Advanced search
Publication Cover
Inverse Problems in Science and Engineering Volume 25, 2017 - Issue 11
Submit an article Journal homepage
289
Views
3
CrossRef citations to date
0
Altmetric
Articles

Optimal parameters identification and sensitivity study for abrasive waterjet milling model

D. AurouxLaboratoire J. A. Dieudonné, Université Nice Sophia Antipolis, Nice cedex 2, France.View further author information
&
V. GrozaLaboratoire J. A. Dieudonné, Université Nice Sophia Antipolis, Nice cedex 2, France.Correspondence[email protected]
View further author information
Pages 1560-1576 | Received 02 Mar 2016, Accepted 15 Dec 2016, Published online: 29 Dec 2016

References

  • Lavrentiev MM, Romanov VG, Shishatskii SP. Ill-posed problems of mathematical problems. Vol. 64. Providence (RI): AMS; 1986.
  • Tarantola A. Inverse problem theory and methods for model parameter estimation. Philadelphia (PA): SIAM; 2005.
  • Aster RC, Borchers B, Thurber CH. Parameter estimation and inverse problems. 2nd ed. Waltham (MA): Elsevier; 2013.
  • Tikhonov AN, Arsenin VY. Solutions of ill-posed problems. New York (NY): Wiley; 1977.
  • Tikhonov AN, Glasko VB. Use of the regularization method in non-linear problems. Zh Vychisl Mat Mat Fiz. 1965;5(3):463–473.
  • Tautenhahn U. Lavrentiev regularization of nonlinear ill-posed problems. Vietnam J Math. 2004;32:29–41.
  • Denisov AM, Zaharov EV, Kalinin AV, et al. Application of Tikhonov regularization method for numerical solution of inverse problem of electrocardiography. MSU Vestnik. 2008;15:5–10.
  • Kaltenbacher B, Neubauer A, Scherzer O. Iterative regularization methods for nonlinear ill-posed problems. Vol. 6, Radon series on computational and applied mathematics. Berlin: Walter de Gruyter GmbH & Co.; 2008.
  • Engl HW, Hanke M, Neubauer A. Regularization of inverse problems. Vol. 375, Mathematics and its applications. Dordrecht: Kluwer Academic; 1996.
  • Axinte DA, Srinivasu DS, Billingham J, et al. Geometrical modelling of abrasive waterjet footprints: a study for 90° jet impact angle. CIRP Ann Manuf Technol. 2010;59:341–346.
  • Kong MC, Anwar S, Billingham J, et al. Mathematical modelling of abrasive waterjet footprints for arbitrarily moving jets: Parti -- single straight paths. Int J Mach Tools Manuf. 2012;53:58–68.
  • Billingham J, Miron CB, Axinte DA, et al. Mathematical modelling of abrasive waterjet footprints for arbitrarily moving jets: Partii -- overlapped single and multiple straight paths. Int J Mach Tools Manuf. 2013;68:30–39.
  • Lozano Torrubia P, Billingham J, Axinte DA. Stochastic simplified modelling of abrasive waterjet footprints. Proc R Soc A. 2016;472:20150836. Available from: http://rspa.royalsocietypublishing.org/content/472/2186/20150836
  • Bilbao Guillerna A, Axinte DA, Billingham J. The linear inverse problem in energy beam processing with an application to abrasive waterjet machining. Int J Mach Tools Manuf. 2015;99:34–42.
  • Gilbert JC, Lemaréchal C. Some numerical experiments with variable storage quasi-newton algorithms. Math Prog. 1989;45:407–435.
  • Liu DC, Nocedal J. On the limited memory bfgs method for large scale optimization. Math Prog. 1989;45:503–528.
  • Veersé F, Auroux D. Some numerical experiments on scaling and updating L-BFGS dianogal preconditioners. INRIA; 2000. ( Research Report 3858).
  • Gilbert JC, Lemaréchal C. 2013. Available from: https://who.rocq.inria.fr/Jean-Charles.Gilbert/modulopt
  • Hascoët L, Pascual V. The tapenade automatic differentiation tool: principles, model, and specification. ACM Trans Math Softw. 2013;39(3):1–20.
  • Quarteroni A. Numerical models for differential problems. Milan: Springer-Verlag; 2009.
  • Lions JL. Optimal control of systems governed by partial differential equations. Berlin: Springer-Verlag; 1971.
  • Lawson CL, Hanson RJ. Solving least squares problems. Philadelphia (PA): SIAM; 1995.
  • Hansen PC, O’Leary DP. The use of the l-curve in the regularization of discrete ill-posed problems. SIAM J Sci Comput. 1993;14:1487–1503.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.