The goal of this work is to understand the effect of process conditions on lack of fusion porosity in parts made using laser powder bed fusion (LPBF) additive manufacturing (AM) process, and subsequently, to detect the onset of process conditions that lead to lack of fusion-related porosity from in-process sensor data. In pursuit of this goal, the objectives of this work are twofold: (1) quantify the count (number), size and location of pores as a function of three LPBF process parameters, namely, the hatch spacing (H), laser velocity (V), and laser power (P); and (2) monitor and identify process conditions that are liable to cause porosity through analysis of in-process layer-by-layer optical images of the build invoking multifractal and spectral graph theoretic features. These objectives are important because porosity has a significant impact on the functional integrity of LPBF parts, such as fatigue life. Furthermore, linking process conditions to defects via sensor signatures is the first step toward in-process quality assurance in LPBF. To achieve the first objective, titanium alloy (Ti–6Al–4V) test cylinders of 10 mm diameter × 25 mm height were built under differing H, V, and P settings on a commercial LPBF machine (EOS M280). The effect of these process parameters on count, size, and location of pores was quantified based on X-ray computed tomography (XCT) images. To achieve the second objective, layerwise optical images of the powder bed were acquired as the parts were being built. Spectral graph theoretic and multifractal features were extracted from the layer-by-layer images for each test part. Subsequently, these features were linked to the process parameters using machine learning approaches. Through these image-based features, process conditions under which the parts were built were identified with the statistical fidelity over 80% (F-score).

References

References
1.
ASTM
, “
Standard Terminology for Additive Manufacturing
,” ASTM International, West Conshohocken, PA, Standard No.
ASTM 52900-15
.http://www.astm.org/cgi-bin/resolver.cgi?ISOASTM52900-15
2.
Gibson
,
I.
,
Rosen
,
D. W.
, and
Stucker
,
B.
,
2010
,
Additive Manufacturing Technologies: Rapid Prototyping to Direct Digital Manufacturing
,
Springer
, New York.
3.
O'Regan
,
P.
,
Prickett
,
P.
,
Setchi
,
R.
,
Hankins
,
G.
, and
Jones
,
N.
,
2016
, “
Metal Based Additive Layer Manufacturing: Variations, Correlations and Process Control
,”
Procedia Comput. Sci.
,
96
, pp.
216
224
.
4.
Guo
,
N.
, and
Leu
,
M. C.
,
2013
, “
Additive Manufacturing: Technology, Applications and Research Needs
,”
Front. Mech. Eng.
,
8
(
3
), pp.
215
243
.
5.
Schmidt
,
M.
,
Merklein
,
M.
,
Bourell
,
D.
,
Dimitrov
,
D.
,
Hausotte
,
T.
,
Wegener
,
K.
,
Overmeyer
,
L.
,
Vollertsen
,
F.
, and
Levy
,
G. N.
,
2017
, “
Laser Based Additive Manufacturing in Industry and Academia
,”
CIRP Ann. Manuf. Technol.
,
66
(2), pp. 561–583.
6.
Everton
,
S. K.
,
Hirsch
,
M.
,
Stravroulakis
,
P.
,
Leach
,
R. K.
, and
Clare
,
A. T.
,
2016
, “
Review of in-Situ Process Monitoring and in-Situ Metrology for Metal Additive Manufacturing
,”
Mater. Des.
,
95
, pp.
431
445
.
7.
Gorelik
,
M.
,
2017
, “
Additive Manufacturing in the Context of Structural Integrity
,”
Int. J. Fatigue
,
94
(
2
), pp.
168
177
.
8.
Seifi
,
M.
,
Gorelik
,
M.
,
Waller
,
J.
,
Hrabe
,
N.
,
Shamsaei
,
N.
,
Daniewicz
,
S.
, and
Lewandowski
,
J. J.
,
2017
, “
Progress Towards Metal Additive Manufacturing Standardization to Support Qualification and Certification
,”
JOM
,
69
(
3
), pp.
439
455
.
9.
Grasso
,
M.
, and
Colosimo
,
B. M.
,
2017
, “
Process Defects and in Situ Monitoring Methods in Metal Powder Bed Fusion: A Review
,”
Meas. Sci. Technol.
,
28
(
4
), p.
044005
.
10.
Sames
,
W. J.
,
List
,
F.
,
Pannala
,
S.
,
Dehoff
,
R. R.
, and
Babu
,
S. S.
,
2016
, “
The Metallurgy and Processing Science of Metal Additive Manufacturing
,”
Int. Mater. Rev.
,
61
(
5
), pp.
315
360
.
11.
Cheng
,
B.
, and
Chou
,
K.
,
2015
, “
Geometric Consideration of Support Structures in Part Overhang Fabrications by Electron Beam Additive Manufacturing
,”
Comput. Aided Des.
,
69
, pp.
102
111
.
12.
Aboulkhair
,
N. T.
,
Everitt
,
N. M.
,
Ashcroft
,
I.
, and
Tuck
,
C.
,
2014
, “
Reducing Porosity in AlSi10 Mg Parts Processed by Selective Laser Melting
,”
Addit. Manuf.
,
1–4
, pp.
77
86
.
13.
Mahmoudi
,
M.
,
Elwany
,
A.
,
Yadollahi
,
A.
,
Thompson
,
S. M.
,
Bian
,
L.
, and
Shamsaei
,
N.
,
2017
, “
Mechanical Properties and Microstructural Characterization of Selective Laser Melted 17-4 PH Stainless Steel
,”
Rapid Prototyping J.
,
23
(
2
), pp.
280
294
.
14.
Bi
,
G.
,
Sun
,
C.
, and
Gasser
,
A.
,
2013
, “
Study on Influential Factors for Process Monitoring and Control in Laser Aided Additive Manufacturing
,”
J. Mater. Process. Technol.
,
213
(
3
), pp.
463
468
.
15.
Imani
,
F.
,
Gaikwad
,
A.
,
Montazeri
,
M.
,
Yang
,
H.
, and
Rao
,
P.
,
2018
, “
Layerwise in-Process Quality Monitoring in Laser Powder Bed Fusion
,”
ASME
Paper No. 6477.
16.
Imani
,
F.
,
Yao
,
B.
,
Chen
,
R.
,
Rao
,
P.
, and
Yang
,
H.
,
2018
, “
Factal Pattern Recognition of Image Profiles for Manufacturing Process Monitoring and Control
,”
ASME
Paper No. 6523.
17.
Yao
,
B.
,
Imani
,
F.
, and
Yang
,
H.
,
2018
, “
Markov Decision Process for Image-Guided Additive Manufacturing
,”
IEEE Rob. Autom. Lett.
,
3
(4), pp. 2792–2798.
18.
Rao
,
S.
,
Cunningham
,
R.
,
Ozturk
,
T.
, and
Rollett
,
A. D.
,
2016
, “
Measurement and Analysis of Porosity in Al-10Si-1 Mg Components Additively Manufactured by Selective Laser Melting
,”
Mater. Perform. Charact.
,
5
(
5
), pp.
701
716
.
19.
Maskery
,
I.
,
Aboulkhair
,
N. T.
,
Corfield
,
M. R.
,
Tuck
,
C.
,
Clare
,
A. T.
,
Leach
,
R. K.
,
Wildman
,
R. D.
,
Ashcroft
,
I. A.
, and
Hague
,
R. J. M.
,
2016
, “
Quantification and Characterisation of Porosity in Selectively Laser Melted Al–Si10–Mg Using X-Ray Computed Tomography
,”
Mater. Charact.
,
111
, pp.
193
204
.
20.
Gong
,
H.
,
Rafi
,
K.
,
Starr
,
T.
, and
Stucker
,
B.
,
2012
, “
Effect of Defects on Fatigue Tests of As-Built Ti-6Al-4V Parts Fabricated by Selective Laser Melting
,”
Solid Freeform Fabrication Symposium
, Austin, TX, Aug. 6–8, pp.
499
506
.http://sffsymposium.engr.utexas.edu/Manuscripts/2012/2012-39-Gong.pdf
21.
DebRoy
,
T.
,
Wei
,
H. L.
,
Zuback
,
J. S.
,
Mukherjee
,
T.
,
Elmer
,
J. W.
,
Milewski
,
J. O.
,
Beese
,
A. M.
,
Wilson-Heid
,
A.
,
De
,
A.
, and
Zhang
,
W.
,
2018
, “
Additive Manufacturing of Metallic Components—Process, Structure and Properties
,”
Prog. Mater. Sci.
,
92
, pp.
112
224
.
22.
Gong
,
H.
,
Rafi
,
K.
,
Gu
,
H.
,
Janaki Ram
,
G. D.
,
Starr
,
T.
, and
Stucker
,
B.
,
2015
, “
Influence of Defects on Mechanical Properties of Ti–6Al–4V Components Produced by Selective Laser Melting and Electron Beam Melting
,”
Mater. Des.
,
86
, pp.
545
554
.
23.
Khairallah
,
S. A.
,
Anderson
,
A. T.
,
Rubenchik
,
A.
, and
King
,
W. E.
,
2016
, “
Laser Powder-Bed Fusion Additive Manufacturing: Physics of Complex Melt Flow and Formation Mechanisms of Pores, Spatter, and Denudation Zones
,”
Acta Mater.
,
108
, pp.
36
45
.
24.
Gong
,
H.
,
Rafi
,
K.
,
Gu
,
H.
,
Starr
,
T.
, and
Stucker
,
B.
,
2014
, “
Analysis of Defect Generation in Ti–6Al–4V Parts Made Using Powder Bed Fusion Additive Manufacturing Processes
,”
Addit. Manuf.
,
1–4
, pp.
87
98
.
25.
King
,
W. E.
,
Barth
,
H. D.
,
Castillo
,
V. M.
,
Gallegos
,
G. F.
,
Gibbs
,
J. W.
,
Hahn
,
D. E.
,
Kamath
,
C.
, and
Rubenchik
,
A. M.
,
2014
, “
Observation of Keyhole-Mode Laser Melting in Laser Powder-Bed Fusion Additive Manufacturing
,”
J. Mater. Process. Technol.
,
214
(
12
), pp.
2915
2925
.
26.
Beuth
,
J.
,
Fox
,
J.
,
Gockel
,
J.
,
Montgomery
,
C.
,
Yang
,
R.
,
Qiao
,
H.
,
Soylemez
,
E.
,
Reeseewatt
,
P.
,
Anvari
,
A.
, and
Narra
,
S.
,
2013
, “
Process Mapping for Qualification Across Multiple Direct Metal Additive Manufacturing Processes
,”
Solid Freeform Fabrication Symposium
, Austin, TX, Aug. 13–15.http://sffsymposium.engr.utexas.edu/Manuscripts/2013/2013-52-Beuth.pdf
27.
Beuth
,
J.
, and
Klingbeil
,
N.
,
2001
, “
The Role of Process Variables in Laser-Based Direct Metal Solid Freeform Fabrication
,”
JOM
,
53
(
9
), pp.
36
39
.
28.
Vasinonta
,
A.
,
Beuth
,
J. L.
, and
Griffith
,
M.
,
2007
, “
Process Maps for Predicting Residual Stress and Melt Pool Size in the Laser-Based Fabrication of Thin-Walled Structures
,”
ASME J. Manuf. Sci. Eng.
,
129
(
1
), pp.
101
109
.
29.
Morgan
,
R. H.
,
Papworth
,
A. J.
,
Sutcliffe
,
C.
,
Fox
,
P.
, and
O'neill
,
W.
,
2002
, “
High Density Net Shape Components by Direct Laser Re-Melting of Single-Phase Powders
,”
J. Mater. Sci.
,
37
(
15
), pp.
3093
3100
.
30.
Montazeri
,
M.
,
Yavari
,
R.
,
Rao
,
P.
, and
Boulware
,
P.
,
2018
, “
In-Process Monitoring of Material Cross-Contamination Defects in Laser Powder Bed Fusion
,”
ASME J. Manuf. Sci. Eng.
, (in press).
31.
Gu
,
H.
,
Gong
,
H.
,
Pal
,
D.
,
Rafi
,
K.
,
Starr
,
T.
, and
Stucker
,
B.
,
2013
, “
Influences of Energy Density on Porosity and Microstructure of Selective Laser Melted 17-4PH Stainless Steel
,”
Solid Freeform Fabrication Symposium
, Austin, TX, Aug. 13–15 p.
474
. http://sffsymposium.engr.utexas.edu/Manuscripts/2013/2013-37-Gu.pdf
32.
Rafi
,
H. K.
,
Pal
,
D.
,
Patil
,
N.
,
Starr
,
T.
, and
Stucker
,
B.
,
2014
, “
Microstructure and Mechanical Behavior of 17-4 Precipitation Hardenable Steel Processed by Selective Laser Melting
,”
J. Mater. Eng. Perform.
,
23
(
12
), pp.
4421
4428
.
33.
Rafi
,
H. K.
,
Starr
,
T.
, and
Stucker
,
B.
,
2013
, “
A Comparison of the Tensile, Fatigue, and Fracture Behavior of Ti–6Al–4V and 15-5 PH Stainless Steel Parts Made by Selective Laser Melting
,”
Int. J. Adv. Manuf. Technol.
,
69
(
5–8
), pp.
1299
1309
.
34.
Mani
,
M.
,
Lane
,
B. M.
,
Donmez
,
M. A.
,
Feng
,
S. C.
, and
Moylan
,
S. P.
,
2017
, “
A Review on Measurement Science Needs for Real-Time Control of Additive Manufacturing Metal Powder Bed Fusion Processes
,”
Int. J. Prod. Res.
,
55
(
5
), pp.
1400
1418
.
35.
Tapia
,
G.
, and
Elwany
,
A.
,
2014
, “
A Review on Process Monitoring and Control in Metal-Based Additive Manufacturing
,”
ASME J. Manuf. Sci. Eng.
,
136
(
6
), p.
060801
.
36.
Mani
,
M.
,
Lane
,
B.
,
Donmez
,
A.
,
Feng
,
S.
,
Moylan
,
S.
, and
Fesperman
,
R.
,
2015
, “
Measurement Science Needs for Real-Time Control of Additive Manufacturing Powder Bed Fusion Processes
,” National Institute of Standards and Technology, Gaithersburg, MD, Report No.
NISTIR 8036
.http://www.come3d.com/ueditor/php/upload/file/20150416/1429164193510688.pdf
37.
Spears
,
T. G.
, and
Gold
,
S. A.
,
2016
, “
In-Process Sensing in Selective Laser Melting (SLM) Additive Manufacturing
,”
Integr. Mater. Manuf. Innovation
,
5
(
1
), p.
2
.
38.
Lane
,
B.
,
Lane
,
B.
,
Moylan
,
S.
,
Moylan
,
S.
,
Whitenton
,
E. P.
,
Whitenton
,
E. P.
,
Ma
,
L.
, and
Ma
,
L.
,
2016
, “
Thermographic Measurements of the Commercial Laser Powder Bed Fusion Process at NIST
,”
Rapid Prototyping J.
,
22
(
5
), pp.
778
787
.
39.
Reutzel
,
E.
, and
Nassar
,
A.
,
2014
, “
A Survey of Sensing and Control Systems for Machine and Process Monitoring of Directed-Energy, Metal-Based Additive Manufacturing
,”
Solid Freeform Fabrication Conference
, Austin, TX, Aug. 4–6, pp.
309
322
.http://sffsymposium.engr.utexas.edu/sites/default/files/2014-027-Reutzel.pdf
40.
Foster
,
B.
,
Reutzel
,
E.
,
Nassar
,
A.
,
Hall
,
B.
,
Brown
,
S.
, and
Dickman
,
C.
,
2015
, “
Optical Layerwise Monitoring of Powder Bed Fusion
,”
Solid Freeform Fabrication Symposium
, Austin, TX, Aug. 10–12, pp.
295
307
.http://sffsymposium.engr.utexas.edu/sites/default/files/2015/2015-24-Foster.pdf
41.
Nassar
,
A.
,
Spurgeon
,
T.
, and
Reutzel
,
E.
,
2014
, “
Sensing Defects During Directed-Energy Additive Manufacturing of Metal Parts Using Optical Emissions Spectroscopy
,”
Solid Freeform Fabrication Symposium
, Austin, TX, Aug. 4–6, pp.
278
287
.http://sffsymposium.engr.utexas.edu/sites/default/files/2014-024-Nassar.pdf
42.
Dunbar
,
A. J.
,
Nassar
,
A. R.
,
Reutzel
,
E. W.
, and
Blecher
,
J. J.
,
2016
, “
A Real-Time Communication Architecture for Metal Powder Bed Fusion Additive Manufacturing
,”
Solid Freeform Fabrication Symposium
, Austin, TX, Aug. 8–10, pp.
67
80
. http://sffsymposium.engr.utexas.edu/sites/default/files/2016/005-Dunbar.pdf
43.
Foster
,
B. K.
,
Reutzel
,
E. W.
,
Nassar
,
A. R.
,
Dickman
,
C. J.
, and
Hall
,
B. T.
,
2015
, “
A Brief Survey of Sensing for Additive Manufacturing
,”
Proc. SPIE.
9489
, p. 94890B.
44.
Abdelrahman
,
M.
,
Reutzel
,
E. W.
,
Nassar
,
A. R.
, and
Starr
,
T. L.
,
2017
, “
Flaw Detection in Powder Bed Fusion Using Optical Imaging
,”
Addit. Manuf.
,
15
, pp.
1
11
.
45.
Boulware
,
P.
,
2016
, “
Final Technical Report to National Institute of Standards and Technology and National Center for Defense Manufacturing and Machining—Measurement Science Innovation Program for Additive Manufacturing: An Evaluation of in-Process Sensing Techniques Through the Use of an Open Architecture Laser Powder Bed Fusion Platform
,” Edison Welding Institute (EWI), Cincinnati, OH, Report No. NIST# 70 NANB13H192-20140097.
46.
Berumen
,
S.
,
Bechmann
,
F.
,
Lindner
,
S.
,
Kruth
,
J.-P.
, and
Craeghs
,
T.
,
2010
, “
Quality Control of Laser- and Powder Bed-Based Additive Manufacturing (AM) Technologies
,”
Phys. Procedia
,
5
(
Pt. B
), pp.
617
622
.
47.
Craeghs
,
T.
,
Clijsters
,
S.
,
Kruth
,
J. P.
,
Bechmann
,
F.
, and
Ebert
,
M. C.
,
2012
, “
Detection of Process Failures in Layerwise Laser Melting With Optical Process Monitoring
,”
Phys. Procedia
,
39
, pp.
753
759
.
48.
Craeghs
,
T.
,
Clijsters
,
S.
,
Yasa
,
E.
,
Bechmann
,
F.
,
Berumen
,
S.
, and
Kruth
,
J.-P.
,
2011
, “
Determination of Geometrical Factors in Layerwise Laser Melting Using Optical Process Monitoring
,”
Opt. Lasers Eng.
,
49
(
12
), pp.
1440
1446
.
49.
Jacobsmuhlen
,
J. Z.
,
Kleszczynski
,
S.
,
Schneider
,
D.
, and
Witt
,
G.
,
2013
, “
High Resolution Imaging for Inspection of Laser Beam Melting Systems
,”
IEEE International Instrumentation and Measurement Technology Conference
(
I2MTC
), Minneapolis, MN, May 6–9, pp.
707
712
.
50.
Kleszczynski
,
S.
,
zur Jacobsmühlen
,
J.
,
Reinarz
,
B.
,
Sehrt
,
J. T.
,
Witt
,
G.
, and
Merhof
,
D.
,
2014
, “
Improving Process Stability of Laser Beam Melting Systems
,”
Fraunhofer Direct Digital Manufacturing Conference
, Berlin, Mar. 12–13.
51.
Kleszczynski
,
S.
,
Zur Jacobsmühlen
,
J.
,
Sehrt
,
J.
, and
Witt
,
G.
,
2012
, “
Error Detection in Laser Beam Melting Systems by High Resolution Imaging
,”
23rd Annual International Solid Freeform Fabrication Symposium
, Austin, TX, Aug. 6–8, pp.
975
987
.http://sffsymposium.engr.utexas.edu/Manuscripts/2012/2012-74-Kleszczynski.pdf
52.
Wegner
,
A.
, and
Witt
,
G.
,
2011
, “
Process Monitoring in Laser Sintering Using Thermal Imaging
,”
SFF Symposium
, Austin, TX, Aug. 8–10, pp.
8
10
.http://sffsymposium.engr.utexas.edu/Manuscripts/2011/2011-30-Wegner.pdf
53.
Calta
,
N. P.
,
Wang
,
J.
,
Kiss
,
A. M.
,
Martin
,
A. A.
,
Depond
,
P. J.
,
Guss
,
G. M.
,
Thampy
,
V.
,
Fong
,
A. Y.
,
Weker
,
J. N.
,
Stone
,
K. H.
,
Tassone
,
C. J.
,
Kramer
,
M. J.
,
Toney
,
M. F.
,
Buuren
,
A. V.
, and
Matthews
,
M. J.
,
2018
, “
An Instrument for in Situ Time-Resolved X-Ray Imaging and Diffraction of Laser Powder Bed Fusion Additive Manufacturing Processes
,”
Rev. Sci. Instrum.
,
89
(
5
), p.
055101
.
54.
Hu
,
D.
, and
Kovacevic
,
R.
,
2003
, “
Sensing, Modeling and Control for Laser-Based Additive Manufacturing
,”
Int. J. Mach. Tools Manuf.
,
43
(
1
), pp.
51
60
.
55.
Barua
,
S.
,
Sparks
,
T.
, and
Liou
,
F.
,
2011
, “
Development of Low-Cost Imaging System for Laser Metal Deposition Processes
,”
Rapid Prototyping J.
,
17
(
3
), pp.
203
210
.
56.
Krauss
,
H.
,
Eschey
,
C.
, and
Zaeh
,
M.
,
2012
, “
Thermography for Monitoring the Selective Laser Melting Process
,”
Solid Freeform Fabiraction Conference
, Austin, TX, Aug. 6–8, pp.
999
1014
.http://sffsymposium.engr.utexas.edu/Manuscripts/2012/2012-76-Krauss.pdf
57.
Rieder
,
H.
,
Alexander
,
D.
,
Spies
,
M.
,
Bamberg
,
J.
, and
Hess
,
T.
,
2014
, “
Online Monitoring of Additive Manufacturing Processes Using Ultrasound
,”
11th European Conference on Non-Destructive Testing
(
ECNDT
), Prague, Czech Republic, Oct. 6–11.https://www.ndt.net/events/ECNDT2014/app/content/Paper/259_Spies.pdf
58.
Krauss
,
H.
,
Zeugner
,
T.
, and
Zaeh
,
M. F.
,
2014
, “
Layerwise Monitoring of the Selective Laser Melting Process by Thermography
,”
Phys. Procedia
,
56
, pp.
64
71
.
59.
Derakhshani
,
M.
,
Berfield
,
T.
, and
Murphy
,
K. D.
,
2018
, “
Dynamic Analysis of a Bi-Stable Buckled Structure for Vibration Energy Harvester
,”
Dynamic Behavior of Materials
, Vol.
1
, Springer, Cham, pp.
199
208
.
60.
Chiu
,
T.-M.
,
Mahmoudi
,
M.
,
Dai
,
W.
,
Elwany
,
A.
,
Liang
,
H.
, and
Castaneda
,
H.
,
2018
, “
Corrosion Assessment of Ti-6Al-4V Fabricated Using Laser Powder-Bed Fusion Additive Manufacturing
,”
Electrochim. Acta
,
279
, pp.
143
151
.
61.
Melvin
,
L. S.
, III
,
Das
,
S.
, and
Beaman
,
S.
, Jr
,
1994
, “
Video Microscopy of Selective Laser Sintering
,”
Solid Freeform Fabrication Symposium
, Austin, TX, Aug. 8–10, pp.
34
41
.http://sffsymposium.engr.utexas.edu/Manuscripts/1994/1994-05-Melvin.pdf
62.
Bartkowiak
,
K.
,
2010
, “
Direct Laser Deposition Process Within Spectrographic Analysis in Situ
,”
Phys. Procedia
,
5
, pp.
623
629
.
63.
Chivel
,
Y.
, and
Smurov
,
I.
,
2010
, “
On-Line Temperature Monitoring in Selective Laser Sintering/Melting
,”
Phys. Procedia
,
5
, pp.
515
521
.
64.
Craeghs
,
T.
,
Clijsters
,
S.
,
Yasa
,
E.
, and
Kruth
,
J.-P.
,
2011
, “
Online Quality Control of Selective Laser Melting
,”
Solid Freeform Fabrication Proceedings
, Austin, TX, Aug. 8–10, pp.
212
226
.http://sffsymposium.engr.utexas.edu/Manuscripts/2011/2011-17-Craeghs.pdf
65.
Craeghs
,
T.
,
Bechmann
,
F.
,
Berumen
,
S.
, and
Kruth
,
J. P.
,
2010
, “
Feedback Control of Layerwise Laser Melting Using Optical Sensors
,”
Phys. Procedia
,
5
, Aug. 8–10, pp.
505
514
.
66.
Heigel
,
J. C.
, and
Lane
,
B. M.
,
2018
, “
Measurement of the Melt Pool Length During Single Scan Tracks in a Commercial Laser Powder Bed Fusion Process
,”
ASME J. Manuf. Sci. Eng.
,
140
(
5
), p.
051012
.
67.
Dunbar
,
A. J.
, and
Nassar
,
A. R.
,
2018
, “
Assessment of Optical Emission Analysis for in-Process Monitoring of Powder Bed Fusion Additive Manufacturing
,”
Virtual Phys. Prototyping
,
13
(
1
), pp.
14
19
.
68.
Stutzman
,
C. B.
,
Nassar
,
A. R.
, and
Reutzel
,
E. W.
,
2018
, “
Multi-Sensor Investigations of Optical Emissions and Their Relations to Directed Energy Deposition Processes and Quality
,”
Addit. Manuf.
,
21
, pp.
333
339
.
69.
Montazeri
,
M.
, and
Rao
,
P.
,
2018
, “
Heterogeneous Sensor-Based Build Condition Monitoring in Laser Powder Bed Fusion Additive Manufacturing Process Using a Spectral Graph Theoretic Approach
,”
ASME J. Manuf. Sci. Eng.
,
140
(9), p. 091002.
70.
Hirsch
,
M.
,
Patel
,
R.
,
Li
,
W.
,
Guan
,
G.
,
Leach
,
R. K.
,
Sharples
,
S. D.
, and
Clare
,
A. T.
,
2016
, “
Assessing the Capability of in-Situ Nondestructive Analysis During Layer Based Additive Manufacture
,”
Addit. Manuf.
,
13
, 135–142.
71.
Smith
,
R. J.
,
Hirsch
,
M.
,
Patel
,
R.
,
Li
,
W.
,
Clare
,
A. T.
, and
Sharples
,
S. D.
,
2016
, “
Spatially Resolved Acoustic Spectroscopy for Selective Laser Melting
,”
J. Mater. Process. Technol.
,
236
, pp.
93
102
.
72.
Solomon
,
C.
, and
Breckon
,
T.
,
2011
,
Fundamentals of Digital Image Processing: A Practical Approach With Examples in Matlab
,
Wiley
, Sussex, UK.
73.
Chung
,
F.
,
1997
,
Spectral Graph Theory
,
American Mathematical Society
, Providence, RI.
74.
Jianbo
,
S.
, and
Malik
,
J.
,
2000
, “
Normalized Cuts and Image Segmentation
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
22
(
8
), pp.
888
905
.
75.
Rao
,
P. K.
,
Beyca
,
O. F.
,
Kong
,
Z.
,
Bukkapatnam
,
S. T.
,
Case
,
K. E.
, and
Komanduri
,
R.
,
2015
, “
A Graph-Theoretic Approach for Quantification of Surface Morphology Variation and Its Application to Chemical Mechanical Planarization Process
,”
IIE Trans.
,
47
(
10
), pp.
1088
1111
.
76.
Tootooni
,
M. S.
,
Liu
,
C.
,
Roberson
,
D.
,
Donovan
,
R.
,
Rao
,
P. K.
,
Kong
,
Z.
, and
Bukkapatnam
,
S. T. S.
,
2016
, “
Online Non-Contact Surface Finish Measurement in Machining Using Graph Theory-Based Image Analysis
,”
J. Manuf. Syst.
,
41
, pp.
266
276
.
77.
Mohar
,
B.
,
1991
, “
Eigenvalues, Diameter, and Mean Distance in Graphs
,”
Graphs Combinatorics
,
7
(
1
), pp.
53
64
.
78.
Imani
,
F.
,
Cheng
,
C.
,
Chen
,
R.
, and
Yang
,
H.
,
2018
, “
Nested Gaussian Process Modeling for High-Dimensional Data Imputation in Healthcare Systems
,”
IISE 2018 Conference & Expo
, Orlando, FL, May 19–22.
79.
Jiang
,
X.
,
Scott
,
P. J.
,
Whitehouse
,
D. J.
, and
Blunt
,
L.
,
2007
, “
Paradigm Shifts in Surface Metrology—Part 2: The Current Shift
,”
Proc. R. Soc. A
,
463
(
2085
), pp.
2071
2099
.
80.
Jiang
,
X.
,
Scott
,
P. J.
,
Whitehouse
,
D. J.
, and
Blunt
,
L.
,
2007
, “
Paradigm Shifts in Surface Metrology. Part 1: Historical Philosophy
,”
Proc. R. Soc. A
,
463
(
2085
), pp.
2049
2070
.
81.
Whitehouse
,
D. J.
,
2002
,
Handbook of Surface and Nanometrology
,
Taylor & Francis
,
New York
.
82.
Yao
,
B.
,
Imani
,
F.
,
Sakpal
,
A.
,
Reutzel
,
E. W.
, and
Yang
,
H.
,
2017
, “
Multifractal Analysis of Image Profiles for the Characterization and Detection of Defects in Additive Manufacturing
,”
ASME J. Manuf. Sci. Eng.
,140
(3), p. 031014.
83.
Kan
,
C.
,
Cheng
,
C.
, and
Yang
,
H.
,
2016
, “
Heterogeneous Recurrence Monitoring of Dynamic Transients in Ultraprecision Machining Processes
,”
J. Manuf. Syst.
,
41
, pp.
178
187
.
84.
Yang
,
H.
, and
Chen
,
Y.
,
2014
, “
Heterogeneous Recurrence Monitoring and Control of Nonlinear Stochastic Processes
,”
Chaos: An Interdiscip. J. Nonlinear Sci.
,
24
(
1
), p.
013138
.
85.
Feder
,
J.
,
1988
,
Fractals
,
Plenum
,
New York
, p.
283
.
86.
Meisel
,
L.
,
Johnson
,
M.
, and
Cote
,
P.
,
1992
, “
Box-Counting Multifractal Analysis
,”
Phys. Rev. A
,
45
(
10
), p.
6989
.
87.
Barnsley
,
M. F.
, and
Demko
,
S.
,
1985
, “
Iterated Function Systems and the Global Construction of Fractals
,”
Proc. R. Soc. London A
,
399
(
1817
), pp.
243
275
.
88.
Chhabra
,
A.
, and
Jensen
,
R. V.
,
1989
, “
Direct Determination of the f (α) Singularity Spectrum
,”
Phys. Rev. Lett.
,
62
(
12
), p.
1327
89.
Fabio
,
D.
,
Reis
,
A.
, and
Riera
,
R.
,
1994
, “
Lacunarity Calculation in the True Fractal Limit
,”
J. Phys. A: Math. General
,
27
(
6
), p.
1827
.
90.
Tolle
,
C. R.
,
McJunkin
,
T. R.
, and
Gorsich
,
D. J.
,
2008
, “
An Efficient Implementation of the Gliding Box Lacunarity Algorithm
,”
Phys. D: Nonlinear Phenom.
,
237
(
3
), pp.
306
315
.
91.
Plotnick
,
R. E.
,
Gardner
,
R. H.
,
Hargrove
,
W. W.
,
Prestegaard
,
K.
, and
Perlmutter
,
M.
,
1996
, “
Lacunarity Analysis: A General Technique for the Analysis of Spatial Patterns
,”
Phys. Rev. E
,
53
(
5
), p.
5461
.
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