Nonlinear parameter identification method for clamps based on neural network proxy model
-
摘要:
提出一种基于定频测试和神经网络代理模型的管路-卡箍系统非线性参数辨识的方法。首先，开展低激励幅值下的模态测试，基于测试数据建立管路-卡箍系统的底层线性模型。其次，开展不同激励幅值和激励频率下的定频测试，构建系统的恒位移和恒速度响应面，基于等效线性化理论对卡箍的动力学参数开展非线性参数表征及辨识。然后，针对等效线性化模型存在响应预测精度不足的问题，开展不同非线性参数下卡箍结构的非线性动力学特性分析，采用神经网络技术定量描述非线性参数对其响应特性的影响规律，并构建其代理模型。最后，基于代理模型及其灵敏度特征，逆向辨识卡箍的非线性刚度和阻尼系数，从而获得该系统的非线性动力学模型。基于该模型的响应预测结果与实测结果高度吻合，在共振峰处的最大频差小于0.007%，响应幅值误差小于1.53%，表明基于辨识结果得到的非线性动力学模型能够准确地预测其非线性振动行为，验证了辨识结果的可靠性。
Abstract:A method for nonlinear parameter identification of pipeline clamp system based on fixed frequency testing and neural network proxy model was proposed. Firstly, modal testing under low excitation amplitudes was conducted, and a bottom level linear model of the pipeline clamp system based on the test data was established. Secondly, fixed frequency tests under different excitation amplitudes and frequencies were performed, the constant displacement and constant velocity response surfaces of the system were constructed, and nonlinear parameter characterization and identification of the dynamic parameters of the clamp based on the equivalent linearization theory were performed. Then, in response to the problem of insufficient response prediction accuracy in the equivalent linearization model, nonlinear dynamic characteristics analysis of the clamp structure under different nonlinear parameters was carried out. Neural network technology was used to quantitatively describe the influence of nonlinear parameters on its response characteristics, and its proxy model was constructed. Finally, based on the proxy model and its sensitivity characteristics, the nonlinear stiffness and damping coefficients of the clamp were identified in reverse, thereby obtaining the nonlinear dynamic model of the system. The response prediction results based on this model were highly consistent with the measured results. The maximum frequency difference at the resonance peak was less than 0.007%, and the response amplitude error was less than 1.53%, indicating that the nonlinear dynamic model obtained based on the identification results can accurately predict its nonlinear vibration behavior, verifying the reliability of the identification results.
-
Key words:
- clamp /
- nonlinear /
- parameter identification /
- neural network /
- fixed frequency test
-
图 9 管路-卡箍系统的原点频响曲线
Figure 9. Origin acceleration frequency response curve of pipe-clamp system
图 16 等效刚度与固有频率关系
Figure 16. Relationship of equivalent stiffness and natural frequency
图 17 等效阻尼与模态阻尼比关系
Figure 17. Relationship of equivalent damping and modal damping ratio
图 18 等效刚度随位移响应幅值的变化关系
Figure 18. Relationship between equivalent stiffness and displacement response amplitude
图 19 等效阻尼随速度响应幅值的变化关系
Figure 19. Relationship between equivalent damping and velocity response amplitude
图 24 线性预测结果与测试结果对比
Figure 24. Comparison of linear prediction results and test results
图 25 非线性预测结果与测试结果对比
Figure 25. Comparison of nonlinear prediction results and test results
表 1 有限元模型参数
Table 1. Parameters of finite element model
密度/（kg/m3） 弹性模量/1011 Pa 泊松比 卡箍质量/g 6837.8 1.6223 0.3 22.5 
下载: 导出CSV
表 2 卡箍线性动力学参数
Table 2. Linear dynamic parameters of clamp
N/mm ky1 kz1 ky2 kz2 3699.82 5618.55 1050.74 4617.39
下载: 导出CSV
表 3 管路-卡箍系统频差和MAC值
Table 3. Frequency error and MAC of pipe-clamp system
阶次 频差/% MAC 1 0 0.997 2 0 0.931 3 −0.054 0.950 4 −0.016 0.997
下载: 导出CSV
表 4 非线性测试参数
Table 4. Parameters of nonlinear testing
参数 数值 频率范围/Hz 540～560 频率间隔/Hz 0.1 电压范围/V 0.25～8 电压间隔/V 0.25 采样率/Hz 8192 采样时长/s 2
下载: 导出CSV
表 5 参数辨识区间
Table 5. Identification interval of parameters
待辨识参数 区间下限 区间上限 k1/104 （N/mm2） −7 −1 k2/106 （N/mm3） −3 −0.01 c1/10−5 （N·s2/mm2） −9 −4 c3/10−7 （N·s4/mm4） 1 5
下载: 导出CSV
表 6 BPNN预测响应误差
Table 6. Prediction response error of BPNN
激励幅值/N 频差/% 响应峰值误差/% 2.5 9.5430 ×10−40.0109 3.5 4.3664 ×10−40.0188 4.5 4.3563 ×10−40.0085
下载: 导出CSV
表 7 非线性参数辨识结果
Table 7. Results of nonlinear parameter identification
待辨识参数 辨识结果 k1/104 （N/mm2） − 6.2077 k2/105 （N/mm3） − 0.0423 c1/10−4 （N·s2/mm2） − 5.0411 c3/10−6 （N·s4/mm4） 2.2395
下载: 导出CSV
-
[1] 李枫, 刘伟, 韦顺超, 等. 航空液压管道卡箍等效刚度及其影响因素研究[J]. 机械科学与技术, 2017, 36(9): 1472-1476. LI Feng, LIU Wei, WEI Shunchao, et al. Research on equivalent stiffness and influence factors of aero-clamps for aircraft hydraulic pipelines[J]. Mechanical Science and Technology for Aerospace Engineering, 2017, 36(9): 1472-1476. (in ChineseLI Feng, LIU Wei, WEI Shunchao, et al. Research on equivalent stiffness and influence factors of aero-clamps for aircraft hydraulic pipelines[J]. Mechanical Science and Technology for Aerospace Engineering, 2017, 36(9): 1472-1476. (in Chinese) [2] 赵国伟, 李德勇, 陈勇. 金属橡胶隔振系统动刚度及减振效能分析[J]. 振动与冲击, 2014, 33(22): 193-197. ZHAO Guowei, LI Deyong, CHEN Yong. Dynamic stiffness and vibration reduction efficiency of metal rubber[J]. Journal of Vibration and Shock, 2014, 33(22): 193-197. (in ChineseZHAO Guowei, LI Deyong, CHEN Yong. Dynamic stiffness and vibration reduction efficiency of metal rubber[J]. Journal of Vibration and Shock, 2014, 33(22): 193-197. (in Chinese) [3] 许建东, 郭宝亭, 朱梓根, 等. 金属橡胶材料的振动特性[J]. 航空动力学报, 2004, 19(5): 619-622. XU Jiandong, GUO Baoting, ZHU Zigen, et al. The vibration performance of metal-rubber material[J]. Journal of Aerospace Power, 2004, 19(5): 619-622. (in ChineseXU Jiandong, GUO Baoting, ZHU Zigen, et al. The vibration performance of metal-rubber material[J]. Journal of Aerospace Power, 2004, 19(5): 619-622. (in Chinese) [4] 李占营, 王建军, 邱明星. 航空发动机管路流固耦合振动的固有频率分析[J]. 航空发动机, 2017, 43(1): 66-70. LI Zhanying, WANG Jianjun, QIU Mingxing. Analysis for natural frequencies of pipe conveying fluid considering fluid-structure interaction[J]. Aeroengine, 2017, 43(1): 66-70. (in ChineseLI Zhanying, WANG Jianjun, QIU Mingxing. Analysis for natural frequencies of pipe conveying fluid considering fluid-structure interaction[J]. Aeroengine, 2017, 43(1): 66-70. (in Chinese) [5] 杨莹, 陈志英. 航空发动机管路流固耦合固有频率计算与分析[J]. 燃气涡轮试验与研究, 2010, 23(1): 42-46, 25. YANG Ying, CHEN Zhiying. Calculation and analysis on natural frequency of fluid structure interaction in aero-engine pipelines[J]. Gas Turbine Experiment and Research, 2010, 23(1): 42-46, 25. (in ChineseYANG Ying, CHEN Zhiying. Calculation and analysis on natural frequency of fluid structure interaction in aero-engine pipelines[J]. Gas Turbine Experiment and Research, 2010, 23(1): 42-46, 25. (in Chinese) [6] 高志辉, 王东海, 孙伟, 等. L型管路系统动力学有限元建模及基于遗传算法的卡箍支撑位置优化[J]. 振动与冲击, 2022, 41(16): 149-157, 254. GAO Zhihui, WANG Donghai, SUN Wei, et al. Establishment of a dynamic finite element model of an L-type pipeline system and optimization of hoop supporting position based on the genetic algorithm[J]. Journal of Vibration and Shock, 2022, 41(16): 149-157, 254. (in ChineseGAO Zhihui, WANG Donghai, SUN Wei, et al. Establishment of a dynamic finite element model of an L-type pipeline system and optimization of hoop supporting position based on the genetic algorithm[J]. Journal of Vibration and Shock, 2022, 41(16): 149-157, 254. (in Chinese) [7] 刘学峰, 张源麟, 张德聪, 等. 航空带垫卡箍刚度及阻尼特性分析与试验验证[J]. 航空动力学报, 2022, 37(2): 274-282. LIU Xuefeng, ZHANG Yuanlin, ZHANG Decong, et al. Analysis and test verification of stiffness and damping characteristics of aviation clamp with cushion[J]. Journal of Aerospace Power, 2022, 37(2): 274-282. (in ChineseLIU Xuefeng, ZHANG Yuanlin, ZHANG Decong, et al. Analysis and test verification of stiffness and damping characteristics of aviation clamp with cushion[J]. Journal of Aerospace Power, 2022, 37(2): 274-282. (in Chinese) [8] ZHANG Genbei, ZANG Chaoping, FRISWELL M I. Measurement of multivalued response curves of a strongly nonlinear system by exploiting exciter dynamics[J]. Mechanical Systems and Signal Processing, 2020, 140: 106474. doi: 10.1016/j.ymssp.2019.106474 [9] BARTON D W, SIEBER J. Systematic experimental exploration of bifurcations with noninvasive control[J]. Physical Review E, Statistical, Nonlinear, and Soft Matter Physics, 2013, 87(5): 052916. [10] 周艳国, 屈文忠. 金属橡胶非线性动力学特性建模方法研究[J]. 噪声与振动控制, 2013, 33(1): 31-36. ZHOU Yanguo, QU Wenzhong. Several practical approaches for nonlinear dynamic modeling of metal rubber[J]. Noise and Vibration Control, 2013, 33(1): 31-36. (in ChineseZHOU Yanguo, QU Wenzhong. Several practical approaches for nonlinear dynamic modeling of metal rubber[J]. Noise and Vibration Control, 2013, 33(1): 31-36. (in Chinese) [11] ARSLAN O, AYKAN M, OZGUVEN H N. Modal identification of non-linear structures and the use of modal model in structural dynamic analysis[R]. Orlando, US: 26th International Modal Analysis Conference, 2008. [12] KERSCHEN G, WORDEN K, VAKAKIS A F, et al. Past, present and future of nonlinear system identification in structural dynamics[J]. Mechanical Systems and Signal Processing, 2006, 20(3): 505-592. doi: 10.1016/j.ymssp.2005.04.008 [13] ZANG C, SCHWINGSHACKL C W, EWINS D J. Model validation for structural dynamic analysis: an approach to the Sandia Structural Dynamics Challenge[J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(29/30/31/32): 2645-2659. [14] SCHWINGSHACKL C W, ZANG C, EWINS D J. The influence of nonlinearity on uncertainty and variability for dynamic models[R]. Sheffield, UK: 1st International Conference on Uncertainty in Structural Dynamics, 2007. [15] ZHANG G, ZANG C. Identification and verification of structural nonlinearities based on vibration tests[R]. Sharjah, United Arab Emirates: 8th International Symposium on Mechatronics and its Applications, 2012. [16] 吕金华, 臧朝平, 张让威, 等. 基于测试数据的卡箍非线性等效建模方法[J]. 航空动力学报, 2019, 34(9): 1944-1952. LÜ Jinhua, ZANG Chaoping, ZHANG Rangwei, et al. Nonlinear equivalent modeling method for clamp based on test data[J]. Journal of Aerospace Power, 2019, 34(9): 1944-1952. (in ChineseLÜ Jinhua, ZANG Chaoping, ZHANG Rangwei, et al. Nonlinear equivalent modeling method for clamp based on test data[J]. Journal of Aerospace Power, 2019, 34(9): 1944-1952. (in Chinese) [17] COOPER S B, DIMAIO D, EWINS D J. Integration of system identification and finite element modelling of nonlinear vibrating structures[J]. Mechanical Systems and Signal Processing, 2018, 102: 401-430. doi: 10.1016/j.ymssp.2017.09.031 [18] 林君哲. 航空发动机液压管路-卡箍系统的非线性振动特性研究[D]. 沈阳: 东北大学, 2018. LIN Junzhe. Study on nonlinear vibration characteristics of aero-engine hydraulic pipeline-clamps system[D]. Shenyang: Northeastern University, 2018. (in ChineseLIN Junzhe. Study on nonlinear vibration characteristics of aero-engine hydraulic pipeline-clamps system[D]. Shenyang: Northeastern University, 2018. (in Chinese) [19] 肖春亮, 马辉. 卡箍非线性刚度辨识及振动特性分析[R]. 广州: 第十八届全国非线性振动暨第十五届全国非线性动力学和运动稳定性学术会议(NVND2021), 2021. [20] FRISWELL M I, MOTTERSHEAD J E. Finite element model updating in structural dynamics [M]. Dordrecht, Netherlands: Kluwer Academic Publishers, 1995. -
点击查看大图
计量
- 文章访问数: 611
- HTML浏览量: 290
- PDF量: 31
- 被引次数: 0