A priori error estimator for reduced-order models based on the higher-order Craig-Bampton method in dynamic substructuring

Abstract

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.