改进VMD及其在时变结构地震响应瞬时频率识别中的应用  

Improved VMD and its application in instantaneous frequencyidentification of seismic responses of time-varying structures

作　　者：王焱楠 尚旭强 黄天立[1] WANG Yan-nan;SHANG Xu-qiang;HUANG Tian-li(School of Civil Engineering,Central South University,Changsha 410075,China)

机构地区：[1]中南大学土木工程学院,湖南长沙410075

出　　处：《振动工程学报》2024年第3期402-413,共12页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(52078486,U1734208);中南大学中央高校基本科研业务费专项资金资助项目(2023ZZTS0410)。

摘　　要：强地震动作用下,结构动力特性因损伤将随时间变化,变分模态分解(Variational Mode Decomposition,VMD)可用于分析结构地震响应的瞬时频率变化规律,揭示地震过程中结构的损伤状态。针对人为预设分解模态数K和二次惩罚因子α参数不准确导致VMD非平稳响应出现模态混叠的问题,提出了一种改进的VMD(Improved VMD,IVMD)算法,结合Hilbert变换(HT)可准确识别非平稳地震激励下时变结构的瞬时频率。采用多重信号分类(Multiple Signal Classification,MUSIC)算法确定分解模态数K,基于整体正交系数和能量比系数构建综合目标函数,并采用樽海鞘算法(Slap Swarm Algorithm,SSA)优化确定二次惩罚因子。在优化确定K和α参数的基础上,结合IVMD和HT识别时变结构地震响应瞬时频率。典型模拟信号和地震激励下4层时变框架结构数值模拟响应表明,相比VMD算法,IVMD算法识别得到的瞬时频率精度更高;12层钢筋混凝土框架结构模型地震模拟振动台试验数据验证了所提方法的实用性。Under the action of strong seismic excitations,structures exhibit time-varying dynamic characteristics due to damage.Variational mode decomposition(VMD)can be used to analyze the instantaneous frequency variation of structural seismic respons-es and reveal the damage condition of structures during earthquake.When VMD is adopted for decomposing the non-stationary re-sponses,there exists the problem of mode aliasing due to the artificially presetting the number of decomposed modes K and the qua-dratic penalty factorα.Aiming at solving this problem,an improved variational mode decomposition(IVMD)algorithm is pro-posed in this study,which,combined with Hilbert transform(HT),can more accurately identify the instantaneous frequencies of time-varying structures under non-stationary seismic excitations.The multiple signal classification(MUSIC)algorithm is used to determine the number of decomposition modes K.The comprehensive objective function is constructed based on the overall orthog-onal coefficient and energy ratio coefficient,and the slap swarm algorithm(SSA)is used to optimize and determine the optimal quadratic penalty factorα.Based on the optimized parameters K andα,IVMD-HT is used to identify the instantaneous frequency of time-varying structures from the seismic responses.A simulated signal and the seismic responses of a 4-layer time-varying frame structure show that the accuracy of identified instantaneous frequencies by using the IVMD algorithm is higher than the identified ones by using the VMD algorithm.The feasibility of the proposed method is verified by using shaking table test data of a 12-story reinforced concrete frame structure model.

关 键 词：地震激励 时变框架结构 振动台试验 瞬时频率识别 变分模态分解 

分 类 号：TU311.3[建筑科学—结构工程] TU323.5