基于混合正则化方法的结构载荷识别与响应重构

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振动与冲击 ›› 2024, Vol. 43 ›› Issue (6) : 104-112.

论文

彭珍瑞，周雪文

作者信息 +

Structural load identification and response reconstruction based on a hybrid regularization method

PENG Zhenrui，ZHOU Xuewen

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文章历史 +

摘要

针对结构载荷识别与响应重构问题中存在的不适定性，提出一种最小平方残差(least square minimal residual, LSMR)算法与Tikhonov正则化方法相结合的混合正则化方法，实现利用结构有限测点的加速度响应识别载荷并重构未知的各类型响应。首先，基于时域状态空间模型构建结构的传递矩阵，并建立载荷识别与响应重构方程；其次，采用混合正则化方法改善载荷识别问题的不适定性，得到载荷的正则化解，并结合响应重构方程的传递矩阵对结构的位移、速度和加速度响应进行重构；最后，通过简支梁数值仿真和试验分析验证所提方法的可行性。结果表明，所提方法能改善重构方程的不适定性，从而对结构未知载荷和各类型响应进行有效重构。

Abstract

To identify the load and reconstruct the unknown response using the acceleration response of the finite structural measurement points, a hybrid regularization method combining the least square minimal residual algorithm and Tikhonov regularization method is proposed to solve the ill-posedness of load identification and response reconstruction of structures. Firstly, the transfer matrix of the structure is constructed based on the time-domain state-space model, and the load identification and response reconstruction equations are established. Secondly, the hybrid regularization method is used to improve the ill-posedness of the load identification, and the regular solution of the load is obtained. The displacement, velocity and acceleration responses of the structure are reconstructed by combining the transfer matrix of the response reconstruction equation. Finally, the proposed method is verified by numerical simulation and experimental analysis of simply supported beams. The results show that the proposed method can improve the ill-posedness of the reconstruction equation and effectively reconstruct the unknown load and various types of response of the structure.

导出引用

彭珍瑞，周雪文. 基于混合正则化方法的结构载荷识别与响应重构[J]. 振动与冲击, 2024, 43(6): 104-112

PENG Zhenrui，ZHOU Xuewen. Structural load identification and response reconstruction based on a hybrid regularization method[J]. Journal of Vibration and Shock, 2024, 43(6): 104-112

参考文献

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