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Technical Brief

Joint Multifractal and Lacunarity Analysis of Image Profiles for Manufacturing Quality Control

[+] Author and Article Information
Farhad Imani

Department of Industrial and Manufacturing Engineering,
Pennsylvania State University,
State College, PA 16802
e-mail: fxi1@psu.edu

Bing Yao

Department of Industrial and Manufacturing Engineering,
Pennsylvania State University,
State College, PA 16802
e-mail: bzy111@psu.edu

Ruimin Chen

Department of Industrial and Manufacturing Engineering,
Pennsylvania State University,
State College, PA 16802
e-mail: rxc91@psu.edu

Prahalad Rao

Department of Mechanical and Materials Engineering,
University of Nebraska,
Lincoln, NE 68588
e-mail: rao@unl.edu

Hui Yang

Department of Industrial and Manufacturing Engineering,
Pennsylvania State University,
State College, PA 16802
e-mail: huy25@psu.edu

1Corresponding author.

Manuscript received March 20, 2018; final manuscript received January 2, 2019; published online February 27, 2019. Assoc. Editor: Dragan Djurdjanovic.

J. Manuf. Sci. Eng 141(4), 044501 (Feb 27, 2019) (7 pages) Paper No: MANU-18-1168; doi: 10.1115/1.4042579 History: Received March 20, 2018; Accepted January 02, 2019

The modern manufacturing industry faces increasing demands to customize products according to personal needs, thereby leading to the proliferation of complex designs. To cope with design complexity, manufacturing systems are increasingly equipped with advanced sensing and imaging capabilities. However, traditional statistical process control methods are not concerned with the stream of in-process imaging data. Also, very little has been done to investigate nonlinearity, irregularity, and inhomogeneity in the image stream collected from manufacturing processes. This paper presents the joint multifractal and lacunarity analysis to characterize irregular and inhomogeneous patterns of image profiles, as well as detect the hidden dynamics in the manufacturing process. Experimental studies show that the proposed method not only effectively characterizes surface finishes for quality control of ultraprecision machining but also provides an effective model to link process parameters with fractal characteristics of in-process images acquired from additive manufacturing. This, in turn, will allow a swift response to processes changes and consequently reduce the number of defective products. The proposed multifractal method shows strong potentials to be applied for process monitoring and control in a variety of domains such as ultraprecision machining and additive manufacturing.

Copyright © 2019 by ASME
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References

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Figures

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Fig. 1

Flow diagram of the research methodology: (a) UPM and (b) LPBF-AM processes

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Fig. 2

Voronoi tessellation with different number of cells: (a) 100 cells, (b) 1000 cells, and (c) 10,000 cells; Delaunay triangulation with different number of cells: (d) 100 cells, (e) 1000 cells, and (f) 10,000 cells

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Fig. 3

Characteristic points in the multifractal spectrum

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Fig. 4

(a) Multifractal spectra of the Voronoi tessellation and Delaunay triangulation in Fig. 2 and (b) lacunarity spectra of the Voronoi tessellation with different cells number in Fig. 2

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Fig. 5

UPM images with smooth surfaces (in-control): (a) Ra = 43.81 nm, (b) Ra = 43.83 nm and rough surfaces (out of control), (c) Ra = 297.58 nm, and (d) Ra = 296.92 nm

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Fig. 6

Multifractal spectra of four UPM images: (a) Ra = 43.81 nm, (b) Ra = 43.83 nm, (c) Ra = 297.58 nm, and (d) Ra = 296.92 nm in Fig. 5

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Fig. 7

Lacunarity spectra of 4 UPM images: (a) Ra = 43.81 nm, (b) Ra = 43.83 nm, (c) Ra = 297.58 nm, and (d) Ra = 296.92 nm in Fig. 5

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Fig. 8

Multifractal spectra of 100 UPM image profiles

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Fig. 9

Lacunarity spectra of UPM image profiles

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Fig. 10

The Hotelling T2 chart of UPM image profiles

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Fig. 11

Process parameter setting of the LPBF-AM cylinders

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Fig. 12

(a) 3D visualization of the XCT scan and (b) the top view of the XCT scan of a cylinder part

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Fig. 13

Multifractal spectra of XCT scan images of the LPBF-AM process

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Fig. 14

Lacunarity spectra of XCT scan images of the LPBF-AM process

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Fig. 15

Normal probability plot for model diagnosis

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