包装件振动可靠性的不确定度量化及灵敏度分析

Uncertainty quantification and sensitivity analysis of package vibration reliability

研究包装件参数不确定性对振动可靠性变化的影响,并分析振动可靠性指标对各不确定参数的灵敏度。采用Karhunen-Loeve展开将具有一定谱特征的平稳随机振动表示在标准正态随机变量空间中,应用一阶可靠性方法分析线性包装件振动可靠性指标。考虑缓冲材料弹性特性、阻尼特性、产品主体和脆弱部件之间的弹性特性、阻尼特性四个随机参数,对这些参数进行等概率转换,将它们用标准正态随机变量等效表示,根据拉丁超立方采样原则,在四维标准正态随机变量空间采样,应用数值分析研究可靠性指标的变化情况。根据可靠性指标的概率分布选取合理的正交混沌多项式类型,应用非嵌入分析法分析混沌多项式的系数。在获得可靠性指标的多项式混沌展开表达后,采用Sobol法分析可靠性指标的全局灵敏度。给出了一个实例分析,介绍了应用多项式混沌展开对振动可靠性指标进行不确定量化的过程及可靠性指数的分析结果。

Here,effects of package parameters uncertainty on its vibration reliability was studied,the sensitivity of reliability index to each package uncertain parameter was analyzed.Karhunen-Loeve expansion was used to express a stationary random vibration with certain spectral characteristics in the standard normal random variable space.The first-order reliability method was applied to analyze the vibration reliability index of linear package.Four random parameters of cushioning material elastic property,cushioning material damping one,elastic one between product main body and vulnerable parts,and damping one between product main body and vulnerable parts were considered.These parameters were converted with equal probability into equivalent standard normal random variables.According to Latin hypercube sampling principle,sampling was done in the four-dimensional standard normal random variable space,and numerical analysis was applied to study the reliability index’s changes.According to the probability distribution of the reliability index,the reasonable type of orthogonal chaotic polynomial was selected,and coefficients of the chaotic polynomial were analyzed using the non-embedding analysis method.After obtaining the polynomial chaos expansion expression of the reliability index,the global sensitivity of the reliability index was analyzed using Sobol method.An example analysis was given here.The uncertainty quantification process of the vibration reliability index using polynomial chaos expansion and analysis results of the reliability index were introduced.