Model reduction based on prior response covariance: enhancing accuracy and adaptability for diverse structural dynamics problems

Efficient model reduction of large-scale structural dynamic systems while maintaining high prediction accuracy is critical for engineering analysis and design. This work proposes a novel framework for model reduction and master degrees of freedom (DOFs) selection. By reformulating model reduction as a full-field response reconstruction problem, the proposed method leverages prior information on system response covariance to construct transformation matrices and select optimal master DOFs set through conditional Gaussian probabilities analysis. The proposed framework demonstrates three key innovations: (1) systematic integration of load and damping characteristics into the response covariance matrix, enabling adaptability to diverse scenarios including non-proportional damping and dense-modal systems; (2) derivation of transformation matrices through conditional Gaussian probabilities analysis, establishing mathematical equivalence to the System Equivalent Reduction and Expansion Process (SEREP) when employing modal-based covariance; (3) a greedy algorithm for optimal master DOFs selection that minimizes prediction covariance through iterative refinement. Two distinct strategies are presented for constructing prior covariance matrices: a modal participation factor approach for systems with well-defined dynamic characteristics, and a time-domain sampling method for structures with complex damping or uncertain modal parameters. Numerical results show that the proposed method significantly enhances accuracy in both time and frequency domain responses with limited master DOFs. Case studies highlight particular effectiveness in challenging scenarios involving narrow-band excitation coinciding with dense modal regions and localized non-proportional damping configurations.