0
Research Papers

Fault Diagnosis in Multistation Assembly Systems Using Spatially Correlated Bayesian Learning Algorithm

[+] Author and Article Information
Kaveh Bastani

Unifund LLC,
Cincinnati, OH 45242

Babak Barazandeh

Department of Industrial and
Systems Engineering,
University of Southern California,
Los Angeles, CA 90007

Zhenyu (James) Kong

Grado Department of Industrial and
Systems Engineering,
Virginia Polytechnic Institute and
State University,
Blacksburg, VA 24061
e-mail: zkong@vt.edu

1Corresponding author.

Manuscript received April 9, 2017; final manuscript received September 17, 2017; published online December 21, 2017. Assoc. Editor: Satish Bukkapatnam.

J. Manuf. Sci. Eng 140(3), 031003 (Dec 21, 2017) (10 pages) Paper No: MANU-17-1238; doi: 10.1115/1.4038184 History: Received April 09, 2017; Revised September 17, 2017

The problem of fault diagnosis for dimensional integrity in multistation assembly systems is addressed in this paper. Fault diagnosis under this context is to identify the process errors which significantly contribute to the large product dimensional variation based on sensor data. The main challenges to be resolved in this paper include (1) the number of measurements is less than the process errors, which is typical in practice, but results in an ill-posed estimation problem, and (2) there exists spatial correlation among the dimensional variation of process errors, which has not been addressed yet by existing literature. A spatially correlated Bayesian learning (SCBL) algorithm to address these challenges is developed. The SCBL algorithm is based on the relevance vector machine (RVM) by exploiting the spatial correlation of dimensional variation from various process errors, which occurs in some circumstances of assembled parts and is well defined in GD&T standards. The proposed algorithm relies on a parametrized prior including the spatial correlation, and eventually leads sparsity in fault diagnosis; hence, the issues with ill-posedness and structured process errors will be addressed. A number of simulation studies are performed to illustrate the superiority of SCBL algorithm over state-of-the-art algorithms in sparse estimation problems when spatial correlation exists among the nonzero elements. A real autobody assembly process is also used to demonstrate the effectiveness of proposed SCBL algorithm.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Huang, W. , Lin, J. , Kong, Z. , and Cegralek, D. , 2007, “ Stream-of-Variation (SOVA) Modeling—II: A Generic 3D Variation Model for Rigid Body Assembly in Multistation Assembly Processes,” ASME J. Manuf. Sci. Eng., 129(4), pp. 832–842. [CrossRef]
Huang, W. , Lin, J. , Kong, Z. , Bezdecny, M. , and Ceglarek, D. , 2007, “ Stream-of-Variation Modeling—Part I: A Generic Three-Dimensional Variation Model for Rigid-Body Assembly in Single Station Assembly Processes,” ASME J. Manuf. Sci. Eng., 129(4), pp. 821–831. [CrossRef]
Apley, D. , and Shi, J. , 1998, “ Diagnosis of Multiple Fixture Faults in Panel Assembly,” ASME J. Manuf. Sci. Eng., 120(4), pp. 793–801. [CrossRef]
Ceglarek, D. , and Shi, J. , 1996, “ Fixture Failure Diagnosis for Autobody Assembly Using Pattern Recognition,” ASME J. Eng. Ind., 118(1), pp. 55–66. [CrossRef]
Ding, Y. , Ceglarek, D. , and Shi, J. , 2002, “ Fault Diagnosis of Multistage Manufacturing Processes by Using State Space Approach,” ASME J. Manuf. Sci. Eng., 124(2), pp. 313–322. [CrossRef]
Kong, Z. , Ceglarek, D. , and Huang, W. , 2008, “ Multiple Fault Diagnosis Method in Multistation Assembly Processes Using Orthogonal Diagonalization Analysis,” ASME J. Manuf. Sci. Eng., 130(1), p. 011014. [CrossRef]
Rong, Q. , Ceglarek, D. , and Shi, J. , 2000, “ Dimensional Fault Diagnosis for Compliant Beam Structure Assemblies,” ASME J. Manuf. Sci. Eng., 122(4), pp. 773–780. [CrossRef]
Zhou, S. , Chen, Y. , and Shi, J. , 2005, “ Statistical Estimation and Testing for Variation Root-Cause Identification of Multistage Manufacturing Processes,” IEEE Trans. Autom. Sci. Eng., 1(1), pp. 73–83. [CrossRef]
Wang, H. , Huang, Q. , and Katz, R. , 2005, “ Multi-Operational Machining Processes Modeling for Sequential Root Cause Identification and Measurement Reduction,” ASME J. Manuf. Sci. Eng., 127(3), pp. 512–521. [CrossRef]
Wang, H. , and Huang, Q. , 2006, “ Error Cancellation Modeling and Its Application to Machining Process Control,” IIE Trans., 38(4), pp. 355–364. [CrossRef]
Bastani, K. , Kong, Z. , Huang, W. , Huo, X. , and Zhou, Y. , 2013, “ Fault Diagnosis Using an Enhanced Relevance Vector Machine (RVM) for Partially Diagnosable Multistation Assembly Processes,” IEEE Trans. Autom. Sci. Eng., 10(1), pp. 124–136. [CrossRef]
Li, S. , and Chen, Y. , 2016, “ A Bayesian Variable Selection Method for Joint Diagnosis of Manufacturing Process and Sensor Faults,” IIE Trans., 48(4), pp. 313–323. [CrossRef]
Kong, Z. , Kumar, R. , Gogineni, S. , Zhou, Y. , and Ceglarek, D. , 2006, “ Mode-Based Tolerance Analysis in Multi-Station Assembly Using Stream of Variation Model,” Trans. NAMRI/SME, 34, pp. 469–476. https://www.researchgate.net/profile/Dariusz_Ceglarek/publication/258837349_Mode-based_tolerance_analysis_in_multi-station_assembly_using_stream_of_variation_model/links/0deec52922b18b77a2000000.pdf
Candès, E. J. , and Wakin, M. B. , 2008, “ An Introduction to Compressive Sampling,” IEEE Signal Process. Mag., 25(2), pp. 21–30. [CrossRef]
Natarajan, B. K. , 1995, “ Sparse Approximate Solutions to Linear Systems,” SIAM J. Comput., 24(2), pp. 227–234. [CrossRef]
Pati, Y. C. , Rezaiifar, R. , and Krishnaprasad, P. , 1993, “ Orthogonal Matching Pursuit: Recursive Function Approximation With Applications to Wavelet Decomposition,” 27th Asilomar Conference on Signals, Systems and Computers (ACSSC), Pacific Grove, CA, Nov. 1–3, pp. 40–44.
Donoho, D. L. , Tsaig, Y. , Drori, I. , and Starck, J. , 2012, “ Sparse Solution of Underdetermined Systems of Linear Equations by Stagewise Orthogonal Matching Pursuit,” IEEE Trans. Inf. Theory, 58(2), pp. 1094–1121. [CrossRef]
Candès, E. J. , and Plan, Y. , 2009, “ Near-Ideal Model Selection by ℓ1 Minimization,” Ann. Stat., 37(5A), pp. 2145–2177. [CrossRef]
Candes, E. , and Tao, T. , 2007, “ The Dantzig Selector: Statistical Estimation When p is Much Larger Than n,” Ann. Stat., 35(6), pp. 2313–2351. [CrossRef]
Chen, S. S. , Donoho, D. L. , and Saunders, M. A. , 1998, “ Atomic Decomposition by Basis Pursuit,” SIAM J. Sci. Comput., 20(1), pp. 33–61. [CrossRef]
Tibshirani, R. , 1996, “ Regression Shrinkage and Selection Via the Lasso,” J. R. Stat. Soc. Ser. B (Methodol.), 58(1), pp. 267–288. http://www.jstor.org/stable/2346178
Tipping, M. E. , 2001, “ Sparse Bayesian Learning and the Relevance Vector Machine,” J. Mach. Learn. Res., 1, pp. 211–244. http://www.jmlr.org/papers/volume1/tipping01a/tipping01a.pdf
Wipf, D. P. , and Rao, B. D. , 2004, “ Sparse Bayesian Learning for Basis Selection,” IEEE Trans. Signal Process., 52(8), pp. 2153–2164. [CrossRef]
Park, T. , and Casella, G. , 2008, “ The Bayesian Lasso,” J. Am. Stat. Assoc., 103(482), pp. 681–686. [CrossRef]
Bastani, K. , Rao, P. K. , and Kong, Z. , 2016, “ An Online Sparse Estimation-Based Classification Approach for Real-Time Monitoring in Advanced Manufacturing Processes From Heterogeneous Sensor Data,” IIE Trans., 48(7), pp. 579–598. [CrossRef]
Ji, S. , Xue, Y. , and Carin, L. , 2008, “ Bayesian Compressive Sensing,” IEEE Trans. Signal Process., 56(6), pp. 2346–2356. [CrossRef]
Zhang, Z. , and Rao, B. D. , 2011, “ Sparse Signal Recovery With Temporally Correlated Source Vectors Using Sparse Bayesian Learning,” IEEE J. Select. Top. Signal Process., 5(5), pp. 912–926. [CrossRef]
Zhang, Z. , and Rao, B. D. , 2013, “ Extension of SBL Algorithms for the Recovery of Block Sparse Signals With Intra-Block Correlation,” IEEE Trans. Signal Process., 61(8), pp. 2009–2015. [CrossRef]
Trefethen, L. N. , and Bau, D., III , 1997, Numerical Linear Algebra, Vol. 50, Society for Industrial and Applied Mathematics, Philadelphia, PA. [CrossRef]
Kong, Z. , Huang, W. , and Oztekin, A. , 2009, “ Variation Propagation Analysis for Multistation Assembly Process With Consideration of GD&T Factors,” ASME J. Manuf. Sci. Eng., 131(5), p. 051010. [CrossRef]
Bastani, K. , Kong, Z. , Huang, W. , and Zhou, Y. , 2016, “ Compressive Sensing–Based Optimal Sensor Placement and Fault Diagnosis for Multi-Station Assembly Processes,” IIE Trans., 48(5), pp. 462–474. [CrossRef]

Figures

Grahic Jump Location
Fig. 2

Multiple feature composite control frame

Grahic Jump Location
Fig. 1

A three-part assembly process is presented. Fixture locators represented by Pij's are used to hold the parts during the operations.

Grahic Jump Location
Fig. 4

The performance comparison of SCBL, BLASSO, and LASSO are presented in normalized mean squared error (MSE). Different correlation structures and different ill-posedness ratio (n/m), are considered in our comparisons. The results are based on 500 replications.

Grahic Jump Location
Fig. 5

Floor-pan assembly in three assembly stations

Grahic Jump Location
Fig. 6

Fault diagnosis performance of SCBL, BLASSO, and LASSO are presented in normalized MSE. Different correlation coefficients varying in the range of (0, 0.9] are considered in the comparisons.

Grahic Jump Location
Fig. 3

SCBL algorithm for mean shift fault diagnosis

Tables

Errata

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