scholarly journals Numerical Verification of 10000-dimensional Linear Systems 10000x Faster

10.29007/gv5q ◽  
2018 ◽  
Author(s):  
Stanley Bak
Keyword(s):  
Model Order Reduction ◽  
Krylov Subspace ◽  
Order Reduction ◽  
Dimensional System ◽  
Numerical Verification ◽  
Model Order ◽  
New Approach ◽  
Counter Example ◽  
Continuous Branch ◽  
Original Approach

Tool Presentation: We evaluate an improved reachability algorithm for linear (and affine) systems implemented in the continuous branch of the Hylaa tool. While Hylaa’s earlier approach required n simulations to verify an n-dimensional system, the new method takes advantage of additional problem structure to produce the same verification result in significantly less time. If the initial states can be defined in i dimensions, and the output variables related to the property being checked are o-dimensional, the new approach needs only min(i,o) simulations to verify the system, or produce a counter-example. In addition to reducing the number of simulations, a second improvement speeds up individual simulations when the dynamics is sparse by using Krylov subspace methods.At ARCH 2017, we used the original approach to verify nine large linear benchmarks taken from model order reduction. Here, we run the new algorithm on the same set of benchmarks, and get an identical verification result in a fraction of the time. None of the benchmarks need more than tens of seconds to complete. The largest system with 10922 dimensions, which took over 24 hours using last year’s method, is verified in 3.4 seconds.

scholarly journals Extracting second-order structures from single-input state-space models: Application to model order reduction

2011 ◽  
Vol 21 (3) ◽  
pp. 509-519 ◽  
Author(s):  
Jérôme Guillet ◽  
Benjamin Mourllion ◽  
Abderazik Birouche ◽  
Michel Basset
Keyword(s):  
State Space ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Second Order ◽  
Input State ◽  
Model Order ◽  
New Approach ◽  
Order Form ◽  
Form Model ◽  
Single Input

Extracting second-order structures from single-input state-space models: Application to model order reductionThis paper focuses on the model order reduction problem of second-order form models. The aim is to provide a reduction procedure which guarantees the preservation of the physical structural conditions of second-order form models. To solve this problem, a new approach has been developed to transform a second-order form model from a state-space realization which ensures the preservation of the structural conditions. This new approach is designed for controllable single-input state-space realizations with real matrices and has been applied to reduce a single-input second-order form model by balanced truncation and modal truncation.

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.

Fast Harmonic MEMS Simulation With Arnoldi Model Order Reduction

2009 ◽  
Author(s):  
David Binion ◽  
Xiaolin Chen
Keyword(s):  
Model Order Reduction ◽  
Krylov Subspace ◽  
Order Reduction ◽  
Simulation Models ◽  
Original Model ◽  
Computational Time ◽  
Mems Devices ◽  
Element Analysis ◽  
Model Order ◽  
Similar Accuracy

Recent years has witnessed a large increase in the use of vibrating Micro-Electro-Mechanical-Systems (MEMS) especially in the expanding wireless telecommunication industry. In particular, the use of microresonators to generate or filter signals has facilitated a reduction in the size of many popular cell phones. Advances in microfabrication have increased the ability to create complex MEMS devices. Finite Element Analysis (FEA) has widely been used in the design of these devices. To obtain accurate simulations of complex MEMS devices, a dense FEA mesh is required resulting in computationally demanding simulation models. Arnoldi Model Order Reduction has been investigated and implemented to improve the computational efficiency of MEMS simulations. Using ANSYS, a popular FEA program, a micro resonator model was created. With Arnoldi, a Krylov subspace was extracted from the model and the model was projected onto the subspace reducing the model size. A harmonic simulation over normal operating frequencies was performed on the reduced model and compared with a simulation of the original model. It was found that the computational time was drastically reduced through the use of Arnoldi while achieving similar accuracy as compared to the original model.

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.

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