On the Use of Proper Generalized Decomposition and Model Reduction Techniques for Structural Optimization Problems

2010 ◽  
Author(s):  
E. Verron ◽  
A. Leygue
Keyword(s):  
Structural Optimization ◽  
Model Reduction ◽  
Optimization Problems ◽  
Proper Generalized Decomposition ◽  
Reduction Techniques

scholarly journals Conservative model reduction for finite-volume models

2018 ◽  
Keyword(s):  
Model Reduction ◽  
Finite Volume ◽  
Optimization Problems ◽  
Posteriori Error ◽  
Galerkin Projection ◽  
Lower State ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Reduction Techniques ◽  
Volume Models

We present a method for model reduction of finite-volume models that guarantees the resulting reduced-order model is conservative, thereby preserving the structure intrinsic to finite-volume discretizations [1]. The proposed reduced-order models associate with optimization problems characterized by (1) a minimum-residual objective function and (2) nonlinear equality constraints that explicitly enforce conservation over subdomains. Conservative Galerkin projection arises from formulating this optimization problem at the time-continuous level, while conservative least- squares Petrov–Galerkin (LSPG) projection associates with a time-discrete formulation. We note that other recent works have also considered ROMs that associate with constrained optimization problems [3, 2], although none are conservative. We equip these approaches with hyper-reduction techniques in the case of nonlinear flux and source terms, and also provide approaches for handling infeasibility. In addition, we perform analyses that include deriving conditions under which conservative Galerkin and conservative LSPG are equivalent, as well as deriving a posteriori error bounds. On a parameterized quasi-1D Euler equation problem, the proposed method not only conserves mass, momentum, and energy globally, but also has significantly lower state-space errors than nonconservative reduced-order models such as standard Galerkin and LSPG projection.

Energy-Based Model Reduction Methodology for Automated Modeling

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Loucas S. Louca ◽  
Jeffrey L. Stein ◽  
Gregory M. Hulbert
Keyword(s):  
Model Reduction ◽  
Order Reduction ◽  
Process Models ◽  
Model Parameters ◽  
Automated Modeling ◽  
Reduced Models ◽  
System Models ◽  
Quarter Car Model ◽  
Reduction Techniques ◽  
Physical Phenomena

In recent years, algorithms have been developed to help automate the production of dynamic system models. Part of this effort has been the development of algorithms that use modeling metrics for generating minimum complexity models with realization preserving structure and parameters. Existing algorithms, add or remove ideal compliant elements from a model, and consequently do not equally emphasize the contribution of the other fundamental physical phenomena, i.e., ideal inertial or resistive elements, to the overall system behavior. Furthermore, these algorithms have only been developed for linear or linearized models, leaving the automated production of models of nonlinear systems unresolved. Other model reduction techniques suffer from similar limitations due to linearity or the requirement that the reduced models be realization preserving. This paper presents a new modeling metric, activity, which is based on energy. This metric is used to order the importance of all energy elements in a system model. The ranking of the energy elements provides the relative importance of the model parameters and this information is used as a basis to reduce the size of the model and as a type of parameter sensitivity information for system design. The metric is implemented in an automated modeling algorithm called model order reduction algorithm (MORA) that can automatically generate a hierarchical series of reduced models that are realization preserving based on choosing the energy threshold below which energy elements are not included in the model. Finally, MORA is applied to a nonlinear quarter car model to illustrate that energy elements with low activity can be eliminated from the model resulting in a reduced order model, with physically meaningful parameters, which also accurately predicts the behavior of the full model. The activity metric appears to be a valuable metric for automating the reduction of nonlinear system models—providing in the process models that provide better insight and may be more numerically efficient.

Application of projection-based model reduction to finite-element plate models for two-dimensional traveling waves

2016 ◽  
Vol 28 (14) ◽  
pp. 1886-1904 ◽  
Author(s):  
Vijaya VN Sriram Malladi ◽  
Mohammad I Albakri ◽  
Serkan Gugercin ◽  
Pablo A Tarazaga
Keyword(s):  
Finite Element ◽  
Model Reduction ◽  
Traveling Waves ◽  
Large Scale ◽  
Fe Model ◽  
Plate Model ◽  
Reduction Techniques ◽  
State Frequency ◽  
Scale Down ◽  
The Stability

A finite element (FE) model simulates an unconstrained aluminum thin plate to which four macro-fiber composites are bonded. This plate model is experimentally validated for single and multiple inputs. While a single input excitation results in the frequency response functions and operational deflection shapes, two input excitations under prescribed conditions result in tailored traveling waves. The emphasis of this article is the application of projection-based model reduction techniques to scale-down the large-scale FE plate model. Four model reduction techniques are applied and their performances are studied. This article also discusses the stability issues associated with the rigid-body modes. Furthermore, the reduced-order models are utilized to simulate the steady-state frequency and time response of the plate. The results are in agreement with the experimental and the full-scale FE model results.

Sign in / Sign up

Export Citation Format

Share Document