Multilevel model order reduction

We present a multilevel Model Order Reduction scheme for enhancing numerical analysis of electromagnetic fields by means of grid based techniques. The scheme allows one to create nested macromodels and combine macromodels with the Fast Frequency Sweep. The implementation of the method is illustrated on the Finite Difference Frequency Domain technique and efficient nodal order reduction algorithm (ENOR) but the concept can easily be applied also for other mesh based methods and other order reduction schemes.     

Least-squares moment matching reduction methods

It is shown how the two apparently different approaches to modelling reduction by least-squares time moment matching give identical results. This property also enables a clear understanding of how the method actually approximates the system. Computational savings are seen to be made by adopting the two-stage approach     

Least-squares design of higher order nonrecursive differentiators

A method is described that can be used to design non-recursive linear-phase higher order differentiators that can perform differentiation over any frequency range. The method is based on formulating the absolute mean-square error between the amplitude responses of the practical and ideal differentiator as a quadratic function. The coefficients of the differentiators are obtained by solving a set of linear equations. This method leads to a lower mean-square error and is computationally more efficient than both the eigenfilter method and the method based on the Remez exchange algorithm. Design of differentiators based on minimization of the relative mean-square error is also carried out. Finally, the method is extended to the design of frequency selective higher order differentiators     

Least-squares Pade reduction: A nonuniqueness property

It is shown that least-squares Pade reduced order models are not unique for a given order. Depending on which reduced denominator coefficient is chosen to be unity. The method is seen to minimise an error index over different subsets of system time moments when calculating this denominator     

An efficient terminal and model order reduction algorithm

The paper proposes an efficient terminal and model order reduction method for compact modeling of interconnect circuits with many terminals. The new method is inspired by the recently proposed terminal reduction method, SVDMOR [P. Feldmann, F. Liu, Sparse and efficient reduced order modeling of linear subcircuits with large number of terminals, in: Proceedings of the International Conference on Computer Aided Design (ICCAD), 2004, pp. 88-92]. But different from SVDMOR, the new method considers higher order moment information for terminal responses during the terminal reduction and separately applies singular value decomposition (SVD) on both input and output terminals for low-rank approximations. This is in contrast to the SVDMOR method where input and output terminal responses are approximated by SVD at the same time, which can lead to large errors when the numbers of inputs and outputs are quite different. We analyze the passivity requirements for SVD-based terminal and model order reduction and show that the combined passive terminal and MOR using SVD method will not lead an effective terminal reduction in general. Our experimental results show that the proposed ESVDMOR method outperforms the SVDMOR method in terms of accuracy for the same reduced model sizes when the numbers of input and output terminals are quite different.     

An aggregating based model order reduction method for power grids

Simulation of power girds has become increasingly computationally expensive. In this paper, we propose a Model Order Reduction (MOR) method for power grids by extending the existing Aggregating based MOR (AMOR) method. In the proposed method, besides resistors and capacitors, current sources are also aggregated to improve MOR efficiency. Moreover, pre-partition and parallelization techniques are employed to decrease reduction time. Numerical results demonstrate that compared to original circuits, the scale of power grids is greatly reduced without much loss of accuracy. The reduced-order models are especially useful in the multiple simulations of different working modes or different environment corners.     

人体头部过载模型阶次的辨识与降阶研究

针对在系统辨识过程中面临的人体头部过载模型阶次辨识问题,介绍了常用的模型阶次辨识方法及利用残差平方和即损失函数J估计模型阶次的原理,并基于20组试验数据开展人体头部过载模型阶次辨识研究。通过系统辨识获得了人体头部过载模型后,采用Gram阵对Hankel奇异值分解方法实施模型简化和降阶处理。通过比较降阶前后模型,表明模型降阶方法是有效和正确的。     

FIR filter order reduction: balanced model truncation andHankel-norm optimal approximation

Two different algorithms for approximating FIR by IIR filters are treated: truncation of the balanced model and the Hankel-norm optimal approximation. Both are assessed for approximation fidelity, as well as for intrinsic computational efficiency. Examples show surprisingly good relative performance of the balanced model truncation, suggesting that frequently this method will be operationally preferable     

Motor car acoustic response modelling and order reduction viabalanced model truncation

A novel practical application of the balanced model truncation (BMT) technique for the accurate and reduced order/complexity magnitude and phase modelling of the acoustic response of a motor car is described and demonstrated. The effectiveness and viability are illustrated through a sample car response modelling example     

Approach to model order reduction for angular response calculationsin periodic structures

A framework for implementing model order techniques for periodic structure analysis is presented. Appropriate choice of the problem formulation, in combination with straightforward Pade approximations, permit the entire angular response to be extrapolated from the solution at a single aspect angle     

Simple model order reduction by truncation with performance verification by fast digital simulation

The availability of fast interactive digital simulation to test the accuracy of low-order models has greatly increased the viability of trying simple truncation methods of model order reduction. The truncation technique is successfully applied in reducing a tenth-order analytical model of an electrode position controller to third-order.     

On a passivity of the Arnoldi based model order reduction forfull-wave electromagnetic modeling

Progress in MEMS and packaging design has made significant changes in the requirements for modeling tools. In order to design a modern microdevice or interconnect system it is no longer sufficient to limit the analysis to quasielectrostatic modeling due to smaller size and higher operation frequencies of the microdevices. On the other hand, a “full-wave” analysis produces huge systems of equations which require tremendous amounts of computational resources. Many model order reduction algorithms were developed in order to solve this problem. But the passivity of the reduced system is still an issue for “full-wave” models. This paper will describe the Arnoldi based model order reduction algorithm for “full-wave” electromagnetic analysis and will show that this algorithm preserves passivity of the reduced system     

Eigenvalue trim approach to exact order reduction for roesser state-space model of multidimensional systems

Multidimensional Systems and Signal Processing - In this paper, a new notion of eigenvalue trim or co-trim for n-D Roesser (state-space) model is first introduced, which reveals the internal...     

Program package for linear-system order reduction

A computer-program package for linear-system order reduction is presented for systems described by a scalar transfer function. It should be useful for system analysis and design purposes. The program is written in FORTRAN IV for use in a conversational mode on a PDP-9 (8k, 18 bit) computer.     

Least-squares model-based halftoning

A least-squares model-based (LSMB) approach to digital halftoning is proposed. It exploits both a printer model and a model for visual perception. It attempts to produce an optimal halftoned reproduction, by minimizing the squared error between the response of the cascade of the printer and visual models to the binary image and the response of the visual model to the original gray-scale image. It has been shown that the one-dimensional (1-D) least-squares problem, in which each row or column of the image is halftoned independently, can be implemented using the Viterbi algorithm to obtain the globally optimal solution. Unfortunately, the Viterbi algorithm cannot be used in two dimensions. In this paper, the two-dimensional (2-D) least-squares solution is obtained by iterative techniques, which are only guaranteed to produce a total optimum. Experiments show that LSMB halftoning produces better textures and higher spatial and gray-scale resolution than conventional techniques. We also show that the least-squares approach eliminates most of the problems associated with error diffusion. We investigate the performance of the LSMB algorithms over a range of viewing distances, or equivalently, printer resolutions. We also show that the LSMB approach gives us precise control of image sharpness.     

Multi-port dynamic compact thermal models of dual-chip package using model order reduction and metaheuristic optimization

Delphi-like boundary condition independent (BCI) compact thermal models (CTMs) are the standard for modelling single die packages. However their extraction, particularly in the transient case, will be time consuming due to complex numerical simulations for a large number of external conditions. Lately, new approaches to extract a BCI dynamical CTM (DCTM), based on model order reduction (MOR) were developed. Despite the numerous advantages of this recent method, the lack of numerical tools to integrate reduced-order models (ROM) makes it difficult to use at board level. In this study, a novel process flow for extracting Delphi-inspired BCI DCTMs is proposed. Thus a detailed three-dimensional model is replaced by a BCI-ROM model using FANTASTIC matrix reduction code to generate the data used in the creation of a Delphi-style BCI DCTM. That hybrid reduction method has been applied, at first on a single-chip package (QFN16) then on a dual-chip package (DFN12). Their derived CTM and DCTM have been compared in term of accuracy and creation time using, or not, MOR reduction technique. The results show that for a similar accuracy, the integration of MOR technique allows minimizing the time-consuming numerical simulations and consequently reduce the thermal network creation time by 80%.     

A novel elementary operation approach with Jordan transformation to order reduction for Roesser state-space model

This paper proposes a novel elementary operation approach to order reduction for the Roesser state-space model of multidimensional (n-D) systems by introducing a new kind of transformation, i.e., the Jordan transformation, which guarantees the establishment of an objective matrix with more general structure than the existing one. Then two basic order reduction techniques are developed which can overcome the difficulty encountered by the existing methods and reveal, for the first time, the fact that the order reduction is still possible even when the column (or row) blocks in the related n-D polynomial matrix are full rank. Furthermore, based on the Jordan transformation, an equivalence relationship between two Roesser models after using the elementary operations among the different blocks will be clarified. Although these operations do not directly lower the total order of the model, the partial orders can be changed so that it may nevertheless yield a possibility for further order reduction. It turns out that this new approach includes our previous elementary operation order reduction approach just as a special case. Examples are given to illustrate the details as well as the effectiveness of the proposed approach.