Partial least squares regression calculation for quantitative analysis of metals submerged in water measured using laser-induced breakdown spectroscopy
Effects of different parameters regarding partial least squares (PLS) regression analysis are investigated for quantitative analysis of water-submerged brass samples. The concentrations of Cu and Zn in various brass alloys were quantified using PLS, and the performance after different signal processing steps (normalization, smoothing, and background subtraction) and database segmentation by excitation temperature is compared. In addition, the effects of averaging numbers on the results are examined. From the results, normalization was found to be the most effective among three established signal processing methods. The effects of both peak and background fluctuations seen in the signals are reduced by normalization. It was found that temperature segmentation of the database in an appropriate range, which should be high enough for reliable peak detection, can further improve the accuracy of PLS calculations. The proposed method is applicable in real time, and can potentially be used for automated fast and accurate measurements of solids at oceanic pressures.
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Mass Fractions of Cu and Zn in the Certified Samplesa
Number
Sample Name
Company
Cu (%)
Zn (%)
Others (%)
1
31X78355.5
MBH Analytical Ltd.
91.25
6.23
2.52
2
31X7835.8
MBH Analytical Ltd.
69.93
24.83
5.24
3
31XB2
MBH Analytical Ltd.
60.13
39.57
0.30
4
31XB20
MBH Analytical Ltd.
58.53
37.03
4.44
5
31XB21
MBH Analytical Ltd.
69.24
29.50
1.26
6
31XB23
MBH Analytical Ltd.
89.57
9.97
0.46
7
C5191
JCBA
93.62
0.02
6.36
8
C2600
JCBA
69.89
30.10
0.01
9
C6871
JCBA
78.08
21.91
0.01
10
C2801
JCBA
60.48
39.50
0.02
11
C3713
JCBA
59.63
39.12
1.25
JCBA: Japan Copper and Brass Association.
Table 2.
List of Cu I Peaks Used in the Temperature Calculationa
[nm]
[]
[eV]
510.6
0.0195
3.82
4
515.3
1.03
6.19
4
521.8
1.22
6.19
6
The wavelength , transition probability , upper level energy , and statistical weight of the atomic lines of the three Cu I peaks are listed. The wavelength and other data were obtained from the NIST [25] and Kurucz spectral databases [26], respectively.
Table 3.
Average and Standard Deviation of the Temperatures Calculated Using the Boltzmann Plot for 400 Randomly Selected Spectra for Each Sample Used in This Work
Sample
Temperature (K)
1
2
3
4
5
6
7
8
9
10
11
Table 4.
PLS Results for Cu and Zn Calculated from Different Signal Processing Methodsa
Cu
Zn
Raw
Norm
Smooth
Bg
All
Raw
Norm
Smooth
Bg
All
LV
2
4
2
2
2
2
4
2
2
2
RMSECV (%)
9.60
3.51
9.65
9.13
3.43
8.21
3.26
8.28
7.82
3.53
Reduction rate (%)
0
63.44 (−)
0.52 (+)
4.90 (−)
64.27 (−)
0
60.29 (−)
0.85 (+)
4.75 (−)
56.88 (−)
Slope
0.47
0.92
0.47
0.50
0.88
0.68
1.02
0.68
0.70
1.02
-intercept
37.07
5.84
37.09
34.94
8.43
10.39
−0.81
10.37
10.04
−0.11
0.34
0.90
0.33
0.39
0.91
0.55
0.91
0.55
0.59
0.92
Labels “Raw,” “Norm,” “Smooth,” “Bg,” and “All” indicate raw spectra, normalized spectra, smoothed spectra, spectra with background subtraction, and spectra after all signal processing steps, respectively.
Table 5.
PLS Results for Cu and Zn for the Segmented Models in a Segmentation Range of 250Ka
Cu 250K range
Zn 250K range
6750–7000K
7000–7250K
7250–7500K
7500–7750K
7750–8000K
8000–8250K
8250–8500K
8500–8750K
6750–7000K
7000–7250K
7250–7500K
7500–7750K
7750–8000K
8000–8250K
8250–8500K
8500–8750K
LV
8
5
3
7
4
5
3
2
8
6
5
7
9
6
5
2
RMSECV(%)
4.30
3.48
2.91
3.08
3.30
2.94
2.30
1.76
5.53
4.03
3.45
3.97
4.02
3.74
3.44
2.33
Slope
1.02
0.99
1.01
1.06
1.03
1.02
0.93
0.97
1.03
1.03
1.02
1.06
1.05
1.06
1.05
1.03
-intercept
−0.68
0.93
−0.82
−4.43
−2.33
−1.43
4.41
1.80
−2.37
−1.44
−1.34
−1.910
−1.82
−1.90
−1.42
−1.32
0.88
0.91
0.94
0.94
0.93
0.94
0.95
0.98
0.83
0.90
0.92
0.91
0.90
0.92
0.93
0.97
The red numbers indicate values that showed better accuracy than in the nonsegmented model under the same conditions.
Table 6.
PLS Results for Cu and Zn for the Temperature-Segmented Modelsa
Cu
Zn
6750–7250K
7250–7750K
7750–8250K
8250–8750K
6750–7250K
7250–7750K
7750–8250K
8250–8750K
LV
5
3
4
2
5
9
2
2
RMSECV (%)
3.66
3.27
3.05
1.95
4.47
4.13
3.95
2.66
Reduction rate (%)
6.71 (+)
4.66 (−)
11.08 (−)
43.15 (−)
26.62 (+)
17.00 (+)
11.90 (+)
24.65 (−)
Slope
0.99
0.98
1.02
0.94
1.03
1.04
0.95
1.03
-intercept
1.05
1.18
−1.56
3.66
−1.19
−1.45
1.30
−0.89
0.91
0.92
0.94
0.97
0.88
0.90
0.89
0.95
The red numbers indicate values that had better accuracy than in the nonsegmented model under the same conditions.
Table 7.
PLS Results for Cu and Zn for the Segmented Models in a Segmentation Range of 1000Ka
Cu 1000K range
Zn 1000K range
7000– 8000K
8000– 9000K
7000– 8000K
8000– 9000K
LV
3
2
5
2
RMSECV(%)
3.59
2.56
4.37
3.06
Slope
0.94
0.92
1.02
1.02
-intercept
4.29
5.23
−0.63
−0.57
0.90
0.95
0.88
0.94
The red numbers indicate values that showed better accuracy than in the nonsegmented model under the same conditions.
Table 8.
PLS Results for Cu and Zn for the Nonsegmented Models with Different Averaging Numbers
Cu no seg.
Zn no seg.
10
30
50
70
10
30
50
70
LV
2
2
2
2
2
4
4
4
RMSECV(%)
3.43
2.40
2.10
1.80
3.53
2.92
2.47
2.27
Slope
0.88
0.92
0.93
0.94
1.02
1.04
1.05
1.06
-intercept
8.43
5.57
4.94
4.19
−0.11
−1.22
−1.23
−1.75
0.91
0.96
0.97
0.98
0.92
0.95
0.96
0.97
Table 9.
PLS Results for Cu and Zn for the Segmented Models in a Range from 8000K to 9000K with Different Averaging Numbers
Cu 8000–9000K
Zn 8000–9000K
10
30
50
70
10
30
50
70
LV
2
2
2
2
2
5
5
5
RMSECV(%)
2.56
1.67
1.47
1.37
3.06
2.32
2.05
1.94
Slope
0.92
0.95
0.95
0.95
1.02
1.05
1.05
1.06
-intercept
5.23
3.51
3.27
3.04
−0.57
−1.51
−1.54
−1.73
0.95
0.98
0.99
0.99
0.94
0.97
0.97
0.98
Tables (9)
Table 1.
Mass Fractions of Cu and Zn in the Certified Samplesa
Number
Sample Name
Company
Cu (%)
Zn (%)
Others (%)
1
31X78355.5
MBH Analytical Ltd.
91.25
6.23
2.52
2
31X7835.8
MBH Analytical Ltd.
69.93
24.83
5.24
3
31XB2
MBH Analytical Ltd.
60.13
39.57
0.30
4
31XB20
MBH Analytical Ltd.
58.53
37.03
4.44
5
31XB21
MBH Analytical Ltd.
69.24
29.50
1.26
6
31XB23
MBH Analytical Ltd.
89.57
9.97
0.46
7
C5191
JCBA
93.62
0.02
6.36
8
C2600
JCBA
69.89
30.10
0.01
9
C6871
JCBA
78.08
21.91
0.01
10
C2801
JCBA
60.48
39.50
0.02
11
C3713
JCBA
59.63
39.12
1.25
JCBA: Japan Copper and Brass Association.
Table 2.
List of Cu I Peaks Used in the Temperature Calculationa
[nm]
[]
[eV]
510.6
0.0195
3.82
4
515.3
1.03
6.19
4
521.8
1.22
6.19
6
The wavelength , transition probability , upper level energy , and statistical weight of the atomic lines of the three Cu I peaks are listed. The wavelength and other data were obtained from the NIST [25] and Kurucz spectral databases [26], respectively.
Table 3.
Average and Standard Deviation of the Temperatures Calculated Using the Boltzmann Plot for 400 Randomly Selected Spectra for Each Sample Used in This Work
Sample
Temperature (K)
1
2
3
4
5
6
7
8
9
10
11
Table 4.
PLS Results for Cu and Zn Calculated from Different Signal Processing Methodsa
Cu
Zn
Raw
Norm
Smooth
Bg
All
Raw
Norm
Smooth
Bg
All
LV
2
4
2
2
2
2
4
2
2
2
RMSECV (%)
9.60
3.51
9.65
9.13
3.43
8.21
3.26
8.28
7.82
3.53
Reduction rate (%)
0
63.44 (−)
0.52 (+)
4.90 (−)
64.27 (−)
0
60.29 (−)
0.85 (+)
4.75 (−)
56.88 (−)
Slope
0.47
0.92
0.47
0.50
0.88
0.68
1.02
0.68
0.70
1.02
-intercept
37.07
5.84
37.09
34.94
8.43
10.39
−0.81
10.37
10.04
−0.11
0.34
0.90
0.33
0.39
0.91
0.55
0.91
0.55
0.59
0.92
Labels “Raw,” “Norm,” “Smooth,” “Bg,” and “All” indicate raw spectra, normalized spectra, smoothed spectra, spectra with background subtraction, and spectra after all signal processing steps, respectively.
Table 5.
PLS Results for Cu and Zn for the Segmented Models in a Segmentation Range of 250Ka
Cu 250K range
Zn 250K range
6750–7000K
7000–7250K
7250–7500K
7500–7750K
7750–8000K
8000–8250K
8250–8500K
8500–8750K
6750–7000K
7000–7250K
7250–7500K
7500–7750K
7750–8000K
8000–8250K
8250–8500K
8500–8750K
LV
8
5
3
7
4
5
3
2
8
6
5
7
9
6
5
2
RMSECV(%)
4.30
3.48
2.91
3.08
3.30
2.94
2.30
1.76
5.53
4.03
3.45
3.97
4.02
3.74
3.44
2.33
Slope
1.02
0.99
1.01
1.06
1.03
1.02
0.93
0.97
1.03
1.03
1.02
1.06
1.05
1.06
1.05
1.03
-intercept
−0.68
0.93
−0.82
−4.43
−2.33
−1.43
4.41
1.80
−2.37
−1.44
−1.34
−1.910
−1.82
−1.90
−1.42
−1.32
0.88
0.91
0.94
0.94
0.93
0.94
0.95
0.98
0.83
0.90
0.92
0.91
0.90
0.92
0.93
0.97
The red numbers indicate values that showed better accuracy than in the nonsegmented model under the same conditions.
Table 6.
PLS Results for Cu and Zn for the Temperature-Segmented Modelsa
Cu
Zn
6750–7250K
7250–7750K
7750–8250K
8250–8750K
6750–7250K
7250–7750K
7750–8250K
8250–8750K
LV
5
3
4
2
5
9
2
2
RMSECV (%)
3.66
3.27
3.05
1.95
4.47
4.13
3.95
2.66
Reduction rate (%)
6.71 (+)
4.66 (−)
11.08 (−)
43.15 (−)
26.62 (+)
17.00 (+)
11.90 (+)
24.65 (−)
Slope
0.99
0.98
1.02
0.94
1.03
1.04
0.95
1.03
-intercept
1.05
1.18
−1.56
3.66
−1.19
−1.45
1.30
−0.89
0.91
0.92
0.94
0.97
0.88
0.90
0.89
0.95
The red numbers indicate values that had better accuracy than in the nonsegmented model under the same conditions.
Table 7.
PLS Results for Cu and Zn for the Segmented Models in a Segmentation Range of 1000Ka
Cu 1000K range
Zn 1000K range
7000– 8000K
8000– 9000K
7000– 8000K
8000– 9000K
LV
3
2
5
2
RMSECV(%)
3.59
2.56
4.37
3.06
Slope
0.94
0.92
1.02
1.02
-intercept
4.29
5.23
−0.63
−0.57
0.90
0.95
0.88
0.94
The red numbers indicate values that showed better accuracy than in the nonsegmented model under the same conditions.
Table 8.
PLS Results for Cu and Zn for the Nonsegmented Models with Different Averaging Numbers
Cu no seg.
Zn no seg.
10
30
50
70
10
30
50
70
LV
2
2
2
2
2
4
4
4
RMSECV(%)
3.43
2.40
2.10
1.80
3.53
2.92
2.47
2.27
Slope
0.88
0.92
0.93
0.94
1.02
1.04
1.05
1.06
-intercept
8.43
5.57
4.94
4.19
−0.11
−1.22
−1.23
−1.75
0.91
0.96
0.97
0.98
0.92
0.95
0.96
0.97
Table 9.
PLS Results for Cu and Zn for the Segmented Models in a Range from 8000K to 9000K with Different Averaging Numbers
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