Wouter Hendrickx

A discussion of "Rational approximation of frequency domain responses by vector fitting"

Vector fitting (VF) is a popular iterative rational approximation technique for sampled data in the frequency domain. VF is nowadays widely investigated and used in the Power Systems and Microwave Engineering communities. The VF methodology is recognized as an elegant version of the Sanathanan-Koerner iteration with a well-chosen basis.

Sequential design and rational metamodelling

Metamodelling techniques are used in many engineering applications for efficient exploration of the design space of complex deterministic simulation systems, and for optimisation purposes and sensitivity analysis. This paper presents a new sequential design and rational metamodelling technique which combines adaptive modelling and sampling algorithms.

Some Remarks on the Vector Fitting Iteration

Vector Fitting (VF) is an iterative technique to construct rational approximations based on multiple frequency domain samples, introduced by Gustavsen and Semlyen [1, 3]. VF is nowadays widely investigated and used in the Power Systems and Microwave Engineering communities. Numerical experiments show that VF has favorable convergence properties. However, so far, no theoretical proof for its convergence, or conditions to guarantee convergence, have been published. This paper gives a description of a general iterative Least-Squares framework for rational approximation and shows that VF fits into this framework.

Adaptive distributed metamodeling

Simulating and optimizing complex physical systems is known to be a task of considerable time and computational complexity. As a result, metamodeling techniques for the efficient exploration of the design space have become standard practice since they reduce the number of simulations needed. However, conventionally such metamodels are constructed sequentially in a one-shot manner, without exploiting inherent parallelism. To tackle this inefficient use of resources we present an adaptive framework where modeler and simulator interact through a distributed environment, thus decreasing model generation and simulation turnaround time. This paper provides evidence that such a distributed approach for adaptive sampling and modeling is worthwhile investigating. Research in this new field can lead to even more innovative automated modeling tools for complex simulation systems.

Grid enabled sequential design and adaptive metamodeling

Metamodeling is emerging as a valuable new tool in simulation: complex computer codes can be approximated by surrogate models (analytic, neural network, SVM, etc.) which can easily be evaluated on-the-fly. Adaptive modeling and sequential design further improve the performance of metamodeling frameworks. Grid computing quickly replaces regular cluster computing when it comes to complex calculations. Several efforts use grid computing to facilitate the exploration of simulator outputs. This contribution combines adaptive modeling and sequential design with distributed, grid-based techniques into one metamodeling framework

Magnitude Vector Fitting to interval data

Vector Fitting is an effective technique for rational approximation of LTI systems. It has been extended to fit the magnitude of the transfer function in absence of phase data. In this paper, magnitude Vector Fitting is modified to work on inequalities which the magnitude of the transfer function has to satisfy, instead of least squares approximation. The new interval version of the magnitude Vector Fitting is proved valuable for multiband filter design and the fitting of noisy magnitude spectra.

Integrating Gridcomputing and Metamodeling

Simulation and optimization of complex mechanical and electronical systems is a very time consuming and computationally intensive task. Therefore, metamodeling techniques are often used for the efficient exploration of the design space, as they reduce the number of simulations needed. However, constructing such metamodels (or surrogate models) is typically done in a sequential fashion. In this paper we argue that this approach can still be improved. We propose a framework where modeler and simulator interact through a distributed environment, (using established grid computing techniques) thus decreasing model generation and simulation turnaround time.

Meta-modelling of microwave devices with rational functions and radial basis functions

A new versatile meta-modelling framework is presented that automatically generates accurate and compact meta-models for passive electrical components. Meta-models or surrogate models are scalable analytical models that mimic the component behaviour over a user-defined design space (consisting of frequency and layout parameters). Both multivariable rational models and radial basis function models can be used to build the meta-models.