Dirk Deschrijver

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

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.

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.

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.

Fast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimization

The use of surrogate based optimization (SBO) is widely spread in engineering design to reduce the number of computational expensive simulations. However, “real-world” problems often consist of multiple, conflicting objectives leading to a set of competitive solutions (the Pareto front). The objectives are often aggregated into a single cost function to reduce the computational cost, though a better approach is to use multiobjective optimization methods to directly identify a set of Pareto-optimal solutions, which can be used by the designer to make more efficient design decisions (instead of weighting and aggregating the costs upfront). Most of the work in multiobjective optimization is focused on multiobjective evolutionary algorithms (MOEAs). While MOEAs are well-suited to handle large, intractable design spaces, they typically require thousands of expensive simulations, which is prohibitively expensive for the problems under study. Therefore, the use of surrogate models in multiobjective optimization, denoted as multiobjective surrogate-based optimization, may prove to be even more worthwhile than SBO methods to expedite the optimization of computational expensive systems. In this paper, the authors propose the efficient multiobjective optimization (EMO) algorithm which uses Kriging models and multiobjective versions of the probability of improvement and expected improvement criteria to identify the Pareto front with a minimal number of expensive simulations. The EMO algorithm is applied on multiple standard benchmark problems and compared against the well-known NSGA-II, SPEA2 and SMS-EMOA multiobjective optimization methods.

Stochastic Modeling-Based Variability Analysis of On-Chip Interconnects

In this paper, a novel stochastic modeling strategy is constructed that allows assessment of the parameter variability effects induced by the manufacturing process of on-chip interconnects. The strategy adopts a three-step approach. First, a very accurate electromagnetic modeling technique yields the per unit length (p.u.l.) transmission line parameters of the on-chip interconnect structures. Second, parameterized macromodels of these p.u.l. parameters are constructed. Third, a stochastic Galerkin method is implemented to solve the pertinent stochastic telegraphers equations. The new methodology is illustrated with meaningful design examples, demonstrating its accuracy and efficiency. Improvements and advantages with respect to the state-of-the-art are clearly highlighted.

Efficient Algorithm for Passivity Enforcement of

This paper presents an efficient and robust algorithm for passivity enforcement of S -parameter-based macromodels. The method computes updated values of the model residues by least squares fitting of nonpassive residuals of the scattering matrix. Several examples show that the proposed method yields accurate passive macromodels at a limited computational cost.

S

This paper presents a robust technique for the macromodeling of time-domain and frequency-domain responses, which are parameterized by one or more design variables. The representation of the multivariate macromodel ensures that stability of the transfer function poles is enforced by construction. Passivity of the parametric macromodel can be enforced in a post-processing step by perturbation of barycentric weights.

-Parameter-Based Macromodels

The increasing operating frequencies in modern designs call for broadband macromodeling techniques. The problem of computing high-accuracy simulation models for high-speed interconnects is of great importance in the modeling arena. Nowadays, many full-wave numerical techniques are available that provide high accuracy, often at a significant cost in terms of memory storage and computing time. Furthermore, designers are usually only interested in a few electrical quantities such as port voltages and currents. So, model order reduction techniques are commonly used to achieve accurate results in a reasonable time. This paper presents a new technique, based on the partial element equivalent circuit method, which allows to generate reduced-order models by adaptively selecting the complexity (order) of the macromodel and suitable frequency samples. Thus, the proposed algorithm allows to limit the computing time while preserving the accuracy. Validation examples are given.