Infrared and Laser Engineering, Volume. 54, Issue 2, 20240455(2025)
Determination of copper content in raw ores via laser-induced breakdown spectroscopy with generalized linear model
Figures & Tables(11)
Table 1. The spectra sets and speciality of copper ore/concentrate
View tableView in ArticleTable 1. The spectra sets and speciality of copper ore/concentrate
Type Spectrum No. Sample name Copper content/ wt.% Training/ validation set 1-10 GWB(E)07 3.84 21-30 ZBK339 8.46 31-40 ZBK337 10.71 41-50 ZBK336 12.79 51-60 ZBK340 16.60 71-80 ZBK338 20.56 81-90 ZBK338 B 24.35 Test set 11-20 ZBK335 6.78 61-70 ZBK340 A 18.04
Table 2. Performance comparison between eight models
View tableView in ArticleTable 2. Performance comparison between eight models
Model Number of variables Training set Test set R2 MSEv MSEp MAPE 注：1 Information content >95%；2 Linear Kernel，c=44.54，g=0.01；3α=0.296，λ= 0.00314 ；4λ=0.00656 ，Linear Kernel，c=91.85，g=0.01；5α=0.08；λ= 0.00729 ，Linear Kernel，c=33.07，g=0.01PLSR1 6 0.9690 1.304 1.843 8.11% OLS 29 0.9835 0.701 2.317 11.58% PSO-SVR2 29 0.9789 0.877 2.496 12.55% Lasso (λ = 0.00656 )21 0.9801 0.831 1.706 10.73% Ridge(k = 0.188) 29 0.9792 0.860 1.180 8.37% Elastic Net3 29 0.9795 0.849 1.231 8.56% Lasso-PSO-SVR4 21 0.9787 0.922 2.061 11.43% Elastic Net-PSO-SVR5 28 0.9792 0.867 2.295 11.89%
Table 3. Fitting MSE of Leave-one-out method
View tableView in ArticleTable 3. Fitting MSE of Leave-one-out method
No. Validated ore Lasso Ridge Elastic Net PLSR Lasso-PSO-SVR Elastic Net-PSO-SVR 1 GWB(E)07 0.2845 0.2331 0.2751 0.4726 0.8589 0.5887 2 ZBK339 0.8911 0.7998 0.8472 1.1641 2.5806 3.4203 3 ZBK337 0.2578 0.2315 0.2436 0.3756 0.6967 0.4848 4 ZBK336 0.7053 0.6497 0.6987 0.9465 2.4479 3.7488 5 ZBK340 0.6974 0.5943 0.658 1.1358 2.4204 2.3746 6 ZBK338 0.7817 0.7133 0.7476 1.1895 2.6855 1.9875 7 ZBK338B 0.8068 0.7389 0.7768 1.2495 2.4473 3.0500 8 ZBK335 0.8722 0.7748 0.8262 1.2711 2.8562 2.8444 9 ZBK340A 0.8464 0.7215 0.7903 1.1519 3.3778 3.5985 Mean 0.683 0.606 0.6515 0.9952 2.264 2.455 Std. deviation 0.243 0.221 0.23 0.3374 0.894 1.225 Tests of normality Statistic 0.771 0.764 0.761 0.756 0.821 0.877 Sig. P 0.009 0.008 0.007 0.006 0.036 0.147
Table 4. Validation MSE of Leave-one-out method
View tableView in ArticleTable 4. Validation MSE of Leave-one-out method
No. Validated ore Lasso Ridge Elastic Net PLSR Lasso-PSO-SVR Elastic Net-PSO-SVR 1 GWB(E)07 67.3145 57.2904 56.3262 60.7289 68.1940 63.2958 2 ZBK339 1.3277 2.4126 1.2947 1.4491 1.6320 1.0263 3 ZBK337 52.2403 51.3192 52.8692 64.4827 47.9133 53.7357 4 ZBK336 13.0786 8.2945 11.414 28.982 30.7940 36.1303 5 ZBK340 28.8767 25.8269 23.751 31.7462 26.3477 31.9675 6 ZBK338 7.6785 3.5496 5.1051 12.4508 13.8712 13.3334 7 ZBK338B 7.4952 14.7490 10.6776 15.3868 21.0660 21.2086 8 ZBK335 3.5487 1.5743 1.3709 0.3661 1.4411 2.5917 9 ZBK340A 2.0556 2.1012 1.6924 4.1519 38.9687 48.6560 Mean 20.402 18.569 18.2779 24.4161 27.803 30.216 Std. deviation 24.116 21.77 21.8001 24.3407 21.769 22.38 Tests of normality Statistic 0.791 0.782 0.769 0.864 0.956 0.949 Sig. P 0.016 0.013 0.009 0.107 0.756 0.678
Table 5. Paired T-Test
View tableView in ArticleTable 5. Paired T-Test
Paired group Sig. P Fitting Validation Lasso vs PLSR 0.008 0.139 Ridge vs PLSR 0.008 0.038 Elastic Net vs PLSR 0.008 0.015
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Jing HE, Quancheng LIU, Zhonggang XIONG, Linyu CHEN. Determination of copper content in raw ores via laser-induced breakdown spectroscopy with generalized linear model[J]. Infrared and Laser Engineering, 2025, 54(2): 20240455
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Received: Oct. 9, 2024
Accepted: --
Published Online: Mar. 14, 2025
The Author Email: CHEN Linyu (chenlinyu@mtc.edu.cn)
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