• CN:11-2187/TH
  • ISSN:0577-6686

机械工程学报 ›› 2019, Vol. 55 ›› Issue (3): 81-89.doi: 10.3901/JME.2019.03.081

• 机械动力学 • 上一篇    下一篇

机械结构冲击载荷稀疏识别方法研究

乔百杰1,2, 陈雪峰1,2, 刘金鑫1,2, 王诗彬1,2   

  1. 1. 西安交通大学机械工程学院 西安 710049;
    2. 西安交通大学机械制造系统工程国家重点实验室 西安 710049
  • 收稿日期:2018-04-09 修回日期:2018-10-19 出版日期:2019-02-05 发布日期:2019-02-05
  • 通讯作者: 陈雪峰(通信作者),男,1975年出生,博士,教授,博士研究生导师。主要研究方向为机械装备动态分析与故障诊断。E-mail:chenxf@xjtu.edu.cn
  • 作者简介:乔百杰,男,1985年出生,博士,讲师。主要研究方向为载荷识别、结构动力学反演理论、航空发动机叶片动应变场重构。E-mail:qiao1224@xjtu.edu.cn
  • 基金资助:
    国家自然科学基金(51705397)、中国博士后基金(2017M610636)和国家重点基础研究发展计划(2015CB057400)资助项目。

Sparse Identification of Impact Force Acting on Mechanical Structures

QIAO Baijie1,2, CHEN Xuefeng1,2, LIU Jinxin1,2, WANG Shibin1,2   

  1. 1. School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049;
    2. The State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University, Xi'an 710049
  • Received:2018-04-09 Revised:2018-10-19 Online:2019-02-05 Published:2019-02-05

摘要: 冲击载荷识别在结构健康监测、动力学优化设计、铣削力测量等领域扮演重要角色。然而,现有的基于L2范数的冲击载荷识别正则化方法在识别精度、稳定性、计算效率、参数选取等方面均存在瓶颈和局限。近年来兴起的稀疏正则化理论为冲击载荷识别提供了一种新的探索途径。充分利用冲击载荷在时域内稀疏的先验信息,提出冲击载荷稀疏识别新方法,通过最小化L1罚函数项取代传统的最小化L2罚函数项,建立基于L1范数的稀疏识别正则化模型,突破基于L2范数的冲击载荷识别方法精度低的瓶颈。基于L1范数的稀疏识别方法与基于L2范数的Tikhonov正则化方法在机械结构单源和多源冲击载荷识别中进行了对比。薄板结构冲击载荷识别试验表明:基于L1范数的正则化解在时域内非常稀疏,冲击载荷非加载区噪声被极大地抑制;稀疏识别方法在重构冲击载荷时间历程、稳定性和计算效率方面均优于传统的Tikhonov方法。

关键词: 冲击载荷识别, 反问题, 稀疏识别, 正则化

Abstract: Impact force identification plays an important role in structural health monitoring, dynamics optimization design, milling force measurement, etc. However, the traditional L2 norm-based regularization methods run into the bottleneck and limitation on identification accuracy, stability, computational efficiency, parameter selection, etc. Sparse regularization theory widely developed in recent years is a promising technique for impact force identification. Considering the prior information that the impact force is sparse in time domain, a general impact force sparse identification model is proposed, where the traditional minimization L2 norm penalty is replaced by the minimization L1 norm penalty. A sparse regularization model based on L1 norm is established, leading to breaking through the limitation of the low identification accuracy of the traditional L2 norm-based regularization methods in impact force identification. The sparse identification method based on L1 norm is examined and compared with the Tikhonov regularization method based on L2 norm under single impact force and multiple impact forces. Experimental results of identifying impact force acting on a thin plate structure demonstrate that the sparse regularization solution based on L1 norm is sufficiently sparse in time domain, where the noise in the unloading stage of impact force is greatly inhibited; the proposed sparse identification method has great advantages of reconstructing impact force history, stability and computational efficiency over the traditional Tikhonov regularization method.

Key words: impact force identification, inverse problem, regularization, sparse identification

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