基于优化Kriging模型的平台结构动力学模型修正
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摘要
以某海洋平台结构试验模型为研究对象,提出了Krigging模型与多目标遗传算法优化相结合的动力学模型修正方法。将模态频率设为修正目标,利用待修正参数与平台模态频率间的Kriging模型代替平台有限元模型进行修正。针对近似误差可能对修正结果产生干扰的问题,提出了一种基于多目标遗传算法的局部加点优化方法,用于优化代理模型的拟合精度。通过力锤激励下的室内模型试验对上述方法进行了验证,结果表明,Kriging模型能够有效拟合平台结构参数与固有频率间的复杂映射关系,所提出的优化方法能够显著改善Kriging模型精度,可应用于实际工程。
A dynamics model updating method combining the Kriging model with the multi-scale objective genetic algorithm(MOGA) optimization for the experimental model of an offshore platform structure was proposed. The modal frequencies were set as updating targets, and the Kriging model between updating parameters and modal frequencies of the platform was set up and, in replacement of the commonly used finite element model, applied to the model updating. In order to solve the problem that approximate error may cause a disturbance to the updating result, the method of MOGA based on an infill-sampling optimization approach was provided. Model tests of the offshore platform model in the lab based on hammer excitation were employed to prove the effectiveness of the method. The results show that the Kriging model can effectively reveal the complex mapping relations between the updating parameters and modal frequencies, and the infill-sampling criteria provided can significantly improve the precision of the Kriging model, which can be applied in actual engineering.
A dynamics model updating method combining the Kriging model with the multi-scale objective genetic algorithm(MOGA) optimization for the experimental model of an offshore platform structure was proposed. The modal frequencies were set as updating targets, and the Kriging model between updating parameters and modal frequencies of the platform was set up and, in replacement of the commonly used finite element model, applied to the model updating. In order to solve the problem that approximate error may cause a disturbance to the updating result, the method of MOGA based on an infill-sampling optimization approach was provided. Model tests of the offshore platform model in the lab based on hammer excitation were employed to prove the effectiveness of the method. The results show that the Kriging model can effectively reveal the complex mapping relations between the updating parameters and modal frequencies, and the infill-sampling criteria provided can significantly improve the precision of the Kriging model, which can be applied in actual engineering.
引文
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[14]张冬冬，郭勤涛．Kriging响应面代理模型在有限元模型确认中的应用[J]．振动与冲击，2013,32(9):187-191.ZHANG Dongdong,GUO Qintao.Application of Kriging response surface in finite element model validation[J].Journal of Vibration and Shock,2013,32(9):187-191．
[15]韩忠华．Kriging模型及代理优化算法研究进展[J]．航空学报，2016,37(11):3197-3225.HAN Zhonghua.Kriging surrogate model and its application to design optimization:a review of recent progress[J].Acta Aeronautica et Astronautica Sinica,2016,37(11):3197-3225．
[16]李志刚，阳霞，任伟新．一座异形斜拉桥的动力有限元模型与验证[J]．振动与冲击，2017,36(12):55-60.LI Zhigang,YANG Xia,REN Weixin.Dynamic finite element model and validation of a special-shaped cable-stayed bridge[J].Journal of Vibration and Shock,2017,36(12):55-60．
[17]游海龙，贾新章，张小波，等．Kriging插值与拉丁超立方试验相结合构造电路元模型[J]．系统仿真学报，2005,17(11):2752-2755.YOU Hailong,JIA Xinzhang,ZHANG Xiaobo,et al.Constructing circuit metamodel using Kriging interpolation integrated with Latin hypercube sampling experiment[J].Journal of System Simulation,2005,17(11):2752-2755.
[2]CHEN J C,WADA B K.Criteria for analysis-test correlation of structural dynamic systems[J].Journal of Applied Mechanics Trans of the ASME,1975,42(2):471-477．
[3]KABE A M.Stiffness matrix adjustment using mode data[J].AIAA Journal,1985,23(9):1431-1436．
[4]STETSON K A,PALMA G E.Inversion of first-order perturbation theory and its application to structural design[J].AIAA Journal,2012,14(4):454-460．
[5]FOX R L,KAPOOR M P.Rates of change of eigenvalues and eigenvectors[J].AIAA Journal,1969,6(12):2426-2429．
[6]LIM K B,JUNKINS J L,WANG B P.Re-examination of eigenvector derivatives[J].Journal of Guidance Control&Dynamics,1987,10(6):581-587．
[7]NELSON R B.Simplified calculation of eigenvector derivatives[J].AIAA Journal,1976,14(9):1201-1205．
[8]OJALVO I U.Efficient computation of mode-shape derivatives for large dynamic systems[J].AIAA Journal,1987,25(10):1386-1390．
[9]FANG S E,PERERA R.Damage identification by response surface based model updating using D-optimal design[J].Mechanical Systems&Signal Processing,2011,25(2):717-733．
[10]宗周红，褚福鹏，牛杰．基于响应面模型修正的桥梁结构损伤识别方法[J]．土木工程学报，2013,46(2):115-122.ZONG Zhouhong,CHU Fupeng,NIU Jie.Damage identification methods of bridge structures using response surface based on finite element model updating[J].China Civil Engineering Journal,2013,46(2):115-122．
[11]CHAKRABORTY S,SEN A.Adaptive response surface based efficient finite element model updating[J].Finite Elements in Analysis&Design,2014,80(3):33-40．
[12]陈喆，何欢，陈国平．基于增广SVM的结构动力学模型修正方法研究[J]．振动与冲击，2017,36(15):194-202.CHEN Zhe,HE Huan,CHEN Guoping.Structural dynamic model updating based on augmented SVM[J].Journal of Vibration and Shock,2017,36(15):194-202．
[13]KRIGE D G.A Statistical approach to some basic mine valuation problems on the witwatersrand[J].Journal of the Chemical,Metallurgical and Mining Engineering Society of South Africa,1951,52(6):119-139．
[14]张冬冬，郭勤涛．Kriging响应面代理模型在有限元模型确认中的应用[J]．振动与冲击，2013,32(9):187-191.ZHANG Dongdong,GUO Qintao.Application of Kriging response surface in finite element model validation[J].Journal of Vibration and Shock,2013,32(9):187-191．
[15]韩忠华．Kriging模型及代理优化算法研究进展[J]．航空学报，2016,37(11):3197-3225.HAN Zhonghua.Kriging surrogate model and its application to design optimization:a review of recent progress[J].Acta Aeronautica et Astronautica Sinica,2016,37(11):3197-3225．
[16]李志刚，阳霞，任伟新．一座异形斜拉桥的动力有限元模型与验证[J]．振动与冲击，2017,36(12):55-60.LI Zhigang,YANG Xia,REN Weixin.Dynamic finite element model and validation of a special-shaped cable-stayed bridge[J].Journal of Vibration and Shock,2017,36(12):55-60．
[17]游海龙，贾新章，张小波，等．Kriging插值与拉丁超立方试验相结合构造电路元模型[J]．系统仿真学报，2005,17(11):2752-2755.YOU Hailong,JIA Xinzhang,ZHANG Xiaobo,et al.Constructing circuit metamodel using Kriging interpolation integrated with Latin hypercube sampling experiment[J].Journal of System Simulation,2005,17(11):2752-2755.