NSU CTRG 2020-2021
Approximation of Large-Scale Dynamical System over a Limited Time Interval. (CTRG-20/SEPS/20)
- Funded by: North South University
- Principle Investigator: Dr. Mohammad Monir Uddin (monir.uddin@northsouth.edu)
- Co-Principle Investigator: Mohammad Niaz Morsed (mohammad.murshed@northsouth.edu)
- Duaration: 1 years (Started from March 2021)
Project Overview
Model order reduction (MOR) is considered as an indispensable subject in the different branches of Science, Engineering and Technology. The demand of MOR is increasing everyday in the different branches of Science, Engineering and Technology. Over the last few decades many methods havebeen developed to perform the model reduction of large-scale dynamical system.Every method has advantages and disad- vantages. Currently time and frequencylimited MOR techniques have taken lot of attentions since in engineering and tech-nology in some applications it is important to minimize the error of the system overa finite time and frequency intervals. More- over time and frequency limited MORhas meaningful physical interpretation and provides more accurate approximations.They are already well established for standard/generalized system. Recently, weare investigating the frequency-limited MOR of descriptor systems which is a partof the project funded by NSU-CTRG (2019- 2020). In this work we will investigatethe time limited MOR using the balanced truncation and Interpolatory projectionmethods. The efficiency of the developed methods will be assessed by applying themapplied to some real world data for the MOR of descriptor systems . The possible significant outcomes of this research are as follows:
- The algorithms and software developed from this research would be interesting and rewarding materials for further research and development in both academics and industries.
- The software can be useful in Industries for the controller design, optimization and simulation of large scale mathematical models.
- With the results of this project besides several journal papers we also can publish a book.
- The researches will be benefited tremendously. The project will help them to acquire knowledge in Control theory, Optimizations, Scientific computing, Mathematical Algorithms and Software. They can see how to apply the Mathematical knowledge in the real life applications.
Team
Project Outcome
In this project we proposed to develop algorithms for the frequency limited model reduction of large-scale sparse descriptor systems. The proposed research work has been successfully done theoretically and some numerical experiments also have been carried out. The results have been shown in the attached papers. Some numerical experiments are being carried out at a automation lab of Shanghai University, China. The project was supposed to be ended by September 2020. Due to pandemic problem it was delayed by three months. In future work we will generalize the ideas obtained here for limited time interval case.
Sumulation & Results
Publications
A computationally effective time-restricted stability preserving H2-optimal model order reduction approach
Results in Control and Optimization
Several approaches for reducing model order on the definite time segments have become the topic of investigation in a series of papers that bring challenges during application in a large-scale setting.JOURNAL
A computationally effective time-restricted stability preserving H2-optimal model order reduction approach
About The Publication
Several approaches for reducing model order on the definite time segments have become the topic of investigation in a series of papers that bring challenges during application in a large-scale setting. The subject of discussion of this paper is the computationally efficient time-restricted H2-optimal model order reduction method of higher dimensional sparse systems that requires the solutions of time-restricted Lyapunov and Sylvester equations. Our discussion is on developing the algorithms to solve these matrix equations that face difficulty when calculating the matrix exponential of the large-scale matrices. As a result, an efficient remedy is also proposed to compute the matrix exponential. Our ideas are also evaluated for index-1 descriptor systems apart from the generalized structure. Numerical analyses are conducted on several benchmark examples to illustrate how accurate and efficient our suggested approaches are by comparing them with the existing methods.
Reduced Order Modeling of a Class of Descriptor System on Certain Domains with the Application to Blood Flow Through the Carotid
SSRN
This study focuses on model order reduction for large-scale sparse index-2 descriptor systems that arise from practical problems governed by the semi-discrete Naiver Stokes equation, such as blood flow through the carotid.JOURNAL
Reduced Order Modeling of a Class of Descriptor System on Certain Domains with the Application to Blood Flow Through the Carotid
About The Publication
This study focuses on model order reduction for large-scale sparse index-2 descriptor systems that arise from practical problems governed by the semi-discrete Naiver Stokes equation, such as blood flow through the carotid. The goal is to reduce the system’s complexity while maintaining its critical properties within a limited frequency and time interval. To achieve this, we implicitly convert the index-2 descriptor system to an equivalent ODE system and then apply the generalized H2 optimal model reduction technique on the altered system for order reduction on the restricted frequency interval. Then this idea is extended to the order reduction in the definite time interval. The main challenge in this approach is to efficiently solve two Sylvester equations obtained from the index-2 descriptor system. We implicitly discuss the efficient solution technique of these Sylvester equation pairs and propose a method based on the Iterative Rational Krylov Algorithm for computing the large-scale matrix logarithm to deal with the significant computational challenge efficiently. To validate the proposed techniques, the authors perform numerical experiments on generated and some existing data of index-2 descriptor systems using the MATLAB interface. The results demonstrate the approximation accuracy and computational efficiency of the proposed techniques.