Order of experimentation for metamodeling tasks

The order in which measurements are carried out, determines the accuracy of models in early stages of the measurement process, i.e. while measurements are still in progress. Reliable models in early stages of the data acquisition phase allow for model-based investigations like optimization runs or an earlier switching to an active learning phase. This paper compares different methods to determine the order of experimentation for regression problems in metamodeling tasks. The data distribution and the data density in the input space are varied for several randomly generated synthetic functions in order to find the most promising determination strategy for the order of experimentation. As an application example, all strategies are also applied to a computational fluid dynamics (CFD) metamodel. The order of experimentation based on the intelligent k-means clustering algorithm turns out to be the best overall order-determination strategy.

[1]  O. Nelles.  Axes-oblique partitioning strategies for local model networks , 2006, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.

[2]  S. Töpfer.  Approximation nichtlinearer Prozesse mit Hinging Hyperplane Baummodellen (Approximation of Nonlinear Processes with Hinging Hyperplane Trees) , 2002 .

[3]  Oliver Nelles,et al.  Extended Deterministic Local Search Algorithm for Maximin Latin Hypercube Designs , 2015, 2015 IEEE Symposium Series on Computational Intelligence.

[4]  Oliver Nelles,et al.  Proposal for a function generator and extrapolation analysis , 2015, 2015 International Symposium on Innovations in Intelligent SysTems and Applications (INISTA).

[5]  Marco Wiering,et al.  2011 INTERNATIONAL JOINT CONFERENCE ON NEURAL NETWORKS (IJCNN) , 2011, IJCNN 2011.

[6]  H. Niederreiter.  Low-discrepancy and low-dispersion sequences , 1988 .

[7]  Tatiana Tambouratzis.  Counter-clustering for Training Pattern Selection , 2000, Comput. J..

[8]  T. Simpson,et al.  Computationally Inexpensive Metamodel Assessment Strategies , 2002 .

[9]  S. Ernst,et al.  Hinging hyperplane trees for approximation and identification , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[10]  G. G. Wang,et al.  Metamodeling for High Dimensional Simulation-Based Design Problems , 2010 .

[11]  Leo Breiman,et al.  Hinging hyperplanes for regression, classification, and function approximation , 1993, IEEE Trans. Inf. Theory.

[12]  Boris Mirkin,et al.  Clustering For Data Mining: A Data Recovery Approach (Chapman & Hall/Crc Computer Science) , 2005 .

[13]  Hisham Hilow.  Comparison among run order algorithms for sequential factorial experiments , 2013, Comput. Stat. Data Anal..

[14]  Oliver Nelles,et al.  Aerodynamic Optimization of Centrifugal Fans Using CFD-Trained Meta-Models , 2016 .

[15]  Sonja Kuhnt,et al.  Design and analysis of computer experiments , 2010 .

[16]  X. Tort-Martorell,et al.  Experimentation order in factorial designs: new findings , 2012 .

[17]  Oliver Nelles,et al.  Model-based design of experiments based on local model networks for nonlinear processes with low noise levels , 2011, Proceedings of the 2011 American Control Conference.