Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Nonparametric-copula-entropy and network deconvolution method for causal discovery in complex manufacturing systems

  • Published:
Journal of Intelligent Manufacturing Aims and scope Submit manuscript

Abstract

To clarify the causality among process parameters is a core issue of data-driven production performance analysis and product quality optimization. The difficulty lies in accurately measuring and distinguishing direct and indirect associations of complex manufacturing systems. In this work, the nonparametric-copula-entropy and network deconvolution method is proposed for causal discovery in complex manufacturing systems. Firstly, based on copula theory and kernel density estimation method, the nonparametric-copula-entropy is introduced to improve the accuracy of association measurement between parameters, and its superiority is verified by comparing with the results of different association measurement methods. Then, the global association matrix is constructed by the nonparametric-copula-entropy, and network deconvolution method is employed to extract the direct information from the global association matrix. The proposed method is tested by using an open gene expression dataset. Finally, as an experimental application, the causal analysis for a diesel engine production line is carried out by the proposed method. The results show that the proposed method can reveal causal relationship between process parameters and quality parameters in the diesel engine production line well, which provide theoretical guidance and implementation approach for the optimal control of complex manufacturing system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Abbreviations

a 1(x i), a 2(x i):

Parameters of multivariate kernel function K(·)

B :

Base-number of logarithmic functions

c(u 1, u 2, …, u N):

Probability density function corresponding to copula function

C(u 1, u 2, …, u N):

Copula function

f(x 1, x 2, …, x N):

Joint probability density function of N random variables X1, X2, …, XN

f 1(x 1), f 2(x 2) …, f N(x N):

Marginal probability density function of N random variables X1, X2, …, XN

F(x 1, x 2, …, x N):

Joint distribution function of N random variables X1, X2, …, XN

F 1(x 1), F 2(x 2) …, F N(x N):

Marginal distribution function of N random variables X1, X2, …, XN

G(·):

Distribution function of univariate kernel function

G :

Global association matrix

G dir :

Direct association matrix

h :

Bandwidth of univariate kernel density estimation

h i :

Bandwidth of multivariate kernel density estimation for the ith random variable

I :

Identity matrix

k(·):

Univariate kernel function

K(·):

Multivariate kernel function

MI(X 1, X 2, …, X N):

Mutual information of multi-dimension random variables X1, X2, …, XN

N :

Number of random variables

n :

Rotational speed

p(x i):

Subfunctions of multivariate kernel function K(·)

P :

Power

T :

Torque

u i :

Independent variable of copula function, ui = Fi(xi)

U i :

Random variable i subject to uniform distribution

U :

Vector form of [u1, u2, …, uN]

x i :

Observation values of the ith random variable

X i :

The ith random variable

AMV:

Association measurement values

AUC:

Area under ROC curve

CE:

Copula entropy

FN:

The numbers of false negatives

FP:

The numbers of false positives

FPR:

False positive rate

KDE:

Kernel density estimation

MES:

Manufacturing execution system

NCE:

Nonparametric copula entropy

ND:

Network deconvolution

OLE:

Object linking and embedding

PDF:

Probability density function

QAS:

Quality assurance system

RMSE:

Root mean square error

ROC:

Receiver operating characteristic

TN:

The numbers of true negatives

TP:

The numbers of true positives

TPR:

True positive rate

WS:

Work station

References

  • Altay, G., & Emmert-Streib, F. (2010). Revealing differences in gene network inference algorithms on the network level by ensemble methods. Bioinformatics, 26(14), 1738–1744.

    Article  Google Scholar 

  • Bastian, M., Heymann, S., & Jacomy, M. (2009). Gephi: an open source software for exploring and manipulating networks. In Third International AAAI Conference on Weblogs and Social Media.

  • Bowman, A. W., & Azzalini, A. (1997). Applied smoothing techniques for data analysis. Oxford University Press Inc.

    Google Scholar 

  • Chen, L., & Guo, S. (2019). Copulas and its application in hydrology and water resources. Springer.

    Book  Google Scholar 

  • Chen, L., Ye, L., Singh, V., Zhou, J., & Guo, S. (2014). Determination of input for artificial neural networks for flood forecasting using the copula entropy method. Journal of Hydrologic Engineering, 19(11), 04014021–04014031.

    Article  Google Scholar 

  • Cover, T. M., & Thomas, J. A. (2012). Elements of information theory. Wiley.

    Google Scholar 

  • Croux, C., & Dehon, C. (2010). Influence functions of the Spearman and Kendall correlation measures. Statistical Methods & Applications, 19(4), 497–515.

    Article  Google Scholar 

  • Embrechts, P., Lindskog, F., & McNeil, A. (2001). Modelling dependence with copulas, rapport technique, Dép. de Math. Inst. Féd. de Technol. de Zurich, Zurich.

  • Fang, L., Zhao, H., Wang, P., Yu, M., Yan, J., Cheng, W., & Chen, P. (2015). Feature selection method based on mutual information and class separability for dimension reduction in multidimensional time series for clinical data. Biomedical Signal Processing and Control, 21, 82–89.

    Article  Google Scholar 

  • Feizi, S., Marbach, D., Médard, M., & Kellis, M. (2013). Network deconvolution as a general method to distinguish direct dependencies in networks. Nature Biotechnology, 31(8), 726.

    Article  Google Scholar 

  • Frigieri, E. P., Ynoguti, C. A., & Paiva, A. P. (2019). Correlation analysis among audible sound emissions and machining parameters in hardened steel turning. Journal of Intelligent Manufacturing, 30(4), 1753–1764.

    Article  Google Scholar 

  • Gu, Y. K., Fan, C. J., Liang, L. Q., & Zhang, J. (2019). Reliability calculation method based on the Copula function for mechanical systems with dependent failure. Annals of Operations Research. https://doi.org/10.1007/s10479-019-03202-5

    Article  Google Scholar 

  • Han, M., & Ren, W. (2015). Global mutual information-based feature selection approach using single-objective and multi-objective optimization. Neurocomputing, 168, 47–54.

    Article  Google Scholar 

  • Hu, L. (2006). Dependence patterns across financial markets: a mixed copula approach. Applied Financial Economics, 16(10), 717–729.

    Article  Google Scholar 

  • Huard, D., Évin, G., & Favre, A. C. (2006). Bayesian copula selection. Computational Statistics & Data Analysis, 51(2), 809–822.

    Article  Google Scholar 

  • Jeon, H. W., Lee, S., & Wang, C. (2019). Estimating manufacturing electricity costs by simulating dependence between production parameters. Robotics and Computer-Integrated Manufacturing, 55, 129–140.

    Article  Google Scholar 

  • Jones, M. C. (1993). Simple boundary correction for kernel density estimation. Statistics and Computing., 3(3), 135–146.

    Article  Google Scholar 

  • Khan, S., Bandyopadhyay, S., Ganguly, A. R., Saigal, S., Erickson, D. J., et al. (2007). Relative performance of mutual information estimation methods for quantifying the dependence among short and noisy data. Physical Review E, 76, 1–15.

    Article  Google Scholar 

  • Kraskov, A., Stögbauer, H., & Grassberger, P. (2004). Estimating mutual information. Physical Review E, 69(6), 066138.

    Article  Google Scholar 

  • Marbach, D., Prill, R. J., Schaffter, T., Mattiussi, C., Floreano, D., & Stolovitzky, G. (2010). Revealing strengths and weaknesses of methods for gene network inference. Proceedings of the National Academy of Sciences, 107(14), 6286–6291.

    Article  Google Scholar 

  • Nicoloutsopoulos, D. (2005). Parametric and Bayesian non-parametric estimation of copulas. Doctoral dissertation, University of London.

  • Patton, A. J. (2002). Applications of Copula Theory in Financial Econometrics, Ph.D. Dissertation, University of California.

  • Qin, W., Zha, D., & Zhang, J. (2018). An effective approach for causal variables analysis in diesel engine production by using mutual information and network deconvolution. Journal of Intelligent Manufacturing, 1–11.

  • Rossi, F., Lendasse, A., François, D., Wertz, V., & Verleysen, M. (2006). Mutual information for the selection of relevant variables in spectrometric nonlinear modelling. Chemometrics and intelligent laboratory systems, 80(2), 215–226.

    Article  Google Scholar 

  • Scott, D. W. (2015). Multivariate density estimation: theory, practice, and visualization. Wiley.

    Google Scholar 

  • Shannon, C. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 379–423.

    Article  Google Scholar 

  • Shi, J., Zhao, J., Li, T., & Chen, L. (2019). Detecting direct associations in a network by information theoretic approaches. Science China Mathematics, 62(5), 823–838.

    Article  Google Scholar 

  • Silverman, B. W. (1986). Density estimation for statistics and data analysis. Monographs on Statistics and Applied Probability, 26.

  • Sklar, M. (1959). Fonctions de repartition an dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris, 8, 229–231.

    Google Scholar 

  • Sun, J. C., et al. (2017). Complex network construction of multivariate time series using information geometry. IEEE Transactions on Systems, Man, and Cybernetics: Systems., 49(1), 107–122.

    Article  Google Scholar 

  • Thomas, R. D., Moses, N. C., Semple, E. A., & Strang, A. J. (2014). An efficient algorithm for the computation of average mutual information: Validation and implementation in Matlab. Journal of Mathematical Psychology, 61, 45–59.

    Article  Google Scholar 

  • Wei, J., Pan, Z., Lin, X., Qin, D., Zhang, A., & Shi, L. (2019). Copula-function-based analysis model and dynamic reliability of a gear transmission system considering failure correlations. Fatigue & Fracture of Engineering Materials & Structures, 42(1), 114–128.

    Article  Google Scholar 

  • Xu, Y. (2005). Applications of Copula-based Models in Portfolio Optimization, Ph.D. Dissertation, University of Miami.

  • Zachariah, M., & Reddy, M. J. (2013). Development of an entropy-copula-based stochastic simulation model for generation of monthly inflows into the Hirakud Dam. ISH Journal of Hydraulic Engineering, 19(3), 267–275.

    Article  Google Scholar 

  • Zhang, X., Zhao, X. M., He, K., Lu, L., Cao, Y., Liu, J., et al. (2012). Inferring gene regulatory networks from gene expression data by path consistency algorithm based on conditional mutual information. Bioinformatics, 28(1), 98.

    Article  Google Scholar 

  • Zhang, X., Zhao, J., Hao, J. K., Zhao, X. M., & Chen, L. (2015). Conditional mutual inclusive information enables accurate quantification of associations in gene regulatory networks. Nucleic Acids Research, 43(5), e31–e31.

    Article  Google Scholar 

  • Zhao, N., & Lin, W. T. (2011). A copula entropy approach to correlation measurement at the country level. Applied Mathematics and Computation, 218(2), 628–642.

    Article  Google Scholar 

Download references

Acknowledgements

This project is supported by Shanghai Aerospace Science and Technology Innovation Fund (No. SAST2016048), and the National Natural Science Foundation (Grant Nos. 51435009 and 51775348).

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China

    Yanning Sun, Wei Qin & Zilong Zhuang

Authors
  1. Yanning Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zilong Zhuang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wei Qin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sun, Y., Qin, W. & Zhuang, Z. Nonparametric-copula-entropy and network deconvolution method for causal discovery in complex manufacturing systems. J Intell Manuf 33, 1699–1713 (2022). https://doi.org/10.1007/s10845-021-01751-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10845-021-01751-w

Keywords

Search

Navigation