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和分析
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摘要
针对传统方法在辨识多股螺旋弹簧(以下简称多股簧)非线性响应模型参数时效率较低、精度较差的问题,提出带噪声统计估计器的自适应无迹卡尔曼滤波(AUKF)算法。该算法通过对多股簧试验数据中的量测(过程)噪声进行递推和估计,能够确保非线性模型参数辨识的收敛性;结合多股簧动态试验对该算法进行检验。研究结果表明:即使在量测噪声级别较高的情况下,AUKF算法也可以准确地求出多股簧的动力学模型参数;在预测多股簧动态响应过程中,若预测振幅和参数辨识所用振幅相差太大则会导致较大的预测误差;当加载速度变化时,多股簧动力学模型中的迟滞部分参数基本不变,但0阶非线性刚度系数和非线性放大因子变化较大。
An adaptive unscented Kalman filter(AUKF) algorithm with noise statistic estimator is developed for the parameters identification of nonlinear response model of stranded wire helical springs.The convergence of parameters identification of nonlinear model could be ensured by recursively estimating measurement noise(or process noise) in the test data of stranded wire helical springs.The effectiveness of AUKF algorithm is verified via dynamic loading experiment.The result demonstrates that the proposed algorithm can accurately determine the model parameters of stranded wire helical springs even with higher levels of measurement noise.In the prediction process of spring response,the predicted amplitude should not be much smaller than the amplitude for parameter identification.When the loading rate is changed,the hysteresis parameters in the dynamic model of stranded wire helical spring are basically unchanged,but the zero-order nonlinear stiffness coefficient and the zero-order nonlinear amplification factor are changed greatly.
An adaptive unscented Kalman filter(AUKF) algorithm with noise statistic estimator is developed for the parameters identification of nonlinear response model of stranded wire helical springs.The convergence of parameters identification of nonlinear model could be ensured by recursively estimating measurement noise(or process noise) in the test data of stranded wire helical springs.The effectiveness of AUKF algorithm is verified via dynamic loading experiment.The result demonstrates that the proposed algorithm can accurately determine the model parameters of stranded wire helical springs even with higher levels of measurement noise.In the prediction process of spring response,the predicted amplitude should not be much smaller than the amplitude for parameter identification.When the loading rate is changed,the hysteresis parameters in the dynamic model of stranded wire helical spring are basically unchanged,but the zero-order nonlinear stiffness coefficient and the zero-order nonlinear amplification factor are changed greatly.
引文
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[19]田波.冲击载荷作用下多股簧动态特性试验研究[D].重庆大学,2014:58-64.TIAN Bo.Experimental study of dynamic characteristics of stranded wire helical springs under shock load[D].Chongqing:Chongqing University,2014:58-64.(in Chinese)
[2]王时龙,周杰,李小勇,等.多股螺旋弹簧[M].北京:科学出版社,2011:47-51.WANG Shi-long,ZHOU Jie,LI Xiao-yong,et al.Stranded wire helical spring[M].Beijing:Science Press,2011:47-51.(in Chinese)
[3]闵建军,王时龙.多股螺旋弹簧动态计算分析[J].机械工程学报,2007,43(3):199-203.MIN Jian-jun,WANG Shi-long.Dynamic design method for stranded wire helical spring[J].Chinese Journal of Mechanical Engineering,2007,43(3):199-203.(in Chinese)
[4]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.
[5]李玲,蔡安江,蔡立刚,等.基于Bouc-Wen模型辨识结合面动态特性研究[J].振动与冲击,2013,32(20):139-144.LI Ling,CAI An-jiang,CAI Li-gang,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)
[6]易琳,王班,郭吉丰.Kevlar绳索非对称迟滞模型及参数识别[J].浙江大学学报:工学版,2015,49(7):1376-1381.YI Lin,WANG Ban,GUO Ji-feng.Modeling and identification of asymmetric hysteresis for Kevlar tether[J].Journal of Zhejiang University:Engineering Science,2015,49(7):1376-1381.(in Chinese)
[7]韩强,董慧慧,郭婕.考虑强度和刚度退化及捏拢效应的钢筋混凝土桥墩滞回模型及其参数识别[J].振动工程学报,2015,28(3):381-393.HAN Qiang,DONG Hui-hui,GUO Jie.Hysteresis model and parameter identification of RC bridge piers considering strength and stiffness degradation and pinching effect[J].Journal of Vibration Engineering,2015,28(3):381-393.(in Chinese)
[8]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.WANG Tao,WU Bin,MENG Li-yan,et al.Effects of initial parameters of constrained UKF on parameter identification for BoucWen model[J].Journal of Heilongjiang University of Science and Technology,2014,24(6):651-657.(in Chinese)
[9]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,2014:30-44.CHENG Cheng.Study of modeling and responses characteristics of stranded wire helical spring under periodic loading[D].Chongqing:Chongqing University,2014:30-44.(in Chinese)
[10]Worden K,Manson G.On the identification of hysteretic systems.Part I:fitness landscapes and evolutionary identification[J].Mechanical Systems and Signal Processing,2012,29(5):201-212.
[11]Fu Z J,Xie W F,Luo W D.Robust on-line nonlinear systems identification using multilayer dynamic neural networks with twotime scales[J].Neurocomputing,2013,113(7):16-26.
[12]Quaranta G,Marano G C,Greco R,et al.Parametric identification of seismic isolators using differential evolution and particle swarm optimization[J].Applied Soft Computing,2014,22(5):458-464.
[13]Ikhouane F,Rodellar J.On the hysteretic Bouc-Wen model[J].Nonlinear Dynamics,2005,42(1):79-95.
[14]Shabbouei H Y,Mohammadi A R,Cocquempot V.A hybrid robust fault tolerant control based on adaptive joint unscented Kalman filter[J].ISA Transactions,2017,66:262-274.
[15]Liu M,Lai J Z,Li Z M,et al.An adaptive cubature Kalman filter algorithm for inertial and land-based navigation system[J].Aerospace Science and Technology,2016,51(2):52-60.
[16]Meng Y,Gao S S,Zhong Y M,et al.Covariance matching based adaptive unscented Kalman filter for direct filtering in INS/GNSS integration[J].Acta Astronautica,2016,120:171-181.
[17]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.ZHAO Lin,WANG Xiao-xu,SUN Ming,et al.Adaptive UKF filtering algorithm based on maximum a posterior estimation and exponential weighting[J].Acta Automatic Sinica,2010,36(7):1007-1019.(in Chinese)
[18]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.Protland,OR,US:IEEE,2005:4051-4055.
[19]田波.冲击载荷作用下多股簧动态特性试验研究[D].重庆大学,2014:58-64.TIAN Bo.Experimental study of dynamic characteristics of stranded wire helical springs under shock load[D].Chongqing:Chongqing University,2014:58-64.(in Chinese)