Page 174 - 《振动工程学报》2026年第5期

第 39 卷第 5 期 振 动 工 程 学 报 Vol. 39 No. 5
2026 年 5 月 Journal of Vibration Engineering May 2026

基 于 滑 动 包 络 中 值 的 趋 势 项 提 取

及 其 在 位 移 反 演 中 的 应 用

高晓建， 何浩祥， 国海楠， 孙澔鼎

（北京工业大学工程抗震与结构诊治北京市重点实验室，北京 100124）

摘要：工程结构的动态位移是结构动力性能分析及健康监测等诸多领域研究的重要物理信息，在部分实际工程中难以实现直
接高精度测量。利用实测的加速度响应和频域积分算法反演非线性位移时精度较差，基于时域积分算法反演则会出现趋势
项。为实现动态位移的精确反演，对时域积分产生趋势项的原因进行剖析，提出基于滑动包络中值 (sliding envelope median，
SEM) 的趋势项提取算法。通过数值算例对 SEM 算法的参数进行敏感性分析，确定参数设置准则。设置不同频率范围和幅值
的线性和非线性数值模拟工况，应用 SEM 算法对各工况下的时域积分结果进行趋势项提取和校正，并与频域积分法、传统多
项式拟合法和基于 EMD 的趋势项去除方法进行对比。结果表明 SEM 算法在非线性工况中的精度优势显著。将多种工况下
的位移响应作为振动台控制输入，通过安装多种传感器对振动台面响应进行采集。利用实测数据对 SEM 算法进行验证并与
其他方法对比。试验结果表明，SEM 算法在参数设置、准确度校正、效率校正以及非线性信号的处理方面具有优势和工程实
用性。
关键词： 位移响应；趋势项提取；位移反演；时域积分；包络中值
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中图分类号：TU317 .1 文献标志码：A DOI：10.16385/j.cnki.issn.1004-4523.202404029

Trend term extraction based on sliding envelope median

and its application in displacement inversion

GAO Xiaojian，HE Haoxiang，GUO Hainan，SUN Haoding
（Beijing Key Laboratory of Earthquake Engineering and Structural Retrofit，Beijing University of Technology，Beijing 100124，China）

Abstract： The dynamical displacement of engineering structures is important physical information for research fields such as structural
dynamic alperformance analysis and health monitoring. However，high-precision direct measurement of displacement is often challenging in
many practical engineering applications. Utilizing the measured acceleration responses and the frequency domain integration algorithms for
displacement inversion tends to yield poor accuracy in nonlinear signal applications，besides the time domain integration algorithms often
suffer from trend terms issues. To achieve accurate inversion of displacement responses， this study analyzes the reasons for trend terms
generated by time domain integration and a trend term extraction algorithm based on sliding envelope median (SEM) is proposed. Sensitivity
analysis of SEM parameters is conducted using numerical examples to determine parameter setting guidelines. Linear and nonlinear numerical
simulation scenarios with different frequency ranges and amplitudes are established. The SEM algorithm is applied to extract andcorrect trend
terms from time domain integration results under various scenarios， and compared with the frequency domain integration method， the
traditional polynomial fitting method， and the trend term removal method based on empirical mode decomposition (EMD). The results
demonstrate that the SEM algorithm exhibits significant advantages in accuracy under nonlinear scenarios. The displacement responses under
various scenarios from the numerical models are used as the inputs for shaking table control，and the responses of the shaking table surface are
collected using multiple sensors. The SEM algorithm is validated using experimental data and compared with other methods. The experimental
results show that the SEM algorithm has advantages and engineering practicality in parameter setting， calibration accuracy， calibration
efficiency，and processing of nonlinear signals.
Keywords：displacement response；trend term extraction；displacement inversion；time-domain integration；envelope median

收稿日期：2024-04-11；修订日期：2024-10-17
基金项目：国家自然科学基金资助项目 (52378469)