参数不确定性内声场分析的封闭区间有限元方法

Enclosing interval finite-element method for the analysis of the interior-acoustic field with parametric uncertainty

针对含有不确定但有界参数的内声场预测问题,主要的区间建模方法为逐单元的区间有限元法(EBE-IFEM)和区间摄动有限元法(IPFEM)。但由于IPFEM在级数展开时存在非保守近似的缺陷,EBE-IFEM在利用拉格朗日乘子法来约束扩增的节点自由度时增加了内存消耗并降低了迭代计算效率,现有方法很难兼备保守的结果和高的计算效率。为此,提出了一种新的封闭区间有限元方法(Enclosing-IFEM),结合“混合节点-单元”(MNE)的组装策略来缩减自由度,该方法能够在满足结果保守性的前提下,提高求解效率。而且,Enclosing-IFEM的区间动力学方程可以直接转化为“并矢积”形式,解决了基于Sherrman-Morrison-Woodbury(S-M-W)级数的区间摄动有限元法(SMW-IPFEM)的动力学拓展问题。最后,将蒙特卡罗方法以及它的区间有限元方法作为参考解,通过两个数值算例验证了Enclosing-IFEM的计算精度和效率。

For the prediction of interior acoustic field with uncertain-but-bounded parameters,the main currently used interval modeling approaches are element-by-element based interval finite-element method(EBE-IFEM) and interval perturbation finite-element method(IPFEM).However,the non-conservative approximation of IPFEM due to neglecting the high-order terms in series expansion,and the increasing memory consumption and low iterative computational efficiency of EBE-IFEM due to the constraints of the expanded nodal freedoms by the Lagrange multiplier method,none of present methods can cope with both the conservative results and high computational efficiency.Therefore,based on the “mixed-nodal-element” assembly way to decrease the freedoms,a new method called enclosing interval finite-element method(Enclosing-IFEM) was proposed to achieve the goals of both well conservativeness and high time-efficiency.Moreover,as the interval dynamic equation of the Enclosing-IFEM can be transformed into the dyadic product formula directly,the problem of Sherrman-Morrison-Woodbury(S-M-W)-series based IPFEM for dynamic analysis was solved.Finally,taking the results by the Monte-Carlo method and other interval finite-element methods as the cross references,both efficiency and accuracy of the Enclosing-IFEM were verified through two numerical examples.