Research on Dynamic Hysteresis Modeling and Parameter Identification of a Wire-cable Vibration Isolator
-
摘要: 对钢丝绳隔振器的动态迟滞特性进行研究。针对小振幅下修正的归一化Bouc-wen模型拟合精度低的问题,在模型中引入一个关于激励位移的非线性函数,建立了隔振器动态迟滞特性模型;采用线性最小二乘法和带噪声统计估计器的自适应无迹卡尔曼滤波算法对模型参数进行识别。结果表明:建立的模型能够很好地描述钢丝绳隔振器动态迟滞特性,采用的参数识别方法可以准确有效地识别出模型参数,试验曲线和识别的模型拟合曲线吻合较好,验证了建立的模型和参数识别方法的有效性。
-
关键词:
- 钢丝绳隔振器 /
- 归一化Bouc-wen模型 /
- 迟滞 /
- 参数识别
Abstract: The dynamic hysteresis characteristics of the wire-cable vibration isolator were studied by experiments. In order to improve the fitting accuracy of the modified normalized Bouc-wen model under the condition of small amplitude, a nonlinear function about excitation displacement was first introduced into the model to complete the modeling of dynamic hysteresis characteristics of the isolator. Then, the linear least square method and adaptive unscented Kalman filter (AUKF) algorithm with noise statistic estimator were developed for model parameter identification. Research results indicated that the established model can well describe the dynamic hysteresis characteristics of the wire-cable vibration isolator, and the model parameters can be identified accurately and effectively by this identification method, the experimental hysteresis curve is consistent with the identified model fitting curve, verifying the effectiveness of the established model and the parameter identification method. -
表 1 模型参数识别结果
参数 N=3, M=2 ke0 -20.704 2 ke1 33.256 3 ke2 1.975 2 ke3 0.125 4 kz0 73.527 6 kz1 6.348 5 kz2 -0.142 4 ρ 1.647 1 σ 2.456 2 n 0.845 7 表 2 两种识别方法下的RMSE和RNL对比
识别方法 预测迟滞环ERMSE/N 预测迟滞环RNL AUKF法 4.770 2 0.972 568 极限环法 5.509 4 0.961 048 表 3 小振幅情况下模型改进前后RMSE和RNL对比
振幅
A/mmERMSE RNL 改进前 改进后 改进前 改进后 1 9.648 6 0.932 565 4.309 5 0.980 462 2 9.345 7 0.940 163 4.068 9 0.985 234 表 4 拟合函数参数数值
加载f(x) 数值 卸载f(x) 数值 a0* 12.890 a1 10.970 a1* -1.834 a2 1.427 a2* 1.051 a3 1.290 a3* 0.188 a4 126.600 a4* -1.400 b1 0.906 a5* 0.820 b2 0.113 b1* -4.462 b3 -0.213 b2* 9.874 b4 -126 b3* -9.702 c1 0.093 b4* 6.168 c2 0.305 b5* -2.280 c3 0.129 ω 1.992 c4 72.080 -
[1] 班书昊, 李晓艳, 蒋学东, 等.钢丝绳隔振器的非线性动力学模型[J].力学与实践, 2012, 34(1):66-69 http://d.wanfangdata.com.cn/Periodical_lxysj201201013.aspxBan S H, Li X Y, Jiang X D, et al. Nonlinear dynamic model on steel-wire isolator[J]. Mechanics in Engineering, 2012, 34(1):66-69(in Chinese) http://d.wanfangdata.com.cn/Periodical_lxysj201201013.aspx [2] Demetriades G F, Constantinou M C, Reinhorn A M. Study of wire rope systems for seismic protection of equipment in buildings[J]. Engineering Structures, 1993, 15(5):321-334 doi: 10.1016/0141-0296(93)90036-4 [3] 熊鑫, 金晶, 吴新跃, 等.钢丝绳隔振器结构抗冲击设计与优化[J].海军工程大学学报, 2017, 29(6):39-43, 66 http://www.cqvip.com/QK/91072A/20176/674259667.htmlXiong X, Jin J, Wu X Y, et al. Anti-shock design and optimization of wire rope isolator structure[J]. Journal of Naval University of Engineering, 2017, 29(6):39-43, 66(in Chinese) http://www.cqvip.com/QK/91072A/20176/674259667.html [4] 白鸿柏, 黄协清.干摩擦振动系统响应计算方法研究综述[J].力学进展, 2001, 31(4):527-534 http://www.cnki.com.cn/Article/CJFDTotal-LXJZ200104006.htmBai H B, Huang X Q. An overview on study of methods of response computation for the dry frictionally damped vibration systems[J]. Advances in Mechanics, 2001, 31(4):527-534(in Chinese) http://www.cnki.com.cn/Article/CJFDTotal-LXJZ200104006.htm [5] Ferri A A. Friction damping and isolation systems[J]. Journal of Mechanical Design, 1995, 117(B):196-206 doi: 10.1115/1.2836456 [6] Wen Y K. Equivalent linearization for hysteretic systems under random excitation[J]. Journal of Applied Mechanics, 1980, 47(1):150-154 doi: 10.1115/1.3153594 [7] Zhao Y, Wang S L, Zhou J, et al. Three-stage method for identifying the dynamic model parameters of stranded wire helical springs[J]. Chinese Journal of Mechanical Engineering, 2015, 28(1):197-207 doi: 10.3901/CJME.2014.0723.123 [8] 李玲, 蔡安江, 蔡立刚, 等.基于Bouc-wen模型辨识别结合面动态特性研究[J].振动与冲击, 2013, 32(20):139-144 http://www.cqvip.com/QK/95775X/201320/47563496.htmlLi L, Cai A J, Cai L G, et al. Dynamic characteristics identification of joint interfaces based on a Bouc-Wen model[J]. Journal of Vibration and Shock, 2013, 32(20):139-144(in Chinese) http://www.cqvip.com/QK/95775X/201320/47563496.html [9] 王涛, 吴斌, 孟丽岩, 等.约束UKF初始参数对Bouc-wen模型参数识别的影响[J].黑龙江科技大学学报, 2014, 24(6):651-657, 666 http://d.wanfangdata.com.cn/Periodical/hljkyxyxb201406022Wang T, Wu B, Meng L Y, et al. Effects of initial parameters of constrained UKF on parameter identification for Bouc-Wen model[J]. Journal of Heilongjiang University of Science and Technology, 2014, 24(6):651-657, 666(in Chinese) http://d.wanfangdata.com.cn/Periodical/hljkyxyxb201406022 [10] 程成.周期载荷下多股簧的动力学模型及响应特性研究[D].重庆: 重庆大学, 2014: 30-44Cheng C. Study of modeling and response characteristics of stranded wire helical springs under periodic loading[D]. Chongqing: Chongqing University, 2014: 30-44(in Chinese) [11] Xie S L, Zhang Y H, Chen C H, et al. Identification of nonlinear hysteretic systems by artificial neural network[J]. Mechanical Systems and Signal Processing, 2013, 34(1-2):76-87 doi: 10.1016/j.ymssp.2012.07.015 [12] 王红霞, 龚宪生, 潘飞, 等.O型钢丝绳隔振器动态迟滞模型参数识别方法研究[J].振动与冲击, 2015, 34(20):155-160 http://www.cnki.com.cn/Article/CJFDTotal-ZDCJ201520026.htmWang H X, Gong X S, Pan F, et al. Parametric identification method for identifying dynamic hysteretic model parameters of O-type wire-cable vibration isolator[J]. Journal of Vibration and Shock, 2015, 34(20):155-160(in Chinese) http://www.cnki.com.cn/Article/CJFDTotal-ZDCJ201520026.htm [13] 丁传俊, 张相炎, 刘宁.基于自适应无迹卡尔曼滤波算法的多股螺旋弹簧动态响应模型参数辨识别和分析[J].兵工学报, 2018, 39(1):28-37 http://www.cqvip.com/QK/94928X/201801/674473289.htmlDing C J, Zhang X Y, Liu N. Adaptive unscented kalman filter algorithm for identifying and analyzing the dynamic response model parameters of stranded wire helical springs[J]. Acta Armamentarii, 2018, 39(1):28-37(in Chinese) http://www.cqvip.com/QK/94928X/201801/674473289.html [14] Ikhouane F, Rodellar J. On the hysteretic Bouc-Wen model part Ⅰ:forced limit cycle characterization[J]. Nonlinear Dynamics, 2005, 42(1):63-78 doi: 10.1007/s11071-005-0069-3 [15] 王红霞, 龚宪生, 潘飞, 等.O型钢丝绳隔振器的三向动态特性[J].振动、测试与诊断, 2016, 36(6):1190-1195Wang H X, Gong X S, Pan F, et al. Research on the dynamic behavior of O type wire-cable vibration isolator in three modes[J]. Journal of Vibration, Measurement & Diagnosis, 2016, 36(6):1190-1195(in Chinese) [16] 张周灿, 谢长君, 曹夏令, 等.基于改进自适应无迹卡尔曼滤波的锂电池SOC估计[J].汽车技术, 2018, (3):10-15 http://www.cnki.com.cn/Article/CJFDTotal-QCJS201803003.htmZhang Z C, Xie C J, Cao X L, et al. SOC estimation of lithium battery based on improved adaptive unscented Kalman filtering[J]. Automobile Technology, 2018, (3):10-15(in Chinese) http://www.cnki.com.cn/Article/CJFDTotal-QCJS201803003.htm [17] Wu Y X, Hu D W, Wu M P, et al. Unscented kalman filtering for additive noise case: augmented vs. non-augmented[C]//Proceedings of the 2005, American Control Conference. Portland, US: IEEE, 2005: 4051-4055 [18] 赵琳, 王小旭, 孙明, 等.基于极大后验估计和指数加权的自适应UKF滤波算法[J].自动化学报, 2010, 36(7):1007-1019 http://www.cqvip.com/QK/90250X/20107/34605552.htmlZhao L, Wang X X, Sun M, et al. Adaptive UKF filtering algorithm based on maximum a posterior estimation and exponential weighting[J]. Acta Automatica Sinica, 2010, 36(7):1007-1019(in Chinese) http://www.cqvip.com/QK/90250X/20107/34605552.html [19] 王红霞.O型钢丝绳隔振器特性研究丝[D].重庆: 重庆大学, 2015: 35-41Wang H X. Research on the property of an O type wire-cable vibration isolator[D]. Chongqing: Chongqing University, 2015: 35-41(in Chinese) [20] 张世强.曲线回归的拟合优度指标的探讨[J].中国卫生统计, 2002, 19(1):9-11 http://www.cnki.com.cn/Article/CJFDTotal-ZGWT200201003.htmZhang S Q. Approach on the fitting optimization index of curve regression[J]. Chinese Journal of Health Statistics, 2012, 19(1):9-11(in Chinese) http://www.cnki.com.cn/Article/CJFDTotal-ZGWT200201003.htm