基础激励下含间隙折叠舵面非线性系统辨识  

System identification of folding rudders with freeplay nonlinearity under base excitation

作　　者：王博[1,2] 马志赛 丁千 张欣[3] 杨宁 WANG Bo;MA Zhisai;DING Qian;ZHANG Xin;YANG Ning(Department of Mechanics,Tianjin University,Tianjin 300350,China;Tianjin Key Laboratory of Nonlinear Dynamics and Control,Tianjin 300350,China;Beijing Institute of Electronic System Engineering,Beijing 100854,China)

机构地区：[1]天津大学力学系,天津300350 [2]天津市非线性动力学与控制重点实验室,天津300350 [3]北京电子工程总体研究所,北京100854

出　　处：《振动与冲击》2020年第4期122-128,135,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金(11802201;51575378;11972245);中国博士后科学基金(2017M621075)

摘　　要：间隙在飞行器折叠舵面中普遍存在且不易准确描述,通过辨识方法获得间隙的真实非线性特性具有重要意义。基于直接参数估计方法建立基础激励下含间隙非线性系统辨识模型,利用相对速度和相对位移的多项式表征非线性系统的恢复力;引入显著因子剔除多项式中影响度较低的基函数,采用最小二乘求解得出恢复力多项式中各项系数,由不同自由度之间的相对关系组装出整个系统的辨识模型;通过比较基于辨识模型的系统响应和实测系统响应之间的均方误差来评价辨识精度。基础激励下含间隙三自由度结构系统数值算例的辨识结果表明:含间隙非线性系统的恢复力可通过增加刚度立方项进行准确逼近;选取折叠舵面上两处测点分别在无间隙和有间隙的工况下进行辨识,辨识所得运动方程均能较好地描述两测点的动力学特性,对含间隙折叠舵面非线性系统的离散化建模与动力学分析具有重要工程意义。Freeplay nonlinearity is ubiquitous in folding rudders of flight vehicles,which is difficult to be accurately described.It is necessary to obtain the real nonlinear characteristics of freeplays by using system identification methods.The identified model of the nonlinear system with freeplays under base excitation was first built using direct parameter estimation.Nonlinear restoring force was expressed by polynomials of relative velocity and displacement.A significance factor was defined to determine whether a term is an important part of the identified model,and the coefficients of the polynomials were solved by the least squares method.Finally,the completed system model can be obtained based on the relationship between different degrees of freedom,and the identification accuracy can be validated via the mean-square error between the estimated and measured responses.Identification results of a three degree of freedom numerical example demonstrate that the restoring force of a nonlinear system with freeplays can be accurately approximated by adding cubic stiffness.Furthermore,the dynamic characteristics of two measuring points on the folding rudder can be well described by the identified model,which is of importance to discretization modeling and dynamic analysis of folding rudders with freeplays.

关 键 词：折叠舵面 基础激励 间隙非线性 系统辨识 

分 类 号：V216[航空宇航科学与技术—航空宇航推进理论与工程] O322[理学—一般力学与力学基础]