基于响应面与灵敏度分析的区间不确定性参数识别方法

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摘要针对工程结构中普遍存在的不确定性，需开展考虑不确定性的有限元建模与模型参数识别。提出了具有区间不确定性参数识别的分步实施方法，第一步首先通过Box-Behnken矩阵设计方法进行响应面的样本点设计，并代入有限元模型计算获得结构的关心固有频率，再基于二次多项式建立固有频率与待识别参数间的响应面模型，最后基于优化方法与自适应响应面思想对区间参数中值进行识别，第二步基于响应面模型并结合灵敏度分析，通过迭代实现区间参数半径的识别。通过一个质量—弹簧系统的数值算例和一组镜架系统工程实例的区间不确定性参数识别，验证了本文所提出方法的可行性和可靠性。参数识别结果表明所提出的方法具有较高的计算效率且可有效地避免区间优化导致的收敛问题。

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	陈学前1
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	沈展鹏1
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关键词 ：响应面模型, 区间不确定性, 参数识别, 灵敏度分析

Abstract：It is necessary to study the finite element (FE) modeling and updating in consideration of the uncertainty, because the uncertainty is widely existent in the engineering structure. A method of interval uncertain parameter identification in the structural dynamics was proposed. In the method, the model updating with interval uncertainty includes two steps. In step one, the samples of the response model are obtained by Box-Behnken design, and the interesting natural frequencies of the model are calculated by the finite element simulation. Then, the response surface model between the natural frequency and the identifying parameters is constructed according to the quadratic polynomial. Lastly,the interval average value of uncertain parameters is identified based on the optimal algorithm and the adaptive response surface model. The interval width of uncertain parameters is identified by combining the response model and the sensitivity analysis in step two. The proposed method has been validated by a numerical mass-spring system and a transport mirror system. The updating results have proved the feasibility and reliability of the method. Also, the results show that the proposed method can improve the efficiency and avoid the questions induced by the interval optimization.

Key words： response surface model interval uncertainty parameter identification sensitivity analysis

收稿日期: 2018-01-23 出版日期: 2019-08-15

引用本文:

陈学前1,2，沈展鹏1,2，刘信恩1,2. 基于响应面与灵敏度分析的区间不确定性参数识别方法[J]. 振动与冲击, 2019, 38(16): 267-273.
CHEN Xueqian1,2, SHEN Zhanpeng1,2, LIU Xin’en1,2. A method of interval uncertain parameter identification based on a response surface model and sensitivity analysis. JOURNAL OF VIBRATION AND SHOCK, 2019, 38(16): 267-273.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2019/V38/I16/267

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