Advertisement

Visual Analysis of a Cold Rolling Process Using Data-Based Modeling

  • Daniel Pérez
  • Francisco J. García-Fernández
  • Ignacio Díaz
  • Abel A. Cuadrado
  • Daniel G. Ordonez
  • Alberto B. Díez
  • Manuel Domínguez
Part of the Communications in Computer and Information Science book series (CCIS, volume 311)

Abstract

In this paper, a method to characterize the chatter phenomenon in a cold rolling process is proposed. This approach is based on obtaining a global nonlinear dynamical MISO model, relating four input variables and the exit strip thickness as the output variable. In a second stage, local linear models are obtained for all working points using sensitivity analysis on the nonlinear model to get input/output small signal models. Each local model is characterized by a high dimensional vector containing the frequency response functions (FRF) of the four SISO resulting models. Finally, the FRF’s are projected on a 2D space, using the t-SNE algorithm, in order to visualize the dynamical changes of the process. Our results show a clear separation between chatter condition and other vibration states, allowing an early detection of chatter as well as being a visual analysis tool to study the chatter phenomenon.

Keywords

dimensionality reduction cold rolling data visualization dynamical systems data-based models 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Roberts, W.L.: Cold rolling of steel. Marcel Dekker, Inc., New York (1978)Google Scholar
  2. 2.
    Yun, I.S., Wilson, W.R.D., Ehmann, K.F.: Review of chatter studies in cold rolling. International Journal of Machine Tools and Manufacture 38(12), 1499–1530 (1998)CrossRefGoogle Scholar
  3. 3.
    Hu, P.H., Ehmann, K.F.: A dynamic model of the rolling process. part I: homogeneous model. International Journal of Machine Tools and Manufacture 40(1), 1–19 (2000)CrossRefGoogle Scholar
  4. 4.
    Cuadrado, A.A., Diaz, I., Diez, A.B., Obeso, F., Gonzalez, J.A.: Visual data mining and monitoring in steel processes. In: 37th IAS Annual Meeting, Conference Record of the Industry Applications Conference, vol. 1, pp. 493–500 (2002)Google Scholar
  5. 5.
    Díaz, I., Domínguez, M., Cuadrado, A., Fuertes, J.: A new approach to exploratory analysis of system dynamics using som. Applications to industrial processes. Expert Systems with Applications 34(4), 2953–2965 (2008)CrossRefGoogle Scholar
  6. 6.
    Kourti, T., MacGregor, J.: Process analysis, monitoring and diagnosis, using multivariate projection methods. Chemometrics and Intelligent Laboratory Systems 28(1), 3–21 (1995)Google Scholar
  7. 7.
    Lee, J.A., Verleysen, M.: Nonlinear dimensionality reduction (2007)Google Scholar
  8. 8.
    Pearson, K.: LIII. On lines and planes of closest fit to systems of points in space. Philosophical Magazine Series 6 2(11), 559–572 (1901)CrossRefGoogle Scholar
  9. 9.
    Hyvärinen, A., Karhunen, J.: Independent component analysis (2001)Google Scholar
  10. 10.
    Kohonen, T.: Self Organizing Maps. Springer (1995)Google Scholar
  11. 11.
    Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)CrossRefGoogle Scholar
  12. 12.
    Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000)CrossRefGoogle Scholar
  13. 13.
    Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation 15(6), 1373–1396 (2003)zbMATHCrossRefGoogle Scholar
  14. 14.
    Van Der Maaten, L., Hinton, G.: Visualizing data using t-SNE. Journal of Machine Learning Research 9, 2579–2605 (2008)zbMATHGoogle Scholar
  15. 15.
    Bushati, N., Smith, J., Briscoe, J., Watkins, C.: An intuitive graphical visualization technique for the interrogation of transcriptome data. Nucleic Acids Research 39(17), 7380–7389 (2011)CrossRefGoogle Scholar
  16. 16.
    Jamieson, A.R., Giger, M.L., Drukker, K., Li, H., Yuan, Y., Bhooshan, N.: Exploring nonlinear feature space dimension reduction and data representation in breast CADx with Laplacian eigenmaps and t-SNE. Medical Physics 37(1), 339–351 (2010)CrossRefGoogle Scholar
  17. 17.
    Huang, G.B., Zhu, Q.Y., Siew, C.K.: Extreme learning machine: Theory and applications. Neurocomputing 70(1-3), 489–501 (2006)CrossRefGoogle Scholar
  18. 18.
    Venter, R., Abd-Rabbo, A.: Modelling of the rolling process–I: Inhomogeneous deformation model. International Journal of Mechanical Sciences 22(2), 83–92 (1980)CrossRefGoogle Scholar
  19. 19.
    Freshwater, I.: Simplified theories of flat rolling–I: the calculation of roll pressure, roll force and roll torque. International Journal of Mechanical Sciences 38(6), 633–648 (1996)zbMATHGoogle Scholar
  20. 20.
    Paton, D.L., Critchley, S.: Tandem mill vibration: Its cause and control. In: Mechanical Working; Steel Processing XXII, Proceedings of the 26th Mechanical Working; Steel Processing Conference, pp. 247–255. Iron and Steel Soc. Inc., Chicago (1985)Google Scholar
  21. 21.
    Meehan, P.A.: Vibration instability in rolling mills: Modeling and experimental results. Journal of Vibration and Acoustics 124(2), 221–228 (2002)CrossRefGoogle Scholar
  22. 22.
    Kimura, Y., Sodani, Y., Nishimura, N., Ikeuchi, N., Mihara, Y.: Analysis of chatter in tandem cold rolling mills. ISIJ International 43(1), 77–84 (2003)CrossRefGoogle Scholar
  23. 23.
    Venkatasubramanian, V.: A review of process fault detection and diagnosis Part III: Process history based methods. Computers & Chemical Engineering 27(3), 327–346 (2003)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716–723 (1974)MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Theil, H.: Economics and information theory. North-Holland Pub. Co., Rand McNally, Amsterdam, Chicago (1967)Google Scholar
  26. 26.
    Simon, H.: Neural networks: a comprehensive foundation. Prentice Hall (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Daniel Pérez
    • 1
  • Francisco J. García-Fernández
    • 1
  • Ignacio Díaz
    • 1
  • Abel A. Cuadrado
    • 1
  • Daniel G. Ordonez
    • 1
  • Alberto B. Díez
    • 1
  • Manuel Domínguez
    • 2
  1. 1.Área de Ingeniería de Sistemas y AutomáticaUniversidad de OviedoSpain
  2. 2.Instituto de Automática y FabricaciónUniversidad de LeónSpain

Personalised recommendations