Research Papers

Multifractal Analysis of Image Profiles for the Characterization and Detection of Defects in Additive Manufacturing

[+] Author and Article Information
Bing Yao, Farhad Imani, Aniket S. Sakpal

Department of Industrial and
Manufacturing Engineering,
The Pennsylvania State University,
University Park, PA 16802

E. W. Reutzel

Applied Research Laboratory
The Pennsylvania State University,
P.O. Box 30,
State College, PA 16804-0030

Hui Yang

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

1Corresponding author.

Manuscript received July 18, 2017; final manuscript received August 30, 2017; published online January 3, 2018. Assoc. Editor: Zhijian J. Pei.

J. Manuf. Sci. Eng 140(3), 031014 (Jan 03, 2018) (13 pages) Paper No: MANU-17-1444; doi: 10.1115/1.4037891 History: Received July 18, 2017; Revised August 30, 2017

Metal-based powder-bed-fusion additive manufacturing (PBF-AM) is gaining increasing attention in modern industries, and is a promising direct manufacturing technology. Additive manufacturing (AM) does not require the tooling cost of conventional subtractive manufacturing processes, and is flexible to produce parts with complex geometries. Quality and repeatability of AM parts remain a challenging issue that persistently hampers wide applications of AM technology. Rapid advancements in sensing technology, especially imaging sensing systems, provide an opportunity to overcome such challenges. However, little has been done to fully utilize the image profiles acquired in the AM process and study the fractal patterns for the purpose of process monitoring, quality assessment, and control. This paper presents a new multifractal methodology for the characterization and detection of defects in PBF-AM parts. Both simulation and real-world case studies show that the proposed approach effectively detects and characterizes various defect patterns in AM images and has strong potential for quality control of AM processes.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Kruth, J.-P. , Leu, M. C. , and Nakagawa, T. , 1998, “Progress in Additive Manufacturing and Rapid Prototyping,” CIRP Ann.-Manuf. Technol., 47(2), pp. 525–540. [CrossRef]
Tammas-Williams, S. , Zhao, H. , Léonard, F. , Derguti, F. , Todd, I. , and Prangnell, P. , 2015, “XCT Analysis of the Influence of Melt Strategies on Defect Population in Ti–6Al–4V Components Manufactured by Selective Electron Beam Melting,” Materi. Charact., 102, pp. 47–61. [CrossRef]
Li, R. , Liu, J. , Shi, Y. , Wang, L. , and Jiang, W. , 2012, “Balling Behavior of Stainless Steel and Nickel Powder During Selective Laser Melting Process,” Int. J. Adv. Manuf. Technol., 59(9–12), pp. 1025–1035. [CrossRef]
Wang, F. , Mao, H. , Zhang, D. , Zhao, X. , and Shen, Y. , 2008, “Online Study of Cracks During Laser Cladding Process Based on Acoustic Emission Technique and Finite Element Analysis,” Appl. Surf. Sci., 255(5), pp. 3267–3275. [CrossRef]
Rao, P. K. , Liu, J. P. , Roberson, D. , Kong, Z. J. , and Williams, C. , 2015, “Online Real-Time Quality Monitoring in Additive Manufacturing Processes Using Heterogeneous Sensors,” ASME J. Manuf. Sci. Eng., 137(6), p. 061007. [CrossRef]
Chivel, Y. , and Smurov, I. , 2010, “On-Line Temperature Monitoring in Selective Laser Sintering/Melting,” Phys. Procedia, 5(Pt. B), pp. 515–521. [CrossRef]
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. https://sffsymposium.engr.utexas.edu/sites/default/files/2015/2015-24-Foster.pdf
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. https://sffsymposium.engr.utexas.edu/Manuscripts/2012/2012-74-Kleszczynski.pdf
Bi, G. , Schürmann, B. , Gasser, A. , Wissenbach, K. , and Poprawe, R. , 2007, “Development and Qualification of a Novel Laser-Cladding Head With Integrated Sensors,” Int. J. Mach. Tools Manuf., 47(3), pp. 555–561. [CrossRef]
Reutzel, E. W. , and Nassar, A. R. , 2015, “A Survey of Sensing and Control Systems for Machine and Process Monitoring of Directed-Energy, Metal-Based Additive Manufacturing,” Rapid Prototyping J., 21(2), pp. 159–167. [CrossRef]
Krauss, H. , Eschey, C. , and Zaeh, M. , 2012, “Thermography for Monitoring the Selective Laser Melting Process,” 23rd Annual International Solid Freeform Fabrication Symposium, Austin, TX, Aug. 6–8, pp. 999–1014. https://sffsymposium.engr.utexas.edu/Manuscripts/2012/2012-76-Krauss.pdf
Rodriguez, E. , Mireles, J. , Terrazas, C. A. , Espalin, D. , Perez, M. A. , and Wicker, R. B. , 2015, “Approximation of Absolute Surface Temperature Measurements of Powder Bed Fusion Additive Manufacturing Technology Using in Situ Infrared Thermography,” Addit. Manuf., 5, pp. 31–39. [CrossRef]
Jacobsmühlen, 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.
Grasso, M. , Laguzza, V. , Semeraro, Q. , and Colosimo, B. M. , 2016, “In-Process Monitoring of Selective Laser Melting: Spatial Detection of Defects Via Image Data Analysis,” ASME J. Manuf. Sci. Eng., 139(5), p. 051001. [CrossRef]
Pavan, M. , Craeghs, T. , Verhelst, R. , Ducatteeuw, O. , Kruth, J.-P. , and Dewulf, W. , 2016, “Ct-Based Quality Control of Laser Sintering of Polymers,” Case Stud. Nondestr. Test. Eval., 6(Pt. B), pp. 62–68. [CrossRef]
Dewulf, W. , Pavan, M. , Craeghs, T. , and Kruth, J.-P. , 2016, “Using X-Ray Computed Tomography to Improve the Porosity Level of Polyamide-12 Laser Sintered Parts,” CIRP Ann.-Manuf. Technol., 65(1), pp. 205–208. [CrossRef]
Megahed, F. M. , Woodall, W. H. , and Camelio, J. A. , 2011, “A Review and Perspective on Control Charting With Image Data,” J. Qual. Technol., 43(2), p. 83. http://asq.org/qic/display-item/index.html?item=33284
Nembhard, H. B. , and Kao, M. S. , 2001, “A Forecast-Based Monitoring Methodology for Process Transitions,” Qual. Reliab. Eng. Int., 17(4), pp. 307–321. [CrossRef]
Liang, Y.-T. , and Chiou, Y.-C. , 2008, “Vision-Based Automatic Tool Wear Monitoring System,” Seventh World Congress on Intelligent Control and Automation (WCICA), Chongqing, China, June 25–27, pp. 6031–6035.
Graham, K. , Krishnapisharody, K. , Irons, G. , and MacGregor, J. , 2007, “Ladle Eye Area Measurement Using Multivariate Image Analysis,” Can. Metall. Q., 46(4), pp. 397–405. [CrossRef]
Jiang, B. , Wang, C.-C. , and Liu, H.-C. , 2005, “Liquid Crystal Display Surface Uniformity Defect Inspection Using Analysis of Variance and Exponentially Weighted Moving Average Techniques,” Int. J. Prod. Res., 43(1), pp. 67–80. [CrossRef]
Kam, K. M. , Zeng, L. , Zhou, Q. , Tran, R. , and Yang, J. , 2013, “On Assessing Spatial Uniformity of Particle Distributions in Quality Control of Manufacturing Processes,” J. Manuf. Syst., 32(1), pp. 154–166. [CrossRef]
Yan, H. , Paynabar, K. , and Shi, J. , 2015, “Image-Based Process Monitoring Using Low-Rank Tensor Decomposition,” IEEE Trans. Autom. Sci. Eng., 12(1), pp. 216–227. [CrossRef]
Kan, C. , and Yang, H. , 2017, “Dynamic Network Monitoring and Control of in Situ Image Profiles From Ultraprecision Machining and Biomanufacturing Processes,” Qual. Reliab. Eng. Int., epub.
Kan, C. , and Yang, H. , 2015, “Network Models for Monitoring High-Dimensional Image Profiles,” IEEE International Conference on Automation Science and Engineering (CASE), Gothenburg, Sweden, Aug. 24–28, pp. 1078–1083.
Jiang, X. , Scott, P. J. , Whitehouse, D. J. , and Blunt, L. , 2007, “Paradigm Shifts in Surface Metrology—Part II: The Current Shift,” Proc. R. Soc. London, Ser. A, 463(2085), pp. 2071–2099. [CrossRef]
Posadas, A. N. , Giménez, D. , Quiroz, R. , and Protz, R. , 2003, “Multifractal Characterization of Soil Pore Systems,” Soil Sci. Soc. Am. J., 67(5), pp. 1361–1369. [CrossRef]
Yang, H. , Chen, Y. , and Leonelli, F. M. , 2016, “Characterization and Monitoring of Nonlinear Dynamics and Chaos in Complex Physiological Systems,” Healthcare Analytics: From Data to Knowledge to Healthcare Improvement, H. Yang and E. K. Lee, eds., Wiley, Hoboken, NJ, pp. 59–93.
Chen, Y. , and Yang, H. , 2016, “Numerical Simulation and Pattern Characterization of Nonlinear Spatiotemporal Dynamics on Fractal Surfaces for the Whole-Heart Modeling Applications,” Eur. Phys. J. B, 89(8), p. 181. [CrossRef]
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. [CrossRef]
Chen, Y. , and Yang, H. , 2016, “Heterogeneous Recurrence Representation and Quantification of Dynamic Transitions in Continuous Nonlinear Processes,” Eur. Phys. J. B, 89(6), pp. 1–11. [CrossRef]
Whitehouse, D. J. , 2002, “Surface and Nanometrology, Markov and Fractal Scale of Size Properties,” Seventh International Symposium on Laser Metrology Applied to Science, Industry, and Everyday Life, Novosibirsk, Russia, Sept. 9–13, pp. 691–707.
Foroutan-Pour, K. , Dutilleul, P. , and Smith, D. L. , 1999, “Advances in the Implementation of the Box-Counting Method of Fractal Dimension Estimation,” Appl. Math. Comput., 105(2–3), pp. 195–210. https://doi.org/10.1016/S0096-3003(98)10096-6
Li, J. , Du, Q. , and Sun, C. , 2009, “An Improved Box-Counting Method for Image Fractal Dimension Estimation,” Pattern Recognit., 42(11), pp. 2460–2469. [CrossRef]
Thomas, T. , and Rosén, B.-G. , 2008, “Implementation of Whitehouse's Method for Calculating Properties of Self-Affine Fractal Profiles,” Proc. Inst. Mech. Eng., Part C, 222(8), pp. 1547–1550. [CrossRef]
Halsey, T. C. , Jensen, M. H. , Kadanoff, L. P. , Procaccia, I. , and Shraiman, B. I. , 1986, “Fractal Measures and Their Singularities: The Characterization of Strange Sets,” Phys. Rev. A, 33(2), p. 1141. [CrossRef]
Chhabra, A. , and Jensen, R. V. , 1989, “Direct Determination of the f (α) Singularity Spectrum,” Phys. Rev. Lett., 62(12), p. 1327. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 1

Three different types of surfaces—(a) rough, (b) sinusoidal, (c) random, and their 2D images (d)–(f)

Grahic Jump Location
Fig. 2

Flowchart of research methodology

Grahic Jump Location
Fig. 3

(a) Illustration of f(q) and α(q) estimated in the range of q values from –3 to 3, (b) Illustration of f(α) spectrum, and (c) Multifractal spectra for the images of rough surface, sinusoidal surface, and random surface in Fig. 1

Grahic Jump Location
Fig. 8

(a) AM image profiles. (Note: 1 — with no defect; 2 — with balling defect; 3 — with crack defect; 4 — with pore defect.) and (b) multifractal spectrum of each image in (a).

Grahic Jump Location
Fig. 4

Examples of simulated patterns with varying degrees of dispersion

Grahic Jump Location
Fig. 5

(a) Actual build components from the AM process, (b) 3D visualization of CT scan, and (c) sliced CT-scan image

Grahic Jump Location
Fig. 6

(a) Four different types of simulated images: 1-random pattern, 2-single cluster, 3-matern cluster, and 4-line pattern (Note: the graphs of 2, 3, and 4 are with dispersion level of L2) and (b) multifractal spectra of the four different graphs

Grahic Jump Location
Fig. 9

Spectra of images with different sizes of pore defects

Grahic Jump Location
Fig. 10

Spectra of images with different number of pore defects

Grahic Jump Location
Fig. 11

Layout of the build setup. Note: The top left corner is the design of experiments to print seven groups of parts under different process conditions, i.e., (H0, V0, P0), H25+=((1+25%)H0, V0, P0), H50+=((1+50%)H0, V0, P0), V25+=(H0(1+25%), V0, P0), V50+=(H0(1+50%), V0, P0), P25−=(H0, V0(1−25%), P0), and P50−=(H0, V0(1−50%), P0).

Grahic Jump Location
Fig. 13

Residual diagnosis of the regression model

Grahic Jump Location
Fig. 7

The variation of single fractal dimension D0 with respect to the dispersion level

Grahic Jump Location
Fig. 12

Multifractal spectra of the 120 CT-scan images



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In