AI 中文总结
针对高阶Craig-Bampton（HCB）方法缺乏先验误差估计器的问题，提出分层估计框架，推导广义CB误差估计器与HCB-1误差估计器，经数值算例验证其有效性。
AI 中文摘要
Craig-Bampton（CB）方法是一种广泛应用的、基于组件模态综合（CMS）的动态子结构技术。高阶Craig-Bampton（HCB）方法通过在残差柔度矩阵的Neumann级数展开中添加残差模态来扩充CB基；其中HCB-n保留至n阶项，并通过系统等价缩减扩展过程（SEREP）缩减回CB规模，在相同模型维度下实现了更高的精度。然而，在不求解全阶问题的情况下评估降阶模型的精度仍是一个基础挑战：若需全阶解来评估误差，模型缩减的目的便无法实现。尽管HCB方法的优越性已得到证实，但尚未有人为其提出先验误差估计器（无需求解全阶特征值问题即可预测特征值误差）。本研究针对这一空白，提出了一种分层估计框架，该框架利用HCB方法的嵌套Ritz子空间结构，其中每阶更高阶解可作为估计前一阶误差的参考。该框架提供：（i）通过瑞利商扰动分析推导的广义CB误差估计器；（ii）以HCB-2特征解为参考的新型HCB-1误差估计器。对不同几何复杂度模型的数值算例验证了这两种估计器的有效性。
英文摘要
The Craig-Bampton (CB) method is a widely used dynamic substructuring technique based on component mode synthesis (CMS). The higher-order Craig-Bampton (HCB) method augments the CB basis with residual modes from a Neumann series expansion of the residual flexibility matrix, where HCB-n retains terms up to the n-th order and is reduced back to the CB size via the System Equivalent Reduction Expansion Process (SEREP), achieving improved accuracy at the same model dimension. However, assessing the accuracy of a reduced model without solving the full-order problem remains a fundamental challenge: if the full-order solution is required to evaluate the error, the purpose of model reduction is defeated. Despite the demonstrated superiority of the HCB method, no a priori error estimator (one that predicts eigenvalue errors without solving the full-order eigenvalue problem) has been proposed for it. The present work addresses this gap with a hierarchical estimation framework that exploits the nested Ritz subspace structure of the HCB method, where each higher-order solution serves as a reference for estimating the error of the preceding order. The framework provides (i) a generalized CB error estimator derived from a Rayleigh quotient perturbation analysis, and (ii) a novel HCB-1 error estimator using the HCB-2 eigensolution as a reference. Numerical examples across models of varying geometric complexity validate both estimators.
Comments25 pages, 10 figures, 7 tables
