Advances in Radio Science www.adv-radio-sci.net 1684-9965 1684-9973 6 Kleinheubacher Berichte 2007 2008 10.5194/ars-6-139-2008 http://www.adv-radio-sci.net/6/139/2008/ http://www.adv-radio-sci.net/6/139/2008/ars-6-139-2008.html http://www.adv-radio-sci.net/6/139/2008/ars-6-139-2008.pdf 139 143 2008-05-26 Macro-modelling via radial basis functionen nets C. Wiegand christopher.wiegand@pb.izm.fraunhofer.de C. Fischer R. Kazemzadeh C. Hedayat W. John U. Hilleringmann University of Paderborn, Department of Electrical Engineering, Sensor Technology Group, Germany Fraunhofer Institute for Reliability and Microintegration (IZM) Advanced System Engineering (ASE), Paderborn, Germany Leibniz University of Hannover Institute of Electromagnetic Theory (TET), Hannover, Germany By the rising complexity and miniaturisation of the device's dimensions, the density of the conductors increases considerably. Referring to this, locally transient interactions between single physical values become apparent. Therefore, for the investigation and optimisation of integrated circuits it is essential to develop suitable models and simulation surroundings which allow for memory and time-efficient calculation of the behaviour. By means of the dynamic reconstruction theory and the radial basis functions nets the so-called black box models are provided. The description of black box models is derived from the input and output behaviour or so-called time series of a dynamic system. Concerning the time series, the black box model adapts its parameters via the extended Kalman filter. This paper provides a modelling approach that enables fast and efficient simulations. Chen, S., Billings, S. A., Cowan, C. F. N., and Grant, P. M.: Non-linear system identification using radial basis functions, Int. J. Control, 21, 2513-2539, 1990a. Chen, S., Billings, S. A., Cowan, C. F. N., and Grant, P. M.: Practical identification of NARMAX models using radial basis functions, Int. J. Control, 52, 1327-1350, 1990b. Chen, S., Chng, E. S., and Alkadhimi, K.: Regularized orthogonal least squares algorithm for constructing radial basis function networks, Int. J. Control, 64, 829-837, 1996. Haykin, S.: Kalman Filtering and Neural Networks, John Wiley & Sons, Inc., New York, Chichester, Weinheim, Brisbane, Singapore, Toronto, 2001. Howlett, R. J. and Jain, L. C.: Radial Basis Funcrion Networks 1 – Recent Developments in Theory and Application, Physica-Verlag, 2001a. Howlett, R. J. and Jain, L. C.: Radial Basis Funcrion Networks 2 – New Advances in Design, Physica-Verlag, 2001b. Sauer, T., Yorke, J. A., and Casdagli, M.: Embedology, J. Stat. Phys., 65, 579-616, 1991. Sing, J. K., Basu, D. K., Nasipuri, M., and Kundu, M.: Improved K-means Algorithm in the Design of RBF Neural Networks, TENCON 2003, Conference on Convergent Technologies for Asia-Pacific Region, 2, 841-845, 2003. Stievano, I. S., Maio, I. A., and Canavero, F. G.: Parametric Macromodels of Digital I/O Ports, IEEE T. Adv. Packaging, Special Selection on EPEP01, 25(2), 255–264, 2002. Wiegand, C., Hedayat, C., John, W., Radic-Weissenfeld, L., and Hilleringmann, U.: Nonlinear Identification of Complex Systems using Radial Basis Function Networks and Model Order Reduction, IEEE International Symposium on EMC, Honolulu Hawaii, USA, 2007a. Wiegand, C., Radic-Weissenfeld, L., Hedayat, C., John, W.: Black Box Model and Singular Value Based Model Order Reduction, 18th International Zurich Symposium on EMC, 2007b. Ahmida, Z. and Charef, A.: Nonlinear Systems Modelling Using RBF Neural Networks: A Ransdom Learning Approach to the Resource Allocating Network Algorithm, Proceedings if the 10th Mediterranean Conference on Control and Automation, 2002.