A family of Craig–Bampton methods considering residual mode compensation

Go, Myeong-Seok; Lim, Jae Hyuk; Kim, Jin-Gyun; Hwang, Ki-ryoung

doi:10.1016/j.amc.2019.124822

Cited by 13 publications

(13 citation statements)

References 23 publications

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“…We here compare the IF‐CMS method with the other well‐known iterative CMS methods: Higher‐order CB (HCB) method 30,35 and iterative CB method 31 . Both the HCB and iterative CB methods were directly motivated from the ECB method that is the first CB approach with the residual flexibility 19 .…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…The condition numbers of the reduced matrices become worse through the iteration process. The HCB method and other related methods simply handled this issue with higher precisions such as 32 or 64 digits, 30,35 but the IF‐CMS formulation resolves it by using the preconditioning process within the standard 16 digit precision.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…The error becomes smaller through the iterative step in the both iterative methods. However, the error of the HCB method diverges from the fourth iteration step since it is implemented in 16 digits 30,35 . Furthermore, the computation efficiency may be deteriorated due to the increased matrices sizes through the iteration step.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Therefore, recently, many researchers have focused on considering residual flexibility in the conventional CMS methods. The most successful first approach considering the residual flexibility in the original CB method is the enhanced CB (ECB) method, 19 which has been a source of inspiration to many extension and application works 20‐30 . The original ECB method only considers the zeroth order of residual flexibility.…”

Section: Introductionmentioning

confidence: 99%

“…Higher precision over 16 digits and/or correction by using reference eigensolutions have been proposed, but this is still significant issue 35 . Go et al recently summarized these approaches well 30 …”

Section: Introductionmentioning

confidence: 99%

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An iterative scheme of flexibility‐based component mode synthesis with higher‐order residual modal compensation

Chung

Kim²,

Chae

et al. 2021

Numerical Meth Engineering

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An Iterative Flexibility‐based Component Mode Synthesis (IF‐CMS) is presented for the model reduction of partitioned structural dynamic systems via localized Lagrange multipliers. A distinct IF‐CMS feature is the inclusion of hierarchical residual flexibility at each iteration, resulting in considerably improved accuracy compared with the classical Craig–Bampton (CB) CMS method. The present IF‐CMS method does not increase the number of substructural modes during the hierarchical iteration process. In particular, to alleviate ill‐conditioning during the iteration steps, the proposed IF‐CMS method adopts the so‐called (qd, α, ub)‐formulation by condensing Lagrange multipliers from the original F‐CMS method. The performance of the proposed method is evaluated through numerical examples, which illustrates improved accuracy over existing CMS methods.

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Section: Numerical Experimentsmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An iterative scheme of flexibility‐based component mode synthesis with higher‐order residual modal compensation

Chung

Kim²,

Chae

et al. 2021

Numerical Meth Engineering

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Enhanced algebraic substructuring for symmetric generalized eigenvalue problems

Kalantzis

Horesh

2022

Numerical Linear Algebra App

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This article proposes a new substructuring algorithm to approximate the algebraically smallest eigenvalues and corresponding eigenvectors of a symmetric positive-definite matrix pencil (A, M). The proposed approach partitions the graph associated with (A, M) into a number of algebraic substructures and builds a Rayleigh-Ritz projection subspace by combining spectral information associated with the interior and interface variables of the algebraic domain. The subspace associated with interior variables is built by computing substructural eigenvectors and truncated Neumann series expansions of resolvent matrices. The subspace associated with interface variables is built by computing eigenvectors and associated leading derivatives of linearized spectral Schur complements. The proposed algorithm can take advantage of multilevel partitionings when the size of the pencil. Experiments performed on problems stemming from discretizations of model problems showcase the efficiency of the proposed algorithm and verify that adding eigenvector derivatives can enhance the overall accuracy of the approximate eigenpairs, especially those associated with eigenvalues located near the origin.

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Real-Time Estimation of Unmeasured Vibro-acoustic Responses Using Inverse Force Identification Technique

Cho

Lee

et al. 2022

Topics in Modal Analysis &Amp; Parameter Identification, Volume 8

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This study aimed to develop a virtual sensing algorithm of structural vibration for the real-time identification of unmeasured information. First, certain local point vibration responses (such as displacement and acceleration) are measured using physical sensors, and the data sets are extended using a numerical model to cover the unmeasured quantities through the entire spatial domain in the real-time computation process. A modified time integrator is then proposed to synchronize the physical sensors and the numerical model using inverse dynamics. In particular, an efficient inverse force identification method is derived using implicit time integration.The second-order ordinary differential formulation and its projection-based reducedorder modeling is used to avoid two times larger degrees of freedom within the state space form. Then, the Tikhonov regularization noise-filtering algorithm is employed instead of Kalman filtering. The performance of the proposed method is investigated on both numerical and experimental testbeds under sinusoidal and random excitation loading conditions. In the experimental test, the algorithm is implemented on a single-board computer, including inverse force identification and unmeasured response prediction. The results show that the virtual sensing algorithm can accurately identify unmeasured information, forces, and displacements throughout the vibration model in real time in a very limited computing environment.

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A family of Craig–Bampton methods considering residual mode compensation

Cited by 13 publications

References 23 publications

An iterative scheme of flexibility‐based component mode synthesis with higher‐order residual modal compensation

An iterative scheme of flexibility‐based component mode synthesis with higher‐order residual modal compensation

Enhanced algebraic substructuring for symmetric generalized eigenvalue problems

Real-Time Estimation of Unmeasured Vibro-acoustic Responses Using Inverse Force Identification Technique

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