parameters of canopy and leaf was analyzed by correlation analysis, the closest relates of hyperspectral parameters with biophysical and biochemical indexes were filtrate and the predictive models of those indexes were established by stepwise regression.
The first independent variables of regression equations of LAI, AFW, ADW were Rg by analyzing the spectral parameters of canopy without exception, and the correlation coefficient reached a significant level, the regression equations of first independent variable as Rg also were significant. It can be used as characteristic variable for LAI, AFW, ADW. the most relevant characteristic variables of Chlorophyll a, Chlorophyll b, carotenoid, total Chlorophyll content are SAVI; the most relevant characteristic variables of total nitrogen and nicotine are the Rg; the most relevant characteristic variables of Leaf moisture content and starch are the Db; the most relevant characteristic variables of total sugar and reducing sugar are the SDb; There are the direct and effective method for finding the characteristic variable of hyperspectral parameters with indexes of biophysical and biochemical of tobacco by the predictive models. useing 25 spectral parameters as independent variables, multiple stepwise regression analysis was performed. all the estimating models of biophysical and biochemical indexes were obtained the significance level. By randomly selected test samples to test, the relationship between the measured values and estimation values were significant in the indexes of biophysical and biochemical of tobacco canopy, indicating the more accurate and the better effect of estimation.
By analyzing the spectral parameters of tobacco leaf shows that the most relevant characteristic variables of Chlorophyll a, Chlorophyll b, carotenoid, total Chlorophyll content areλr, the most relevant characteristic variables of total sugar and starch are Db, the most relevant characteristic variables of reducing sugar and total nitrogen are Rg, and the most relevant characteristic variables of leaf moisture content are (SDr-SDb)/(SDr+SDb). the most relevant characteristic variables of nicotine are SDr, The coefficient of determination of estimating models of tobacco biophysical and biochemical indexes were significant. The test show that the good predictive effect can be obtained by the estimating models by the sample randomly selected.
(3) The relationships between Mineral elements、neutral aroma components、quality indexes of flue-cured tobacco and the hyperspectral parameters of canopy、leaf、cured tobacco leaf were analyzed, and the estimating models of those indexes were established by stepwise regression. The test indicating that the correlation relationship was exist between the hyperspectral parameters of tobacco and the mineral elements、neutral aroma components、quality indexes in different levels of water and nitrogen, and those parameters can be predicted accurately by the stepwise regression model. Consequently, it is feasible to predict the indexes of physiological and biochemical by the hyperspectral estimating models and the results can be used as the reference for monitoring the growth of tobacco and tobacco field management.
(4) Although, most techniques of spectrum analysis have been studied and applied for precision agriculture. Currently, the models were established through extracting vegetation indexes by the hyperspectral reflectance. Estimation of vegetation index esmethod can achieve good results in predicting a variety of physiological and biochemical indexes of tobacco, but because of its general information using only a few wavelengths, the model predictive ability and stability cannot be guaranteed. The PCA method can effectively reduce dimension, and keeping the original important spectrum information. The information of each wave band can be excavated to achieve complementarities of information between each band, and to reduce the random interference from the little band. Therefore, the PCA method is dependable and universal fit. The neural network method has a strong nonlinear mapping ability, and it does not require normal distribution of data. The neural network model has strong ability of linear and nonlinear fitting, Has the incomparable superiority in the data fitting and simulation,but it is difficult to explain the decision by neural networks and the process of producing output.
引文
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