基于混合Copula模型的铝电解槽多参数相关性分析

doi:10.3969/j.issn.0438-1157.2014.04.024

化工学报 ›› 2014, Vol. 65 ›› Issue (4): 1327-1332.DOI: 10.3969/j.issn.0438-1157.2014.04.024

基于混合Copula模型的铝电解槽多参数相关性分析

易军¹, 李太福^1,2, 张元涛¹, 周伟¹, 田应甫³

1 重庆科技学院电气与信息工程学院, 重庆 401331;
2 重庆大学自动化学院, 重庆 400044;
3 重庆天泰铝业有限公司, 重庆 401328

收稿日期:2013-08-19 修回日期:2013-11-28 出版日期:2014-04-05 发布日期:2013-12-02
通讯作者: 易军（1973—），男，博士，副教授。
作者简介:易军（1973—），男，博士，副教授。
基金资助:
国家自然科学基金项目（51374268，51075418，61174015）；重庆市自然科学基金项目（cstc2012jjB40006，cstc2013jjB40007，cstc2012jjA90011）；重庆市教委科学技术研究项目（KJ121410）；重庆科技学院校内科研基金项目（CK2011B04，CK2013Z10）。

Multi-parameter correlation analysis based on mixed Copula model for aluminum reduction cell

YI Jun¹, LI Taifu^1,2, ZHANG Yuantao¹, ZHOU Wei¹, TIAN Yingfu³

1 School of Electronic & Information Engineering, Chongqing University of Science and Technology, Chongqing 401331, China;
2 School of Automation, Chongqing University, Chongqing 400044, China;
3 Chongqing Tiantai Aluminum Corporation Ltd., Chongqing 401328, China

Received:2013-08-19 Revised:2013-11-28 Online:2014-04-05 Published:2013-12-02
Supported by:
supported by the National Natural Science Foundation of China (51374268, 51075418, 61174015), the Natural Science Foundation of Chongqing (cstc2012jjB40006, cstc2013jjB40007, cstc2012jjA90011) and the Campus Research Foundation of Chongqing University of Science and Technology (CK2011B04, CK2013Z10).

摘要/Abstract

摘要： 针对铝电解大型预焙槽操作参数较多且彼此耦合性强，难以进行准确的概率分布描述和相关性分析问题，提出一种基于混合Copula模型的铝电解槽多参数相关性分析方法。在铝电解槽参数分布类型未知的情况下，首先利用非参数核密度函数估计建立变量的边缘密度函数；再构建基于混合Copula模型的多变量联合分布函数，并通过权重参数调节不同类型Copula函数的贡献比重；最后利用极大似然法对模型参数进行估计。对取自某厂170 kA铝电解槽的1824组真实样本数据进行实验，结果得到的3种距离指标分别是0.3169、0.6239和0.9276，均优于其他单一Copula函数，表明本方法是对超低电压下具有非稳态非均一特征的多参数进行相关性分析的一种有效途径。

关键词: 相关性分析, Copula, 模型, 分布, 电解

Abstract: It is difficult to accurately describe probability distribution and to do correlation analysis of operating multiple parameters in aluminum reduction cells. A correlation analysis method based on mixed Copula model was proposed to resolve the problem. First of all, non-parametric kernel density estimation method was used to establish edge density function of variables in the case of unknown distribution type. Secondly, proportion of contribution of different Copula functions could be adjusted by weight parameters in the joint distribution function of multiple parameters. Finally, the maximum likelihood method was used to estimate the mixed model parameters. By using 1824 groups real data of 170 kA operating aluminum smelter from a factory, test results showed that this method was better than other single Copula function because three distance indicators were 0.3169, 0.6239 and 0.9276. It was an effective way under super-low-voltage condition to do multi-parameter correlation analysis with non-steady-state and non-uniform features.

Key words: correlation analysis, Copula, model, distributions, electrolysis

中图分类号:

TQ821
TF391

易军, 李太福, 张元涛, 周伟, 田应甫. 基于混合Copula模型的铝电解槽多参数相关性分析[J]. 化工学报, 2014, 65(4): 1327-1332.

YI Jun, LI Taifu, ZHANG Yuantao, ZHOU Wei, TIAN Yingfu. Multi-parameter correlation analysis based on mixed Copula model for aluminum reduction cell[J]. CIESC Journal, 2014, 65(4): 1327-1332.

参考文献

[1] Li Hesong(李贺松). Research for Aluminum Reduction Cells on Unsteady Heterogeneous Information Models and Technology of Energy Saving(铝电解槽非稳态非均一信息模型及节能技术)[M]. Beijing: Metallurgical Industry Press, 2008
[2] Yin Xueyan(尹雪岩), Liu Fei(刘飞). Dynamic non-Gaussian process monitoring method based on DIFA and its application [J]. CIESC Journal (化工学报), 2011,62(5):1345-1349
[3] Tabsh I, Dupuis M. Simulation of the dynamic response of aluminum reduction cells [J]. Light Metals, 1997: 443-447
[4] Tang H Q, Urata N, Read C M, Stejer S L. Response of hall-heroult cell to step-changes in operating conditions: measurements and dynamic simulations[J]. Light Metals, 1998: 349-357
[5] Yurkov V, Mann V. A simple dynamic real-time model for aluminum reduction cell control system [J]. Light Metals, 2005: 423-428
[6] Arkhipov G V, Rozin A V. The aluminum reduction cell closed system of 3D mathematical models [J]. Light Metals, 2005: 589-592
[7] Knizhnik A V, Kuzakov A A, Zelberg B I, Veselkov V V. Application of mathematical methods to optimize aluminum production in pre-baked anode cells [J]. Light Metals, 2008: 437-442
[8] Severo D S, Gusberti V. A modeling approach to estimate bath and metal heat transfer coefficients[J]. Light Metals, 2009: 557-562
[9] Claudia C, Rainer K, Eike C B, Aleksey M. A mixed Copula model for insurance claims and claim sizes[J]. Scandinavian Actuarial Journal, 2012: 4:1-31
[10] Tang Xiaosong(唐小松), Li Dianqing(李典庆), Zhou Chuangbing(周创兵), Fang Guoguang(方国光). Probabilistic analysis of load-displacement hyperbolic curves of single pile using Copula [J]. Rock and Soil Mechanics (岩土力学), 2012, 33(1):171-178
[11] Sklar A. Fonctions de repartition an dimensions et leurs marges[J]. Publ. Inst. Statist, Univ. Paris, 1959, 8: 229-231
[12] Nelsen R B. Concordance and Copulas: A survey. Distributions with Given Marginals and Statistical Modeling[M]. Dordrecht: Kluwer Academic Publishers, 2002: 169-178
[13] Nelsen R B. An Introduction to Copulas[M]. 2ed. New York: Springer, 2006
[14] Hu Shunbo, Jiang Zhaolin, Zhu Xiangrong. Research on Parzen window based on improved Gaussian matrix in medical image registration[J]. Journal of Computational Information Systems, 2012, 8(12):5103-5110
[15] Ricci R G. On differential properties of Copulas [J]. Fuzzy Sets and Systems, 2013, 220:78-87
[16] Qu Leming, Yin Wotao. Copula density estimation by total variation penalized likelihood with linear equality constraints[J]. Computational Statistics and Data Analysis, 2012, 56(2): 384-398
[17] Berna Y, Senay Y. A comparison of various tests of normality[J]. Journal of Statistical Computation and Simulation, 2007, 77(2): 175-183
[18] Šlman M. On Kendall’s autocorrelations [J]. Communications in Statistics—Theory and Methods, 2012, 41(10): 1733-1738
[19] Jeff T T, Chang Chia-Hao, Rhonda C M. On the use of Spearman’s correlation coefficient for testing ordered alternatives[J]. Journal of Statistical Computation and Simulation, 2011, 81(11):1381-1392
[20] Salim B, Faouzi E, Eddin N, Tarek Z. On the multivariate two-sample problem using strong approximations of empirical Copula processes [J]. Communications in Statistics—Theory and Methods, 2011, 40(8): 1490-1509
[21] Ju Zhaojie, Liu Honghai. Recognizing hand grasp and manipulation through empirical Copula [J]. International Journal of Social Robotics, 2010, 2(3):321-328

基于混合Copula模型的铝电解槽多参数相关性分析

Multi-parameter correlation analysis based on mixed Copula model for aluminum reduction cell

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