Accuracy improvement of quantitative LIBS analysis of coal properties using a hybrid model based on a wavelet threshold de-noising and feature selection method

Peng Lu; Peng Lu; Zhuang Zhuo; Wenhao Zhang; Jing Tang; Hailong Tang; Jingqi Lu

doi:10.1364/AO.394746

Applied Optics
Vol. 59,
Issue 22,
pp. 6443-6451
(2020)
•https://doi.org/10.1364/AO.394746

Accuracy improvement of quantitative LIBS analysis of coal properties using a hybrid model based on a wavelet threshold de-noising and feature selection method

Peng Lu, Zhuang Zhuo, Wenhao Zhang, Jing Tang, Hailong Tang, and Jingqi Lu

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Peng Lu, Zhuang Zhuo, Wenhao Zhang, Jing Tang, Hailong Tang, and Jingqi Lu, "Accuracy improvement of quantitative LIBS analysis of coal properties using a hybrid model based on a wavelet threshold de-noising and feature selection method," Appl. Opt. 59, 6443-6451 (2020)

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- Spectroscopy
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About this Article
History
- Original Manuscript: April 10, 2020
- Revised Manuscript: June 1, 2020
- Manuscript Accepted: June 20, 2020
- Published: July 23, 2020

Abstract

A hybrid model based on a wavelet threshold de-noising (WTD) and recursive feature elimination with cross-validation (RFECV) method was proposed to improve the measurements in quantitative analysis of coal properties using laser-induced breakdown spectroscopy (LIBS). First, a modified threshold of WTD was proposed based on wavelet coefficient theory. Interference of noise in the LIBS spectrum was reduced by using this modified method. Then, the RFECV method was applied to extract effective features from the de-noised LIBS spectrum. Finally, support vector regression (SVR) models of coal properties were established by the selected features. A validation set was used to verify the effectiveness and robustness of the hybrid model. The improvement of the hybrid model on the quantitative analysis of each index of coal properties (heat value, ash, volatile content) was studied and discussed. By using the proposed model, the determination coefficient (${{\rm{R}}^2}$), root mean square error of prediction, average relative error, and relative standard deviation were all significantly improved over the original spectra model. The results demonstrated that the proposed model could effectively improve the accuracy and precision of LIBS quantitative analysis for coal properties.

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Calibration Method	Validation Set Results	References
PLSR	Ash: $A R E = 6.94 %$	[16]
Dominant factor based PLS	Heat value: $R M S E P = 1.33 M J / k g$ , $A R E = 3.68 %$ , Volatile: $R M S E P = 1.41 %$ , $A R E = 5.47 %$ , Ash: $R M S E P = 3.49 %$ , $A R E = 12 %$	[18]
PCA and SVR	Heat value: $R M S E P = 0.85 M J / k g$ , $A R E = 2.71 %$ , $A A E = 0.65 M J / k g$ Volatile: $R M S E P = 1.22 %$ , $A R E = 4.42 %$ , Ash: $R M S E P = 1.82 %$ , $A R E = 5.48 %$	[19]
ANN	Heat value: $R M S E P = 0.48 M J / k g$ Volatile: $R M S E P = 0.85 %$ Ash: $R M S E P = 0.82 %$	[17]
PSO and KELM	Heat value: $R M S E P = 0.70 M J / k g$ Volatile: $R M S E P = 1.09 %$ Ash: $R M S E P = 2.05 %$	[20]
Hybrid model	Heat value: $A A E = 0.856 M J / k g$ Volatile: $A A E = 0.664 %$ Ash: $A A E = 1.661 %$	[22]
WT-MIV-KEML	Heat value: $R M S E P = 0.6151 M J / k g$	[21]

Sample No.	Heat Value (MJ/kg)	Ash (wt. %)	Volatile Content (wt. %)	Sample No.	Heat Value (MJ/kg)	Ash (wt. %)	Volatile Content (wt. %)
C1	14.46	34.18	28.52	C19	15.69	33.09	27.78
C2	36.01	20.48	21.24	C20	13.90	33.87	28.46
C3	40.58	18.47	19.39	C21	28.23	28.01	22.97
C4	38.71	18.11	20.24	C22	32.27	23.02	22.02
C5	10.26	34.02	29.83	C23	24.04	28.08	24.74
C6	12.94	34.69	28.71	C24	7.73	36.55	30.74
C7	26.44	29.84	23.31	C25	27.95	28.24	23.08
C8	23.05	30.25	24.07	C26	17.42	32.21	27.35
C9	35.48	12.11	21.97	V27	13.62	29.62	29.74
C10	37.08	12.22	21.26	V28	16.26	30.12	27.06
C11	31.80	14.00	20.65	V29	39.10	23.61	19.72
C12	11.98	11.30	30.56	V30	42.21	17.04	17.9
C13	9.62	33.64	29.83	V31	10.09	11.00	31.86
C14	25.35	28.5	23.72	V32	8.25	31.68	32.60
C15	6.97	33.18	29.50	V33	34.14	13.64	20.98
C16	31.50	26.48	21.54	V34	22.80	18.50	26.95
C17	18.41	32.08	26.77	V35	25.88	30.43	22.45
C18	20.45	31.64	25.95	V36	29.66	13.77	21.64

Coal Property	Model	RMSEP	R^2 (%)	ARE (%)	MeanRSD (%)
Heat value (MJ/kg)	SVR	1.7536	97.65	3.87	3.83
	$W T D + R F E C V + S V R$	1.0281	99.19	2.16	2.21
Ash (wt. %)	SVR	1.2854	97.18	3.27	2.27
	$W T D + R F E C V + S V R$	0.7281	99.10	1.79	1.49
Volatile content (wt. %)	SVR	0.7426	97.77	1.63	2.14
	$W T D + R F E C V + S V R$	0.5073	98.96	0.89	1.92

Calibration Method	Validation Set Results	References
PLSR	Ash: $A R E = 6.94 %$	[16]
Dominant factor based PLS	Heat value: $R M S E P = 1.33 M J / k g$ , $A R E = 3.68 %$ , Volatile: $R M S E P = 1.41 %$ , $A R E = 5.47 %$ , Ash: $R M S E P = 3.49 %$ , $A R E = 12 %$	[18]
PCA and SVR	Heat value: $R M S E P = 0.85 M J / k g$ , $A R E = 2.71 %$ , $A A E = 0.65 M J / k g$ Volatile: $R M S E P = 1.22 %$ , $A R E = 4.42 %$ , Ash: $R M S E P = 1.82 %$ , $A R E = 5.48 %$	[19]
ANN	Heat value: $R M S E P = 0.48 M J / k g$ Volatile: $R M S E P = 0.85 %$ Ash: $R M S E P = 0.82 %$	[17]
PSO and KELM	Heat value: $R M S E P = 0.70 M J / k g$ Volatile: $R M S E P = 1.09 %$ Ash: $R M S E P = 2.05 %$	[20]
Hybrid model	Heat value: $A A E = 0.856 M J / k g$ Volatile: $A A E = 0.664 %$ Ash: $A A E = 1.661 %$	[22]
WT-MIV-KEML	Heat value: $R M S E P = 0.6151 M J / k g$	[21]

Sample No.	Heat Value (MJ/kg)	Ash (wt. %)	Volatile Content (wt. %)	Sample No.	Heat Value (MJ/kg)	Ash (wt. %)	Volatile Content (wt. %)
C1	14.46	34.18	28.52	C19	15.69	33.09	27.78
C2	36.01	20.48	21.24	C20	13.90	33.87	28.46
C3	40.58	18.47	19.39	C21	28.23	28.01	22.97
C4	38.71	18.11	20.24	C22	32.27	23.02	22.02
C5	10.26	34.02	29.83	C23	24.04	28.08	24.74
C6	12.94	34.69	28.71	C24	7.73	36.55	30.74
C7	26.44	29.84	23.31	C25	27.95	28.24	23.08
C8	23.05	30.25	24.07	C26	17.42	32.21	27.35
C9	35.48	12.11	21.97	V27	13.62	29.62	29.74
C10	37.08	12.22	21.26	V28	16.26	30.12	27.06
C11	31.80	14.00	20.65	V29	39.10	23.61	19.72
C12	11.98	11.30	30.56	V30	42.21	17.04	17.9
C13	9.62	33.64	29.83	V31	10.09	11.00	31.86
C14	25.35	28.5	23.72	V32	8.25	31.68	32.60
C15	6.97	33.18	29.50	V33	34.14	13.64	20.98
C16	31.50	26.48	21.54	V34	22.80	18.50	26.95
C17	18.41	32.08	26.77	V35	25.88	30.43	22.45
C18	20.45	31.64	25.95	V36	29.66	13.77	21.64

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Applied Optics