小样本结构参数不确定性量化及传递分析的信息扩散方法

Structural Parameter Uncertainty Quantification and Propagation Analysis based on Information Diffusion Theory using Limited Data

如何准确估计不确定性参数的概率密度函数是结构不确定性分析的一个重要环节。而这一环节常因实测 数据有限而难以实现。为此,提出基于信息扩散理论的小样本结构参数不确定性量化及传递分析方法。首先基于有限 样本数据,采用信息扩散理论估计不确定性参数服从的概率密度函数,进而采用接受-拒绝法生成随机数并进行统计分 析得到不确定性参数的均值和标准差。其次,根据不确定性参数量化结果,基于响应面模型快速计算参数不确定性引 起的结构响应变异程度。最后,以4自由度弹簧 质量系统和钢板材料参数不确定性量化及传递分析试验来验证所提 方法的可行性及可靠性。分析结果表明:所提方法在概率分布未知、实测数据大于20个的情况下可有效地量化参数的 不确定性及其引起的结构响应的变异程度。

An accurate determination of probability density function of uncertainty parameters is a key link for structural uncertainty analysis.However,in actual engineering,it is often difficult to realize the key link because of the limited measurement data.In this paper,the structure parameter uncertainty quantification and propagation analysis method based on information diffusion theory using limited data is proposed.First of all,the information diffusion theory is used to estimate the probability density function of the limited measured data.Then,the random sample is generated using the acceptance-rejection method and the mean value and the standard difference value of the uncertainty parameters are obtained by performing the statistical analysis.Finally,on the basis of parameter uncertainty quantification,the structural response variableness caused by parameter uncertainty is quickly calculated using response surface model.The proposed method is validated by a 4-DOF mass-spring system and a set of experimental steel plates.The results show that the variation of the structural response caused by the variation of the parameters can be effectively quantified using the proposed method with the unknown probability distribution of the uncertain parameters when the number of the measurement samples is greater than 20.