Structural load identification and response reconstruction based on improved multiplicative regularization

MU Yuanbo; YIN Hong; PENG Zhenrui

doi:10.16579/j.issn.1001.9669.2026.02.009

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Structural load identification and response reconstruction based on improved multiplicative regularization

·Vibration·Noise·Monitoring·Diagnosis· | 更新时间：2026-02-12

- Structural load identification and response reconstruction based on improved multiplicative regularization
- Journal of Mechanical Strength Vol. 48, Issue 2, Pages: 72-79(2026)
- 作者机构：
  
  兰州交通大学机电工程学院，兰州 730070
- 作者简介：
  
  PENG Zhenrui, E-mail: pzrui@163.com
- 基金信息：
  
  National Natural Science Foundation of China(62161018)
- DOI：10.16579/j.issn.1001.9669.2026.02.009
  CLC： TH113.1
- Received：18 March 2024，
  
  Revised：2024-04-19，
  
  Published：15 February 2026
- 稿件说明：
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牟元博，殷红，彭珍瑞. 基于改进乘法正则化的结构载荷识别与响应重构［J］. 机械强度，2026，48（2）：72-79.

MU Yuanbo，YIN Hong，PENG Zhenrui. Structural load identification and response reconstruction based on improved multiplicative regularization［J］. Journal of Mechanical Strength，2026，48（2）：72-79.
牟元博，殷红，彭珍瑞. 基于改进乘法正则化的结构载荷识别与响应重构［J］. 机械强度，2026，48（2）：72-79. DOI： 10.16579/j.issn.1001.9669.2026.02.009.

MU Yuanbo，YIN Hong，PENG Zhenrui. Structural load identification and response reconstruction based on improved multiplicative regularization［J］. Journal of Mechanical Strength，2026，48（2）：72-79. DOI： 10.16579/j.issn.1001.9669.2026.02.009.

摘要

目的

为提高传统乘法正则化方法识别载荷和重构响应的精度，提出一种考虑测量噪声影响的改进乘法正则化方法来识别载荷，并将识别出的载荷用于重构响应。

方法

首先，基于状态空间模型构建载荷识别和响应重构方程；其次，对测量响应进行奇异熵增量去噪，构造目标函数识别结构的外部载荷，重新定义全局加权矩阵，引入可根据奇异值大小而选择性修正的全局平滑算子，以提高载荷满足约束的程度；再次，采用迭代加权最小二乘法求解基于去噪后的测量响应和传递矩阵建立的目标函数，得到载荷的稳定解，并重构未测量位置的响应；最后，对简支梁模型进行数值仿真和试验分析，验证本文方法的有效性。

结果

结果表明，提出的方法可以改善重构方程的不适定性，能较准确地识别载荷，并重构未测量位置的动态响应。

Abstract

Objective

To improve the accuracy of loads identification and responses reconstruction for the traditional multiplicative regularization method

an improved multiplicative regularization method considering the influence of measurement noise was proposed to identify the loads

and the responses were reconstructed using the identified loads.

Methods

Firstly

the load identification and response reconstruction equations were constructed based on the state space model. Secondly

the singular entropy increment denoising of the measurement responses was carried out

the objective function was constructed to identify the external loads of the structure

the global weighting matrix was redefined

and the global smoothing operator that can be selectively modified according to the magnitude of the singular value was introduced to improve the degree to which the load satisfies the constraints. Thirdly

the iterative weighted least squares method was adopted to solve the objective function based on the denoised measurement responses and the transfer matrix

the stable solution of the load was obtained and the responses of the unmeasured positions were reconstructed. Finally

the numerical simulation and the test analysis for the simply supported beam model were carried out to verify the effectiveness of the proposed method.

Results

The results show that the proposed method can improve the ill-posedness of the reconstruction equations

identify the loads accurately and reconstruct the dynamic responses of the unmeasured positions.

关键词

Keywords

references

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