Inferring 3D ellipsoids based on cross-sectional images with applications to porosity control of additive manufacturing

ABSTRACT

This article develops a series of statistical approaches that can be used to infer size distribution, volume number density, and volume fraction of three-dimensional (3D) ellipsoidal particles based on two-dimensional (2D) cross-sectional images. Specifically, this article first establishes an explicit linkage between the size of the ellipsoidal particles and the size of cross-sectional elliptical contours. Then an efficient Quasi-Monte Carlo EM algorithm is developed to overcome the challenge of 3D size distribution estimation based on the established complex linkage. The relationship between the 3D and 2D particle number densities is also identified to estimate the volume number density and volume fraction. The effectiveness of the proposed method is demonstrated through simulation and case studies.

KEYWORDS:

• Ellipsoid intersection
• quasi-Monte Carlo
• expectation maximization
• additive manufacturing
• porosity

Additional information

Notes on contributors

Jianguo Wu

Jianguo Wu is an assistant professor in the Industrial Engineering and Management Department, Peking University, Beijing, China. Between 2015 and 2017 he was an assistant professor in the Department of Industrial Manufacturing and Systems Engineering at the University of Texas–El Paso. He received a B.S. degree in mechanical engineering from Tsinghua University, Beijing, China, in 2009, an M.S. degree in mechanical engineering from Purdue University in 2011, and an M.S. degree in statistics in 2014 and Ph.D. degree in industrial and systems engineering in 2015, both from the University of Wisconsin–Madison. His research focuses on statistical modeling, monitoring and analysis of advanced manufacturing and engineering/service systems for quality control and reliability improvement through integrated application of metrology, engineering domain knowledge, and advanced data analytics. He is a member of INFORMS, IISE, and SME.

Yuan Yuan

Yuan Yuan is a research scientist at IBM Research–Singapore. She received her B.E. degree (2006) from Tsinghua University, Beijing, China, M.S. degrees in industrial and systems engineering (2010) and statistics (2011), and Ph.D. degree in industrial and systems engineering (2014) from the University of Wisconsin–Madison. Her research mainly focuses on data analytics, in particular developing innovative and generic data-driven modeling and analysis methodologies for complex systems with massive data. She has received a number of awards including the QSR Best Student Paper Award from the Institute for Operations Research and the Management Sciences (INFORMS) (2014) and the featured article award of IE Magazine (2010).

Haijun Gong

Haijun Gong is an assistant professor in the Manufacturing Engineering Department at Georgia Southern University. He completed his Ph.D. in industrial engineering in 2013 at the University of Louisville. His research interests include additive manufacturing and 3D printing process development, mechanical testing and materials characterization of 3D printed metals, simulation of the laser melting process, and physical phenomena in the selective laser melting and electron beam melting processes.

Tzu-Liang (Bill) Tseng

Tzu-Liang (Bill) Tseng is a professor and chair of the Department of IMSE at UTEP. He received his M.S. degrees in industrial engineering from the University of Wisconsin–Madison in 1993 (manufacturing systems) and 1995 (decision sciences), respectively, and Ph.D. in industrial engineering from the University of Iowa in 1999. His research areas cover quality assurance in additive manufacturing, industrial data analytics, and cyber-based decision support systems. He is currently serving as an editor of Journal of CSI and sits on the editorial boards of JDMMM and AJIBM. He is currently a Senior Member of IISE and SME and the Program Chair of Manufacturing Division of ASEE.