Layer Classification Algorithm in Terahertz Thickness Measurement Technology

Jie Lin; Ji Qi; Yuqi Zhang; Wei Zhang; Yuang Chen; Mingxia He; Qiuhong Qu; Yizhu Zhang

doi:10.3788/CJL240955

Chinese Journal of Lasers, Volume. 51, Issue 18, 1801017(2024)

Layer Classification Algorithm in Terahertz Thickness Measurement Technology

Jie Lin^1,2, Ji Qi^1,2, Yuqi Zhang^2,3, Wei Zhang², Yuang Chen¹, Mingxia He^1,2, Qiuhong Qu², and Yizhu Zhang^1,2、*

Author Affiliations

¹School of Precision Instrument and Opto-Electronics Engineering, Tianjin University, Tianjin 300072, China

²Sichuan Innovation Research Institute of Tianjin University, Chengdu 610213, Sichuan , China

³School of Electronics and Information Engineering, Tiangong University, Tianjin 300387, China

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Figures & Tables(9)

Fig. 1. THz-TDS scanning system. (a) Schematic diagram of system; (b) picture of system

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Fig. 2. Paint coating sample and measurement point distribution. (a) Different coating regions of the paint coating sample;

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Fig. 3. Terahertz reflection data of paint layer with different number of layers. (a) 100 scans of the single-layer paint; (b) 100 scans of the double-layer paint; (c) 200 scans of the triple-layer paint; (d) time domain reflection waveform of the single-layer paint; (e) time domain reflection waveform of the double-layer paint; (f) time domain reflection waveform of the triple-layer paint

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Fig. 4. Confusion matrix of the test set by different methods. (a) GS-SVM; (b) WOA-SVM; (c) SSA-SVM; (d) ISSA-SVM;

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Fig. 5. AUC scores and the ROC curves of the test set by different methods. (a) GS-SVM; (b) WOA-SVM; (c) SSA-SVM;

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Fig. 6. Measurement results of paint coating thickness for multi-coated sample

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Table 1. Formulas of 29 time domain and frequency domain features in comprehensive feature set

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Table 1. Formulas of 29 time domain and frequency domain features in comprehensive feature set

Class	Feature	Formula
Time domain	Mean value	$\bar{x} = \frac{1}{N} \sum_{i = 1}^{N} x_{i}$
	RMS	$X_{R M S} = \sqrt[]{\frac{1}{N} \sum_{i = 1}^{N} x_{i}^{2}}$
	Root amplitude value	$X_{f} = \sqrt[]{\frac{1}{N} \sum_{i = 1}^{N} \sqrt[]{\| x_{i} \|}}$
	Mean absolute value	$\| \bar{x} \| = \frac{1}{N} \sum_{i = 1}^{N} \sqrt[]{\| x_{i} \|}$
	Skewness	$α = \frac{1}{N} \sum_{i = 1}^{N} {[(x_{i} - \bar{x}) / σ]}^{3}$
	Kurtosis	$β = \frac{1}{N} \sum_{i = 1}^{N} {[(x_{i} - \bar{x}) / σ]}^{4}$
	Variance	$σ^{2} = \frac{1}{N} \sum_{i = 1}^{N} (x_{i} {- \bar{x})}^{2}$
	Maximum value	$X_{m a x} = m a x (x_{i})$
	Minimum value	$X_{m i n} = m i n (x_{i})$
	Peak-to-peak value	$X_{P P} = X_{m a x} - X_{m i n}$
	Waveform indicator	$S = X_{R M S} / \| \bar{x} \|$
	Peak indicator	$C = X_{m a x} / X_{R M S}$
	Impulse indicator	$I = X_{m a x} / \| \bar{x} \|$
	Margin index	$L = X_{m a x} / X_{f}$
	Skewness indicator	$K_{α} = α / X_{R M S}$
	Kurtosis indicator	$K_{β} = β / X_{R M S}$
Frequency domain	Mean frequency	$F_{17} = \frac{1}{K} \sum_{k = 1}^{K} s (k)$
	Spectral RMS value	$F_{18} = \sqrt[]{\frac{1}{K - 1} {\sum_{k = 1}^{K} [s (k) - F_{17}]}^{2}}$
	Signal skewness	$F_{19} = [\sum_{k = 1}^{K} {(s (k) - F_{17})}^{3}] / [(K - 1) F_{18}^{3}]$
	Signal kurtosis	$F_{20} = [\sum_{k = 1}^{K} {(s (k) - F_{17})}^{4}] / [(K - 1) F_{18}^{4}]$
	Frequency centroid	$F_{21} = (\sum_{k = 1}^{K} f_{k} \cdot s (k)) / (\sum_{k = 1}^{K} s (k))$
	Spectral standard deviation	$F_{22} = \sqrt[]{\frac{1}{K - 1} \sum_{k = 1}^{K} (f_{k} - F_{21})^{2} \cdot s (k)}$
	RMS frequency	$F_{23} = \sqrt[]{(\sum_{k = 1}^{K} {f_{k}}^{2} \cdot s (k)) / (\sum_{k = 1}^{K} s (k))}$
	Third-order central frequency	$F_{24} = \sqrt[3]{(\sum_{k = 1}^{K} {f_{k}}^{3} \cdot s (k)) / (\sum_{k = 1}^{K} f_{k}^{2} \cdot s (k))}$
	Fourth-order central frequency	$F_{25} = \sqrt[4]{(\sum_{k = 1}^{K} {f_{k}}^{4} \cdot s (k)) / (\sum_{k = 1}^{K} f_{k}^{2} \cdot s (k))}$
	Frequency centroid ratio	$F_{26} = F_{22} / F_{21}$
	Frequency skewness	$F_{27} = [\sum_{k = 1}^{K} (f_{k} - F_{21})^{3} \cdot s (k)] / [(K - 1) F_{22}^{3}]$
	Frequency kurtosis	$F_{28} = [\sum_{k = 1}^{K} (f_{k} - F_{21})^{4} \cdot s (k)] / [(K - 1) F_{22}^{4}]$
	Standard deviation frequency	$F_{29} = \sqrt[]{[\sum_{k = 1}^{K} (f_{k} - F_{21})^{1 / 2} \cdot s (k)] / [(K - 1) F_{22}^{1 / 2}]}$

Table 2. Comparison of layer classification results for SVM parameters optimized by different methods

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Table 2. Comparison of layer classification results for SVM parameters optimized by different methods

Classification method	Optimal value		Accuracy		Running time /s
Classification method	C	g	Training set	Test set	Running time /s
GS-SVM	64.0000	0.125	99.29%（278/280）	98.33%（118/120）	32.86
WOA-SVM	0.1782	26.780	97.14%（272/280）	92.50%（111/120）	0.65
SSA-SVM	24.3000	22.000	100.00%（280/280）	95.00%（114/120）	0.55
ISSA-SVM	19.5930	30.000	100.00%（280/280）	96.67%（116/120）	0.66
KPCA-ISSA-SVM	9.5300	26.000	100.00%（280/280）	98.33%（118/120）	0.46

Table 3. Precision rate, recall rate, and F1 score of SVM model optimized by different methods

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Table 3. Precision rate, recall rate, and F1 score of SVM model optimized by different methods

Classification method	P			R			F1 score
Classification method	Class 1	Class 2	Class 3	Class 1	Class 2	Class 3	Class 1	Class 2	Class 3
GS-SVM	0.97	1.00	0.98	1.00	0.93	1.00	0.98	0.97	0.99
WOA-SVM	1.00	0.77	1.00	0.93	1.00	0.88	0.97	0.87	0.94
SSA-SVM	1.00	0.85	0.98	0.97	0.97	0.93	0.98	0.91	0.96
ISSA-SVM	1.00	0.91	0.98	0.93	0.97	0.98	0.97	0.94	0.98
KPCA-ISSA-SVM	0.94	1.00	1.00	1.00	0.97	0.98	0.97	0.98	0.99

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Jie Lin, Ji Qi, Yuqi Zhang, Wei Zhang, Yuang Chen, Mingxia He, Qiuhong Qu, Yizhu Zhang. Layer Classification Algorithm in Terahertz Thickness Measurement Technology[J]. Chinese Journal of Lasers, 2024, 51(18): 1801017

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Paper Information

Category: laser devices and laser physics

Received: Jun. 12, 2024

Accepted: Jul. 22, 2024

Published Online: Sep. 9, 2024

The Author Email: Zhang Yizhu (zhangyizhu@tju.edu.cn)

DOI:10.3788/CJL240955

CSTR:32183.14.CJL240955

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology