A study is conducted to determine the sensitivity of 2 topologically distinct metamodel types to variations in the experimental design brought about by sequential adaptive sampling strategies. The study focuses on examples encountered in crashworthiness design. Three sampling strategies are considered for updating the experimental designs, namely (i) a single stage approach, (ii) a sequential approach and (iii) a sequential domain reduction approach with higher densities in local regions. The experimental design type is the Space Filling Method based on maximizing the minimum distance between any two design points within a subdomain. Feedforward Neural Networks (NN) and Radial Basis Function Networks (RBF) are compared with respect to their sensitivity when applied to these strategies. A large set of independent checkpoints, constructed using a Latin Hypercube Sampling method is used to evaluate the accuracy of the various strategies. Five examples are used in the evaluation, namely (i) simple two-variable two-bar truss, (ii) the 21 variable Svanberg problem, (iii) a 7 variable full vehicle crash example, (iv) a 11 variable knee impact crash example and (v) a 5 variable head impact example. The examples reveal two main characteristics, namely that, while expensive to construct, NN committees tend to be superior in predictability whereas RBF networks, although much cheaper to construct can, in some cases, be highly sensitive to irregularity of experimental designs caused by subdomain updating. However, this conclusion cannot be extended to the three crash problems tested, since the RBF networks performed consistently well for these examples.
[1]
A. N. Tikhonov,et al.
Solutions of ill-posed problems
,
1977
.
[2]
Martin A. Riedmiller,et al.
A direct adaptive method for faster backpropagation learning: the RPROP algorithm
,
1993,
IEEE International Conference on Neural Networks.
[3]
Heekuck Oh,et al.
Neural Networks for Pattern Recognition
,
1993,
Adv. Comput..
[4]
C. Lee Giles,et al.
What Size Neural Network Gives Optimal Generalization? Convergence Properties of Backpropagation
,
1998
.
[5]
H. Fang,et al.
Global response approximation with radial basis functions
,
2006
.
[6]
Ruichen Jin,et al.
On Sequential Sampling for Global Metamodeling in Engineering Design
,
2002,
DAC 2002.
[7]
Jaroslav Haslinger.
Shape Optimization
,
2009,
Encyclopedia of Optimization.
[8]
Douglas C. Montgomery,et al.
Response Surface Methodology: Process and Product Optimization Using Designed Experiments
,
1995
.
[9]
Nielen Stander,et al.
On the robustness of a simple domain reduction scheme for simulation‐based optimization
,
2002
.
[10]
T. Simpson,et al.
Comparative studies of metamodeling techniques under multiple modeling criteria
,
2000
.
[11]
M. E. Johnson,et al.
Minimax and maximin distance designs
,
1990
.
[12]
A. E. Hoerl,et al.
Ridge regression: biased estimation for nonorthogonal problems
,
2000
.
[13]
Manolis Papadrakakis,et al.
Structural optimization using evolution strategies and neural networks
,
1998
.
[14]
S. Rippa,et al.
Numerical Procedures for Surface Fitting of Scattered Data by Radial Functions
,
1986
.