Influence of Selection Criterion on RBF Topology Selection for Crashworthiness Optimization

The performance of radial basis function networks largely depends on the choice of topology i.e., location and number of centers, radius of influence. Thus finding the best network is a multi"level optimization prob lem. It is obvious that different criteria for optimization would result in different network topologies. A systematic study is carried out to compare the most widely used root mean square error criterion for topology selection with cross"validat ion based methods like PRESS or PRESS"ratio. The main focus here is to find the cri terion that best approximates the response typically encountered in crashworthiness simulations. Based on a suite of analytical examples and crashworthiness simulation problems, it was concluded that the PRESS"based selection criterion performs the be st and offers the least variation with the choice of experimental design, sampling density, and the nature of the problem.

[1]  M. J. L. Orr,et al.  Recent advances in radial basis function networks , 1999 .

[2]  R. Haftka,et al.  Ensemble of surrogates , 2007 .

[3]  Marco Anghileri,et al.  Multi-objective optimisation of composite absorber shape under crashworthiness requirements , 2004 .

[4]  Bryan Glaz,et al.  Surrogate based optimization of helicopter rotor blades for vibration reduction in forward flight , 2006 .

[5]  J. Utans,et al.  Selecting neural network architectures via the prediction risk: application to corporate bond rating prediction , 1991, Proceedings First International Conference on Artificial Intelligence Applications on Wall Street.

[6]  R. L. Hardy.  Multiquadric equations of topography and other irregular surfaces , 1971 .

[7]  Bernard Yannou,et al.  Metamodeling of Combined Discrete/Continuous Responses , 2001 .

[8]  H. Zimmermann.  Towards global optimization 2: L.C.W. DIXON and G.P. SZEGÖ (eds.) North-Holland, Amsterdam, 1978, viii + 364 pages, US $ 44.50, Dfl. 100,-. , 1979 .

[9]  Tim Andersen,et al.  Cross validation and MLP architecture selection , 1999, IJCNN'99. International Joint Conference on Neural Networks. Proceedings (Cat. No.99CH36339).

[10]  Mark J. L. Orr,et al.  Regularization in the Selection of Radial Basis Function Centers , 1995, Neural Computation.

[11]  G. Golub,et al.  Generalized cross-validation for large scale problems , 1997 .

[12]  Ping Zhang.  Model Selection Via Multifold Cross Validation , 1993 .

[13]  John Mark,et al.  Introduction to radial basis function networks , 1996 .

[14]  Bryan Glaz,et al.  Surrogate based optimization of helicopter rotor blades for vibration reduction in forward flight , 2008 .

[15]  A. Kurdila,et al.  Adaptation of centers of approximation for nonlinear tracking control , 1992 .

[16]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[17]  Ranjan Ganguli,et al.  Structural damage detection in a helicopter rotor blade using radial basis function neural networks , 2003 .

[18]  Achille Messac,et al.  Extended Radial Basis Functions: More Flexible and Effective Metamodeling , 2004 .

[19]  T. W. Layne,et al.  A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models , 1998 .

[20]  Mark J. L. Orr.  Local Smoothing of Radial Basis Function Networks , 1995 .

[21]  Atam P. Dhawan,et al.  Space Shuttle Main Engine sensor modeling using radial-basis-function neural networks , 1994 .

[22]  Marios K. Karakasis,et al.  On the use of metamodel-assisted, multi-objective evolutionary algorithms , 2006 .

[23]  Masoud Rais-Rohani,et al.  A comparative study of metamodeling methods for multiobjective crashworthiness optimization , 2005 .

[24]  Naira Hovakimyan,et al.  Adaptive Control Design Methodology for Nonlinear-in-Control Systems in Aircraft Applications , 2007 .

[25]  Raphael T. Haftka,et al.  Error measures for noise-free surrogate approximations , 2008 .

[26]  Layne T. Watson,et al.  Pitfalls of using a single criterion for selecting experimental designs , 2008 .

[27]  Narasimhan Sundararajan,et al.  Stable Neuro-Flight-Controller Using Fully Tuned Radial Basis Function Neural Networks , 2001 .

[28]  Christoph W. Ueberhuber.  Numerical computation : methods, software, and analysis , 1997 .

[29]  John Moody,et al.  Architecture Selection Strategies for Neural Networks: Application to Corporate Bond Rating Predicti , 1995, NIPS 1995.

[30]  Gene H. Golub,et al.  Generalized cross-validation as a method for choosing a good ridge parameter , 1979, Milestones in Matrix Computation.

[31]  Ken J. Craig,et al.  Automotive crashworthiness design using response surface‐based variable screening and optimization , 2005 .

[32]  K.S. Nikita,et al.  Cross-validation and neural network architecture selection for the classification of intracranial current sources , 2004, 7th Seminar on Neural Network Applications in Electrical Engineering, 2004. NEUREL 2004. 2004.

[33]  T. Simpson,et al.  Comparative studies of metamodeling techniques under multiple modeling criteria , 2000 .

[34]  Wei Shyy,et al.  Shape optimization of supersonic turbines using global approximation methods , 2002 .

[35]  Surjya K. Pal,et al.  Flank wear prediction in drilling using back propagation neural network and radial basis function network , 2008, Appl. Soft Comput..

[36]  Sharif Rahman,et al.  A hybrid surrogate and pattern search optimization method and application to microelectronics , 2006 .

[37]  Wu Li,et al.  Principal Component Regression for Fitting Wing Weight Data of Subsonic Transports , 2006 .