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.

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.

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.

Approximate Decoupling of the Equations of Motion of Linear Underdamped Systems

1988 ◽  
Vol 55 (3) ◽  
pp. 716-720 ◽  
Author(s):  
S. M. Shahruz ◽  
F. Ma
Keyword(s):  
Linear System ◽  
Error Bound ◽  
Error Bounds ◽  
Equations Of Motion ◽  
Diagonal Matrix ◽  
Common Procedure ◽  
Damping Matrix ◽  
Diagonally Dominant

One common procedure in the solution of a normalized damped linear system with small off-diagonal damping elements is to replace the normalized damping matrix by a selected diagonal matrix. The extent of approximation introduced by this method of decoupling the system is evaluated, and tight error bounds are derived. Moreover, if the normalized damping matrix is diagonally dominant, it is shown that decoupling the system by neglecting the off-diagonal elements indeed minimizes the error bound.

Some Remarks About the Decoupling Approximation of Damped Linear Systems

2009 ◽  
Author(s):  
Matthias Morzfeld ◽  
Nopdanai Ajavakom ◽  
Fai Ma
Keyword(s):  
Linear Systems ◽  
Approximation Error ◽  
Driving Frequency ◽  
Finite Range ◽  
Diagonal Dominance ◽  
Damping Matrix ◽  
Modal Damping ◽  
Diagonally Dominant ◽  
Decoupling Approximation ◽  
Damped Systems

A common approximation in the analysis of non-classically damped systems is to ignore the off-diagonal elements of the modal damping matrix. This procedure is termed the decoupling approximation. It is generally believed that errors due to the decoupling approximation should be negligible if the modal damping matrix is diagonally dominant. In addition, the errors are expected to decrease as the modal damping matrix becomes more diagonally dominant. It is shown numerically in this paper that, over a finite range, errors due to the decoupling approximation can increase monotonically at any specified rate while the modal damping matrix becomes more diagonally dominant with its off-diagonal elements decreasing continuously in magnitude. These unexpected drifts in errors due to the decoupling approximation can be observed at any driving frequency. Small off-diagonal elements in the modal damping matrix may not be sufficient to ensure small errors due to the decoupling approximation. Error-criteria based solely upon diagonal dominance of the modal damping matrix cannot be accurate.

An Efficient Technique for the Approximate Analysis of Vibro-Impact

1983 ◽  
Vol 105 (3) ◽  
pp. 332-336 ◽  
Author(s):  
R. K. Miller ◽  
B. Fatemi
Keyword(s):  
Approximate Solution ◽  
Substantial Reduction ◽  
Solution Procedure ◽  
Computational Effort ◽  
Mean Square ◽  
Base Excitation ◽  
Weighted Mean ◽  
Linearization Technique ◽  
Adjacent Structures ◽  
Impact Problems

An approximate solution procedure is presented for a class of steady vibro-impact problems consisting of adjacent structures separated by a gap and subjected to harmonic base excitation. The procedure is based on a weighted mean-square linearization technique, and is capable of substantial reduction of computational effort over that required for an exact numerical simulation. As an illustration of the general approach, a detailed analysis of an example problem is presented, together with a comparison of results with an exact solution. It is shown for the example problem that the level of accuracy of the approximate solution is adequate for many applications.

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 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.

Normalization Bernstein Basis For Solving Fractional Fredholm-Integro Differential Equation

2018 ◽  
pp. 491
Author(s):  
Abdul Khaleq O. Al-Jubory ◽  
Shaymaa Hussain Salih
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Linear System ◽  
Differential Equations ◽  
Bernstein Basis ◽  
Traditional Methods ◽  
Integro Differential Equation

In this work, we employ a new normalization Bernstein basis for solving linear Freadholm of fractional integro-differential equations  nonhomogeneous  of the second type (LFFIDEs). We adopt Petrov-Galerkian method (PGM) to approximate solution of the (LFFIDEs) via normalization Bernstein basis that yields linear system. Some examples are given and their results are shown in tables and figures, the Petrov-Galerkian method (PGM) is very effective and convenient and overcome the difficulty of traditional methods. We solve this problem (LFFIDEs) by the assistance of Matlab10.   

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.

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