Classification of Rubber Soles by X-ray Fluorescence Spectrometry Based on Multiple Linear Regression

Lanze Zhang; Hong Jiang; Jintong Liu; Jiageng Wang; Ji Man

doi:10.3788/LOP202158.1430002

Journals >Laser & Optoelectronics Progress >Volume 58 >Issue 14 >Page 1430002 > Article

Laser & Optoelectronics Progress
Vol. 58, Issue 14, 1430002 (2021)

Classification of Rubber Soles by X-ray Fluorescence Spectrometry Based on Multiple Linear Regression

Lanze Zhang¹, Hong Jiang^1、*, Jintong Liu¹, Jiageng Wang², and Ji Man³

Author Affiliations

¹School of Investigation, People's Public Security University of China, Beijing 100038, China

²Fengtai Branch of Beijing Municipal Public Security Bureau, Beijing 100071, China

³Beijing Huayi Hongsheng Technology Co., Ltd., Beijing 100123, China

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DOI: 10.3788/LOP202158.1430002 Cite this Article Set citation alerts

Lanze Zhang, Hong Jiang, Jintong Liu, Jiageng Wang, Ji Man. Classification of Rubber Soles by X-ray Fluorescence Spectrometry Based on Multiple Linear Regression[J]. Laser & Optoelectronics Progress, 2021, 58(14): 1430002 Copy Citation Text

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Fig. 1. Score of shoe types

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Fig. 2. Flow chart of multivariate linear regression classification method

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No.	Brand	Shoe type	Male or female
1	AOKANG	Leather shoe	Female
2	YONGLIANG	Leather shoe	Male
3	NIKE	Casual shoe	Male
4	Unknown	Running shoe	Male
5	Crocodile	Leather shoe	Male
6	Louis	Leather shoe	Male
7	YONGLIANG	Leather shoe	Male (special sole material)
8	PLOVER	Leather shoe	Male
9	GA	Leather shoe	Male (military sole material)
10	Camel	Leather shoe	Male
11	SHEN TA	Casual shoe	Female
12	JRV NALI	Leather shoe	Male
13	DAPHNE	Leather shoe	Female
14	People's Public Security University of China	Leather shoe	Male
15	DAPHNE	Leather shoe	Female
No.	Brand	Shoe type	Male or female
16	Z.Suo	Casual shoe	Male
17	Warrior	Casual shoe	Male
18	LiNing	Basketball shoe	Male
19	ANTA	Basketball shoe	Male
20	OLUNPO	Leather shoe	Male
21	361°	Basketball shoe	Male
22	NIKE	Basketball shoe	Male
23	Unknown	Leather shoe	Male
24	AOKANG	Leather shoe	Female
25	YANG DA	Casual shoe	Male
26	NIKE	Running shoe	Male
27	361°	Casual shoe	Male
28	NIKE	Slipper	Male
29	YINGYUEGU	Leather shoe	Male
30	MISTRAL	Casual shoe	Male
31	PUMA	Casual shoe	Male
32	SENDA	Leather shoe	Male
33	NIKE	Soccer shoe	Male
34	NiuAiKe	Leather shoe	Male
35	AOKANG	Leather shoe	Male
36	AOKANG	Leather shoe	Male
37	Adidas	Casual shoe	Male
38	People's Public Security University of China	Leather shoe	Male
39	People's Public SecurityUniversity of China	Leather shoe	Male
40	People's Public Security University of China	Leather shoe	Male

Table 1. List of relevant information of rubber sole samples

Variable	Explanation of variables
Kind	Leather shoes are marked as 1 and other types of shoes are marked as 0
Gender	1 for men's shoes and 0 for women's shoes
Element	Seven kinds of elements in rubber sole

Table 2. Variable description

Kind	Frequency	Proportion /%	Cumulative proportion /%
Leather shoe	23	57.5	57.5
Casual shoe	9	22.5	80.0
Basketball shoe	4	10.0	90.0
Running shoe	2	5.0	95.0
Football shoe	1	2.5	97.5
Slipper	1	2.5	100.0

Table 3. Descriptive statistical results of types of shoes

Element	Mean /10^-6	Std. Dev. /10^-6	Min /10^-6	Max /10^-6
Ca	22572.8	29050.95	135	128227
Ti	6010.625	11462.14	0	49237
Zn	9464.025	6429.343	32	26219
Pb	386.525	1372.053	0	7975
Fe	605.175	1027.582	0	4959
Cu	69.25	55.83802	0	201
Sb	69.575	53.30747	0	285

Table 4. Statistical analysis of sample element content

Variable	Robust
Variable	η_Coef	E_Std	t	P	[95%Conf. Interval]
Gender	-0.2304934	0.2608486	-0.88	0.384	-0.7624976	0.3015108
Ca	-4.44×10^-6	1.68×10^-6	-2.65	0.013	-7.86×10^-6	-1.02×10^-6
Zn	6.05×10^-6	0.0000129	0.47	0.641	-0.0000202	0.0000323
Fe	0.0001524	0.00008	1.91	0.066	-0.0000107	0.0003154
Sb	0.0010258	0.0006019	1.7	0.098	-0.0002018	0.0022534
Cu	-0.0022586	0.0012021	-1.88	0.07	-0.0047104	0.0001931
Ti	-0.0000199	4.46×10^-6	-4.46	0	-0.000029	-0.0000108
Pb	-0.0000317	0.0000385	-0.82	0.417	-0.0001103	0.0000469
Cons	0.9443076	0.3006426	3.14	0.004	0.3311431	1.557472

Table 5. Re-regression results of sample element content

Variable	Element content /10^-6
Variable	Ca	Cu	Ti	Fe	Sb
Others	28689.18	80.35	12992.82	170.53	58.06
Leather shoe	18052.00	61.04	849.87	926.43	78.09

Table 6. Average element content of different shoes

Variable	η_Coef	E_Std	t	P	α
Ca	-4.45×10^-6	2.18×10^-6	-2.04	0.049	-0.2581123
Cu	-0.0022486	0.0011303	-1.99	0.055	-0.2507974
Ti	-0.0000198	5.51×10^-6	-3.59	0.001	-0.4522083
Fe	0.0001799	0.0000635	2.83	0.008	0.3693422
Cons	0.8409447	0.1178095	7.14	0

Table 7. Standardized regression results of each element in the sample

Variable	F_VIF	1/F_VIF
Fe	1.11	0.897329
Ca	1.05	0.95281
Ti	1.04	0.958093
Cu	1.04	0.958947
Mean F_VIF	1.06

Table 8. Test results of multicollinearity

Sample No.	Element content /10^-6
Sample No.	Ca	Fe	Cu	Ti
28	1261	0	30	0
32	2285	0	72	2074
35	21528	1170	123	0
38	16272	0	24	2394
39	2934	0	8	1365

Table 9. Element content of misclassified samples

Variable	Element content /10^-6							Score rating
Variable	Ca	Cu		Ti		Fe		Score rating
Yongliang leather shoe	2172		0		0		647	0.947675
Yongliang leather shoe (combustion group)	2312		0		0		601	0.938776
Crocodile leather shoe	17573		0		0		888	0.922496
Crocodile leather shoe (bloodstain group)	16326		0		0		828	0.917251
Z. Suo casual shoe	80073		0		21045		0	0.067929
Z. Suo casual shoe (soil group)	79074		0		20315		0	0.086828
Huili casual shoe (paint group)	854		0		23679		0	0.3683
Yangda casual shoe (control group)	107806		47		9354		0	0.070315
Yangda casual shoe (ink group)	109634		60		9706		0	0.025979

Table 10. Sample regression results of simulating the real situation of cases

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