Tom Dhaene

Macromodeling of Multiport Systems Using a Fast Implementation of the Vector Fitting Method

Broadband macromodeling of large multiport systems by vector fitting can be time consuming and resource demanding when all elements of the system matrix share a common set of poles. This letter presents a robust approach which removes the sparsity of the block-structured least-squares equations by a direct application of the QR decomposition. A 60-port printed circuit board example illustrates that considerable savings in terms of computation time and memory requirements are obtained.

Orthonormal Vector Fitting: A Robust Macromodeling Tool for Rational Approximation of Frequency Domain Responses

Vector Fitting is widely accepted as a robust macromodeling tool for approximating frequency domain responses of complex physical structures. In this paper, the Orthonormal Vector Fitting technique is presented, which uses orthonormal rational functions to improve the numerical stability of the method. This reduces the numerical sensitivity of the system equations to the choice of starting poles significantly and limits the overall macromodeling time

Selection of lumped element models for coupled lossy transmission lines

A practical method is developed for selecting the minimal number of lumped elements needed to represent a lossy transmission line if a certain accuracy is desired in a well-defined frequency range. This method, which uses dimensionless transmission line parameters, can be used in a wide range of applications and is also extended to hybrid equivalent circuits, consisting of ideal single lossless lines and resistors. For completeness, a lumped element model for coupled lossy lines is presented which uses the same dimensionless parameters and the same criteria as proposed for single lines. An example of coupled transmission line structure including skin-effect losses illustrates the approach. >

A Novel Hybrid Sequential Design Strategy for Global Surrogate Modeling of Computer Experiments

Many complex real-world systems can be accurately modeled by simulations. However, high-fidelity simulations may take hours or even days to compute. Because this can be impractical, a surrogate model is often used to approximate the dynamic behavior of the original simulator. This model can then be used as a cheap, drop-in replacement for the simulator. Because simulations can be very expensive, the data points, which are required to build the model, must be chosen as optimally as possible. Sequential design strategies offer a huge advantage over one-shot experimental designs because they can use information gathered from previous data points in order to determine the location of new data points. Each sequential design strategy must perform a trade-off between exploration and exploitation, where the former involves selecting data points in unexplored regions of the design space, while the latter suggests adding data points in regions which were previously identified to be interesting (for example, highly nonlinear regions). In this paper, a novel hybrid sequential design strategy is proposed which uses a Monte Carlo-based approximation of a Voronoi tessellation for exploration and local linear approximations of the simulator for exploitation. The advantage of this method over other sequential design methods is that it is independent of the model type, and can therefore be used in heterogeneous modeling environments, where multiple model types are used at the same time. The new method is demonstrated on a number of test problems, showing that it is a robust, competitive, and efficient sequential design strategy.

Efficient space-filling and non-collapsing sequential design strategies for simulation-based modeling

Simulated computer experiments have become a viable cost-effective alternative for controlled real-life experiments. However, the simulation of complex systems with multiple input and output parameters can be a very time-consuming process. Many of these high-fidelity simulators need minutes, hours or even days to perform one simulation. The goal of global surrogate modeling is to create an approximation model that mimics the original simulator, based on a limited number of expensive simulations, but can be evaluated much faster. The set of simulations performed to create this model is called the experimental design. Traditionally, one-shot designs such as the Latin hypercube and factorial design are used, and all simulations are performed before the first model is built. In order to reduce the number of simulations needed to achieve the desired accuracy, sequential design methods can be employed. These methods generate the samples for the experimental design one by one, without knowing the total number of samples in advance. In this paper, the authors perform an extensive study of new and state-of-the-art space-filling sequential design methods. It is shown that the new sequential methods proposed in this paper produce results comparable to the best one-shot experimental designs available right now.

Advancements in Iterative Methods for Rational Approximation in the Frequency Domain

Rational approximation of frequency-domain responses is commonly used in electromagnetic transients programs for frequency-dependent modeling of transmission lines and to some extent, network equivalents (FDNEs) and transformers. This paper analyses one of the techniques [vector fitting (VF)] within a general iterative least-squares scheme that also explains the relation with the polynomial-based Sanathanan-Koerner iteration. Two recent enhancements of the original VF formulation are described: orthonormal vector fitting (OVF) which uses orthonormal functions as basis functions instead of partial fractions, and relaxed vector fitting (RVF), which uses a relaxed least-squares normalization for the pole identification step. These approaches have been combined into a single approach: relaxed orthonormal vector fitting (ROVF). The application to FDNE identification shows that ROVF offers more robustness and better convergence than the original VF formulation. Alternative formulations using explicit weighting and total least squares are also explored.

Adaptive CAD-model building algorithm for general planar microwave structures

A new adaptive technique is presented for building multidimensional parameterized analytical models for general planar microwave structures with a predefined accuracy and based on full-wave electromagnetic (EM) simulations. The models can be incorporated in a circuit simulator and the time required to calculate the circuit representation of a practical network is reduced by several orders of magnitude compared to full EM simulations. Furthermore, the accuracy of the results is significantly better compared to the circuit models used in state-of-the-art computer-aided design tools.

Robust Parametric Macromodeling Using Multivariate Orthonormal Vector Fitting

A robust multivariate extension of the orthonormal vector fitting technique is introduced for rational parametric macromodeling of highly dynamic responses in the frequency domain. The technique is applicable to data that is sparse or dense, deterministic or a bit noisy, and grid-based or scattered in the design space. For a specified geometrical parameter combination, a SPICE equivalent model can be calculated.

Efficient Multi-Objective Simulation-Driven Antenna Design Using Co-Kriging

A methodology for fast multi-objective antenna optimization is presented. Our approach is based on response surface approximation (RSA) modeling and variable-fidelity electromagnetic (EM) simulations. In the design process, a computationally cheap RSA surrogate model constructed from sampled coarse-discretization EM antenna simulations is optimized using a multi-objective evolutionary algorithm. The initially determined Pareto optimal set representing the best possible trade-offs between conflicting design objectives is then iteratively refined. In each iteration, a limited number of high-fidelity EM model responses are incorporated into the RSA model using co-kriging. The enhanced RSA model is subsequently re-optimized to yield the refined Pareto set. Combination of low- and high-fidelity simulations as well as co-kriging results in the low overall optimization cost. The proposed approach is validated using two UWB antenna examples.

A novel sequential design strategy for global surrogate modeling

In mathematical/statistical modeling of complex systems, the locations of the data points are essential to the success of the algorithm. Sequential design methods are iterative algorithms that use data acquired from previous iterations to guide future sample selection. They are often used to improve an initial design such as a Latin hypercube or a simple grid, in order to focus on highly dynamic parts of the design space. In this paper, a comparison is made between different sequential design methods for global surrogate modeling on a real-world electronics problem. Existing exploitation and exploration-based methods are compared against a novel hybrid technique which incorporates both an exploitation criterion, using local linear approximations of the objective function, and an exploration criterion, using a Monte Carlo Voronoi tessellation. The test results indicate that a considerable improvement of the average model accuracy can be achieved by using this new approach.