基于改进正则化的多点平稳随机载荷识别方法  

Multi-point Stationary Random Load Identification Method Based on Improved Regularization

作　　者：井雯 姜金辉[1] 许锋[1] 包欢迎 陈爽[1] JING Wen;JIANG Jinhui;XU Feng;BAO Huanying;CHEN Shuang(State Key Laboratory of Mechanics and Control for Aerospace Structures,Nanjing University of Aeronautics and Astronautics Nanjing,210016,China)

机构地区：[1]南京航空航天大学航空航天结构力学及控制全国重点实验室,南京210016

出　　处：《振动.测试与诊断》2025年第2期219-224,406,共7页Journal of Vibration,Measurement & Diagnosis

基　　金：国家自然科学基金资助项目(12372066,U23B6009);航空科学基金资助项目(20240013052002);江苏高校“青蓝工程”资助项目。

摘　　要：针对随机载荷识别中的病态逆问题影响识别精度、制约工程应用的问题,根据频响函数矩阵大小奇异值对识别结果稳定性影响程度的不同,在逆虚拟激励法的基础上提出一种改进正则化方法。首先,在识别过程中采用变正则化参数方式,对较小的奇异值采用较大的正则化参数修正,对较大的奇异值采用较小的正则化参数修正,以提高识别精度;其次,通过平板结构仿真分析了该方法与直接求逆法、传统Tikhonov正则化方法在5%和10%响应测量噪声水平下的载荷识别精度;最后,进行了简支梁多点平稳随机载荷试验,验证了方法的可行性。研究结果表明,与直接求逆法和传统Tikhonov正则化相比,该方法提高了载荷识别精度,对响应测量噪声具有良好的鲁棒性。The ill-conditioned inverse problem in identification of random loads seriously affects the identification accuracy and restricts the engineering applications.Aiming at this problem,a new improved regularization method is proposed based on the inverse virtual excitation method from the viewpoint that the singular value of the frequency response function matrix has different influences on the stability of the identification result.In order to improve the identification accuracy,the method changes the pattern of the traditional regularization parameters that are invariant,and adopts the changing regularization parameters in the identification process.The smaller singular value is corrected with the larger regularization parameter,and the larger singular value is corrected with the smaller regularization parameter.The load identification accuracy of this method with the direct inversion method and the traditional Tikhonov regularization method at 5% and 10% response measurement noise levels are analyzed through the simulation of a plate structure.In addition,a multi-point stationary random load test of a simply supported beam is carried out to further verify the feasibility of the method.The research results show that,compared with the direct inversion method and the traditional Tikhonov regularization,this method can effectively improve the load identification accuracy and has good robustness to the response measurement noise.

关 键 词：随机载荷识别 病态逆问题 TIKHONOV正则化 改进正则化 

分 类 号：TH113.1[机械工程—机械设计及理论] TU311.3[建筑科学—结构工程] O324[理学—一般力学与力学基础]