噪声与振动控制2025，Vol.45Issue(3)：21-27,48,8.DOI:10.3969/j.issn.1006-1355.2025.03.004
改进Tikhonov正则化的激励修正与结构响应重构
Improved Tikhonov Regularization for Excitation Correction and Structural Response Reconstruction
摘要
Abstract
An improved Tikhonov regularization method for excitation correction and structural response reconstruc-tion was proposed to address the difficulty of accurately identifying the excitation in structural response reconstruction and the discrete ill-posedness during the reconstruction process.Firstly,a transfer matrix was constructed based on the state space model,and external excitation identification and response reconstruction equations of the structure were introduced.Secondly,the Tikhonov regularization method was improved to enhance the discrete ill-posedness,and the regularization so-lution of the excitation was obtained.The local weighted regression was used for correction of this solution.Combining with the transfer matrix at the corresponding position,the response at the unmeasured point was reconstructed.Finally,the appli-cability of the proposed method was verified through numerical simulation of a simply supported beam and an experimental analysis of a cantilever beam.The results indicate that the proposed method can utilize the measured responses to reconstruct the excitation and the responses at unmeasured positions with high accuracy,and improve the discrete ill-posedness during the reconstruction process.关键词
振动与波/激励修正/响应重构/不适定性/正则化/局部加权回归Key words
vibration and wave/excitation correction/response reconstruction/ill-posedness/regularization/local weighted regression分类
机械工程引用本文复制引用
张大伟,殷红,彭珍瑞..改进Tikhonov正则化的激励修正与结构响应重构[J].噪声与振动控制,2025,45(3):21-27,48,8.基金项目
国家自然科学基金资助项目(62161018) （62161018）
