Stochastic Process Prediction of Clutch Remaining Life Based on Oil Spectral Data

Jiang ZHANG; Jun-jie CUI; Chang-song ZHENG; Yong LIU; Ya-jun LIU; Jian SHEN

doi:10.3964/j.issn.1000-0593(2022)08-2631-06

Journals >Spectroscopy and Spectral Analysis >Volume 42 >Issue 8 >Page 2631 > Article

Spectroscopy and Spectral Analysis
Vol. 42, Issue 8, 2631 (2022)

Stochastic Process Prediction of Clutch Remaining Life Based on Oil Spectral Data

Jiang ZHANG^1,*, Jun-jie CUI^1,1;, Chang-song ZHENG^{2,2; *;}, Yong LIU^{1,1; *;}..., Ya-jun LIU^3,3; and Jian SHEN^1,1;|Show fewer author(s)

Author Affiliations

¹1. College of Mechatronics Engineering, North University of China, Taiyuan 030051, China

²2. School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China

³3. Inner Mongolia North Heavy Industry Group Co., Ltd., Baotou 014000, China

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DOI: 10.3964/j.issn.1000-0593(2022)08-2631-06 Cite this Article

Jiang ZHANG, Jun-jie CUI, Chang-song ZHENG, Yong LIU, Ya-jun LIU, Jian SHEN. Stochastic Process Prediction of Clutch Remaining Life Based on Oil Spectral Data[J]. Spectroscopy and Spectral Analysis, 2022, 42(8): 2631 Copy Citation Text

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Fig. 1. Structural principle diagram of integrated transmission device and wet clutch

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Fig. 2. Physical drawing of wet clutch comprehensive test bench

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Fig. 3. Experimental flow chart

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Fig. 4. Elemental spectrum

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Fig. 5. Accumulation diagram of Cu and Pb elements

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Fig. 6. Degradation increment diagram
(a): Cu increment diagram; (b): Pb increment diagram

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Fig. 7. Histogram of normal distribution of incremental statistics
(a): Cu increment statistics chart; (b): Pb increment statistics chart

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Fig. 8. Prediction diagram of univariate wiener process

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Fig. 9. Prediction diagram of binary wiener process

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Fig. 10. Residual life prediction deviation

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Copula	分布函数表达式
Frank	$C (u, v) = - \frac{1}{α} \ln (1 + \frac{[\exp (- αu) - 1] [\exp (- αv) - 1]}{\exp (- α) - 1})$
Caucasian	$\begin{array}{l} C (u, v) = msubsup msubsup \frac{1}{2 π \sqrt[]{1 - α^{2}}} \cdot \\ \exp (- \frac{x^{2} - 2 αxy + y^{2}}{2 (1 - α^{2})}) d x d y \end{array}$
Gumbel	$C (u, v) = e xp (- ({(- \ln u)}^{α} + {(- \ln v)}^{α})^{\frac{1}{α}})$
Clayton	$C (u, v) = \max ((u^{- α} + v^{- α} {- 1)}^{- \frac{1}{α}}, 0)$

Table 1. Common copula functions

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Copula	Frank	Caucasian	Gumbel	Clayton
AIC	-19.22	-11.42	-7.36	-8.24

Table 2. AIC values of common copula functions

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模型	η¹	η²	σ¹	σ²	α
30	0.548 148 148	0.496 296 296	0.649 8	0.953 5	0.842
60	0.291 228 070	0.228 070 175	0.904 0	1.378 8	0.839
90	0.298 850 575	0.232 183 908	1.241 2	1.681 6	0.822
120	0.261 538 462	0.229 914 530	1.387 7	2.008 1	0.847
150	0.219 727 891	0.159 863 946	1.608 5	2.226 2	0.854
180	0.175 706 215	0.206 779 661	1.969 6	2.172 8	0.874
210	0.147 342 995	0.138 164 251	2.014 0	2.440 5	0.822
240	0.158 649 789	0.127 426 160	1.953 2	2.480 8	0.814

Table 3. Estimated value of model coefficient

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预测时刻 /h	试验值	一元模型		二元模型
预测时刻 /h	试验值	预测/h	偏差/%	预测/h	偏差/%
30	245	165	32.7	188	23.3
60	215	120	44.2	131	39.0
90	185	87	52.9	117	36.8
120	155	78	49.7	110	29.0
150	125	67	46.4	99	20.8
180	95	60	35.2	77	18.9
210	65	57	12.3	61	6.2
240	35	39	11.4	41	17.1

Table 4. Comparison between prediction results and test results

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