覆冰四分裂导线舞动模型的稀疏识别  

Sparse Identification of Galloping Model of Iced Quad Bundle Conductors

作　　者：陈黎兵 刘小会[1,2,3] 伍川 叶中飞 张博 CHEN Libing;LIU Xiaohui;WU Chuan;YE Zhongfei;ZHANG Bo(School of Civil Engineering,Chongqing Jiaotong University,Chongqing 400074,China;Inner Mongolia Power(Group)Co.,Ltd.,Inner Mongolia Power Research Institute Branch,Hohhot 010020,Inner Mongolia,China;State Key Laboratory of Bridge and Tunnel Engineering in Mountain Areas,Chongqing Jiaotong University,Chongqing 400074,China;Henan Electric Power Research Institute,Zhengzhou 450052,Henan,China)

机构地区：[1]重庆交通大学土木工程学院,重庆400074 [2]内蒙古电力(集团)有限责任公司内蒙古电力科学研究院分公司,内蒙古呼和浩特010020 [3]重庆交通大学省部共建山区桥梁及隧道工程国家重点实验室,重庆400074 [4]国网河南省电力公司电力科学研究院,河南郑州450052

出　　处：《力学季刊》2022年第4期923-933,共11页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(51308570);重庆市自然科学基金(cstc2021jcyj-msxmX0166);内蒙古电力公司博士后项目。

摘　　要：输电线路的舞动严重威胁着电力系统运行的安全性与稳定性,准确地建立覆冰导线舞动模型变得尤为重要.为此,采用一种基于数据驱动的稀疏识别算法,该算法可从数据中有效识别出动力系统的控制方程并降低计算量.本文基于数据驱动稀疏识别算法对覆冰四分裂导线舞动方程进行识别.首先基于Hamilton原理推导出覆冰四分裂导线的振动偏微分方程,接着通过Galerkin方法将该偏微分方程转化为常微分方程,然后建立气动荷载模型,将气动力引入到舞动方程中,进而得到最终的覆冰四分裂导线舞动常微分方程,最后,通过数值计算得到该方程数据并采用非线性动力学稀疏识别(SINDy)算法对其进行稀疏识别.结果表明:SINDy算法在无噪声数据中可准确地识别出覆冰四分裂导线舞动方程;在数据导数噪声幅值为0.2以下时,正确识别出舞动方程的项数且系数均值误差在0.22%以内;在数据导数噪声幅值为0.3以上时,开始识别出额外项,导致识别出三次非线性高阶项q3的系数最大相对误差显著增大,在0.5的噪声幅值时达到58.78%,但最终识别出舞动幅值的最大偏差仅为2.1%.通过调整稀疏促进参数及时间步长来修正舞动模型可提高模型识别精度,证实了SINDy算法对数据导数噪声有较强的适应性.本文研究成果可为输电线路舞动模型的建立提供一定参考.The galloping of transmission lines seriously threatens the safety and stability of power system. It is particularly important to accurately establish a galloping model of iced conductor. Therefore, a data-driven sparse identification algorithm is adopted, which can effectively identify the control equations of the dynamic system from the data and reduce the calculation cost.In this paper, the galloping equation of the iced quad bundle conductors is identified based on the data-driven sparse recognition algorithm. Firstly, based on Hamilton’s principle, the partial differential galloping equation of the iced quad bundle conductors is derived. Then, the partial differential equation is converted into an ordinary differential equation via the Galerkin method. Next, the aerodynamic load model is established, and the aerodynamic force is introduced into the galloping equation, obtaining the final ordinary differential galloping equation of the iced quad bundle conductors. Finally, the equation data are obtained by numerical simulation and the Sparse Identification of Nonlinear Dynamics(SINDy) algorithm is used to conduct the sparse identification.The results show that the SINDy algorithm can accurately identify galloping equation of the iced quad bundle conductors from the noise-free data. When the noise amplitude of the data derivative is below 0.2, the number of terms of the galloping equation can be correctly identified and the mean error of coefficients is within 0.22 %. Additional terms start to be identified when the noise amplitude of data derivative is above 0.3, which leads to a significant increase in the maximum relative error of the coefficients of the identified cubic nonlinear higher-order terms q3, reaching 58.78 % at a noise amplitude of 0.5. However, the maximum deviation of the final identified galloping amplitude is only 2.1 %. The identification accuracy of the model can be improved by updating the galloping model through adjusting the sparsity promotion parameter and the time step, which proves

关 键 词：覆冰导线 四分裂 数据驱动 稀疏识别 舞动方程 

分 类 号：O322[理学—一般力学与力学基础]