刘星,张靓靓,高名杨,周明明

• 1:中国三峡建工(集团)有限公司
• 2:长江水利委员会水文局长江下游水文水资源勘测局
• 3:江苏省水利勘测设计研究院有限公司
• 4:河海大学水利水电学院

摘要(Abstract)：

【目的】Duffing振子是一种典型的非线性动力系统，混沌状态的判断是利用Duffing振子进行水工结构动力响应信号检测的基础准则。Duffing振子系统进入混沌状态时，系统状态时序图和相图会变得更为无序和复杂，可以对系统状态进行直观反映，但直接将二者作为系统混沌状态的判断依据，存在较为模糊和主观性较大的问题。为了对Duffing振子系统状态时序图和相图的复杂程度进行定量描述，以便更准确地利用二者对Duffing振子系统混沌状态的判断，【方法】提出了一种利用系统内状态量的时序图和相图盒维数的指数组合的指标，将该指标是否发生突变作为利用Duffing振子进行信号检测时的混沌状态的判断依据。【结果】所提出的Duffing振子混沌状态识别指标在Duffing方程的仿真分析、正弦波仿真信号检测和悬臂梁锤击动力响应信号检测试验中分别表现出22.611%、17.514%和30.975%的相对变化率。同时振子对应的李雅普诺夫指数也由负转正，但Duffing方程的仿真分析结果显示李雅普诺夫指数作为识别指标更为敏感，在振子系统的时序图和相图未明显表现出混沌状态时，其已经由负转正。【结论】由试验结果可知：可以根据所提出识别指标是否发生突变进行识别振子混沌状态，达到信号检测的目的。同时，所提出的混沌状态识别指标以时序图和相图的复杂程度直接作为判断标准，与其他指标相比更为直接和合理。悬臂梁动力响应信号检测试验初步验证了所选取的识别指标应用到具体工作中的可行性，有望应用于结构损伤识别，共振发现等工作中。

关键词(KeyWords)： 动力响应信号;Duffing振子;信号检测;非线性动力系统;混沌判据

Abstract:

Keywords:

基金项目(Foundation): 国家重点研发计划课题(2018YFC1508603);; 中央高校专项资金资助项目(2019B70514)

作者(Author): 刘星,张靓靓,高名杨,周明明

DOI: 10.13928/j.cnki.wrahe.2023.11.012

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