Stability determination in turning using persistent homology and time series analysis

ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE)

Volumn 4B, Issue , 2014, Pages

  Khasawneh, Firas A ^a   Munch, Elizabeth ^b  

^a SUNY POLYTECHNIC INSTITUTE   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICAL SYSTEMS; HOPF BIFURCATION; STOCHASTIC SYSTEMS;

DELAY DYNAMICAL SYSTEMS; EULER-MARUYAMA METHOD; HIGH-DIMENSIONAL; LOSS OF STABILITY; PERSISTENT HOMOLOGY; SELF-EXCITED VIBRATIONS; STOCHASTIC DELAY; TOPOLOGICAL DATA ANALYSIS;

TIME SERIES ANALYSIS;

EID: 84926429906     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/IMECE2014-40221     Document Type: Conference Paper

References (52)

1. Quintana, G., and Ciurana, J., 2011. "Chatter in machining processes: A review". International Journal of Machine Tools and Manufacture, 51(5), pp. 363-376.
2. Kuske, R., 2006. "Multiple-scales approximation of a coherence resonance route to chatter". Computing in Science Engineering, 8(3), pp. 35-43.
3. Buckwar, E., Kuske, R., L'Esperance, B., and Soo, T, 2006. "Noise-sensitivity in machine tool vibrations". International Journal of Bifurcation and Chaos, 16(08), pp. 2407-2416.
4. Klamecki, B., 2004. "Enhancement of the low-level components of milling vibration signals by stochastic resonance". Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 218(1), pp. 33-41.
5. Yilmaz, A., AL-Regib, E., and Ni, J., 2002. "Machine tool chatter suppression by multi-level random spindle speed variation". Journal of Manufacturing Science and Engineering, 124(2), pp. 208-216.
6. Barrio, M., Burrage, K., Leier, A., and Tian, T., 2006. "Oscillatory regulation of hes1: Discrete stochastic delay modelling and simulation". PLoS Comput Biol, 2(9), 09, p. e117.
7. Tian, T., Burrage, K., Burrage, P. M., and Carletti, M., 2007. "Stochastic delay differential equations for genetic regulatory networks". Journal of Computational and Applied Mathematics, 205(2), pp. 696-707. Special issue on evolutionary problems.
8. Mackey, M. C., Nechaeva, I. G., 1995. "Solution moment stability in stochastic differential delay equations". Phys. Rev. E, 52(4), Oct, pp. 3366-3376.
9. Guillouzic, S., L'Heureux, I., and Longtin, A., 1999. "Small delay approximation of stochastic delay differential equations". Phys. Rev. E, 59, Apr, pp. 3970-3982.
10. Elbeyli, O., Sun, J., and Unal, G., 2005. "A semi-discretization method for delayed stochastic systems". Communications in Nonlinear Science and Numerical Simulation, 10(1), pp. 85-94.
11. Frank, T. D., Beek, P. J., 2001. "Stationary solutions of linear stochastic delay differential equations: Applications to biological systems". Phys. Rev. E, 64, Jul, p. 021917.
12. Buckwar, E., 2000. "Introduction to the numerical analysis of stochastic delay differential equations". Journal of Computational and Applied Mathematics, 125(1-2), pp. 297-307. Numerical Analysis 2000. Vol. VI: Ordinary Differential Equations and Integral Equations.
13. Mao, X., and Sabanis, S., 2003. "Numerical solutions of stochastic differential delay equations under local lipschitz condition". Journal of Computational and Applied Mathematics, 151(1), pp. 215-227.
14. Yuan, C., and Glover, W., 2006. "Approximate solutions of stochastic differential delay equations with markovian switching". Journal of Computational and Applied Mathematics, 194(2), pp. 207-226.
15. Buckwar, E., and Winkler, R., 2007. "Multi-step maruyama methods for stochastic delay differential equations". Stochastic Analysis and Applications, 25(5), pp. 933-959.
16. Hu, Y., Mohammed, S.-E. A., and Yan, F., 2004. "Discrete-time approximations of stochastic delay equations: The milstein scheme". Annals of Probability, 32(1A), pp. 265-314.
17. Baker, C. T. H., and Buckwar, E., 2005. "Exponential stability in p-th mean of solutions, and of convergent euler-type solutions, of stochastic delay differential equations". J. Comput. Appl. Math., 184(2), Dec., pp. 404-427.
18. Luo, J., 2007. "A note on exponential stability in pth mean of solutions of stochastic delay differential equations". Journal of Computational and Applied Mathematics, 198(1), pp. 143-148.
19. Mao, X., 2007. "Exponential stability of equidistant euler-maruyama approximations of stochastic differential delay equations". Journal of Computational and Applied Mathematics, 200(1), pp. 297-316.
20. Jolliffe, I., 2005. Principal Component Analysis. John Wiley & Sons, Ltd.
21. Abdi, H., Williams, L. J., 2010. "Principal component analysis". Wiley Interdisciplinary Reviews: Computational Statistics, 2(4), pp. 433-459.
22. Borg, I., and Groenen, P. J. F, 2005. Modern Multidimensional Scaling: Theory and Applications. Springer.
23. Roweis, S., and Saul, L., 2000. "Nonlinear dimensionality reduction by locally linear embedding". Science, 290(5500), p. 2323-2326.
24. Belkin, M., and Niyogi, P., 2003. "Laplacian eigenmaps for dimensionality reduction and data representation". Neural Computation, 15(6), pp. 1373-1396.
25. Donoho, D. L., and Grimes, C., 2003. "Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data". Proceedings of the National Academy of Sciences, 100(10), pp. 5591-5596.
26. Zhang, Z., and Zha, H., 2002. "Principal manifolds and nonlinear dimension reduction via local tangent space alignment". SIAM Journal of Scientific Computing, 26, pp. 313-338.
27. Coifman, R. R., and Lafon, S., 2006. "Diffusion maps". Applied and Computational Harmonic Analysis, 21(1), pp. 5-30. Special Issue: Diffusion Maps and Wavelets.
28. Nadler, B., Lafon, S., Coifman, R. R., Kevrekidis, I. G., 2006. "Diffusion maps, spectral clustering and reaction coordinates of dynamical systems". Applied and Computational Harmonic Analysis, 21(1), pp. 113-127. Special Issue: Diffusion Maps and Wavelets.
29. Singer, A., Coifman, R. R., 2008. "Non-linear independent component analysis with diffusion maps". Applied and Computational Harmonic Analysis, 25(2), pp. 226-239.
30. Brown, J., and Gedeon, T., 2012. "Structure of the afferent terminals in terminal ganglion of a cricket and persistent homology". PLoS ONE, 7(5), 05, p. e37278.
31. Nicolau, M., and Levine., A. J., and Carlsson, G., 2011. "Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival". Proceedings of the National Academy of Sciences, 108(17), pp. 7265-7270.
32. de Silva, V., and Ghrist, R., 2007. "Coverage in sensor networks via persistent homology". Algebraic & Geometric Topology, 7, Apr., pp. 339-358.
33. Munch, E., Shapiro, M., and Harer, J., 2012. "Failure filtrations for fenced sensor networks". The International Journal of Robotics Research, 31(9), pp. 1044-1056.
34. Carlsson, G., Ishkhanov, T., de Silva, V., and Zomorodian, A., 2008. "On the local behavior of spaces of natural images". International Journal of Computer Vision, 76, pp. 1-12. 10.1007/s11263-007-0056-x.
35. Munkres, J. R., 1993. Elements of Algebraic Topology. Addison Wesley.
36. Hatcher, A., 2002. Algebraic Topology. Cambridge University Press.
37. Edelsbrunner, H., and Harer, J., 2010. Computational Topology: An Introduction. American Mathematical Society.
38. Edelsbrunner, H., Letscher, D., and Zomorodian, A., 2000. "Topological persistence and simplification". in Foundations of Computer Science, 2000. Proceedings. 41st Annual Symposium on, pp. 454-463.
39. Perea, J. A., and Harer, J., 2013. "Sliding windows and persistence: An application of topological methods to signal analysis". arXiv: 1307.6188.
40. Berwald, J., Gidea, M., and Vejdemo-Johansson, M., 2013. "Automatic recognition and tagging of topologically different regimes in dynamical systems". arXiv: 1312.2482.
41. de Silva, V., Skraba, P., and Vejdemo-Johansson, M., 2012. "Topological analysis of recurrent systems". In NIPS 2012 Workshop on Algebraic Topology and Machine Learning.
42. Emrani, S., Gentimis, T., and Krim, H., 2014. "Persistent homology of delay embeddings and its application to wheeze detection". Signal Processing Letters, IEEE, 21(4), April, pp. 459-463.
43. Kantz, H., and Schreiber, T., 2004. Nonlinear Time Series Analysis. Cambridge University Press.
44. Takens, F., 1981. "Detecting strange attractors in turbulence". In Dynamical Systems and Turbulence, Warwick 1980, D. Rand and L.-S. Young, eds., Vol. 898 of Lecture Notes in Mathematics. Springer Berlin Heidelberg, pp. 366-381.
45. Insperger, T., and Barton., D. A., and Stepan, G., 2008. "Criticality of hopf bifurcation in state-dependent delay model of turning processes". International Journal of Non-Linear Mechanics, 43(2), pp. 140-149.
46. Oksendal, B., 2007. Stochastic differential equations, 6th ed. Springer.
47. Altintaş, Y., and Budak, E., 1995. "Analytical prediction of stability lobes in milling". CIRP Annals, 44(1), pp. 357-362.
48. Insperger, T., and Stépán, G., 2004. "Updated semi-discretization method for periodic delay-differential equations with discrete delay". International Journal for Numerical Methods, 61, pp. 117-141.
49. Butcher, E. A., Bobrenkov, O. A., 2011. "On the chebyshev spectral continuous time approximation for constant and periodic delay differential equations". Communications in Nonlinear Science and Numerical Simulation, 16(3), pp. 1541-1554.
50. Khasawneh, F. A., Mann, B. P., 2011. "A spectral element approach for the stability of delay systems". International Journal for Numerical Methods in Engineering, 87(6), pp. 566-592.
51. Higham, D., 2001. "An algorithmic introduction to numerical simulation of stochastic differential equations". SIAM Review, 43(3), pp. 525-546.
52. Harer, J., Slaczedek, J., and Bendich, P., 2014. "Ripscollapse: discrete morse theory and fast computation of onedimensional persistence.". Manuscript, Duke University.