A priori error estimator for reduced-order models based on the higher-order Craig-Bampton method in dynamic substructuring
Abstract
The higher-order Craig-Bampton (HCB) method improves reduced-model accuracy through successive residual-mode enrichments. This study proposes an a priori estimator for the eigenvalue error remaining in the first-order HCB model (HCB-1) without using the full-order eigensolution. The estimator is defined as the relative difference between the HCB-1 and HCB-2 eigenvalues. Under symmetric Ritz approximation assumptions, ordered positive eigenvalues, nested augmented spaces, and preservation of retained eigenvalues by the System Equivalent Reduction Expansion Process (SEREP), the estimator is shown to be non-negative and to provide a lower bound on the relative HCB-1 eigenvalue error. A projection-based expression and an exact error identity are also derived, clarifying the conditions under which the estimator is accurate and showing that the lower-bound property alone does not guarantee a prescribed tolerance. Numerical results for a plate, an elbow pipe, and a reactor pressure vessel show estimation-to-error ratios of about 0.85-0.99, while a cost assessment reports the additional expense associated with the HCB-2 reference solution.
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BibTeX
@misc{kim2026priori,
title = {{A priori error estimator for reduced-order models based on the higher-order Craig-Bampton method in dynamic substructuring}},
author = {Jaemin Kim and Seung-Hwan Boo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.05625},
eprint = {2608.05625},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.05625},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A priori error estimator for reduced-order models based on the higher-order Craig-Bampton method in dynamic substructuring
AU - Jaemin Kim
AU - Seung-Hwan Boo
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2608.05625
UR - https://arxiv.org/abs/2608.05625
AB - The higher-order Craig-Bampton (HCB) method improves reduced-model accuracy through successive residual-mode enrichments. This study proposes an a priori estimator for the eigenvalue error remaining in the first-order HCB model (HCB-1) without using the full-order eigensolution. The estimator is defined as the relative difference between the HCB-1 and HCB-2 eigenvalues. Under symmetric Ritz approximation assumptions, ordered positive eigenvalues, nested augmented spaces, and preservation of retained eigenvalues by the System Equivalent Reduction Expansion Process (SEREP), the estimator is shown to be non-negative and to provide a lower bound on the relative HCB-1 eigenvalue error. A projection-based expression and an exact error identity are also derived, clarifying the conditions under which the estimator is accurate and showing that the lower-bound property alone does not guarantee a prescribed tolerance. Numerical results for a plate, an elbow pipe, and a reactor pressure vessel show estimation-to-error ratios of about 0.85-0.99, while a cost assessment reports the additional expense associated with the HCB-2 reference solution.
ER -