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

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振动与冲击 ›› 2024, Vol. 43 ›› Issue (14) : 148-155.

论文

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

陈林1,2，王亚南1,2，程昊3，刘军江1,2，乔百杰1,2，陈雪峰1,2

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

CHEN Lin1,2,WANG Yanan1,2,CHENG Hao3,LIU Junjiang1,2,QIAO Baijie1,2,CHEN Xuefeng1,2

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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，本文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。

Abstract

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 identify 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, this paper proposes a novel frequency-domain non-convex sparse regularization method for impact force identification based on the spatial sparse prior of impact forces. The proposed method combines the non-convex advantages of the generalized minmax concave penalty with the convexity-preserving characteristics, and utilizes the forward-backward splitting algorithm 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. Results indicated that the proposed method can accurately localize the impact positions and reconstruct the time history of impact forces, both in the case of even-determined and 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 L1 regularization.

导出引用

陈林1, 2, 王亚南1, 2, 程昊3, 刘军江1, 2, 乔百杰1, 2, 陈雪峰1, 2. 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[J]. 振动与冲击, 2024, 43(14): 148-155

CHEN Lin1, 2, WANG Yanan1, 2, CHENG Hao3, LIU Junjiang1, 2, QIAO Baijie1, 2, CHEN Xuefeng1, 2 . Frequency-domain non-convex sparse regularization method for impact force identification based on spatial sparsity prior[J]. Journal of Vibration and Shock, 2024, 43(14): 148-155

参考文献

[1] 赵林虎, 周丽. 复合材料蜂窝夹芯结构低速冲击位置识别研究[J]. 振动与冲击, 2012, 31(02):67-71+108. ZHAO Lin-hu, ZHOU Li. Localization of low-velocity impact on a composite honeycomb sandwitch structure [J]. Journal of vibration and shock, 2012, 31(02): 67-71+108. [2] 黄志超, 骆强, 赖家美, 等. 环氧树脂/玻璃纤维/碳纤维混杂复合板低速冲击及损伤检测[J]. 中国塑料, 2021, 35(06): 46-52. HUANG Zhi-chao, LUO Qiang, LAI Jiamei, et al. Low⁃velocity Impact and Damage Detection of Epoxy/Glass and Carbon Fiber Composite Plates [J]. CHINA PLASTICS, 2021, 35(06): 46-52. [3] 严刚, 孙浩. 基于贝叶斯压缩感知的复合材料结构冲击载荷识别研究[J]. 振动工程学报, 2018, 31(03): 483-489. YAN Gang, Sun Hao. Identification of impact force for composite structure using Bayesian compressive sensing [J]. Journal of Vibration Engineering, 2018, 31(03): 483-489. [4] Liu J, Sun X, Han X, et al. Dynamic load identification for stochastic structures based on Gegenbauer polynomial approximation and regularization method[J]. Mechanical Systems and Signal Processing, 2015, 56: 35-54. [5] Jacquelin E, Bennani A, Hamelin P. Force reconstruction: analysis and regularization of a deconvolution problem [J]. Journal of sound and vibration, 2003, 265(1): 81-107. [6] 郭荣, 房怀庆, 裘剡, 等. 基于Tikhonov正则化及奇异值分解的载荷识别方法[J]. 振动与冲击, 2014, 33(06): 53-8. GUO Rong, FANG Huai-qing, QIU Shan, et al. Novel load identification method based on the combination of Tikhonov regularization and singular value decomposition [J]. Journal of vibration and shock, 2014, 33(06): 53-8. [7] Yan G, Sun H, Büyüköztürk O. Impact load identification for composite structures using Bayesian regularization and unscented Kalman filter [J]. Structural Control and Health Monitoring, 2017, 24(5): e1910. [8] Rezayat A, Nassiri V, De Pauw B, et al. Identification of dynamic forces using group-sparsity in frequency domain [J]. Mechanical Systems and Signal Processing, 2016, 70: 756-68. [9] 乔百杰, 陈雪峰, 刘金鑫, 等. 机械结构冲击载荷稀疏识别方法研究[J]. 机械工程学报, 2019, 55(03): 81-89. QIAO Bai-jie, CHEN Xue-feng, LIU Jin-xin, et al. Sparse identification of impact force acting on mechanical structures [J]. Journal of Mechanical Engineering, 2019, 55(03): 81-89. [10] Pan C, Yu L, Liu H, et al. Moving force identification based on redundant concatenated dictionary and weighted l1-norm regularization [J]. Mechanical Systems and Signal Processing, 2018, 98: 32-49. [11] 陈辉, 缪炳荣, 赵浪涛, 等. 基于L1范数正则化和最小二乘优化的冲击载荷识别研究[J]. 噪声与振动控制, 2023, 43(01): 62-67+99. CHEN Hui, MIAO Bing-rong, ZHAO Lang-tao, et al. Research on impact load identification based on L1-norm regularization and least squares optimization [J]. Noise and Vibration Control, 2023, 43(01): 62-67+99. [12] Xu Z, Chang X, Xu F, et al. regularization: A thresholding representation theory and a fast solver [J]. IEEE Transactions on neural networks and learning systems, 2012, 23(7): 1013-27. [13] Aucejo M, De Smet O. A generalized multiplicative regularization for input estimation [J]. Mechanical Systems and Signal Processing, 2021, 157: 107637. [14] Zhou R, Wang Y, Qiao B, et al. Impact force identification on composite panels using fully overlapping group sparsity based on Lp-norm regularization [J]. Structural Health Monitoring, 2023, 0(0). doi: 10.1177/14759217231165701. [15] Chartrand R, Yin W. Nonconvex sparse regularization and splitting algorithms [J]. Splitting methods in communication, imaging, science, and engineering, 2016: 237-49. [16] Rezayat A, Nassiri V, De Pauw B, et al. Identification of dynamic forces using group-sparsity in frequency domain [J]. Mechanical Systems and Signal Processing, 2016, 70: 756-68. [17] Liu J, Li K. Sparse identification of time-space coupled distributed dynamic load [J]. Mechanical Systems and Signal Processing, 2021, 148: 107177. [18] Daubechies I, Defrise M, De Mol C. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint [J]. Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences, 2004, 57(11): 1413-57. [19] Selesnick I. Sparse regularization via convex analysis [J]. IEEE Transactions on Signal Processing, 2017, 65(17): 4481-94. [20] 杨力, 魏中浩, 张冰尘, 等. 基于广义最小最大凹惩罚项的ISAR稀疏成像方法 [J]. 中国科学院大学学报, 2019, 36(02): 244-50. YANG Li，WEI Zhong-hao，ZHANG Bing-chen，et al． ISAR sparse imaging algorithm based on generalized minimax concave penalty ［J］． Journal of University of Chinese Academy of Sciences, 2019, 36(2): 244-250． [21] Hansen P C. Analysis of discrete ill-posed problems by means of the L-curve [J]. SIAM review, 1992, 34(4): 561-580.