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Bayesian Network Learning for Data-Driven Design

[+] Author and Article Information
Zhen Hu

Assistant Professor, Department of Industrial and Manufacturing Systems Engineering, University of Michigan-Dearborn, 2340 Heinz Prechter Engineering Complex (HPEC), Dearborn, MI, 48128
zhennhu@umich.edu

Sankaran Mahadevan

Professor, Department of Civil and Environmental Engineering, Vanderbilt University, 272 Jacobs Hall, VU Mailbox: PMB 351831, Nashville, TN, 37235
sankaran.mahadevan@vanderbilt.edu

1Corresponding author.

ASME doi:10.1115/1.4039149 History: Received May 16, 2017; Revised January 15, 2018

Abstract

Bayesian Networks (BNs) are being studied in recent years for system diagnosis, reliability analysis, and design of complex engineered systems. In several practical applications, BNs need to be learned from available data before being used for design or other purposes. Current BN learning algorithms are mainly developed for networks with only discrete variables. Engineering design problems often consist of both discrete and continuous variables. This paper develops a framework to handle continuous variables in BN learning by integrating learning algorithms of discrete BNs with Gaussian mixture models (GMMs). We first make the topology learning more robust by optimizing the number of Gaussian components in the univariate GMMs currently available in the literature. Based on the BN topology learning, a new Multivariate Gaussian Mixture (MGM) strategy is developed to improve the accuracy of conditional probability learning in the BN. A method is proposed to address this difficulty of MGM modeling with data of mixed discrete and continuous variables by mapping the data for discrete variables into data for a standard normal variable. The proposed framework is capable of learning BNs without discretizing the continuous variables or making assumptions about their CPDs. The applications of the learned BN to uncertainty quantification and model calibration are also investigated. The results of a mathematical example and an engineering application example demonstrate the effectiveness of the proposed framework.

Copyright (c) 2018 by ASME
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