scholarly journals Certified POD-Based Multiobjective Optimal Control of Time-Variant Heat Phenomena

2018 ◽  
Author(s):  
Stefan Banholzer ◽  
Eugen Makarov ◽  
Stefan Volkwein
Keyword(s):  
Optimal Control ◽  
Reference Point ◽  
Model Order Reduction ◽  
Optimization Problems ◽  
Order Reduction ◽  
Point Method ◽  
Model Order ◽  
Reference Point Method ◽  
Multiobjective Optimal Control ◽  
Proper Orthogonal

Many optimization problems in applications can be formulated using several objective functions, which are conflicting with each other. This leads to the notion of multiobjective or multicriterial optimization problems. Here, we investigate the application of the Euclidean reference point method in combination with model-order reduction to multiobjective optimal control problems. Since the reference point method transforms the multiobjective optimal control problem into a series of scalar optimization problems, the method of proper orthogonal decomposition (POD) is introduced as an approach for model-order reduction.

Recent Advances in Computational Methods for Microsystems

2013 ◽  
Vol 745 ◽  
pp. 13-25 ◽  
Author(s):  
Alberto Corigliano ◽  
Martino Dossi ◽  
Stefano Mariani
Keyword(s):  
Model Order Reduction ◽  
Computing Time ◽  
Order Reduction ◽  
Orthogonal Decomposition ◽  
Coupled Problems ◽  
Strong Reduction ◽  
Model Order ◽  
Solution Strategies ◽  
Reduction Methods ◽  
Proper Orthogonal

An algorithm, which combines the use of Domain Decomposition and Model Order Reduction methods based on Proper Orthogonal Decomposition, is proposed. The algorithm allows for the efficient handling of electro-mechanical coupled problems in MEMS, with a strong reduction of computing time with respect to standard monolithic or staggered solution strategies. Examples of coupled electro-mechanical problems, concerning a vibrating beam subject to variable electrostatic forces, are presented and discussed.

scholarly journals A Review of Model Order Reduction Methods for Large-Scale Structure Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Kuan Lu ◽  
Kangyu Zhang ◽  
Haopeng Zhang ◽  
Xiaohui Gu ◽  
Yulin Jin ◽  
...  
Keyword(s):  
Complex Systems ◽  
Model Order Reduction ◽  
Large Scale ◽  
Order Reduction ◽  
Large Scale Structure ◽  
Scale Structure ◽  
High Dimensional ◽  
Model Order ◽  
Reduction Methods ◽  
Proper Orthogonal

The large-scale structure systems in engineering are complex, high dimensional, and variety of physical mechanism couplings; it will be difficult to analyze the dynamic behaviors of complex systems quickly and optimize system parameters. Model order reduction (MOR) is an efficient way to address those problems and widely applied in the engineering areas. This paper focuses on the model order reduction of high-dimensional complex systems and reviews basic theories, well-posedness, and limitations of common methods of the model order reduction using the following methods: center manifold, Lyapunov–Schmidt (L-S), Galerkin, modal synthesis, and proper orthogonal decomposition (POD) methods. The POD is a powerful and effective model order reduction method, which aims at obtaining the most important components of a high-dimensional complex system by using a few proper orthogonal modes, and it is widely studied and applied by a large number of researchers in the past few decades. In this paper, the POD method is introduced in detail and the main characteristics and the existing problems of this method are also discussed. POD is classified into two categories in terms of the sampling and the parameter robustness, and the research progresses in the recent years are presented to the domestic researchers for the study and application. Finally, the outlooks of model order reduction of high-dimensional complex systems are provided for future work.

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