改进 VMD 及其在时变结构地震响应 瞬时频率识别中的应用
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TU311.3;TU323.5

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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)


Improved VMD and its application in instantaneous frequency identification of seismic responses of time-varying structures
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    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(Im‐ proved 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。

    Abstract:

    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 factor α. 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 factor α. Based on the optimized parameters K and α, 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.

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王焱楠,尚旭强,黄天立.改进 VMD 及其在时变结构地震响应 瞬时频率识别中的应用[J].振动工程学报,2024,37(3):402~413.[WANG Yan-nan, SHANG Xu-qiang, HUANG Tian-li. Improved VMD and its application in instantaneous frequency identification of seismic responses of time-varying structures[J]. Journal of Vibration Engineering,2024,37(3):402~413.]

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  • 在线发布日期: 2024-03-28
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