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表 1中列出了两批苹果的SSC测量值。两批苹果的测量方法相同。第1批和第2批的SSC分别在7.80 °Brix~15.10 °Brix和8.70 °Brix~16.10 °Brix范围内。第1批苹果作为校正集,第2批苹果作为预测集。
表 1 苹果SSC统计结果
Table 1. Statistical results of apple SSC
batch minimum/°Brix maximum/°Brix average value/°Brix standard deviation 1 7.80 15.10 12.59 1.34 2 8.70 16.10 13.07 1.18 -
由于样品对不同频率近红外光的选择性吸收,通过样品后的近红外光线在某些波长范围内会变弱,光谱前端(350 nm~600 nm)和后端(850 nm~1150 nm)存在一些噪声信号,有效信息少,故将有效波长范围定为600 nm~850 nm。两批苹果的光谱相似,仅光谱强度存在差异;在645 nm处的波峰与果皮颜色有关,675 nm处波谷受叶绿素的影响[19],758 nm处波谷受O—H伸缩振动的倍频吸收影响[20]。采用多元散射校正和S-G卷积平滑(平滑点数为3)组合作为光谱预处理方法来消除其它背景的干扰。图 2a、图 2b分别为两批苹果的原始漫透射光谱和预处理后的光谱图,预处理后的光谱消除了散射影响和噪声,光谱差异明显减小,减小外界信息的干扰。
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在600 nm~850 nm范围内,经过预处理后建立SSC预测模型,结果见图 3。其中标准决定系数Rc2和预测决定系数Rp2分别为0.8989和0.7151。与标准场方根误差(root mean square error of criterion, RMSEC)相比,RMSEP明显增加到0.6281,且存在较大的预测偏差0.3649,表明在第1批上训练的模型不适用于第2批。造成这种结果的原因可能是苹果保存时间的不同,导致其内部理化性质的改变。
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利用BIPLS将光谱波段划分为等间隔的子区间建立PLS回归模型,采用10~25个间隔数,选出RMSEC值最小的子区间组合,表 2为不同区间个数的BIPLS模型选取结果。当区间个数为14时,RMSEC最小。
表 2 不同区间总数划分结果
Table 2. Division results of the total number of different intervals
number of intervals RMSEC number of subinterval combinations number of variables 10 0.4618 6 334 11 0.4737 9 273 12 0.4707 7 194 13 0.4673 7 179 14 0.4480 7 166 15 0.4656 12 266 16 0.4593 7 145 17 0.4584 10 197 18 0.4577 10 184 19 0.4691 15 264 20 0.4532 11 183 21 0.4603 15 238 22 0.4647 14 211 23 0.4565 16 232 24 0.4532 11 152 25 0.4590 11 147 利用全部子区间建模,并根据表现依次去除较差子区间,由表 2可知, RMSEC最好为0.4480,使用7个子区间建模。所选区间分别为第3、4、8、9、11、13、14子区间,对应波长区间为637.1 nm~672.7 nm、727.6 nm~ 762.8 nm、781.4 nm~798.5 nm、817 nm~850.2 nm共计166个变量,对筛选的子区间变量建模, 结果如图 4所示。Rc2=0.8802,Rp2=0.7788,RMSEC为0.4649,RMSEP为0.5984,B=-0.3341。与未选择变量的PLS模型相比,Rp2增加,RMSEP和B降低,模型性能有所改善。
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图 5显示了使用CARS进行变量选择过程。选择的变量数随着采样次数的增加逐渐减少,采样次数为36时, RMSEC值最小为0.4113,对应的变量数为55个,采样次数继续增加,RMSEC随之增加。
对筛选后的变量建模结果如图 6所示。其Rp2增加到0.7915,RMSEP减少到0.5810,B减少到0.2627。使用CARS进行变量选择剔除了光谱中的冗余信息,简化模型,提高了模型性能。
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使用K-S算法从第2批苹果分别挑选出5个、10个、15个、20个苹果进行模型更新,模型更新总体上提高了BIPLS模型的性能,结果见表 3。随着更新样品数量的增加模型性能得到提高,用20个样品更新模型得到了最佳的性能。更新后的模型Rp2从0.7788增加到0.8169,RMSEP从0.5984降低到0.4866,B从-0.3841降低到0.1146。
表 3 BIPLS结合模型更新的结果
Table 3. Results of BIPLS combined with model update
BIPLS Rp2 RMSEP B no new sample 0.7788 0.5984 -0.3841 5 samples from batch 2 0.7809 0.5610 0.2368 10 samples from batch 2 0.7975 0.5333 0.1779 15 samples from batch 2 0.8131 0.5079 0.1218 20 samples from batch 2 0.8169 0.4866 0.1146 与BIPLS建模一样,CARS建模更新后的模型的预测效果有所改善,如表 4所示。用20个样品更新模型得到了最佳的性能。与未更新的糖度预测模型相比,Rp2从0.7915增加到0.8506,RMSEP从0.5810降低到0.4358,B从0.2627降低到0.1045。
表 4 CARS结合模型更新的结果
Table 4. Results of CARS combined with model update
CARS Rp2 RMSEP B no new sample 0.7915 0.5810 0.2627 5 samples from batch 2 0.8361 0.4672 0.1828 10 samples from batch 2 0.8457 0.4583 0.1602 15 samples from batch 2 0.8501 0.4358 0.1159 20 samples from batch 2 0.8506 0.4358 0.1045
变量选择结合模型更新以改进苹果的糖度检测
Variable selection combined with model updating to improve soluble solids content detection in apples
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摘要: 为了获得稳健的近红外光谱模型,采用变量选择结合模型更新的方法,以240个红富士苹果为对象,取得近红外漫透射光谱和糖度数据,建立偏最小二乘回归模型,对苹果糖度含量进行预测,并采用后向区间偏最小二乘法和竞争性自适应重加权算法,对建模变量进行了选择,通过将新批次中的一些样品加入到旧批次中重新校准来实现模型更新。结果表明, 变量选择可以提高模型性能,预测决定系数提高到0.7915,预测均方根误差降低到0.5810,预测偏差降至0.2627;结合模型更新策略,可以进一步降低预测均方根误差和预测偏差; 仅使用20个样品进行模型更新已经明显改善了模型性能,预测决定系数提高到0.8506,预测均方根误差降到0.4358,预测偏差降到0.1045。这一结果对于多种水果建立稳健的近红外光谱模型是有帮助的。Abstract: In order to obtain a robust near infrared spectral model, a method based on variate selection and model updating was adopted. 240 Red Fuji apples were used to obtain near infrared diffuse transmission spectra and soluble solids content data, and a partial least squares regression model was developed to predict apple soluble solids content. The modelling variates were selected by using backward interval partial least squares and competitive adaptive reweighting algorithms. The model was updated by adding some samples from the new batch to the old batch and recalibrating. The results indicate that the model performance can be improved by variable selection, with the prediction coefficient of determination increasing to 0.7915, the root mean square error of prediction decreasing to 0.5810 and the prediction bias decreasing to 0.2627. Combining the model update strategy, the root mean square error of prediction and the prediction bias were further reduced. Model updating using only 20 samples has already led to a significant improvement in model performance, with the prediction coefficient of determination improving to 0.8506, the root mean square error of prediction decreasing to 0.4358 and the prediction bias decreasing to 0.1045, the result that is useful for robust near infrared spectroscopy modelling of a wide range of fruits.
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表 1 苹果SSC统计结果
Table 1. Statistical results of apple SSC
batch minimum/°Brix maximum/°Brix average value/°Brix standard deviation 1 7.80 15.10 12.59 1.34 2 8.70 16.10 13.07 1.18 表 2 不同区间总数划分结果
Table 2. Division results of the total number of different intervals
number of intervals RMSEC number of subinterval combinations number of variables 10 0.4618 6 334 11 0.4737 9 273 12 0.4707 7 194 13 0.4673 7 179 14 0.4480 7 166 15 0.4656 12 266 16 0.4593 7 145 17 0.4584 10 197 18 0.4577 10 184 19 0.4691 15 264 20 0.4532 11 183 21 0.4603 15 238 22 0.4647 14 211 23 0.4565 16 232 24 0.4532 11 152 25 0.4590 11 147 表 3 BIPLS结合模型更新的结果
Table 3. Results of BIPLS combined with model update
BIPLS Rp2 RMSEP B no new sample 0.7788 0.5984 -0.3841 5 samples from batch 2 0.7809 0.5610 0.2368 10 samples from batch 2 0.7975 0.5333 0.1779 15 samples from batch 2 0.8131 0.5079 0.1218 20 samples from batch 2 0.8169 0.4866 0.1146 表 4 CARS结合模型更新的结果
Table 4. Results of CARS combined with model update
CARS Rp2 RMSEP B no new sample 0.7915 0.5810 0.2627 5 samples from batch 2 0.8361 0.4672 0.1828 10 samples from batch 2 0.8457 0.4583 0.1602 15 samples from batch 2 0.8501 0.4358 0.1159 20 samples from batch 2 0.8506 0.4358 0.1045 -
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