Approximate Solution of Nonclassically Damped Systems

1991 ◽  
Author(s):  
F. Ma ◽  
J. H. Hwang
Keyword(s):  
Approximate Solution ◽  
Large Scale ◽  
Computational Effort ◽  
Frequency Separation ◽  
Common Procedure ◽  
Damping Matrix ◽  
Complex Modes ◽  
Modal Coupling ◽  
Order Of Magnitude ◽  
Damped Systems

Abstract In analyzing a nonclassically damped linear system, one common procedure is to neglect those damping terms which are nonclassical, and retain the classical ones. This approach is termed the method of approximate decoupling. For large-scale systems, the computational effort at adopting approximate decoupling is at least an order of magnitude smaller than the method of complex modes. In this paper, the error introduced by approximate decoupling is evaluated. A tight error bound, which can be computed with relative ease, is given for this method of approximate solution. The role that modal coupling plays in the control of error is clarified. If the normalized damping matrix is strongly diagonally dominant, it is shown that adequate frequency separation is not necessary to ensure small errors.

Characterization of Modal Coupling in Nonclassically Damped Systems

1992 ◽  
Author(s):  
F. Ma ◽  
I. W. Park ◽  
J. S. Kim
Keyword(s):  
Large Scale ◽  
Substantial Reduction ◽  
Computational Effort ◽  
Frequency Separation ◽  
Common Procedure ◽  
Damping Matrix ◽  
Natural Modes ◽  
Modal Damping ◽  
Modal Coupling ◽  
Damped Systems

Abstract A common procedure in the solution of a nonclassically damped linear system is to neglect the off-diagonal elements of the associated damping matrix. For a large-scale system, substantial reduction in computational effort is achieved by this method of decoupling the system. Clearly, the decoupling approximation is valid only if modal coupling can somehow be neglected. The purpose of this paper is to study the characteristics of modal coupling, which is amenable to a complex representation. An analytical formulation that facilitates the evaluation of modal coupling is developed. Contrary to widely accepted beliefs, it is shown that neither frequency separation of the natural modes nor strong diagonal dominance of the modal damping matrix would be sufficient to suppress the sometimes significant effect of modal coupling.

On the Approximate Solution of Nonclassically Damped Linear Systems

1993 ◽  
Vol 60 (3) ◽  
pp. 695-701 ◽  
Author(s):  
J. H. Hwang ◽  
F. Ma
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Error Bound ◽  
Large Scale ◽  
Substantial Reduction ◽  
Approximation Error ◽  
Computational Effort ◽  
Common Procedure ◽  
Damping Matrix ◽  
Modal Damping

A common procedure in the solution of a nonclassically damped linear system is to neglect the off-diagonal elements of the associated modal damping matrix. For a large-scale system, substantial reduction in computational effort is achieved by this method of decoupling the system. In the present paper, the error introduced by disregarding the off-diagonal elements is evaluated, and a quadrature formula for the approximation error is derived. A tight error bound is then obtained. In addition, an effective scheme to improve the accuracy of the approximate solution is outlined.

Characteristics of Modal Coupling in Nonclassically Damped Systems Under Harmonic Excitation

1994 ◽  
Vol 61 (1) ◽  
pp. 77-83 ◽  
Author(s):  
I. W. Park ◽  
J. S. Kim ◽  
F. Ma
Keyword(s):  
Harmonic Excitation ◽  
Frequency Separation ◽  
Diagonal Dominance ◽  
Normal Coordinates ◽  
Damping Matrix ◽  
Damped System ◽  
Natural Modes ◽  
Modal Damping ◽  
Modal Coupling ◽  
Damped Systems

The normal coordinates of a nonclassically damped system are coupled by nonzero off-diagonal elements of the modal damping matrix. The purpose of this paper is to study the characteristics of modal coupling, which is amenable to a complex representation. An analytical formulation is developed to facilitate the evaluation of modal coupling. Contrary to widely accepted beliefs, it is shown that enhancing the diagonal dominance of the modal damping matrix or increasing the frequency separation of the natural modes need not diminish the effect of modal coupling. The effect of modal coupling may even increase. It is demonstrated that, within the practical range of engineering applications, neither diagonal dominance of the modal damping matrix nor frequency separation of the natural modes would be sufficient for neglecting modal coupling.

scholarly journals On Decoupling the Equations of Motion of Nonclassically Damped Systems

1989 ◽  
Author(s):  
F. Ma ◽  
J. H. Hwang
Keyword(s):  
Approximate Solution ◽  
Linear Systems ◽  
Error Bounds ◽  
Equations Of Motion ◽  
Effective Procedure ◽  
Common Procedure ◽  
Damping Matrix ◽  
Alternative Techniques ◽  
Damped Systems

One common procedure in the solution of a damped linear systems with small off-diagonal damping elements is to neglect the off-diagonal elements of the normalized damping matrix. The extent of approximation introduced by this method of decoupling the system is evaluated, and tight error bounds are derived by alternative techniques. An effective procedure to improve the accuracy of the approximate solution is outlined.

Diagonal Dominance and the Decoupling Approximation in Damped Discrete Linear Systems

2007 ◽  
Author(s):  
Matthias Morzfeld ◽  
Nopdanai Ajavakom ◽  
Fai Ma
Keyword(s):  
Diagonal Element ◽  
Diagonal Dominance ◽  
Damping Matrix ◽  
Damped System ◽  
Modal Damping ◽  
Principal Coordinates ◽  
Discrete Linear Systems ◽  
Modal Coupling ◽  
Decoupling Approximation ◽  
Damped Systems

The principal coordinates of a non-classically damped linear system are coupled by nonzero off-diagonal element of the modal damping matrix. In the analysis of non-classically damped systems, a common approximation is to ignore the off-diagonal elements of the modal damping matrix. This procedure is termed the decoupling approximation. It is widely accepted that if the modal damping matrix is diagonally dominant, then errors due to the decoupling approximation must be small. In addition, it is intuitively believed that the more diagonal the modal damping matrix, the less will be the errors in the decoupling approximation. Two quantitative measures are proposed in this paper to measure the degree of being diagonal dominant in modal damping matrices. It is demonstrated that, over a finite range, errors in the decoupling approximation can continuously increase while the modal damping matrix becomes more and more diagonal with its off-diagonal elements decreasing in magnitude continuously. An explanation for this unexpected behavior is presented. Within a practical range of engineering applications, diagonal dominance of the modal damping matrix may not be sufficient for neglecting modal coupling in a damped system.

Permeability characterization of the Soultz and Ogachi large‐scale reservoir using induced microseismicity

Geophysics ◽  
2002 ◽  
Vol 67 (1) ◽  
pp. 204-211 ◽  
Author(s):  
Pascal Audigane ◽  
Jean‐Jacques Royer ◽  
Hideshi Kaieda
Keyword(s):  
Large Scale ◽  
Pressure Oscillation ◽  
Data Sets ◽  
Active Volume ◽  
Common Procedure ◽  
Order Of Magnitude ◽  
Different Depths ◽  
The Difference

Hydraulic fracturing is a common procedure to increase the permeability of a reservoir. It consists in injecting high‐pressure fluid into pilot boreholes. These hydraulic tests induce locally seismic emission (microseismicity) from which large‐scale permeability estimates can be derived assuming a diffusion‐like process of the pore pressure into the surrounding stimulated rocks. Such a procedure is applied on six data sets collected in the vicinity of two geothermal sites at Soultz (France) and Ogachi (Japan). The results show that the method is adequate to estimate large‐scale permeability tensors at different depths in the reservoir. Such an approach provides permeability of the medium before fracturing compatible with in situ measurements. Using a line source formulation of the diffusion equation rather than a classical point source approach, improvements are proposed for accounting in situation where the injection is performed on a well section. This technique applied to successive fluid‐injection tests indicates an increase in permeability by an order of magnitude. The underestimates observed in some cases are attributed to the difference of scale at which the permeability is estimated (some 1 km3 corresponding to the seismic active volume of rock compared to a few meters around the well for the pumping or pressure oscillation tests). One advantage of the proposed method is that it provides permeability tensor estimates at the reservoir scale.

scholarly journals Computational Issues in Damping Identification for Large Scale Problems

1997 ◽  
Author(s):  
Deborah F. Pilkey ◽  
Kevin P. Roe ◽  
Daniel J. Inman
Keyword(s):  
High Performance ◽  
Large Scale ◽  
Least Squares Method ◽  
Diagnostic Techniques ◽  
Computational Effort ◽  
Analytical Models ◽  
High Performance Fortran ◽  
Damping Matrix ◽  
Large Scale Problems ◽  
Vibration Responses

Abstract Damage detection and diagnostic techniques using vibration responses that depend on analytical models provide more information about a structure’s integrity than those that are not model based. The drawback of these approaches is that some form of a workable model is required. Typically, models of practical structures and their corresponding computational effort are very large. One method of detecting damage in a structure is to measure excess energy dissipation, which can be seen in damping matrices. Calculating damping matrices is important because there is a correspondence between a change in the damping matrix and the change in the health of a structure. The objective of this research is to investigate the numerical problems associated with computing damping matrices using inverse methods. Two damping identification methods are tested for efficiency in large-scale applications. One is an iterative routine, and the other a least squares method. Numerical simulations have been performed on multiple degree-of-freedom models to test the effectiveness of the algorithm and the usefulness of parallel computation for the problems. High Performance Fortran is used to parallelize the algorithm.

scholarly journals Amalgamation of cloud-based colonoscopy videos with patient-level metadata to facilitate large-scale machine learning

2021 ◽  
Vol 09 (02) ◽  
pp. E233-E238
Author(s):  
Rajesh N. Keswani ◽  
Daniel Byrd ◽  
Florencia Garcia Vicente ◽  
J. Alex Heller ◽  
Matthew Klug ◽  
...  
Keyword(s):  
Machine Learning ◽  
Large Scale ◽  
Medical Center ◽  
Academic Medical Center ◽  
Procedure Time ◽  
Image Capture ◽  
Common Procedure ◽  
Patient Level Data ◽  
Patient Level ◽  
Level Data

Abstract Background and study aims Storage of full-length endoscopic procedures is becoming increasingly popular. To facilitate large-scale machine learning (ML) focused on clinical outcomes, these videos must be merged with the patient-level data in the electronic health record (EHR). Our aim was to present a method of accurately linking patient-level EHR data with cloud stored colonoscopy videos. Methods This study was conducted at a single academic medical center. Most procedure videos are automatically uploaded to the cloud server but are identified only by procedure time and procedure room. We developed and then tested an algorithm to match recorded videos with corresponding exams in the EHR based upon procedure time and room and subsequently extract frames of interest. Results Among 28,611 total colonoscopies performed over the study period, 21,170 colonoscopy videos in 20,420 unique patients (54.2 % male, median age 58) were matched to EHR data. Of 100 randomly sampled videos, appropriate matching was manually confirmed in all. In total, these videos represented 489,721 minutes of colonoscopy performed by 50 endoscopists (median 214 colonoscopies per endoscopist). The most common procedure indications were polyp screening (47.3 %), surveillance (28.9 %) and inflammatory bowel disease (9.4 %). From these videos, we extracted procedure highlights (identified by image capture; mean 8.5 per colonoscopy) and surrounding frames. Conclusions We report the successful merging of a large database of endoscopy videos stored with limited identifiers to rich patient-level data in a highly accurate manner. This technique facilitates the development of ML algorithms based upon relevant patient outcomes.

scholarly journals Nebula: ultra-efficient mapping-free structural variant genotyper

2021 ◽  
Author(s):  
Parsoa Khorsand ◽  
Fereydoun Hormozdiari
Keyword(s):  
Large Scale ◽  
Structural Variants ◽  
Sequencing Technologies ◽  
Generic Framework ◽  
Common Genetic Variants ◽  
Order Of Magnitude ◽  
Complex Events ◽  
Comparable Accuracy ◽  
Using Data ◽  
Computational Resources

Abstract Large scale catalogs of common genetic variants (including indels and structural variants) are being created using data from second and third generation whole-genome sequencing technologies. However, the genotyping of these variants in newly sequenced samples is a nontrivial task that requires extensive computational resources. Furthermore, current approaches are mostly limited to only specific types of variants and are generally prone to various errors and ambiguities when genotyping complex events. We are proposing an ultra-efficient approach for genotyping any type of structural variation that is not limited by the shortcomings and complexities of current mapping-based approaches. Our method Nebula utilizes the changes in the count of k-mers to predict the genotype of structural variants. We have shown that not only Nebula is an order of magnitude faster than mapping based approaches for genotyping structural variants, but also has comparable accuracy to state-of-the-art approaches. Furthermore, Nebula is a generic framework not limited to any specific type of event. Nebula is publicly available at https://github.com/Parsoa/Nebula.

Efficient and High-Quality Seeded Graph Matching: Employing Higher-order Structural Information

2021 ◽  
Vol 15 (3) ◽  
pp. 1-31
Author(s):  
Haida Zhang ◽  
Zengfeng Huang ◽  
Xuemin Lin ◽  
Zhe Lin ◽  
Wenjie Zhang ◽  
...  
Keyword(s):  
Large Scale ◽  
Graph Matching ◽  
Structural Information ◽  
Experimental Studies ◽  
Higher Order ◽  
Personalized Pagerank ◽  
Matching Accuracy ◽  
Approximation Techniques ◽  
Order Of Magnitude ◽  
Matching Score

Driven by many real applications, we study the problem of seeded graph matching. Given two graphs and , and a small set of pre-matched node pairs where and , the problem is to identify a matching between and growing from , such that each pair in the matching corresponds to the same underlying entity. Recent studies on efficient and effective seeded graph matching have drawn a great deal of attention and many popular methods are largely based on exploring the similarity between local structures to identify matching pairs. While these recent techniques work provably well on random graphs, their accuracy is low over many real networks. In this work, we propose to utilize higher-order neighboring information to improve the matching accuracy and efficiency. As a result, a new framework of seeded graph matching is proposed, which employs Personalized PageRank (PPR) to quantify the matching score of each node pair. To further boost the matching accuracy, we propose a novel postponing strategy, which postpones the selection of pairs that have competitors with similar matching scores. We show that the postpone strategy indeed significantly improves the matching accuracy. To improve the scalability of matching large graphs, we also propose efficient approximation techniques based on algorithms for computing PPR heavy hitters. Our comprehensive experimental studies on large-scale real datasets demonstrate that, compared with state-of-the-art approaches, our framework not only increases the precision and recall both by a significant margin but also achieves speed-up up to more than one order of magnitude.

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