基于空间稀疏先验的冲击载荷识别频域非凸稀疏正则化方法  

Frequency-domain non-convex sparse regularization method for impact force identification based on spatial sparsity prior

作　　者：陈林[1,2] 王亚南 程昊 刘军江[1,2] 乔百杰 陈雪峰 CHEN Lin;WANG Yanan;CHENG Hao;LIU Junjiang;QIAO Baijie;CHEN Xuefeng(National Key Lab of Aerospace Power System and Plasma Technology,Xi’an Jiaotong University,Xi’an 710049,China;School of Mechanical Engineering,Xi’an Jiaotong University,Xi’an 710049,China;Beijing Institute of Structure and Environment Engineering,Beijing 100076,China)

机构地区：[1]西安交通大学航空动力系统与等离子体技术全国重点实验室,西安710049 [2]西安交通大学机械工程学院,西安710049 [3]北京强度环境研究所,北京100076

出　　处：《振动与冲击》2024年第14期148-155,188,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金(51705397)。

摘　　要：复合材料因其强度高、刚度高、密度小等优点而广泛应用于航空、航天等领域。但由于其抗冲击性差,监测作用于复合材料结构上的冲击载荷对于结构快速检测损伤十分重要。经典的Tikhonov正则化方法在欠定情况下求解载荷识别问题时容易在载荷非加载区识别出虚假力;近年来兴起的L1范数稀疏正则化方法在识别冲击载荷时常低估载荷的幅值。为了突破这些方法的局限以实现更高精度的冲击载荷识别,该研究基于冲击载荷的空间稀疏先验,提出一种新的冲击载荷识别频域非凸稀疏正则化方法。所提出的方法结合了广义极小极大凹惩罚项的非凸优势以及非凸保凸的特性,利用向前向后分裂算法进行凸优化求解,既避免了非凸优化容易收敛到局部最优解的问题,又促进了解的稀疏。分别在复合材料梁和复合材料层合板上开展了冲击载荷试验验证,试验结果表明,无论在正定还是欠定的情况下,所提出方法能在精准定位冲击位置的同时重构冲击载荷的时间历程,且该方法在促进解稀疏和识别载荷幅值方面的表现都优于L1正则化方法,其中幅值识别精度能比L1正则化提升50%以上。Composite materials are widely used in aviation,aerospace and other fields because of their advantages such as high strength,high stiffness and low density.However,due to its poor impact resistance,monitoring the impact force acting on the composite structure is very important for timely detection of structural damage.The classic Tikhonov regularization method tends to obtain false forces in the non-loaded area when solving the force identification problem under the under-determined condition.The well-known L1 sparse regularization method is prone to underestimate the amplitude of the impact force.In order to break through the limitations of these methods and identify impact forces with higher accuracy,a novel frequency-domain non-convex sparse regularization method was proposed for impact force identification based on the spatial sparse prior of impact forces.In the proposed method,the non-convex advantage of the generalized minmax concave penalty term was combined with the convexity-preserving characteristics,and the forward-backward splitting algorithm was utilized for convex optimization.This approach avoids the problem of non-convex optimization converging to local optima and promotes sparsity of the solution.Laboratory impact tests were conducted on composite beams and laminated composite plates to validate the proposed method.The results indicate that the proposed method can accurately localize the impact positions and reconstruct the time history of impact forces,in the case of either even-determined or under-determined scenarios.The performance of the proposed method in promoting solution sparsity and identifying force amplitudes is superior to the L1 regularization method,with an improvement of over 50%in amplitude identification accuracy compared to the L1 regularization method.

关 键 词：复合材料 冲击载荷识别 非凸正则化 稀疏先验 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3