Author Affiliations
College of Information Science and Engineering, Central South University, Changsha, Hunan 410083, Chinashow less
Fig. 1. Original spectral signals of Zn(II),Cu(II),Co(II)
Fig. 2. Derivative denoising spectral signals of Zn(II), Cu(II), Co(II)
Fig. 3. (a) Spectral signals of different mass concentrations of Cu(II) in the background of high mass concentration of Zn(II)and trace concentration of Co(II); (b) relationship between Cu(II) mass concentration and spectral signal at 9 wavelength points
Fig. 4. Correlation coefficient-stability value of wavelength variables of trace Cu(II)
Fig. 5. Stability value of wavelength variables with MC-UVE PLS method
Fig. 6. CVmse of models with different number of wavelength variables
Fig. 7. Scatter plots of predicted and measured mass concentrations of Cu(II)
Wavelength /nm | Fitting method | Fitting function |
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| Linear fitting | 2.8×10-3c+3.8×10-3 | 500 | Nonlinear fitting | -2.2×10-5c3+6.1×10-5c2+2.9×10-3c+3.6×10-3 | | Partition fitting | 1) -6.1×10-4c3+1.8×10-3c2+1.4×10-3c+3.9×10-3;2) 2.5×10-3c+4.5×10-3 | | Linear fitting | 9.1×10-4c+2.4×10-3 | 520 | Nonlinear fitting | -1.8×10-6c3-6.0×10-5c2+1.2×10-3c+2.2×10-3 | | Partition fitting | 1) -5.4×10-4c3+1.5×10-3c2-1.3×10-4c+2.4×10-3;2) 7.1×10-4c+3.0×10-3 | | Linear fitting | 3.8×10-4c+2.6×10-3 | 540 | Nonlinear fitting | -1.3×10-6c3-5.4×10-5c2+6.3×10-4c+2.4×10-3 | | Partition fitting | 1) -4.5×10-4c3+1.2×10-3c2-3.2×10-4c+2.6×10-3;2) 2.2×10-4c+3.1×10-3 |
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Table 1. Fitting functions of Cu(II) mass concentration c and spectral signal at different wavelengths
Ion | SVM model | Penalty parameter C | Kernel function parameter σ |
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| PSO-SVC | 4.1095 | 0.10 | Cu(II) | PSO-SVR with low concentration interval | 8.8250 | 0.01 | | PSO-SVR with high concentration interval | 4.1604 | 0.01 |
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Table 2. Parameters of SVM model
Item | Predicted interval of mass concentration |
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High | Low |
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True interval of | High | 5 | 0 | mass concentration | Low | 0 | 9 |
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Table 3. Confusion matrix of mass concentration interval prediction results for Cu(II)
Ion | Model | Wavelength number | Maximum relative error /% | R2 /% | RMSEP |
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| PLS | 401 | 13.78 | 98.16 | 0.1424 | | PSO-SVR | 401 | 97.53 | 93.23 | 0.2835 | | CARS PLS | 46 | 10.88 | 99.06 | 0.1020 | Cu(II) | MC-UVE PLS | 67 | 8.13 | 98.99 | 0.1057 | | MC -UVE LS SVM | 67 | 14.79 | 99.18 | 0.0986 | | VR-S SVR | 50 | 8.32 | 99.47 | 0.0794 | | VR-S C-SVR | 50 | 6.94 | 99.61 | 0.0678 |
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Table 4. Modeling results based on seven methods