采用灰色Savitzky-Golay滤波的商用车推力杆橡胶球铰非对称迟滞建模
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摘要
为了建立准确高效的推力杆迟滞特性模型,根据力的分解原理,将滞回力分解为广义非线性弹性力和广义非线性阻尼力,并分别采用等效线性阻尼模型、等效分段线性阻尼模型、非对称Bouc-Wen模型和高阶多项式模型对橡胶球铰的迟滞非线性进行建模。引入灰色关联度指标,对Savitzky-Golay滤波算法进行改进,采用布谷鸟算法对滤波器的参数进行优化,并应用该滤波器对试验采集到的滞回特性数据进行去噪平滑。以滤波后的试验数据与各迟滞模型计算数据的误差平方和最小化为目标,分别对各模型的参数进行识别。结果表明:所提出的灰色Savitzky-Golay滤波方法具有很好的平滑滤波效果,滤波前后信号的灰色关联度大于0.8,而非对称Bouc-Wen迟滞特性模型具有相对较高的精度和较低的复杂度,其建模误差小于10%。研究结果可为汽车和其他机械装置上的橡胶件迟滞非线性建模和信号滤波去噪提供参考。
The description of complex asymmetric and nonlinear hysteresis characteristics of the rubber hinge on commercial vehicle thrust rod is directly related to the accuracy of vehicle modeling and performance simulation. According to the principle of force decomposition, the hysteresis force is decomposed into generalized nonlinear elastic force and damping force. The equivalent linear damping model and piecewise linear damping model, the asymmetric Bouc-Wen model and the high-order polynomial model are employed to model the hysteresis nonlinearity of a rubber ball hinge. The grey correlation degree index is introduced to improve the Savitzky-Golay filter algorithm, and the filter parameters are optimized using cuckoo search algorithm to filter the hysteresis characteristic data collected from experiments. The parameters of each model are identified based on the goal of minimizing the sum of squared errors between the filtered data and the simulation values of each hysteresis model. The results show that the proposed grey Savitzky-Golay filtering method has a good smoothing effect, and the grey correlation degree of the data before and after filtering is large than 0.8; while the asymmetric Bouc-Wen hysteresis characteristic model has relatively high accuracy and low complexity, and the modeling error is below 10%. This research may provide reference for nonlinear hysteresis modeling, data filtering and denoising of the rubber components in vehicles and other mechanical devices.
The description of complex asymmetric and nonlinear hysteresis characteristics of the rubber hinge on commercial vehicle thrust rod is directly related to the accuracy of vehicle modeling and performance simulation. According to the principle of force decomposition, the hysteresis force is decomposed into generalized nonlinear elastic force and damping force. The equivalent linear damping model and piecewise linear damping model, the asymmetric Bouc-Wen model and the high-order polynomial model are employed to model the hysteresis nonlinearity of a rubber ball hinge. The grey correlation degree index is introduced to improve the Savitzky-Golay filter algorithm, and the filter parameters are optimized using cuckoo search algorithm to filter the hysteresis characteristic data collected from experiments. The parameters of each model are identified based on the goal of minimizing the sum of squared errors between the filtered data and the simulation values of each hysteresis model. The results show that the proposed grey Savitzky-Golay filtering method has a good smoothing effect, and the grey correlation degree of the data before and after filtering is large than 0.8; while the asymmetric Bouc-Wen hysteresis characteristic model has relatively high accuracy and low complexity, and the modeling error is below 10%. This research may provide reference for nonlinear hysteresis modeling, data filtering and denoising of the rubber components in vehicles and other mechanical devices.
引文
[1] 闻邦椿. 工程非线性振动 [M]. 北京: 科学出版社, 2007: 285-290.
[2] 何子述, 夏威. 现代数字信号处理及其应用 [M]. 北京: 清华大学出版社, 2009: 163-216.
[3] CANDAN ?, INAN H. A unified framework for derivation and implementation of Savitzky-Golay filters [J]. Signal Processing, 2014, 104(6): 203-211.
[4] LUO J, YING K, HE P, et al. Properties of Savitzky-Golay digital differentiators [J]. Digital Signal Processing, 2005, 15(2): 122-136.
[5] ACHARYA D, RANI A, AGARWAL S, et al. Application of adaptive Savitzky-Golay filter for EEG signal processing [J]. Perspectives in Science, 2016, 8(C): 677-679.
[6] 史文库, 柯俊, 王倩, 等. V型推力杆的极限载荷分析与球铰结构优化 [J]. 西安交通大学学报, 2013, 47(10): 132-136. SHI Wenku, KE Jun, WANG Qian, et al. Ultimate load analysis and ball joint structure optimization of V-type thrust rods [J]. Journal of Xi’an Jiaotong University, 2013, 47(10): 132-136.
[7] FENG G, SHI W, ZHANG H, et al. Research on the fatigue life prediction method of thrust rod [J]. Mathematical Problems in Engineering, 2016(10): 1-9.
[8] 江洪, 成中书, 张丛. 空气悬架导向机构纵向推力杆的优化设计 [J]. 机械设计与制造, 2010(6): 1-3. JIANG Hong, CHENG Zhongshu, ZHANG Cong. Optimization design of longitudinal thrust rod for air suspension steering mechanism [J]. Mechanical Design and Manufacturing, 2010(6): 1-3.
[9] ISMAIL M, IKHOUANE F, RODELLAR J. The hysteresis Bouc-Wen model: a survey [J]. Archives of Computational Methods in Engineering, 2009, 16(2): 161-188.
[10] ORTIZ G A, ALVAREZ D A, BEDOYZ-RUIZ D. Identification of Bouc-Wen type models using the transitional Markov chain Monte Carlo method [J]. Computers & Structures, 2015, 146: 252-269.
[11] ZIMMERMANN B, KOHLER A. Optimizing Savitzky-Golay parameters for improving spectral resolution and quantification in infrared spectroscopy [J]. Applied Spectroscopy, 2013, 67(8): 892-902.
[12] 刘思峰, 杨英杰, 吴利丰. 灰色系统理论及其应用 [M]. 8版. 北京: 科学出版社, 2018: 55-57.
[13] KAYACAN E, ULUTAS B, KAYNAK O. Grey system theory-based models in time series prediction [J]. Expert Systems with Applications, 2010, 37(2): 1784 -1789.
[14] YANG X S, DEB S. Engineering optimisation by cuckoo search [J]. International Journal of Mathematical Modelling & Numerical Optimisation, 2010, 1(4): 330-343.
[15] GANDOMI A H, YANG X S, ALAVI A H. Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems [J]. Engineering with Computers, 2013, 29(2): 245-245.
[16] YANG X S, DEB S. Multiobjective cuckoo search for design optimization [J]. Computers & Operations Research, 2013, 40(6): 1616-1624.
[2] 何子述, 夏威. 现代数字信号处理及其应用 [M]. 北京: 清华大学出版社, 2009: 163-216.
[3] CANDAN ?, INAN H. A unified framework for derivation and implementation of Savitzky-Golay filters [J]. Signal Processing, 2014, 104(6): 203-211.
[4] LUO J, YING K, HE P, et al. Properties of Savitzky-Golay digital differentiators [J]. Digital Signal Processing, 2005, 15(2): 122-136.
[5] ACHARYA D, RANI A, AGARWAL S, et al. Application of adaptive Savitzky-Golay filter for EEG signal processing [J]. Perspectives in Science, 2016, 8(C): 677-679.
[6] 史文库, 柯俊, 王倩, 等. V型推力杆的极限载荷分析与球铰结构优化 [J]. 西安交通大学学报, 2013, 47(10): 132-136. SHI Wenku, KE Jun, WANG Qian, et al. Ultimate load analysis and ball joint structure optimization of V-type thrust rods [J]. Journal of Xi’an Jiaotong University, 2013, 47(10): 132-136.
[7] FENG G, SHI W, ZHANG H, et al. Research on the fatigue life prediction method of thrust rod [J]. Mathematical Problems in Engineering, 2016(10): 1-9.
[8] 江洪, 成中书, 张丛. 空气悬架导向机构纵向推力杆的优化设计 [J]. 机械设计与制造, 2010(6): 1-3. JIANG Hong, CHENG Zhongshu, ZHANG Cong. Optimization design of longitudinal thrust rod for air suspension steering mechanism [J]. Mechanical Design and Manufacturing, 2010(6): 1-3.
[9] ISMAIL M, IKHOUANE F, RODELLAR J. The hysteresis Bouc-Wen model: a survey [J]. Archives of Computational Methods in Engineering, 2009, 16(2): 161-188.
[10] ORTIZ G A, ALVAREZ D A, BEDOYZ-RUIZ D. Identification of Bouc-Wen type models using the transitional Markov chain Monte Carlo method [J]. Computers & Structures, 2015, 146: 252-269.
[11] ZIMMERMANN B, KOHLER A. Optimizing Savitzky-Golay parameters for improving spectral resolution and quantification in infrared spectroscopy [J]. Applied Spectroscopy, 2013, 67(8): 892-902.
[12] 刘思峰, 杨英杰, 吴利丰. 灰色系统理论及其应用 [M]. 8版. 北京: 科学出版社, 2018: 55-57.
[13] KAYACAN E, ULUTAS B, KAYNAK O. Grey system theory-based models in time series prediction [J]. Expert Systems with Applications, 2010, 37(2): 1784 -1789.
[14] YANG X S, DEB S. Engineering optimisation by cuckoo search [J]. International Journal of Mathematical Modelling & Numerical Optimisation, 2010, 1(4): 330-343.
[15] GANDOMI A H, YANG X S, ALAVI A H. Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems [J]. Engineering with Computers, 2013, 29(2): 245-245.
[16] YANG X S, DEB S. Multiobjective cuckoo search for design optimization [J]. Computers & Operations Research, 2013, 40(6): 1616-1624.