改进的平行六面体凸模型识别动力学不确定参数区间的方法
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摘要
提出了一种改进的平行六面体凸模型,以便更普遍地描述不确定参数之间的相关性。结合逆响应面模型,建立了一种动力学不确定参数区间识别方法。首先,采用改进的平行六面体二维模型描述结构动力学响应频率的不确定域相关分布,再构建其多维模型,并通过仿射坐标变换将其转化为标准参数空间中的区间形式;然后,以此参数空间内的响应频率为输入,结构不确定参数为输出,构建能避免区间扩张问题的完全平方项区间逆响应面模型;进而进行区间运算,识别动力学不确定参数区间;最后,以一个3自由度质量弹簧系统仿真算例和一个螺栓连接框架结构模态实验进行了验证。结果说明:此方法能够有效性地识别结构的动力学不确定参数区间,具有较高的识别精度。
An improved parallelepiped convex model is proposed to describe the wide correlation between uncertain parameters.In combination with response surface method,a dynamic uncertain parameter identification method based on non-probabilistic convex model is presented.First of all,the improved parallelepiped two-dimensional model is used to describe the correlation distribution of the dynamic response frequencies of the structure and then to construct the multidimensional model,which is transformed into the interval form of standard parameter space by affine coordinate transformation.Then,taking the response frequency in the standard parameter space as the input and the structure uncertain parameter as the output,we construct the complete-quadratic-term interval inverse response surface model,which can avoid the interval expansion problem caused by interval operation and directly carry out the interval operation to identify the interval of dynamic uncertain parameters.Finally,this method is verified by a simulation example of a 3 DOF mass spring system and a modal experiment of a bolt connection frame.The results show that the proposed method can effectively identify the dynamic uncertain parameters of the structure with a high accuracy.
An improved parallelepiped convex model is proposed to describe the wide correlation between uncertain parameters.In combination with response surface method,a dynamic uncertain parameter identification method based on non-probabilistic convex model is presented.First of all,the improved parallelepiped two-dimensional model is used to describe the correlation distribution of the dynamic response frequencies of the structure and then to construct the multidimensional model,which is transformed into the interval form of standard parameter space by affine coordinate transformation.Then,taking the response frequency in the standard parameter space as the input and the structure uncertain parameter as the output,we construct the complete-quadratic-term interval inverse response surface model,which can avoid the interval expansion problem caused by interval operation and directly carry out the interval operation to identify the interval of dynamic uncertain parameters.Finally,this method is verified by a simulation example of a 3 DOF mass spring system and a modal experiment of a bolt connection frame.The results show that the proposed method can effectively identify the dynamic uncertain parameters of the structure with a high accuracy.
引文
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[3]Mottershead J E,Eriswell M I,Ng G H T.Geometric parameters for finite element model updating of joints and constraints[J].Mechanical Systems and Signal Processing,1996,10(0):171-182.
[4]Khodaparast H H,Mottershead J E,Friswell M I.Perturbation methods for the estimation of parameter variability in stochastic model updating[J].Mechanical Systems&Signal Processing,2008,22(8):1751-1773.
[5]Chen L,Rao S S.Fuzzy finite-element approach for the vibration analysis of imprecisely-defined systems[J].Finite Elements in Analysis&Design,2013,27(12):69-83.
[6]Jaulin L,Kieffer M,Didrit O,et al.Applied Interval Analysis[M].Springer Berlin,2001.
[7]苏静波,邵建国.基于区间分析的工程结构不确定性研究现状与展望[J].力学进展,2005,35(3):338-344.Su Jing-bo,Shao Jian-guo.Current research and prospects on interval analysis in engineering structure uncertainty analysis[J].Progress of Mechanics,2005,35(3):338-344.
[8]王晓军,王磊,贾晓,等.基于非概率凸模型可靠性的结构优化设计[J].北京航空航天大学学报,2012,38(5):630-635.Wang Xiao-jun,Wang Lei,Jia Xiao,et al.Structural optimization design based on mom-probabilistic convex modeling reliability[J].Journal of Beijing University of Aeronautics and Asteonautics,2012,38(5):630-635.
[9]骆勇鹏,黄方林,韩建平,等.灵敏度的模态区间分析方法及其在不确定性参数识别中的应用[J].振动工程学报,2016,29(4):577-584.Luo Yong-peng,Huang Fang-ping,Han Jian-ping,et al.A sensitivity modal interval analysis method and its application to uncertain parameter identification[J].Journal of Vibration Engineering,2016,29(4):577-584.
[10]Nehi H M,Hamidi F.Upper and lower bounds for the optimal values of the interval bilevel linear programming problem[J].Applied Mathematical Modelling,2015,39(5-6):1650-1664.
[11]Jiang C,Han X,Lu G Y,et al.Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique[J].Computer Methods in Applied Mechanics&Engineering,2011,200(33-36):2528-2546.
[12]Ni B Y,Jiang C,Han X.An improved multi-dimensional parallelepiped non-probabilistic model for structural uncertainty analysis[J].Applied Mathematical Model-ling,2016,40(7-8):4727-4745.
[13]Jiang C,Zhang Q F,Han X,et al.Multidimensional parallelepiped model-a new type of non-probabilistic convex model for structural uncertainty analysis[J].International Journal for Numerical Methods in Engineering,2015,103(1):31-59.
[14]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.
[15]方圣恩,张秋虎,林友勤,等.不确定参数识别的区间响应面模型修正方法[J].振动工程学报,2015,28(1):73-81.Fang Sheng-en,Zhang Qiu-hu,Lin You-qin,et al.Uncertain parameter identification using interval response surface modal updating[J].Journal of Vibration Engineering,2015,28(1):73-81.
[16]张根辈,臧朝平,王晓伟,等.螺栓连接框架结构的有限元模型修正[J].工程力学,2014,31(4):26-33.Zhang gen-bei,Zang chao-ping,Wang Xiao-wei,et al.Finite element model updating of a framed structure with bolted joints[J].Engineering Mechanics,2014,31(4):26-33.
[17]Zang C,Ewins D J.Model validation for structural dynamics in the aero-engine design process[J].Frontiers of Energy&Power Engineering in China,2009,3(4):480-488.
[18]Isukapalli S S,Balakrishnan S,Georgopoulos P G.Computationally efficient uncertainty propagation and reduction using the stochastic response surface method[C].IEEE Conference on Decision and Control,2005,2:2237-2243.