scholarly journals Toward Optimality of Proper Generalised Decomposition Bases

2019 ◽  
Vol 24 (1) ◽  
pp. 30 ◽  
Author(s):  
Shadi Alameddin ◽  
Amélie Fau ◽  
David Néron ◽  
Pierre Ladevèze ◽  
Udo Nackenhorst
Keyword(s):  
Greedy Algorithms ◽  
Order Reduction ◽  
Nonlinear Material ◽  
Proper Generalized Decomposition ◽  
Model Order ◽  
Reduced Order ◽  
Structural Problems ◽  
Low Dimensional ◽  
Value Decomposition ◽  
The Greedy Algorithm

The solution of structural problems with nonlinear material behaviour in a model order reduction framework is investigated in this paper. In such a framework, greedy algorithms or adaptive strategies are interesting as they adjust the reduced order basis (ROB) to the problem of interest. However, these greedy strategies may lead to an excessive increase in the size of the ROB, i.e., the solution is no more represented in its optimal low-dimensional expansion. Here, an optimised strategy is proposed to maintain, at each step of the greedy algorithm, the lowest dimension of a Proper Generalized Decomposition (PGD) basis using a randomised Singular Value Decomposition (SVD) algorithm. Comparing to conventional approaches such as Gram–Schmidt orthonormalisation or deterministic SVD, it is shown to be very efficient both in terms of numerical cost and optimality of the ROB. Examples with different mesh densities are investigated to demonstrate the numerical efficiency of the presented method.

scholarly journals Toward Optimality of Proper Generalised Decomposition Bases

2019 ◽  
Author(s):  
Shadi Alameddin ◽  
Amélie Fau ◽  
David Néron ◽  
Pierre Ladevèze ◽  
Udo Nackenhorst
Keyword(s):  
Model Order Reduction ◽  
Greedy Algorithms ◽  
Order Reduction ◽  
Nonlinear Material ◽  
Reduced Basis ◽  
Model Order ◽  
Reduced Order ◽  
Structural Problems ◽  
Low Dimensional ◽  
The Greedy Algorithm

The solution of structural problems with nonlinear material behaviour in a model order reduction framework is investigated in this paper. In such a framework, greedy algorithms or adaptive strategies are interesting as they adjust the reduced order basis (ROB) to the problem of interest. However, these greedy strategies may lead to an excessive increase in the size of the reduced basis, i.e. the solution is no more represented in its optimal low-dimensional expansion. Here, an optimised strategy is proposed to maintain, at each step of the greedy algorithm, the lowest dimension of the PGD basis using a randomised SVD algorithm. Comparing to conventional approaches such as Gram-Schmidt orthonormalisation or deterministic SVD, it is shown to be very efficient both in terms of numerical cost and optimality of the reduced basis. Examples with different mesh densities are investigated to demonstrate the numerical efficiency of the presented method.

scholarly journals Study of methods for dimension reduction of complex dynamic linear systems models

2018 ◽  
Vol 226 ◽  
pp. 04036
Author(s):  
Yuriy M. Manatskov ◽  
Torsten Bertram ◽  
Danil V. Shaykhutdinov ◽  
Nikolay I. Gorbatenko
Keyword(s):  
Linear Systems ◽  
Main Idea ◽  
Computation Time ◽  
Order Reduction ◽  
Complex Dynamic ◽  
Model Order ◽  
Reduced Order ◽  
Advantages And Disadvantages ◽  
Optimization Stage ◽  
Linear Systems Of Equations

Complex dynamic linear systems of equations are solved by numerical iterative methods, which need much computation and are timeconsuming ones, and the optimization stage requires repeated solution of these equation systems that increases the time on development. To shorten the computation time, various methods can be applied, among them preliminary (estimated) calculation or oversimple models calculation, however, while testing and optimizing the full model is used. Reduced order models are very popular in solving this problem. The main idea of a reduced order model is to find a simplified model that may reflect the required properties of the original model as accurately as possible. There are many methods for the model order reduction, which have their advantages and disadvantages. In this article, a method based on Krylov subspaces and SVD methods is considered. A numerical experiments is given.

scholarly journals A Robust Computational Technique for Model Order Reduction of Two-Time-Scale Discrete Systems via Genetic Algorithms

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Othman M. K. Alsmadi ◽  
Zaer S. Abo-Hammour
Keyword(s):  
Genetic Algorithms ◽  
Time Scale ◽  
Model Order Reduction ◽  
Fitness Function ◽  
Order Reduction ◽  
Discrete Systems ◽  
Computational Technique ◽  
Model Order ◽  
New Approach ◽  
Reduced Order

A robust computational technique for model order reduction (MOR) of multi-time-scale discrete systems (single input single output (SISO) and multi-input multioutput (MIMO)) is presented in this paper. This work is motivated by the singular perturbation of multi-time-scale systems where some specific dynamics may not have significant influence on the overall system behavior. The new approach is proposed using genetic algorithms (GA) with the advantage of obtaining a reduced order model, maintaining the exact dominant dynamics in the reduced order, and minimizing the steady state error. The reduction process is performed by obtaining an upper triangular transformed matrix of the system state matrix defined in state space representation along with the elements ofB,C, andDmatrices. The GA computational procedure is based on maximizing the fitness function corresponding to the response deviation between the full and reduced order models. The proposed computational intelligence MOR method is compared to recently published work on MOR techniques where simulation results show the potential and advantages of the new approach.

scholarly journals Suboptimal Control Using Model Order Reduction

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Avadh Pati ◽  
Awadhesh Kumar ◽  
Dinesh Chandra
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Higher Order ◽  
Reduced Order Model ◽  
Suboptimal Control ◽  
Order Model ◽  
Model Order ◽  
Markov Parameters ◽  
Reduced Order ◽  
Partial Feedback

A Padé approximation based technique for designing a suboptimal controller is presented. The technique uses matching of both time moments and Markov parameters for model order reduction. In this method, the suboptimal controller is first derived for reduced order model and then implemented for higher order plant by partial feedback of measurable states.

scholarly journals Model Order Reduction for Real-Time Hybrid Simulation: Comparing Polynomial Chaos Expansion and Neural Network methods

2021 ◽  
Author(s):  
Nikolaos Tsokanas ◽  
Thomas Simpson ◽  
Roland Pastorino ◽  
Eleni Chatzi ◽  
Bozidar Stojadinovic
Keyword(s):  
Real Time ◽  
Hybrid Model ◽  
Model Order Reduction ◽  
Polynomial Chaos ◽  
Hybrid Simulation ◽  
Order Reduction ◽  
Chaos Expansion ◽  
Model Order ◽  
Reduced Order ◽  
Simulation Time

Hybrid simulation is a method used to investigate the dynamic response of a system subjected to a realistic loading scenario by combining numerical and physical substructures. To ensure high fidelity of the simulation results, it is often necessary to conduct hybrid simulation in real-time. One of the challenges arising in real-time hybrid simulation originates from high-dimensional nonlinear numerical substructures and, in particular, from the computational cost linked to the computation of their dynamic responses with sufficient accuracy. It is often the case that the simulation time-step must be decreased to capture the dynamic behavior of numerical substructures, thus resulting in longer computation. When such computation takes longer than the actual simulation time, time delays are introduced and the simulation timescale becomes distorted. In such a case, the only viable solution for doing hybrid simulation in real-time is to reduce the order of such complex numerical substructures.In this study, a model order reduction framework is proposed for real-time hybrid simulation, based on polynomial chaos expansion and feedforward neural networks. A parametric case study encompassing a virtual hybrid model is used to validate the framework. Selected numerical substructures are substituted with their respective reduced-order models. To determine the robustness of the framework, parameter sets are defined to cover the design space of interest. A comparison between the full- and reduced-order hybrid model response is delivered. The attained results demonstrate the performance of the proposed framework.

Fast Multiphysics MEMS Simulation With Arnoldi Model Order Reduction

2008 ◽  
Author(s):  
David Binion ◽  
Xiaolin Chen
Keyword(s):  
Model Order Reduction ◽  
Krylov Subspace ◽  
Order Reduction ◽  
Full Scale ◽  
Solution Time ◽  
System Level ◽  
Computational Time ◽  
Mems Devices ◽  
Model Order ◽  
Reduced Order

Modeling and simulation of Micro Electro Mechanical Systems has become increasingly important as the complexity of MEMS devices increases. In particular, thermal effects on MEMS devices has become a growing topic of interest. Through the FEA, detailed solutions can be obtained to investigate the multiphysics coupling and the transient behavior of a MEMS device at the component level. For system-level integration and simulation, the FEA discretization often results in large full-scale models, which can be computationally demanding or even prohibitive to solve. Model order reduction (MOR) was investigated in this study to reduce problem size for complex dynamic system modeling. The Arnoldi method was implemented for MOR to improve the computational efficiency while preserving the input-output behavior of coupled MEMS simulation. Using this method, a low dimensional Krylov subspace was extracted from the full-scale system model. Reduced order solution of the transient temperature distributions was then determined by projecting the system onto the extracted Krylov subspace and solving the reduced system. An electro thermal MEMS actuator was studied for various inputs. To compare results, the full-scale analyses were performed using the commercial FEA program ANSYS. It was found that the computational time of MOR was only a fraction of the full-scale solution time, with the relative errors ranging from 1.1% to 4.5% at different positions on the actuator. Our results show that the reduced order modeling via Alnoldi can significantly decrease the transient analysis solution time without much loss in accuracy for coupled-field MEMS simulation.

scholarly journals Reduced Order Controller Design for Symmetric, Non-Symmetric and Unstable Systems Using Extended Cross-Gramian

Machines ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 48 ◽  
Author(s):  
Azhar ◽  
Zulfiqar ◽  
Liaquat ◽  
Kumar
Keyword(s):  
Model Order Reduction ◽  
Controller Design ◽  
Order Reduction ◽  
Original System ◽  
Computational Effort ◽  
Model Order ◽  
Unstable Systems ◽  
Reduced Order ◽  
The Cross ◽  
Symmetric Systems

In model order reduction and system theory, the cross-gramian is widely applicable. The cross-gramian based model order reduction techniques have the advantage over conventional balanced truncation that it is computationally less complex, while providing a unique relationship with the Hankel singular values of the original system at the same time. This basic property of cross-gramian holds true for all symmetric systems. However, for non-square and non-symmetric dynamical systems, the standard cross-gramian does not satisfy this property. Hence, alternate approaches need to be developed for its evaluation. In this paper, a generalized frequency-weighted cross-gramian-based controller reduction algorithm is presented, which is applicable to both symmetric and non-symmetric systems. The proposed algorithm is also applicable to unstable systems even if they have poles of opposite polarities and equal magnitudes. The proposed technique produces an accurate approximation of the reduced order model in the desired frequency region with a reduced computational effort. A lower order controller can be designed using the proposed technique, which ensures closed-loop stability and performance with the original full order plant. Numerical examples provide evidence of the efficacy of the proposed technique.

scholarly journals Passivity Preserving Model Order Reduction Using the Reduce Norm Method

Electronics ◽  
2020 ◽  
Vol 9 (6) ◽  
pp. 964
Author(s):  
Namra Akram ◽  
Mehboob Alam ◽  
Rashida Hussain ◽  
Asghar Ali ◽  
Shah Muhammad ◽  
...  
Keyword(s):  
Integrated Circuits ◽  
Integrated Circuit ◽  
Model Order Reduction ◽  
High Speed ◽  
Order Reduction ◽  
Reliable Operation ◽  
Model Order ◽  
Reduced Order ◽  
Reduction Methods ◽  
On Chip

Modeling and design of on-chip interconnect, the interconnection between the components is becoming the fundamental roadblock in achieving high-speed integrated circuits. The scaling of interconnect in nanometer regime had shifted the paradime from device-dominated to interconnect-dominated design methodology. Driven by the expanding complexity of on-chip interconnects, a passivity preserving model order reduction (MOR) is essential for designing and estimating the performance for reliable operation of the integrated circuit. In this work, we developed a new frequency selective reduce norm spectral zero (RNSZ) projection method, which dynamically selects interpolation points using spectral zeros of the system. The proposed reduce-norm scheme can guarantee stability and passivity, while creating the reduced models, which are fairly accurate across selected narrow range of frequencies. The reduced order results indicate preservation of passivity and greater accuracy than the other model order reduction methods.

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