Research on Time-domain Identification Method of Excitation Force using Kalman Filter
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摘要: 激振力识别属于结构动力学中的第二类反问题,为识别振动系统的激励力,本文基于卡尔曼滤波器和最小方差估计的方法,分别建立了以系统位移和加速度为输入参数的激振力时域识别方法。推导了两种方法的识别公式,并对两种方法的识别结果和识别结果的稳健性进行了仿真分析。仿真结果表明,两种方法对噪声方差初值的设定均不敏感;以加速度幅值为输入的方法识别精度优于以位移幅值为输入的方法;以位移幅值为输入的方法识别结果稳健性较好。最后采用力锤敲击试验验证了识别方法的有效性和精度。Abstract: In order to effectively identify the excitation force of a vibration system, based on the Kalman filter and the minimum variance estimation method, two time-domain identification methods of the excitation force with system displacement and acceleration as input parameters are established respectively. The identification formulas of these two methods are derived, and the identification results and robustness of the two methods are simulated and analyzed. The simulation results show that the two methods are insensitive to the initial setting of the variance of the noise. The recognition accuracy of the method with acceleration as input is better than the method with displacement as input. The robustness of the identification results of the method with displacement as input is better than the method with acceleration as input. Finally, the effectiveness and accuracy of the time-domain identification methods are verified by hammer knock test.
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表 1 结构参数和状态变量初值的取值
参数及单位 原始参数 增大 减小 刚度/(N·m-1) 20 23 17 阻尼系数/(N·s·m-1) 0.500 0.575 0.425 位移/m -0.050 0 -0.042 5 -0.057 5 速度/(m·s-1) 0.20 0.22 0.18 表 2 初始参数取值正交表
试验号 刚度/(N·m-1) 阻尼系数/(N·s·m-1) 位移初值/m 速度初值/(m·s-1) 1 20 0.500 -0.050 0 0.20 2 20 0.425 -0.057 5 0.18 3 20 0.575 -0.042 5 0.22 4 17 0.500 -0.057 5 0.22 5 17 0.425 -0.042 5 0.20 6 17 0.575 -0.050 0 0.18 7 23 0.500 -0.042 5 0.18 8 23 0.425 -0.050 0 0.22 9 23 0.575 -0.057 5 0.20 表 3 5个参考点处的激振力识别结果相对误差
% 试验号 点1 点2 点3 点4 点5 均值 1 -0.75 -0.46 -1.00 -0.64 -1.18 0.81 2 -3.15 -3.72 -5.94 -7.71 -9.03 5.91 3 1.67 2.82 3.95 6.46 6.67 4.31 4 -1.08 -3.97 5.69 2.15 2.38 3.05 5 0.53 -3.29 4.63 -1.15 -1.77 2.27 6 -0.05 -6.94 -0.27 -6.15 -9.46 4.57 7 -0.08 2.77 -8.51 -4.68 -6.48 4.50 8 -1.38 6.61 -0.66 6.46 9.06 4.83 9 -2.46 1.99 -6.90 -0.28 -0.71 2.47 表 4 各因子的各水平识别结果相对误差平均值
水平 相对误差平均值/% 刚度 阻尼系数 位移初值 速度初值 1 3.67 2.79 3.40 1.85 2 3.30 4.34 3.69 4.99 3 3.93 3.78 3.81 4.06 表 5 振动系统结构参数
质量/kg 刚度/(N·m-1) 阻尼系数/(N·s·m-1) 4.087 311 000 0.05 -
[1] TAO J S, LIU G R, LAM K Y. Excitation force identification of an engine with velocity data at mounting points[J]. Journal of Sound and Vibration, 2001, 242(2): 321-331 doi: 10.1006/jsvi.2000.3351 [2] 刘晓昂. 基于整车振动控制的动力总成悬置系统设计方法[D]. 广州: 华南理工大学, 2016LIU X A. Design methods of the powertrain mounting system based on vibration control of vechicle level[D]. Guangzhou: South China University of Technology, 2016 (in Chinese) [3] CHAO M, HONGXING H, FENG X. The identification of external forces for a nonlinear vibration system in frequency domain[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2014, 228(9): 1531-1539 doi: 10.1177/0954406213509085 [4] 周玙, 刘莉, 周思达, 等. 基于应变模态参数的结构瞬态载荷识别方法研究[J]. 振动与冲击, 2019, 38(6): 199-205 https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201906030.htmZHOU Y, LIU L, ZHOU S D, et al. Transient load identification of structural dynamic systems based on strain modal parameters[J]. Journal of Vibration and Shock, 2019, 38(6): 199-205 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201906030.htm [5] 王能建, 任春平, 刘春生. 一种新型分数阶Tikhonov正则化载荷重构技术及应用[J]. 振动与冲击, 2019, 38(6): 121-126, 158 https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201906018.htmWANG N J, REN C P, LIU C S. Novel fractional order Tikhonov regularization load reconstruction technique and its application[J]. Journal of Vibration and Shock, 2019, 38(6): 121-126, 158 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201906018.htm [6] LI Z F, LI D, XU X L, et al. New normalized LMS adaptive filter with a variable regularization factor[J]. Journal of Systems Engineering and Electronics, 2019, 30(2): 259-269 doi: 10.21629/JSEE.2019.02.05 [7] WU A L, LOH C H, YANG J N, et al. Input force identification: application to soil-pile interaction[J]. Structural Control & Health Monitoring, 2009, 16(2): 223-240 https://ui.adsabs.harvard.edu/abs/2008SPIE.6932E..23L/abstract [8] LIN D C. Input estimation for nonlinear systems[J]. Inverse Problems in Science and Engineering, 2010, 18(5): 673-689 doi: 10.1080/17415971003698623 [9] NAETS F, CUADRADO J, DESMET W. Stable force identification in structural dynamics using Kalman filtering and dummy-measurements[J]. Mechanical Systems and Signal Processing, 2015, 50-51: 235-248 doi: 10.1016/j.ymssp.2014.05.042 [10] ZHANG C, GAO Y W, HUANG J P, et al. Damage identification in bridge structures subject to moving vehicle based on extended Kalman filter with 1 1-norm regularization[J]. Inverse Problems in Science and Engineering, 2020, 28(2): 144-174 doi: 10.1080/17415977.2019.1582650 [11] LOURENS E, REYNDERS E, DE ROECK G. An augmented Kalman filter for force identification in structural dynamics[J]. Mechanical Systems and Signal Processing, 2012, 27: 446-460 doi: 10.1016/j.ymssp.2011.09.025 [12] 张雪蕊, 刘祚时, 程素平, 等. 改进的Kalman滤波算法在飞行器测距中的应用研究[J]. 机械设计与制造, 2020(2): 158-161 https://www.cnki.com.cn/Article/CJFDTOTAL-JSYZ202002039.htmZHANG X R, LIU Z S, CHENG S P, et al. Application of improved Kalman filter algorithm in obstacle ranging of aircraft[J]. Machinery Design & Manufacture, 2020(2): 158-161 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSYZ202002039.htm [13] FENG W, LI Q F, LU Q H. Force localization and reconstruction based on a novel sparse Kalman filter[J]. Mechanical Systems and Signal Processing, 2020, 144: 106890 doi: 10.1016/j.ymssp.2020.106890 [14] GILLIJINS S, DE MOOR B. Unbiased minimum-variance input and state estimation for linear discrete-time systems with direct feedthrough[J]. Automatica, 2007, 43(5): 934-937 doi: 10.1016/j.automatica.2006.11.016 [15] 张志, 孟少平, 周臻, 等. 振动台试验加速度积分方法[J]. 振动测试与诊断, 2013, 33(4): 627-633, 725 https://wenku.baidu.com/view/7ce73fc06bec0975f465e2fe?fr=xueshuZHANG Z, ZHENG S P, ZHOU Z, et al. Numerical integration method of acceleration recodes for shaking table test[J]. Journal of Vibration, Measurement & Diagnosis, 2013, 33(4): 627-633, 725 (in Chinese) https://wenku.baidu.com/view/7ce73fc06bec0975f465e2fe?fr=xueshu