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

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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.

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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

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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).

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Authors and Affiliations

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

    Yanning Sun, Wei Qin & Zilong Zhuang

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  1. Yanning Sun
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  2. Wei Qin
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  3. Zilong Zhuang
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Correspondence to Wei Qin.

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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

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