Showing papers on "Model order reduction published in 2006"

Model-order reduction using variational balanced truncation with spectral shaping

Abstract: This paper presents a spectrally weighted balanced truncation (SBT) technique for tightly coupled integrated circuit interconnects, when the interconnect circuit parameters change as a result of statistical variations in the manufacturing process. The salient features of this algorithm are the inclusion of the parameter variation in the RLCK interconnect, the guaranteed passivity of the reduced transfer function, and the availability of provable spectrally weighted error bounds for the reduced-order system. This paper shows that the variational balanced truncation technique produces reduced systems that accurately follow the time- and frequency-domain responses of the original system when variations in the circuit parameters are taken into consideration. Experimental results show that the new variational SBT attains, in average, 30% more accuracy than the variational Krylov-subspace-based model-order reduction techniques.

On the Selection of Spectral Zeros for Generating Passive Reduced Order Models

Abstract: As process technology continues to scale into the nanoscale regime, passive components and interconnect plays an ever increasing role in realization of mixed-signal systems. In this paper, the authors develop a new method for the model order reduction of passive components and interconnect using frequency selective projection methods with interpolation points based on the spectral-zeros of the RLC interconnect model's transfer function. The methodology uses imaginary part of the spectral zeros for frequency selective adaptive projection and provides stable as well as passive reduced order models. The results indicate that our method provides more accurate approximations than techniques based on balanced truncation and moment matching

Model order reduction of linear networks with massive ports via frequency-dependent port packing

Abstract: Model order reduction has been a driving force for reducing analysis complexity of VLSI systems containing large linear networks. However, most existing reduction techniques are only applicable to networks with a small number of ports, failing to fulfill an even stronger need of reducing massively interconnected subsystems such as power grids and wide buses. In this paper, a port packing scheme is presented wherein the correlation between circuit ports is explored in a frequency-dependent manner. In the proposed McPack (multiport circuit packing) algorithm, port packing is combined with a practical realization of the recently developed tangential interpolation scheme for model reduction. McPack performs feasible moment matching for networks with many ports in the sense of tangential interpolation. With guaranteed passivity, extensibility to multi-point expansion as well as comparable complexity, McPack systematically introduces frequency-domain port packing into the existing projection-based model order reduction framework. For several large networks with high port count, the presented algorithm is shown to be significantly more accurate than the standard block-moment matching algorithm as well as other recently developed alternative.

Model order reduction for large scale engineering models developed in ANSYS

Abstract: We present the software mor4ansys that allows engineers to employ modern model reduction techniques to finite element models developed in ANSYS. We focus on how one extracts the required information from ANSYS and performs model reduction in a C++ implementation that is not dependent on a particular sparse solver. We discuss the computational cost with examples related to structural mechanics and thermal finite element models.

Macromodel Generation for BioMEMS Components Using a Stabilized Balanced Truncation Plus Trajectory Piecewise-Linear Approach

Abstract: In this paper, we present a technique for automatically extracting nonlinear macromodels of biomedical microelectromechanical systems devices from physical simulation. The technique is a modification of the recently developed trajectory piecewise-linear approach, but uses ideas from balanced truncation to produce much lower order and more accurate models. The key result is a perturbation analysis of an instability problem with the reduction algorithm, and a simple modification that makes the algorithm more robust. Results are presented from examples to demonstrate dramatic improvements in reduced model accuracy and show the limitations of the method.

Dynamic patterns and model order reduction in small-signal models of doubly fed induction generators for wind power applications

Abstract: This paper investigates the dynamic patterns that arise in the small-signal models of doubly fed induction generators for wind power applications. Dynamic patterns are associations between eigenvalues and state variables of linear dynamic systems that can be identified using participation factors. Based on the identified dynamic patterns, reduced order models are proposed and compared with detailed models.

On symbolic model order reduction

Abstract: Symbolic model order reduction (SMOR) is a macromodeling technique that generates reduced-order models while retaining the parameters in the original models. Such symbolic reduced-order models can be repeatedly simulated with a greater efficiency for varying model parameters. Although the model-order-reduction concept has been extensively developed in literature and widely applied in a variety of problems, model order reduction from a symbolic perspective has not been well studied. Several methods developed in this paper include symbol isolation, nominal projection, and first-order approximation. These methods can be applied to models having only a few parametric elements and to models having many symbolic elements. Of special practical interest are models that have slightly varying parameters such as process related variations, for which efficient reduction procedures can be developed. Each technique proposed in this paper has been tested by circuit examples. Experiments show that the proposed methods are efficient and effective for many circuit problems

Fast interval-valued statistical modeling of interconnect and effective capacitance

Abstract: Correlated interval representations of range uncertainty offer an attractive solution to approximating computations on statistical quantities. The key idea is to use finite intervals to approximate the essential mass of a probability density function (pdf) as it moves through numerical operators; the resulting compact interval-valued solution can be easily interpreted as a statistical distribution and efficiently sampled. This paper first describes improved interval-valued algorithms for asymptotic wave evaluation (AWE)/passive reduced-order interconnect macromodeling algorithm (PRIMA) model order reduction for tree-structured interconnect circuits with correlated resistance, inductance, and capacitance (RLC) parameter variations. By moving to a much faster interval-valued linear solver based on path-tracing ideas, and making more optimal tradeoffs between interval- and scalar-valued computations, the delay statistics roughly 10/spl times/ faster than classical Monte Carlo (MC) simulation, with accuracy to within 5% can be extracted. This improved interval analysis strategy is further applied in order to build statistical effective capacitance (C/sub eff/) models for variational interconnect, and show how to extract statistics of C/sub eff/ over 100/spl times/ faster than classical MC simulation, with errors less than 4%.

Fast analysis of structured power grid by triangularization based structure preserving model order reduction

Abstract: In this paper, a triangularization based structure preserving (TBS) model order reduction is proposed to verify power integrity of on-chip structured power grid. The power grid is represented by interconnected basic blocks according to current density, and basic blocks are further clustered into compact blocks, each with a unique pole distribution. Then, the system is transformed into a triangular system, where compact blocks are in its diagonal and the system poles are determined only by the diagonal blocks. Finally, projection matrices are constructed and applied for compact blocks separately. The resulting macromodel has more matched poles and is more accurate than the one using flat projection. It is also sparse and enables a two-level analysis for simulation time reduction. Compared to existing approaches, TBS in experiments achieves up to 133/spl times/ and 109/spl times/ speedup in macromodel building and simulation respectively, and reduces waveform error by 33/spl times/.

Resampling Plans for Sample Point Selection in Multipoint Model-Order Reduction

Abstract: Multipoint projection methods have gained much notoriety in model-order reduction of linear, nonlinear, and parameter-varying systems. A well-known difficulty with such methods lies in the need for clever point selection to attain model compactness and accuracy. In this paper, the authors present a method for sample point selection in multipoint projection-based model-order reduction. The proposed technique, which is borrowed from the statistical modeling area, is based on resampling schemes to estimate error and can be coupled with recently proposed order reduction schemes to efficiently produce accurate models. Two alternative implementations are presented: 1) a rigorous linear-matrix-inequality-based technique and 2) a simpler, more efficient, heuristic search. The goal of this paper is to answer two questions. First, can this alternative metric be effective in selecting sample points in the sense of placing points in regions of high error without recourse to evaluation of the larger system? Second, if the metric is effective in this sense, under what conditions are substantial improvements in the model reduction efficiency achieved? Results are shown that indicate that the metric is indeed effective in a variety of settings, therefore opening the possibility for performing adaptive error control

Wideband passive multiport model order reduction and realization of RLCM circuits

Abstract: This paper presents a novel compact passive modeling technique for high-performance RF passive and interconnect circuits modeled as high-order resistor-inductor-capacitor-mutual inductance circuits. The new method is based on a recently proposed general s-domain hierarchical modeling and analysis method and vector potential equivalent circuit model for self and mutual inductances. Theoretically, this paper shows that s-domain hierarchical reduction is equivalent to implicit moment matching at around s=0 and that the existing hierarchical reduction method by one-point expansion is numerically stable for general tree-structured circuits. It is also shown that hierarchical reduction preserves the reciprocity of passive circuit matrices. Practically, a hierarchical multipoint reduction scheme to obtain accurate-order reduced admittance matrices of general passive circuits is proposed. A novel explicit waveform-matching algorithm is proposed for searching dominant poles and residues from different expansion points based on the unique hierarchical reduction framework. To enforce passivity, state-space-based optimization is applied to the model order reduced admittance matrix. Then, a general multiport network realization method to realize the passivity-enforced reduced admittance based on the relaxed one-port network synthesis technique using Foster's canonical form is proposed. The resulting modeling algorithm can generate the multiport passive SPICE-compatible model for any linear passive network with easily controlled model accuracy and complexity. Experimental results on an RF spiral inductor and a number of high-speed transmission line circuits are presented. In comparison with other approaches, the proposed reduction is as accurate as passive reduced-order interconnect macromodeling algorithm in the high-frequency domain due to the enhanced multipoint expansion, but leads to smaller realized circuit models. In addition, under the same reduction ratio, realized models by the new method have less error compared with reduced circuits by time-constant-based reduction techniques in time domain.

Two Algorithms for Fast and Accurate Passivity-Preserving Model Order Reduction

Abstract: This paper presents two recently developed algorithms for efficient model order reduction. Both algorithms enable the fast solution of continuous-time algebraic Riccati equations (CAREs) that constitute the bottleneck in the passivity-preserving balanced stochastic truncation (BST). The first algorithm is a Smith-method-based Newton algorithm, called Newton/Smith CARE, that exploits low-rank matrices commonly found in physical system modeling. The second algorithm is a project-and-balance scheme that utilizes dominant eigenspace projection, followed by a simultaneous solution of a pair of dual CAREs through completely separating the stable and unstable invariant subspaces of a Hamiltonian matrix. The algorithms can be applied individually or together. Numerical examples show the proposed algorithms offer significant computational savings and better accuracy in reduced-order models over those from conventional schemes

Rational Krylov for eigenvalue computation and model order reduction

Abstract: A rational Krylov algorithm for eigenvalue computation and model order reduction is described. It is shown how to implement it as a modified shift-and-invert spectral transformation Arnoldi decomposition. It is shown how to do deflation, locking converged eigenvalues and purging irrelevant approximations. Computing reduced order models of linear dynamical systems by moment matching of the transfer function is considered. Results are reported from one illustrative toy example and one practical example, a linear descriptor system from a computational fluid dynamics application.

Compact modeling and fast simulation of on-chip interconnect lines

Abstract: An efficient methodology to extract compact models for microstrip lines on lossy silicon substrate is presented. The transversal magnetic field equations are solved by dual finite integration technique (dFIT), a numerical method which allows the accuracy control of the computed frequency dependent line parameters. Several techniques are used to accelerate the process of p.u.l. parameters extraction, such as minimal virtual boundary, minimal mesh and minimal frequency samples set. The solution of the transmission line equations with frequency dependent parameters is then approximated by a rational function of appropriate degree in order to extract the compact model and its SPICE equivalent circuit. The behavior of the obtained compact model of order 10 shows good agreement with respect to the measured data

Modelling requirements for the design of active stability control strategies for a high speed bogie

Abstract: The paper presents the findings of a study on active stability control and simulation for a railway bogie vehicle. For control design a plan-view partial railway vehicle model is described. This is a simplified model derived from research experience and appropriate modelling, and a frequency domain analysis illustrates the problems associated with system instability. A multi-body dynamics software, SIMPACK is used to generate a detailed non-linear full vehicle model for simulation and control assessment. Model order reduction methods, both empirically and analytically based, are used to simplify the linear model generated from SIMPACK for further system analysis and control designs based upon the complex model. Comparisons between the simplified plan-view model and the exported reduced-order model are presented.

Progress in industrial mathematics at ECMI 2004

Abstract: Theme: Aerospace.- The MEGAFLOW Project - Numerical Flow Simulation for Aircraft.- Gradient Computations for Optimal Design of Turbine Blades.- Fast Numerical Computing for a Family of Smooth Trajectories in Fluids Flow.- Optimal Control of an ISS-Based Robotic Manipulator with Path Constraints.- Rigorous Analysis of Extremely Large Spherical Reflector Antennas: EM Case.- Theme: Electronic Industry.- Simulation and Measurement of Interconnects and On-Chip Passives: Gauge Fields and Ghosts as Numerical Tools.- Eigenvalue Problems in Surface Acoustic Wave Filter Simulations.- Diffraction Grating Theory with RCWA or the C Method.- Relocation of Electric Field Domains and Switching Scenarios in Superlattices.- Quantum Kinetic and Drift-Diffusion Equations for Semiconductor Superlattices.- Model Order Reduction of Nonlinear Dynamical Systems.- Electrolyte Flow and Temperature Calculations in Finite Cylinder Caused by Alternating Current.- Numerical Simulation of the Problem Arising in the Gyrotron Theory.- A Deterministic Multicell Solution to the Coupled Boltzmann-Poisson System Simulating the Transients of a 2D-Silicon MESFET.- Some Remarks on the Vector Fitting Iteration.- Krylov Subspace Methods in the Electronic Industry.- On Nonlinear Iteration Methods for DC Analysis of Industrial Circuits.- Implementing Efficient Array Traversing for FDTD-lumped Element Cosimulation.- Thermal Modeling of Bottle Glass Pressing.- Simulation of Pulsed Signals in MPDAE-Modelled SC-Circuits.- A More Efficient Rigorous Coupled-Wave Analysis Algorithm.- Iterative Solution Approaches for the Piezoelectric Forward Problem.- Hydrodynamic Modeling of an Ultra-Thin Base Silicon Bipolar Transistor.- Warped MPDAE Models with Continuous Phase Conditions.- Exact Closure Relations for the Maximum Entropy Moment System in Semiconductor Using Kane's Dispersion Relation.- Reduced Order Models for Eigenvalue Problems.- DRK Methods for Time-Domain Oscillator Simulation.- Digital Linear Control Theory Applied To Automatic Stepsize Control In Electrical Circuit Simulation.- Theme: Chemical Technology.- On the Dynamics of a Bunsen Flame.- Index Analysis for Singular PDE Models of Fuel Cells.- On the Modeling of the Phase Separation of a Gelling Polymeric Mixture.- Iso-Surface Analysis of a Turbulent Diffusion Flame.- A Simplified Model for Non-Isothermal Crystallization of Polymers.- Numerical Simulation of Cylindrical Induction Heating Furnaces.- Thermal Radiation Effect on Thermal Explosion in a Gas Containing Evaporating Fuel Droplets..- Local Defect Correction for Laminar Flame Simulation.- Development of a Hierarchical Model Family for Molten Carbonate Fuel Cells with Direct Internal Reforming (DIR-MCFC).- Modelling of Filtration and Regeneration Processes in Diesel Particulate Traps.- Modelling the Shelf Life of Packaged Olive Oil Stored at Various Conditions.- Nonlinear Model Reduction of a Dynamic Two-dimensional Molten Carbonate Fuel Cell Model.- Liquid/Solid Phase Change with Convection and Deformations: 2D Case.- Mathematical Modelling of Mass Transport Equations in Fixed-Bed Absorbers.- Injection Vapour Model in a Porous Medium Accounting for a Weak Condensation.- Multigrid Solution of Three-Dimensional Radiative Heat Transfer in Glass Manufacturing.- DEM Simulations of the DI Toner Assembly.- Modeling of Drying Processes in Pore Networks.- Mathematical Modelling of Flow through Pleated Cartridge Filters.- Comparison of Some Mixed Integer Non-linear Solution Approaches Applied to Process Plant Layout Problems.- A Mathematical Model of Three-Dimensional Flow in a Scraped-Surface Heat Exchanger.- Theme: Life Sciences.- Transmission Line Matrix Modeling of Sound Wave Propagation in Stationary and Moving Media.- Viscous Drops Spreading With Evaporation And Applications To DNA Biochips.- Similarity-Based Object Recognition of Airborne Fungi in Digital Images.- Rivalling Optimal Control in Robot-Assisted Surgery.- Theme: Materials.- A Multiphase Model for Concrete: Numerical Solutions and Industrial Applications.- Modelling the Glass Press-Blow Process.- Real-Time Control of Surface Remelting.- Fast Shape Design for Industrial Components.- Modeling of Turbulence Effects on Fiber Motion.- Design Optimisation of Wind-Loaded Cylindrical Silos Made from Composite Materials.- Two-Dimensional Short Wave Stability Analysis of the Floating Process.- Optimization in high-precision glass forming.- A Mathematical Model for the Mechanical Etching of Glass.- FPM + Radiation = Mesh-Free Approach in Radiation Problems.- Theme: Geophysics.- Multiscale Methods and Streamline Simulation for Rapid Reservoir Performance Prediction.- Theme: Financial Mathematics.- ONE FOR ALL The Potential Approach to Pricing and Hedging.- The Largest Claims Treaty ECOMOR.- American Options With Discrete Dividends Solved by Highly Accurate Discretizations.- Semi-Lagrange Time Integration for PDE Models of Asian Options.- Fuzzy Binary Tree Model for European Options.- Effective Estimation of Banking Liquidity Risk.- Theme: Water Flow.- Multiphase Flow and Transport Modeling in Heterogeneous Porous Media.- The Unsteady Expansion and Contraction of a Two-Dimensional Vapour Bubble Confined Between Superheated or Subcooled Plates.- Animating Water Waves Using Semi-Lagrangian Techniques.- A Filtered Renewal Process as a Model for a River Flow.- A Parallel Finite Element Method for Convection-Diffusion Problems.- Modelling The Flow And Solidification of a Thin Liquid Film on a Three-Dimensional Surface.- Numerical Schemes for Degenerate Parabolic Problems.- Finite Element Modified Method of Characteristics for Shallow Water Flows: Application to the Strait of Gibraltar.- LDC with compact FD schemes for convection-diffusion equations.- A Finite-Dimensional Modal Modelling of Nonlinear Fluid Sloshing.- Other Contributions.- On the Reliability of Repairable Systems: Methods and Applications.- New Schemes for Differential-Algebraic Stiff Systems.- Wavelet and Cepstrum Analyses of Leaks in Pipe Networks.- Robust Design Using Computer Experiments.- Non-Classical Shocks for Buckley-Leverett: Degenerate Pseudo-Parabolic Regularisation.- A Multi-scale Approach to Functional Signature Analysis for Product End-of-Life Management.- Aspects of Multirate Time Integration Methods in Circuit Simulation Problems.- Exploiting Features for Finite Element Model Generation.- Implicit Subgrid-Scale Models in Space-Time VMS Discretisations.- Multiscale Change-Point Analysis of Inhomogeneous Poisson Processes Using Unbalanced Wavelet Decompositions.- Robust Soft Sensors Based on Ensemble of Symbolic Regression-Based Predictors.- Two-Dimensional Patterns in High Frequency Plasma Discharges.- A Mathematical Model for the Motion of a Towed Pipeline Bundle.- Operators and Criteria for Integrating FEA in the Design Workflow: Toward a Multi-Resolution Mechanical Model.- Wavelet Analysis of Sound Signal in Fluid-filled Viscoelastic Pipes.- Coarse-Grained Simulation and Bifurcation Analysis Using Microscopic Time-Steppers.- Optimal Prediction in Molecular Dynamics.- From CAD to CFD Meshes for Ship Geometries.- Integration of Strongly Damped Mechanical Systems by Runge-Kutta Methods.- Numerical Simulation of SMA Actuators.

Parametric Model Reduction for Fast Simulation of Cyclic Voltammograms

Abstract: Model order reduction is a well-established technique for fast simulation of large-scale models based on ordinary differential equations, especially those in the field of integrated circuits and microelectro-mechanical systems. In this paper, we propose the use of parametric model reduction for fast simulation of a cyclic voltammogram. Instead of being considered as a time varying system, the model for a cyclic voltammogram is treated as a system with a parameter (applied voltage) which is to be preserved during model reduction. Because voltage is preserved in the symbolic form during model reduction, we can simulate the cyclic voltammogram with a reduced system and therefore invest much less time and memory as compared with direct simulation based on the original large-scale model. We present our approach for a case study based on scanning electrochemical microscopy.

Krylov Model Order Reduction of Finite Element Models of Electromagnetic Structures with Frequency-Dependent Material Properties

Abstract: Krylov subspace-based model order reduction (MOR) of finite element models of electromagnetic structures is not readily applicable when the electromagnetic properties of the materials exhibit arbitrary frequency dependence. This paper presents a methodology for overcoming this hurdle. The proposed Krylov MOR process is demonstrated through its application to the expedient broadband analysis of the impact of skin-effect loss on the transmission properties of a microstrip bandpass filter and the extraction of the propagation characteristics of a microstrip line on a dielectric substrate with frequency-dependent permittivity described by a Debye model.

A fast block structure preserving model order reduction for inverse inductance circuits

Abstract: Most existing RCL-1 circuit reductions stamp inverse inductance L-1 elements by a second-order nodal analysis (NA). The NA formulation uses nodal voltage variables and describes inductance by nodal susceptance. This leads to a singular matrix stamping in general. We introduce a new circuit stamping for RCL-1 circuits using branch vector potentials. The new circuit stamping results in a first-order circuit matrix that is semi-positive definite and non-singular. We call this as vector-potential based nodal analysis (VNA). It enables an accurate and passive reduction. In addition, to preserve the structure of state matrices such as sparsity and hierarchy, we represent the flat VNA matrix in a bordered-block diagonal (BBD) form. This enables us to build and simulate the macromodel efficiently. In experiments performed on several test cases, our method achieves up to 15times faster modeling building time, up to 33times faster simulation time, and as much as 67times smaller waveform error compared to SAPOR, the best existing second order RCL-1 reduction method

The Multiple Point Global Lanczos Method for Multiple-Inputs Multiple-Outputs Interconnect Order Reductions

Abstract: The global Lanczos algorithm for solving the RLCG interconnect circuits is presented in this paper. This algorithm is an extension of the standard Lanczos algorithm for multiple-inputs multiple-outputs (MIMO) systems. A new matrix Krylov subspace will be developed first. By employing the congruence transformation with the matrix Krylov subspace, the two-side oblique projection-based method can be used to construct a reduced-order system. It will be shown that the system moments are still matched. The error of the 2q-th order system moment will be derived analytically. Furthermore, two novel model-order reduction techniques called the multiple point global Lanczos (MPGL) method and the adaptive-order global Lanczos (AOGL) method which are both based on the multiple point moment matching are proposed. The frequency responses using the multiple point moment matching method have higher coherence to the original system than those using the single point expansion method. Finally, simulation results on frequency domain will illustrate the feasibility and the efficiency of the proposed methods.

Projection-Based Approximation Methods for the Optimal Control of Smart Oil Fields

Abstract: Computational improvements of instrumented large-scale reservoir simulation are becoming one of the main research topics in the oil industry. In particular, the problem of closed-loop control is capturing a great deal of interest for reliable reservoir management. One of the main difficulties in designing controllers for large-scale reservoir systems has to do with the high dimensional state-space and parameter uncertainties. Hence, lower dimensional models, linear or nonlinear, that approximate the full order system are desirable to either mitigate the cost of large-scale reservoir simulation or design efficient closed-loop control systems. This work aims to compare recent advances in model order reduction techniques applied to reservoir simulation. In general, the problem of reducing the order of a large-scale model is known as approximation of dynamical systems. Several techniques have been developed in the linear dynamical systems framework, namely, the Balanced Truncation, Moment Matching by Krylov techniques, among others and in the nonlinear setting, namely the use of the Proper Orthogonal Decomposition (POD) and its variants. They all share a common approach: they are based on projection techniques. This work provides a comparative analysis of these techniques with particular emphasis on Krylov approaches since they are becoming one of the most active areas of research in large-scale optimal control but yet, they has not been broadly reported within the reservoir community. Preliminary computational experiments reveal that these methods offer promising opportunities to design closed-loop low-order controllers for the management of large-scale smart fields.

Model Order Reduction of Nonlinear Dynamical Systems

Abstract: Some propositions for approximation of the controllability and observability gramians for nonlinear systems are presented. This enables a balancing type model reduction to be performed for nonlinear systems in the same manner as for linear systems.

An Extended SVD-based Terminal and Model Order Reduction Algorithm

Abstract: The paper proposes a new combined terminal and model order reduction method for compact modeling of interconnect circuits. The new method extends the existing SVDMOR method [3] by using higher order moment information for terminal responses during the terminal reduction and by applying separate SVD low-rank approximations on input and output terminals respectively. This is in contrast to SVDMOR method where input and output terminal responses are SVD approximated at the same time, which can lead to large error when the numbers of inputs and outputs are quite different. We analyze the passivity requirement for combined terminal and model order reduction and show the passivity enforcement may significantly hamper the terminal reduction effects. We also improve the computation efficiency of SVDMOR. Our experimental results show that ESVDMOR outperforms the SVDMOR in terms of accuracy for the similar reduced model sizes in a number of interconnect circuits when the input and output terminals are different.

Order Reduction for a Control-Oriented Model of the Water Dynamics in Fuel Cells

Abstract: Predicting the water dynamics and estimating humidity and flooding conditions in a low-temperature fuel cell are critical for robust operation and long life. Previous work by McKay et al [1] shows that the fuel cell anode, cathode, and membrane water dynamics and gaseous species concentrations can be accurately modeled by discretizing the partial differential equations that describe mass transport into three segments. Avoiding sensitivities associated with over-parameterization, and allowing for the real-time computations necessary for embedded controllers, requires in-depth investigation of the model order. In this paper the model from [1] is formulated into a bond graph representation. The objective is to establish the necessary model order for the fuel cell model using the Model Order Reduction Algorithm (MORA) [2], where an energy-based metric termed the Activity is used to quantify the contribution of each element of the model. Activity is a scalar quantity that is determined from the generalized effort and flow through each element of the model. We show the degree of model order reduction and provide a guideline for appropriate discretization.Copyright © 2006 by ASME and Toyota Technical Center, USA Inc.

Nonlinear Thermal Reduced Model for Power Semiconductor Devices

Abstract: The challenge in terms of accurate prediction of electrical behavior, reliability and thermal management of semiconductor power devices goes through the coupling of multi physics analysis and especially through the coupling of nonlinear thermal models with nonlinear electrical models. In order to obtain a precise nonlinear thermal model which can be implemented as an equivalent SPICE (simulation program integrated circuits especially) subcircuit in circuit simulators, we present a methodology based on a model order reduction technique applied to a three dimensional finite element thermal description. This reduction method is based on the Ritz vector approach. In order to take into account the nonlinear thermal properties of materials, an extension of the method based on the Kirchoff transformation and an interpolation formula is proposed. This method, theoretically suitable only for homogeneous structures, exhibits in practice a very good accuracy for heterogeneous structures. Another improvement in the nonlinear transient response relies on the self consistent calculation of a coefficient related to the thermal conductivity approximation law. Thus, obtaining directly in time domain a nonlinear thermal reduced model for inhomogeneous structure is possible. The complete model has been successfully implemented in circuit simulator for several power devices and for various nonlinear materials such as GaAs, GaN or silicon. The nonlinear behavior has been validated on a wide range of input power and baseplate temperature. The influence of the interpolation formula is discussed for strongly nonlinear materials. Thermal infrared and electrical measurements have been performed to validate the simulation results