Benefits and Application of Tree Structures in Gaussian Process Models to Optimize Magnetic Field Shaping Problems
Recent years have witnessed the development of powerful numerical methods to emulate realistic physical systems and their integration into the industrial product development process. Today, finite element simulations have become a standard tool to help with the design of technical products. However, when it comes to multivariate optimization, the computation power requirements of such tools can often not be met when working with classical algorithms. As a result, a lot of attention is currently given to the design of computer experiments approach. One goal of this work is the development of a sophisticated optimization process for simulation based models. Within many possible choices, Gaussian process models are most widely used as modeling approach for the simulation data. However, these models are strongly based on stationary assumptions that are often not satisfied in the underlying system. In this work, treed Gaussian process models are investigated for dealing with non-stationarities and compared to the usual modeling approach. The method is developed for and applied to the specific physical problem of the optimization of 1D magnetic linear position detection.
KeywordsGaussian process surrogates Non-stationarity Simulation data Tree models
This work is part of the Competence Centre ASSIC, which is funded within the R&D Program COMET - Competence Centers for Excellent Technologies by the Federal Ministries of Transport, Innovation and Technology (BMVIT), of Economics and Labor (BMWA). The funding program is managed on their behalf by the Austrian Research Promotion Agency (FFG), the Austrian provinces Carinthia and Styria provide additional funding.
- 5.Fang, K.-T. Li, R. Sudjianto A.: Design and Modeling for Computer Experiments. Chapman & Hall/CRC (2006)Google Scholar
- 7.Johnson, S.G.: The nlopt nonlinear-optimization package. http://ab-initio.mit.edu/nlop (2008). Accessed 25 Nov 2015
- 9.Ortner, M.: Improving magnetic linear position measurement by field shaping. In: Conference proceedings - The 9th International Conference on Sensing Technology, Auckland, New Zealand, Dec. 8–Dec. 10 2015Google Scholar
- 10.Paciorek, C.J.: Nonstationary Gaussian Processes for Regression and Spatial Modelling. Ph.D thesis, Carnegie Mellon University (2003)Google Scholar
- 11.Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning. The MIT Press (2006)Google Scholar
- 15.Simpson, T.W., Lin, D.K.J., Chen, W.: Sampling strategies for computer experiments: design and analysis. Int. J. Reliab. Appl. 2, 209–240 (2001)Google Scholar