Reduced-order Modeling Approach Research Articles

Laguerre-Based Bandlimited Reduced-Order Modeling

A new bandlimited Laguerre basis for application to reduced-order modeling (ROM) is proposed. It is derived from the original Laguerre basis by means of a judiciously chosen rational frequency transformation, shown to be orthonormal over a narrow-band frequency interval. By means of projecting the original transfer function onto this bandlimited Laguerre basis, we obtain a new ROM technique, which does not belong to the class of Krylov methods, but to the rather more general family of projection techniques. Pertinent features of the new method are the reduction in computational effort, the fact that a more efficient ROM approach is obtained by focusing on a frequency band at a time and the better extrapolation power of the new method, as compared to previous methods. The feasibility of the new method is illustrated by means of three examples.

Design across length scales: a reduced-order model of polycrystal plasticity for the control of microstructure-sensitive material properties

Development of techniques for the control of material properties of polycrystal materials that are inherently dependent on preferred orientations (texture) is addressed. To account for the infinite degrees of freedom of microstructural features, a model reduction on the micro-scale is introduced. Reduced-order models are developed to model the evolution of microstructure described by an orientation distribution function using a finite element discretization of the orientation space. This reduced-order modeling approach is based on the technique of proper orthogonal decomposition (POD) and the method of snapshots. Furthermore, novel design problems are introduced for the control of microstructure based on realistic polycrystalline plasticity. Specifically, a gradient based optimization framework is introduced using a multi-length scale continuum sensitivity method (CSM). The model reduction is extended to the sensitivity analysis and is a key element for the success of computational design of deformation processes. Numerical examples that highlight the benefits of the continuum sensitivity method and model reduction are presented. In addition, the potential of the presented techniques towards process design for obtaining desired material properties is demonstrated with the control at a material point of the elastic modulus in fcc copper. A desired distribution of the elastic modulus is achieved through an optimal selection of the velocity gradient.

A proper orthogonal decomposition approach to microstructure model reduction in Rodrigues space with applications to optimal control of microstructure-sensitive properties

A novel reduced-order modeling approach to represent crystallographic texture in polycrystals is presented. This method involves generation of a reduced orthogonal basis for representing polycrystal texture in Rodrigues space. The reduced basis is generated from the textures obtained from different deformation modes (shear, uniaxial tension, etc.) using proper orthogonal decomposition and the method of snapshots. This model reduction can account for all essential information needed to describe the microstructure and leads to tremendous savings in computational time. Based on the above method a multiscale model for microstructure evolution during deformation is proposed driven by the macroscale velocity gradient. A continuum sensitivity-based gradient optimization framework is introduced in the above model for control of microstructure-sensitive material properties. Emphasis is given to relevant design problems that demonstrate the effectiveness of the above method for optimal control of texture-dependent material properties during deformation such as the magnetic hysteresis losses, the yield stress and the Lankford parameter R.

SYSTEM LEVEL SIMULATIONS OF MEMS BASED ON REDUCED ORDER FINITE ELEMENT MODELS

Reduced Order Modeling (ROM) of MEMS has become state of the art for fast component and system level simulations. Based on the well known modal decomposition technique, the automatic generated macromodel is no longer simplified to rigid body and lumped parameter approximations. It retains the true flexible characteristics of electromechanical structures and is able to capture mechanical nonlinearities (Stress-Stiffening), electrostatic fringing fields and large signal behavior with the same order of accuracy as the corresponding FE-model. After a brief description of the ROM approach, the following paper is focused on a new capability of the macromodel which couples nodal degree of freedoms of the FE-model and modal degrees of freedom used for the internal governing equations of the ROM. The new interface is necessary to model temporary displacement constrains, to couple several ROMs together and to analyze system with mechanical contact.

Transient analysis of electro‐osmotic transport by a reduced‐order modelling approach

AbstractTransient behaviour of electro‐osmotic transport in typical electrokinetic channels is studied in this paper. The time needed for the electro‐osmotic flow to reach steady‐state exhibits multiple time scales depending on whether the flow is governed by either a viscous force, electrokinetic force or by a combination of both. When an intersection is present in the electrokinetic channel, such as in a cross or a T‐channel, the flow in the main channel and in the intersection gets to steady‐state at different times.A weighted Karhunen–Loève (KL) decomposition method is proposed in this paper to generate the global basis function for reduced‐order simulation. The key idea in a weighted KL approach is that, instead of minimizing a least‐squares measure of ‘error’ between the linear subspace spanned by the basis functions and the observation space, we minimize the weighted ‘error’ between the two spaces. The global basis functions in a weighted KL approach can be generated by computing the singular value decomposition (SVD) of the matrix containing the weighted snapshots. We show that the weighted KL decomposition based reduced‐order model is computationally more efficient and can capture the multiple time scales encountered in electro‐osmotic transport much more effectively compared to the classical KL decomposition based reduced‐order model. Copyright © 2003 John Wiley & Sons, Ltd.

Reduced-Order Models for Nonlinear Unsteady Aerodynamics

Two reduced-order modeling approaches for the evaluation of nonlinear aerodynamic forces based on CFD computations are presented. These reducedorder models (ROMs) provide a means for rapid calculation of frequency-domain generalized aerodynamic forces, which can be used in traditional flutter analysis scheme, to calculate flutter characteristics about nonlinear steady flows. Two ROMs are presented, one that is based on the Volterra theory for nonlinear systems, and a new ROM that is based on step (indicial) responses. ROM kernels are identified directly from input-output relations, and the study focuses on issues of kernel identification and their effect on the quality of the ROM. First- and second-order ROMs are generated for the response of the AGARD 445.6 wing to forced-harmon ic excitation of its elastic modes. Responses computed from the ROMs are compared to responses obtained directly from a CFD analysis in which the boundary conditions are excited harmonically. Results show that the quality of the Volterra ROM is very sensitive to the amplitudes of the impulse inputs used for identification. The step-response ROM is shown to be more accurate than the Volterra ROM and less sensitive to the amplitude used for its identification.

A reduced-order approach for optimal control of fluids using proper orthogonal decomposition

In this article, a reduced-order modeling approach, suitable for active control of fluid dynamical systems, based on proper orthogonal decomposition (POD) is presented. The rationale behind the reduced-order modeling is that numerical simulation of Navier–Stokes equations is still too costly for the purpose of optimization and control of unsteady flows. The possibility of obtaining reduced-order models that reduce the computational complexity associated with the Navier–Stokes equations is examined while capturing the essential dynamics by using the POD. The POD allows the extraction of a reduced set of basis functions, perhaps just a few, from a computational or experimental database through an eigenvalue analysis. The solution is then obtained as a linear combination of this reduced set of basis functions by means of Galerkin projection. This makes it attractive for optimal control and estimation of systems governed by partial differential equations (PDEs). It is used here in active control of fluid flows governed by the Navier–Stokes equations. In particular, flow over a backward-facing step is considered. Reduced-order models/low-dimensional dynamical models for this system are obtained using POD basis functions (global) from the finite element discretizations of the Navier–Stokes equations. Their effectiveness in flow control applications is shown on a recirculation control problem using blowing on the channel boundary. Implementational issues are discussed and numerical experiments are presented. Copyright © 2000 John Wiley & Sons, Ltd.

A Reduced-Order Method for Simulation and Control of Fluid Flows

This article presents a reduced-order modeling approach for simulation and control of viscous incompressible flows. The reduced-order models suitable for control and which capture the essential physics are developed using the reduced-basis method. The so-called Lagrange approach is used to define reduced bases and the basis functions in this approach are obtained from the numerical solutions. The feasibility of this method for flow control is demonstrated on boundary control problems in closed cavity and in wall-bounded channel flows. Control action is effected through boundary surface movement on a part of the solid wall. Our formulation of the reduced-order method applied to flow control problems leads to a constrained minimization problem and is solved by applying Newton-like methods to the necessary conditions of optimality. Through our computational experiments we demonstrate the feasibility and applicability of the reduced-order method for simulation and control of fluid flows.

Optimal actuator placement for large scale systems: A reduced-order modelling approach

A recently developed, extended balanced realization, reduced order modelling technique for large-scale distributed systems is applied to the problem of optimal actuator placement for hyperthermia treatments. Extended balanced realization develops low-order models whose state reconstructions are robust to actuator and sensor placement changes, and hence can be effectively used to find optimal placements in a computationally efficient manner. This optimization approach has been tested on simulations of a scanned focused, ultrasound hyperthermia system and found to be robust and accurate over a wide range of models, and the savings in computational costs were found to be significant.