Goal-oriented, model-constrained optimization for reduction of large-scale systems

Bui-Thanh, Tan; Willcox, Karen; Ghattas, Omar; Waanders, Bart van Bloemen

doi:10.1016/j.jcp.2006.10.026

Cited by 183 publications

(228 citation statements)

References 27 publications

(44 reference statements)

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“…This can avoid the expensive computation of full-order trial solutions typically needed in a POD-greedy approach. Furthermore, in [24] the POD procedure was extended to incorporate goal-oriented quantities related to specific outputs of interest over the entire range of parameters.…”

Section: Optimality (Or Near-optimality)mentioning

confidence: 99%

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

Lassila

Manzoni

Quarteroni

et al. 2014

Reduced Order Methods for Modeling and Computational Reduction

164

179

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This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities -which are mainly related either to nonlinear convection terms and/or some geometric variability -that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and -in the unsteady case -long-time stability of the reduced model. Moreover, we provide an extensive list of literature references.

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Section: Optimality (Or Near-optimality)mentioning

confidence: 99%

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

Lassila

Manzoni

Quarteroni

et al. 2014

Reduced Order Methods for Modeling and Computational Reduction

164

179

View full text Add to dashboard Cite

show abstract

“…For POD, the basis vector can be conveniently solved by various numerical methods, and therefore recognized as a straightforward application of the approximation on the SVD e.g. (Ravindran, 2000;Afanasiev and Hinze, 2001;Atwell, et al, 2001;Cohen, et al, 2006;Bui-Thanh, et al, 2007).…”

Section: ) Proper Orthogonal Decomposition (Pod)mentioning

confidence: 99%

“…For example, proposed a Goal-oriented model-constrained reduction algorithm to adopt the POD into the MPC. The goal oriented model constrained reduction algorithm is taken from (Bui-Thanh, et al, 2007), in which more information can be acquired to address the accuracy issues of the reduced model. Such a method enforces the reduced order governing equations to be constraints and the cost is targeted to minimize the output error, while the POD minimizes the error of state prediction over the entire domain .…”

Section: ) Proper Orthogonal Decomposition (Pod)mentioning

confidence: 99%

1-Bit processing based model predictive control for fractionated satellite missions

Bai

2014

Acta Astronautica

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In this thesis, a 1-bit processing based Model Predictive Control (OBMPC) structure is proposed for a fractionated satellite attitude control mission. Despite the appealing advantages of the MPC algorithm towards constrained MIMO control applications, implementing the MPC algorithm onboard a small satellite is certainly challenging due to the limited onboard resources. The proposed design is based on the 1-bit processing concept, which takes advantage of the affine relation between the 1-bit state feedback and multi-bit parameters to implement a multiplier free MPC controller.As multipliers are the major power consumer in online optimization, the OBMPC structure is proven to be more efficient in comparison to the conventional MPC implementation in term of power and circuit complexity. The system is in digital control nature, affected by quantization noise introduced by Δ∑ modulators. The stability issues and practical design criteria are also discussed in this work.Some other aspects are considered in this work to complete the control system. Firstly, the implementation of the OBMPC system relies on the 1-bit state feedbacks. Hence, 1-bit sensing components are needed to implement the OBMPC system. While the ∆∑ modulator based Microelectromechanical systems (MEMS) gyroscope is considered in this work, it is possible to implement this concept into other sensing components.Secondly, as the proposed attitude mission is based on the wireless inter-satellite link (ISL), a state estimator is required. However, conventional state estimators will once again introduce multi-bit signals, and compromise the simple, direct implementation of the OBMPC controller. Therefore, the 1-bit state estimator is also designed in this work to satisfy the requirements of the proposed fractionated attitude control mission.The simulation for the OBMPC is based on a 2U CubeSat model in a fractionated satellite structure, in which the payload and actuators are separated from the controller and controlled via the ISL. Matlab simulations and FPGA implementation based performance analysis shows that the OBMPC is feasible for fractionated satellite missions and is advantageous over the conventional MPC controllers. V VI

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“…Surrogate functions and reduced-order meta-models have also been used in control systems to reduce the order of the overall transfer function [3]. [4] proposed a goal-oriented, model-constrained optimization framework. A popular physics-based meta-modeling technique consists of carrying out the approximation on the full vector fields using PCA and Galerkin projection [5] in CFD [6] as well as in structural analysis [7].…”

Section: Introduction Literature Reviewed and Motivation For Researchmentioning

confidence: 99%

Towards simultaneous reduction of both input and output spaces for interactive simulation-based structural design

Raghavan¹,

Xia²,

Breitkopf³

et al. 2013

Computer Methods in Applied Mechanics and Engineering

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International audienceEngineering design problems generally involve a high-dimensional input space of design variables yielding an output space by means of costly high-fidelity evaluations. In order to decrease the overall cost, reduced-order models for the output space such as Proper Orthogonal Decomposition (POD) and Proper Generalized Decomposition (PGD) are an active area of research. However, little research has been conducted into alleviating the problems associated with a high-dimensional input space. In addition to higher dimensionality being an impediment to efficient design by itself, complex shapes involve a high number of explicit/implicit constraints restricting the design space. Geometric parameterization methods in traditional CAD present difficulties in expressing these constraints leading to a high failure rate and the generation of inadmissible shapes. In this paper, we propose a simultaneous meta-modeling protocol for both input and output spaces. We perform a reparametrization of the input space using constrained shape interpolation by introducing the concept of an alpha-manifold of admissible meshed shapes. The output space is reduced using constrained Proper Orthogonal Decomposition. By simultaneously using metamodeling for both spaces, we facilitate interactive design space exploration for the purpose of design. The proposed approach is applied to the industrial problem of designing a car engine intake port

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Goal-oriented, model-constrained optimization for reduction of large-scale systems

Cited by 183 publications

References 27 publications

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

1-Bit processing based model predictive control for fractionated satellite missions

Towards simultaneous reduction of both input and output spaces for interactive simulation-based structural design

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