Application of Hierarchical Extreme Learning Machine in Prediction of Insulator Pollution Degree Using Hyperspectral Images
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摘要: 高光谱图像具有图谱合一、光谱范围广及分辨率高等优势，能精细化地反映物质微观特性. 为此，引入高光谱成像技术以非接触式预测绝缘子污秽度. 考虑到极限学习机具有学习效率高和泛化能力强等优点，提出基于正则化约束极限学习机的绝缘子污秽度预测（extreme learning machine-insulator pollution degree prediction，ELM-IPDP）模型. 此外，为进一步提升预测性能，引入层次极限学习机从复杂的高光谱图像中学习出有效、抽象、判决性特征表示，继而建立基于层次极限学习机的绝缘子污秽度预测（hierarchical ELM-IPDP，HELM-IPDP）模型. 在不同的训练集与测试集比例和不同隐含层神经元个数的情况下分别进行实验，从实验结果可知：ELM-IPDP模型和HELM-IPDP模型的预测性能基本上随着隐含层神经元个数和训练样本的增加而不断提高；当训练集与测试集比例为9∶1时，ELM-IPDP模型的均方根误差和相关系数分别为0.040 3和0.944 7，而HELM-IPDP模型的均方根误差和相关系数分别提升到0.022 3和0.972 0.Abstract: Hyperspectral images possess merging properties of image and spectrum, wide spectral range, and high spectral resolution, which can finely reflect the material microscopic characteristics. To this end, hyperspectral imaging technology is introduced to research the insulator pollution degree in a non-contact way. Considering that extreme learning machine (ELM) has high learning efficiency and strong generalization ability, we construct a ELM with regularization constraint based insulator pollution degree prediction (ELM-IPDP) model. Besides, in order to further improve the prediction performance, hierarchical ELM (HELM) is utilized to learn the effective, abstract, and discriminative feature representations from the complex hyperspectral images, and the HELM based insulator pollution degree prediction (HELM-IPDP) model is proposed. Experiments are performed with different amounts of training data and numbers of neurons in hidden layers. Experimental results show that the prediction performance is basically improved with the increase of numbers of neurons in hidden layer and training samples. Specifically, when the proportion of training sample and test sample is 9∶1, root mean squared error (RMSE) and correlation coefficient of the ELM-IPDP model are 0.040 3 and 0.944 7, while those of the HELM-IPDP model are up to 0.022 3 and 0.972 0, respectively.
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图 3 使用SG + MSC算法得到的光谱曲线
Figure 3. Spectrum curves obtained by using Savitzky-Golay and multiplicative scatter correction algorithms
图 4 不同绝缘子污秽度的平均光谱曲线
Figure 4. Average spectrum curves for different insulator pollution degrees
图 6 不同L值与r、RMSE预测性能
Figure 6. Different values of L versus prediction performance of r and RMSE
表 1 第Ⅱ、Ⅲ、Ⅳ级间的SAD值
Table 1. SAD values between the Ⅱ，Ⅲ，and Ⅳ levels
污秽级 第Ⅱ级 第Ⅲ级 第Ⅳ级 第Ⅱ级 0 0.103 7 0.208 4 第Ⅲ级 0.103 7 0 0.104 7 第Ⅳ级 0.208 4 0.104 7 0 
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表 2 不同训练集样本量下ELM-IPDP和HELM-IPDP模型的预测结果
Table 2. Predicted results of training sets with different train sample sizes for ELM-IPDP and HELM-IPDP models
比值（训练集组数/
测试集组数）ELM-IPDP模型 HELM-IPDP模型 eRMSE-T rT eRMSE-P rP eRMSE-T rT eRMSE-P rP 5∶5 （108/108） 0.035 7 0.909 9 0.044 2 0.927 9 0.031 7 0.919 8 0.035 4 0.921 9 6∶4 （130/86） 0.034 6 0.918 5 0.044 5 0.933 0 0.033 7 0.913 9 0.033 7 0.925 1 7∶3 （151/65） 0.034 3 0.920 6 0.042 5 0.932 8 0.030 0 0.934 6 0.031 2 0.934 8 8∶2 （173/43） 0.034 1 0.921 0 0.042 9 0.932 0 0.031 6 0.927 6 0.028 5 0.942 1 9∶1 （194/22） 0.034 4 0.919 2 0.040 3 0.944 7 0.031 0 0.930 7 0.022 3 0.972 0 注：eRMSE-T 和 eRMSE-P 为训练集和测试集的 RMSE；rT 和 rP 为训练集和测试集的 r.
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