X-Ray Fluorescence Spectral Inspection of Plastic Express Packaging Bags Based on K-means and Within-Cluster Sum of Squared Errors

Zhuang Chen; Hong Jiang; Dingcheng Hao; Ji Man

doi:10.3788/LOP202259.1130001

Laser & Optoelectronics Progress, Volume. 59, Issue 11, 1130001(2022)

X-Ray Fluorescence Spectral Inspection of Plastic Express Packaging Bags Based on K-means and Within-Cluster Sum of Squared Errors

Zhuang Chen1... Hong Jiang2,*, Dingcheng Hao3 and Ji Man4 |Show fewer author(s)

Author Affiliations

¹Judicial Police Academy (Public Security Branch), Gansu University of Political Science and Law, Lanzhou 730000, Gansu , China

²School of Criminal Investigation, People's Public Security University of China, Beijing 100038, China

³Xigu Branch of Lanzhou City Public Security Bureau of Gansu Province, Lanzhou 730000, Gansu , China

⁴Beijing Huayi Hongsheng Technology Co., Ltd., Beijing 100123, China

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Figures & Tables(10)

Fig. 1. Spectral curves of samples 15^# and 16^#

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Fig. 2. Classification of 60 plastic express bag samples

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Fig. 3. Relationship between SSE and K value

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Table 1. Spectral data of sample 9^#
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Table 1. Spectral data of sample 9^#
Duration /s Mass fraction /（μg·g^-1）
Ca Ti Fe Zn Sn
30 32553 2870 76 15 66
40 32959 2978 87 17 67
50 34207 3323 84 17 94
60 36387 3104 86 17 73
70 32581 3110 86 17 71
80 35183 3108 86 16 74
90 34287 3104 85 18 73
100 35383 3117 88 17 73

Table 2. Relative standard deviations of Ca and Ti contents in sample 9^# under different time conditions

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Table 2. Relative standard deviations of Ca and Ti contents in sample 9^# under different time conditions

Duration /s	Element	Mass fraction /（μg·g^-1）			Relative standard deviation /%
Duration /s	Element	1	2	3	Relative standard deviation /%
30	Ca	29642	33316	33897	8.03
30	Ti	2560	2987	3063	9.45
40	Ca	32700	34889	31288	5.51
40	Ti	2997	3154	2783	6.25
50	Ca	32299	35784	34538	5.16
50	Ti	3191	3532	3246	5.51
60	Ca	36025	35018	37938	4.04
60	Ti	3045	3028	3239	3.78
70	Ca	34051	31599	31913	4.10
70	Ti	3257	3014	3059	4.16
80	Ca	35773	36007	33769	3.50
80	Ti	3126	3201	2997	3.32
90	Ca	33767	36001	33093	4.43
90	Ti	3074	3188	3035	3.26
100	Ca	36896	35341	33912	4.22
100	Ti	3210	3089	3052	2.65

Table 3. Spectral data of sample 55^#

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Table 3. Spectral data of sample 55^#

Element	Mass fraction /（μg·g^-1）										Relative standard deviation /%
Element	1	2	3	4	5	6	7	8	9	10	Relative standard deviation /%
Cl	5163	5524	5308	4946	4959	5349	5311	5577	5488	5520	4.08
Ca	24801	25384	26201	24903	25732	25573	23670	26186	26205	27025	3.49
Ti	2159	2129	2180	2048	2226	2214	2013	2208	2231	2137	3.29
Fe	107	112	100	100	104	113	114	106	107	111	3.85
Zn	52	53	55	104	53	53	51	49	51	54	3.22
Sn	74	75	79	113	73	79	73	71	77	76	3.37

Table 4. ANOVA results

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Table 4. ANOVA results

Element	Mean square	Freedom	Error		F	Significance
Element	Mean square	Freedom	Mean square	Freedom	F	Significance
Cl	9.520	5	0.211	54	45.087	0
Ca	6.603	5	0.481	54	13.723	0
Ti	9.051	5	0.255	54	35.555	0
Fe	11.495	5	0.028	54	406.795	0
Sn	9.365	5	0.225	54	41.536	0
Zn	10.097	5	0.158	54	64.011	0
Cu	11.476	5	0.030	54	382.889	0
Ag	4.106	5	0.712	54	5.764	0
Sb	3.116	5	0.804	54	3.875	0.005

Table 5. Clustering results of K-means

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Table 5. Clustering results of K-means

Clustering category	Number	Sample No.
1	21	2^#，3^#，4^#，8^#，9^#，14^#，19^#，25^#，30^#，33^#，35^#，36^#，39^#，40^#，42^#，43^#，44^#，53^#，57^#，58^#，60^#
2	19	13^#，15^#，22^#，27^#，29^#，31^#，32^#，37^#，45^#-52^#，54^#，56^#，59^#
3	16	5^#-7^#，12^#，16^#-18^#，20^#，21^#，23^#，24^#，26^#，28^#，34^#，38^#，41^#
4	2	1^#，11^#
5	1	55^#
6	1	10^#

Table 6. Coefficients of canonical discriminant functions

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Table 6. Coefficients of canonical discriminant functions

Element	Function 1	Function 2	Function 3	Function 4	Function 5
Cl	-0.148	1.370	1.864	0.360	0.018
Ca	-0.666	-0.478	0.733	1.135	0.375
Ti	0.131	1.361	-0.936	1.121	0.165
Fe	4.996	-0.665	0.900	0.674	0.578
Sn	0.888	-0.062	0.002	-0.029	1.819
Zn	0.195	0.135	-0.404	-0.635	1.137
Cu	2.138	0.842	-0.604	0.074	-2.973
Ag	-0.037	0.504	-0.220	-0.674	0.019
Sb	0.044	-0.128	0.041	-0.107	-0.706

Table 7. Test results of Wilks’ Lambda
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Table 7. Test results of Wilks’ Lambda
Function Wilks’ Lambda Chi square Freedom Significance
Functions 1-5 0 446.398 45 0
Functions 2-5 0.012 227.502 32 0
Functions 3-5 0.089 124.747 21 0
Functions 4-5 0.374 50.636 12 0
Function 5 0.740 15.476 5 0.009

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Zhuang Chen, Hong Jiang, Dingcheng Hao, Ji Man. X-Ray Fluorescence Spectral Inspection of Plastic Express Packaging Bags Based on K-means and Within-Cluster Sum of Squared Errors[J]. Laser & Optoelectronics Progress, 2022, 59(11): 1130001

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