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buckling phenomena on the left longitudinal rail and a fold on the floor of the vehicle,
which appear in earlier time steps. In total, 15 bifurcation points have been identified,
representing statistically independent sources of scatter. The whole scatter in the
model can be decomposed over the corresponding basis functions
(y). In this way
the dimensionality of the problem is reduced to 15 variables (g-coefficients)
completely describing the stochastic behavior of the model.
Ψ
6
Conclusions
We have presented and discussed methods for nonlinear metamodeling of a
simulation database featuring continuous exploration of simulation results, tolerance
prediction and rapid interpolation of bulky FEM data. For the purpose of robust
optimization, the approach has been extended by the methods of reliability and causal
analysis. The efficiency of the methods has been demonstrated for several application
cases from automotive industry.
Further plans include to use the results of causal analysis as a basis for
modifications of a simulation model for improving its stability. We also plan to
consider non-linear relationships between stochastic variables. Linear methods such
as PCA and GS determine only a linear span over principal components, while some
stochastic variables can become non-linear functions of others. For determination of
such dependencies the methods of curvilinear component analysis (CCA) can be
applied.
Acknowledgements. Many thanks to the team of Prof. Steve Kan at the NCAC and
the Ford company for providing the publically available LS-DYNA models and to
Andreas Hoppe and Josef Reicheneder at AUDI for providing PamCrash B-pillar
model. The availability of these models fosters method developments for crash
simulation. We are also grateful to Michael Taeschner and Georg Dietrich
Eichmueller (VW) and to Thomas Frank and Wolfgang Fassnacht (Daimler) for
fruitful discussions.
References
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Challenges of the 21st Century" (2000), http://www-stat.stanford.edu/
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3. Jones, D.R., Schonlau, M., Welch, W.J.: Efficient Global Optimization of Expensive
Black-Box Functions. J. Glob. Opt. 13, 455-492 (1998)
4. Keane, A.J., Leary, S.J., Sobester, A.: On the Design of Optimization Strategies Based on
Global Response Surface Approximation Models. J. Glob. Opt. 33, 31-59 (2005)
5. Buhmann, M.D.: Radial Basis Functions: Theory and Implementations. Cambridge
University Press, Cambridge (2003)
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