In this paper we show how the implicit filtering algorithm can be applied to problems in parameter identification and optimization from automotive valve train design. We extend our previous work by using a more refined model of the valve train and exploiting parallelism in a different way. We apply the parameter identification results to obtain optimal profiles for camshaft lobes.
This is a preview of subscription content,to check access.
Access this article
L. Armijo, “Minimization of functions having Lipschitz-continuous first partial derivatives,” Pacific J. Math. vol. 16, pp. 1-3, 1966.
K. R. Bailey, B. G. Fitzpatrick, and M. A. Jeffries, “Least squares estimation of hydraulic conductivity from field data,” Technical Report CRSC-TR95-8, North Carolina State University, Center for Research in Scientific Computation, 1995.
D. B. Bertsekas, “On the Goldstin-Levitin-Polyak gradient projection method,” IEEE Trans. Autom. Control vol. 21, pp. 174-184, 1976.
D. B. Bertsekas, “Projected Newton methods for optimization problems with simple constraint,” SIAM J. Control Optim. vol. 20, pp. 221-246, 1982.
D. M. Bortz and C. T. Kelley, “The simplex gradient and noisy optimization problems,” in Progress in Systems and Control Theory, vol. 24: Computational Methods in Optimal Design and Control, J.T. Borggaard, J. Burns, E. Cliff, and S. Schreck eds. pp. 77-90, 1998.
C. G. Broyden, “Quasi-Newton methods and their application to function minimization,” Math. Comp. vol. 21, pp. 368-381, 1967.
C. G. Broyden “A new double-rank minimization algorithm,” AMS Notices vol. 16, p. 670, 1969.
J. Cash and A. Karp, “A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides,” ACM transactions an Mathematical Software vol. 16, pp. 201-222, 1990.
C. Cheng, “Analysis and optimal design of three dimensional valve train by steam,” Ph.D. thesis, North Carolina State University, 1997.
C. Chia, NonlinearAnalysis of Plates. McGraw Hill International Book Company, 1980.
J. W. David, C. Y. Cheng, T. D. Choi, C. T. Kelley, and J. Gablonsky, “Optimal design of high speed mechanical systems,” Technical Report CRSC-TR97-18, North Carolina State University, Center for Research in Scientific Computation. Mathematical Modeling and Scientific Computing, to appear.
J. W. David, C. T. Kelley, and C. Y. Cheng, “Use of implicit filtering algorithm for mechanical system parameter identification,” SAE Paper 960358, 1996 SAE International Congress and Exposition Conference Proceedings, Modeling of CI and SI Engines, pp. 189-194, 1996.
J. E. Dennis and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, No. 16 in Classics in Applied Mathematics. Philadelphia: SIAM, 1996.
M. Etheridge, “Preliminary performance of carbon-carbon valves in high speed pushrod type valve trains,” Master's thesis, North Carolina State University, Raleigh, North Carolina, 1998.
M. C. Etheridge, J. W. David, and W. L. Roberts, “Dynamic modeling of high speed pushrod type valve trains,” submitted to the Journal of Mechanical Systems and Signal Processing.
A. V. Fiacco and G. P. McCormick, Nonlinear Programming, No. 4 in Classics in Applied Mathematics. Philadelphia: SIAMI, 1990.
R. Fletcher, “A new approach to variable metric methods,” Comput. J. vol. 13, pp. 317-322, 1970.
P. Gilmore, “An algorithm for optimizing functions with multiple minima,” Ph.D. thesis, North Carolina State University, Raleigh, North Carolina, 1993a.
P. Gilmore, “IFFCO: Implicit filtering for constrained optimization,” Technical Report CRSC-TR93-7, Center for Research in Scientific Computation, North Carolina State University, 1993b.
P. Gilmore and C. T. Kelley, “An implicit filtering algorithm for optimization of functions with many local minima,” SIAM J. Optim vol. 5, pp. 269-285, 1995.
P. Gilmore, C. T. Kelley, C. T. Miller, and G. A. Williams, “Implicit filtering and optimal design problems,” In Progress in Systems and Control Theory, Vol. 19: Optimal Design and Control, J. Borggaard, J. Burkhardt, M. Gunzburger, and J. Peterson, eds. pp. 159-176, 1995. Proceedings of the Workshop on Optimal Design and Control, Blackburg VA, April 8-9, 1994.
D. Goldfarb, “A family of variable metric methods derived by variational means,” Math. Comp. vol. 24, pp. 23-26, 1970.
C. T. Kelley, Iterative Methods for Optimization, No. 18 in Frontiers in Applied Mathematics. Philadelphia: SIAM, 1999.
D. Kim and J. David, “A combined model for high speed valve train dynamics (partly linear and partly nonlinear),” SAE Technical Paper 901726, 1990.
J. Mottershead, “Finite elements for dynamical analysis of helical rods,” International Journal of Mechanical Science vol. 22, no. 5-A, pp. 267-283, 1980.
J. Mottershead, “The large displacements and dynamic stability of springs using helical finite elements,” International Journal of Mechanical Science vol. 24, no. 9, pp. 547-558, 1982.
D. Park, “Design and optimization of valve train cam profiles in high speed IC engines,” M.S. Thesis, North Carolina State University 1994.
P. Pernambuco-Wise, P. Gilmore, and Y. Eyssa, “An optimization code for pulse magnets,” Physica B to appear.
W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes, Cambridge University Press, 1992.
K. Radhakrishnan and A. C. Hindmarsh, “Description and use of LSODE, the livermore solver for ordinary differential equations,” Technical Report URCL-ID-113855, Lawrence Livermore National Laboratory, 1993.
D. F. Shanno, “Conditioning of quasi-Newton methods for function minimization,” Math. Comp. vol. 24, pp. 647-657, 1970.
D. Stoneking, G. Bilbro, R. Trew, P. Gilmore, and C.T. Kelley, “Yield optimization using a GaAs process simulator coupled to a physical device model,” IEEE Transactions on Microwave Theory and Techniques vol. 40, pp. 1353-1363, 1992.
D. E. Stoneking, G. L. Bilbro, R. J. Trew, P. Gilmore and C. T. Kelley, “Yield optimization using a GaAs process simulator coupled to a physical device model,” in Proceedings IEEE/Cornell Conference on Advanced Concepts in High Speed Devices and Circuits, pp. 374-383, 1991.
T. A. Winslow, R. J. Trew, P. Gilmore, and C. T. Kelley, “Doping profiles for optimum class B performance of GaAs MESFET amplifiers,” in Proceedings IEEE/Cornell Conference on Advanced Concepts in High Speed Devices and Circuits, pp. 188-197, 1991a.
T. A. Winslow, R. J. Trew, P. Gilmore, and C. T. Kelley, “Simulated performance optimization of GaAs MESFET amplifiers,” in Proceedings IEEE/Cornell Conference on Advanced Concepts in High Speed Devices and Circuits, pp. 393-402, 1991b.
W. Wittrick, “On elastic wave propagation in helical springs,” International Journal of Mechanical Science vol. 8, pp. 25-47, 1966.
About this article
Cite this article
Choi, T.D., Eslinger, O.J., Kelley, C.T. et al. Optimization of Automotive Valve Train Components with Implicit Filtering. Optimization and Engineering 1, 9–27 (2000). https://doi.org/10.1023/A:1010071821464