Showing papers on "Model order reduction published in 1997"

PRIMA: passive reduced-order interconnect macromodeling algorithm

Abstract: This paper describes PRIMA, an algorithm for generating provably passive reduced order N-port models for RLC interconnect circuits. It is demonstrated that, in addition to requiring macromodel stability, macromodel passivity is needed to guarantee the overall circuit stability once the active and passive driver/load models are connected. PRIMA extends the block Arnoldi technique to include guaranteed passivity. Moreover, it is empirically observed that the accuracy is superior to existing block Arnoldi methods. While the same passivity extension is not possible for MPVL, we observed comparable accuracy in the frequency domain for all examples considered. Additionally a path tracing algorithm is used to calculate the reduced order macromodel with the utmost efficiency for generalized RLC interconnects.

A block rational Arnoldi algorithm for multipoint passive model-order reduction of multiport RLC networks

Abstract: Recent work in the area of model-order reduction for RLC interconnect networks has been focused on building reduced-order models that preserve the circuit-theoretic properties of the network, such as stability, passivity, and synthesizability. Passivity is the one circuit-theoretic property that is vital for the successful simulation of a large circuit netlist containing reduced-order models of its interconnect networks. Non-passive reduced-order models may lead to instabilities even if they are themselves stable. In this paper, we address the problem of guaranteeing the accuracy and passivity of reduced-order models of multiport RLC networks at any finite number of expansion points. The novel passivity-preserving model-order reduction scheme is a block version of the rational Arnoldi algorithm. The scheme reduces to that of the PRIMA algorithm when applied to a single expansion point at zero frequency. Although the treatment of this paper is restricted to expansion points that are on the negative real axis, it is shown that the resulting passive reduced-order model is superior in accuracy to the one that would result from expanding the original model around a single point. Nyquist plots are used to illustrate both the passivity and the accuracy of the reduced-order models.

A block rational Arnoldi algorithm for multipoint passive model-order reduction of multiport RLC networks

Abstract: Work in the area of model-order reduction for RLC interconnect networks has focused on building reduced-order models that preserve the circuit-theoretic properties of the network, such as stability, passivity, and synthesizability (Silveira et al, 1996) Passivity is the one circuit-theoretic property that is vital for the successful simulation of a large circuit netlist containing reduced-order models of its interconnect networks Non-passive reduced-order models may lead to instabilities even if they are themselves stable We address the problem of guaranteeing the accuracy and passivity of reduced-order models of multiport RLC networks at any finite number of expansion points The novel passivity-preserving model-order reduction scheme is a block version of the rational Arnoldi algorithm (Ruhe, 1994) The scheme reduces to that of (Odabasioglu et al, 1997) when applied to a single expansion point at zero frequency Although the treatment of this paper is restricted to expansion points that are on the negative real axis, it is shown that the resulting passive reduced-order model is superior in accuracy to the one that would result from expanding the original model around a single point Nyquist plots are used to illustrate both the passivity and the accuracy of the reduced order models

On some simple, autoregression-based estimation and identification techniques for ARMA models

Abstract: SUMMARY We examine simple estimators for general ARMA models and a corresponding identification method. Both estimation and identification are based on a matrix formed from the coefficients of an autoregressive approximation to the process of interest. We show that a zero determinant of this matrix is necessary and sufficient for the existence of a common factor in autoregressive and moving average lag polynomials, and therefore for redundant parameters in the model. Simulation results suggest a close match between the empirical finite-sample distribution of the test statistic for model order reduction and its asymptotic distribution.

FastPep: a fast parasitic extraction program for complex three-dimensional geometries

Abstract: In this paper we describe a computationally efficient approach to generating reduced-order models from PEEC-based three-dimensional electromagnetic analysis programs. It is shown that a recycled multipole-accelerated approach applied to recent model order reduction techniques requires nearly two orders of magnitude fewer floating point operations than direct techniques thus allowing the analysis of larger, more complex three-dimensional geometries.

Convex invertible cones of state space systems

Abstract: In the paper [CL1] the notion of a convex invertible cone,cic, of matrices was introduced and its geometry was studied In that paper close connections were drawn between thiscic structure and the algebraic Lyapunov equation In the present paper the same geometry is extended to triples of matrices andcics of minimal state space models are defined and explored This structure is then used to study balancing, Hankel singular values, and simultaneous model order reduction for a set of systems State spacecics are also examined in the context of the so-called matrix sign function algorithm commonly used to solve the algebraic Lyapunov and Riccati equations

FastPep: a fast parasitic extraction program for complex three-dimensional geometries

Abstract: In this paper we describe a computationally efficient approach to generating reduced-order models from PEEC-based three-dimensional electromagnetic analysis programs. It is shown that a recycled multipole-accelerated approach applied to recent model order reduction techniques requires nearly two orders of magnitude fewer floating point operations than direct techniques thus allowing the analysis of larger, more complex three-dimensional geometries.

Generating reduced order models via PEEC for capturing skin and proximity effects

Abstract: In the past, model order reduction techniques have been successfully employed for 3-D PEEC (Partial Element Equivalent Circuit) interconnect models. This paper explores the difficulties in generating low order models when PEEC-like models include volume filaments to accurately capture skin and proximity effects.

Parameter-dependent model order reduction

Abstract: L In this paper we consider the optimal model reduction problem where the plant 2 model depends on parameters that are measurable. Such cases occur in many on-line as well as off-line applications and the question that arises is how to update the reduced order model without complete re-solution of the problem. A method of approximation of the updated reduced-order model, which is based on its series expansion, is given. A similar approach is used to develop a new algorithm for the numerical solution of the nominal problem. The algorithm compares well, in terms of computation effort and convergence properties, with homotopic methods which are the common way of solving the equations.

Efficient formulation and model-order reduction for the transient simulation of three-dimensional VLSI interconnect

Abstract: Accurately accounting for three-dimensional (3-D) geometry and distributed RC effects in on-chip interconnect is important for predicting crosstalk in memory cells, analog circuits, and regions of congested routing in digital circuits. In this paper we describe a multipole-accelerated, mixed surface-volume formulation, and a preconditioned model-order reduction algorithm for distributed RC, or electroquasistatic, simulation of 3-D integrated circuit interconnect. The difficulties arising from the ill conditioning inherent in the dynamic problem is effectively resolved by a combined surface-volume approach. Results are presented to demonstrate that the computational cost for extracting a complete reduced-order model is order N, where N is the number of surface unknowns. Finally, the multipole-accelerated code is used to investigate the accuracy of the one-dimensional diffusion equation for long RC lines.

µ Controllers: Mixed and Fixed

Abstract: A method is presented for synthesis of fixed order controllers with robustness to mixed real and complex uncertainties. The capabilities of the method are demonstrated on a two-mass/spring benchmark problem and on a flexible satellite example. Several fixed order mixed controllers are designed. A comparison with both full order and reduced order controllers indicates that the method is capable of synthesizing low order controllers achieving robust performance levels similar to full order designs, and superior to reduced order controllers.

Model Order Reduction by Selective Sensitivity

Abstract: Many industrial structures are represented by models with a large number of degrees of freedom, thus making their use complex and costly Model order reduction alleviates this problem by elaborating lower-dimensional models that satisfy some properties of the re® ned model We present a model order reduction procedure based on the concept of selective sensitivity This reduction method has the property of preserving energies and static or dynamic behaviors of the re® ned model in the reduced model while preserving the essence of its topology

A Finite Element, Reduced Order, Frequency Dependent Model of Viscoelastic Damping

Abstract: (ABSTRACT) This thesis concerns itself with a finite element model of nonproportional viscoelastic damping and its subsequent reduction. The Golla-Hughes-McTavish viscoelastic finite element has been shown to be an effective tool in modeling viscoelastic damping. Unlike previous models, it incorporates physical data into the model in the form of a curve fit of the complex modulus. This curve fit is expressed by minioscillators. The frequency dependence of the complex modulus is accounted for by the addition of internal, or dissipation, coordinates. The dissipation coordinates make the viscoelastic model several times larger than the original. The trade off for more accurate modeling of viscoelasticity is increased model size. Internally balanced model order reduction reduces the order of a state space model by considering the controllability/observability of each state. By definition, a model is internally balanced if its controllability and observability grammians are equal and diagonal. The grammians serve as a ranking of the controllability/observability of the states. The system can then be partitioned into most and least controllable/observable states; the latter can be statically reduced out of the system. The resulting model is smaller, but the transformed coordinates bear little resemblance to the original coordinates. A transformation matrix exists that transforms the reduced model back into original coordinates, and it is a subset of the transformation matrix leading to the balanced model. This whole procedure will be referred to as Yae's method within this thesis. By combining GHM and Yae's method, a finite element code results that models nonproportional viscoelastic damping of a clamped-free, homogeneous, Euler-Bernoulli beam, and is of a size comparable to the original elastic finite element model. The modal data before reduction compares well with published GHM results, and the modal data from the reduced model compares well with both. The error between the impulse response before and after reduction is negligible. The limitation of the code is that it cannot model sandwich beam behavior because it is based on Euler-Bernoulli beam theory; it can, however, model a purely viscoelastic beam. The same method, though, can be applied to more sophisticated beam models. Inaccurate results occur when modes with frequencies beyond the range covered by the curve fit appear in the model, or when poor data are used. For good data, and within the range modeled by the curve fit, the code gives accurate modal data and good impulse response predictions.

Model order reduction for optimal bounding ellipsoid channel models

Abstract: This paper presents a new algorithm for performing model order reduction for Volterra series channel models of high-density digital magnetic recording channels. We employ a set-membership approach to the problem in which a set of consistent modeling solutions bounded by an optimal ellipsoid is first developed for the channel. We then present a new algorithm for finding the minimum number of coefficients in the Volterra series expansion which preserves the accuracy, in a least-squares sense, of the reduced order model in comparison with the original model.

Reduction/expansion studies for damage identification of continuous aerospace structures

Abstract: Performing damage Identification on aerospace structures typically suggests large order models, high spatial density measurements (although significantly less dense than the models), high modal density data, and complicated loading conditions. Therefore, model order reduction and/or mode shape expansion are critical technologies which bridge the gap between the experimental data and the analytical models for such structures. In fact,the lack of insight and/or algorithms for reduction/expansion may be the primary roadblock to operational implementation of damage identification on a vast array of aerospace and civil structures. This observational study has looked at the processes of model order reduction and expansion for damage identification using three novel concepts. First, the processes of model order reduction, mode shape expansion, and damage identification are coupled problems which are studied and applied in an integrated fashion. It was concluded that a traditional reduction or expansion procedure can produce relatively large errors in exactly the parameters needed to locate damage, the dynamic residual. Second, a more complete reordering of the unmeasured, or omitted partition, has provided an increased understanding of the coupled problems listed above as well as the effects of sparsity-preserving reduction processes. Third, a series representation to the matrix inverse was used to preserve some of the original load path information in a reduced model using dynamic condensation. The objective of this study is to develop new understanding of the reduction/expansion process.

Convergence and Boundedness of Probability-One Homotopies for Model Order Reduction

Abstract: Committee Chairman: Layne T. Watson Mathematics (ABSTRACT) The optimal model reduction problem, whether formulated in the H 2 or H ∞ norm frameworks, is an inherently nonconvex problem and thus provides a nontrivial computational challenge. This study systematically examines the requirements of probability-one homotopy methods to guarantee global convergence. Homotopy algorithms for nonlinear systems of equations construct a continuous family of systems, and solve the given system by tracking the continuous curve of solutions to the family. The main emphasis is on guaranteeing transversality for several homotopy maps based upon the pseudogramian formulation of the optimal projection equations and variations based upon canonical forms. These results are essential to the probability-one homotopy approach by guaranteeing good numerical properties in the computational implementation of the homotopy algorithms. ACKNOWLEDGEMENTS. I would like to take this opportunity to express my deepest appreciation to my major advisor, Dr. Layne T. Watson, for his excellent guidance, timely advice and encouragement during the entire course of this project. I especially thank him for the immeasurable amount of time he has devoted. Without his support, the achievement of this research would be impossible. I would like to thank Dr. Dennis Bernstein for his help to enhance this study and great effort in preparing this dissertation. Appreciation must also be expressed to Dr. Joseph Ball for his valuable advice on determining the research emphasis, and his conscientious counsels and suggestion. I also would like to express my thanks to Drs. for serving on my graduate committee and, for the time and efforts they have devoted to overseeing my doctoral work. Special thanks to Dr. William Greenberg who initiated me into the graduate study in the Department of Mathematics at Virginia Tech and helped me to get through all of the " hoops " to complete this joint project. His genuine friendship and help has been a source of strength and wisdom. I am extremely grateful to my father, Professor Lin Wang, for inspiring the desire to learn and the strength to achieve in both the path of study and the course of life. Although a return of his love and dedication would be surely impossible, I would like to say " Thanks father, here is your daughter who is dedicating this thesis, as well as all of her achievement to you ". Appreciation is extended to all individuals for their support and friendship which made this work possible …

Coupled Circuit-Interconnect Modeling and Simulation

Abstract: In this paper we discuss generating low order models for efficient coupled circuit-interconnect simulation. The ever increasing speeds and shrinking feature sizes that are typical of state of the art integrated circuits designs have made coupling due to interconnect and packaging a very important, sometimes dominant, factor in system performance. The ability to efficiently perform coupled circuit-interconnect simulation before fabrication is essential in order to detect signal degradation due to delays or crosstalk. We first discuss methods of generating models for both two and three dimensional interconnect and then present a general, guaranteed-stable, model order reduction technique to reduce the order of the interconnect models.