For the vibro-acoustic system with interval and random uncertainties, polynomial chaos expansions have received broad and persistent attention. Nevertheless, the cost of the computation process increases sharply with the increasing number of uncertain parameters. This study presents a novel interval and random polynomial expansion method, called Sparse Grids’ Sequential Sampling-based Interval and Random Arbitrary Polynomial Chaos (SGS-IRAPC) method, to obtain the response of a vibro-acoustic system with interval and random uncertainties. The proposed SGS-IRAPC retains the accuracy and the simplicity of the traditional arbitrary polynomial chaos method, while avoiding its inefficiency. In the SGS-IRAPC, the response is approximated by the moment-based arbitrary polynomial chaos expansion and the expansion coefficient is determined by the least squares approximation method. A new sparse sampling scheme combined the sparse grids’ scheme with the sequential sampling scheme which is employed to generate the sampling points used to calculate the expansion coefficient to decrease the computational cost. The efficiency of the proposed surrogate method is demonstrated using a typical mathematical problem and an engineering application.

中文翻译：

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不确定振动声系统区间和随机响应分析的一种新的稀疏多项式展开方法

对于具有区间和随机不确定性的振动声系统，多项式混沌展开一直受到广泛而持久的关注。然而，随着不确定参数数量的增加，计算过程的成本急剧增加。本研究提出了一种新的区间和随机多项式展开方法，称为稀疏网格的基于序列采样的区间和随机任意多项式混沌 (SGS-IRAPC) 方法，以获得具有区间和随机不确定性的振动声学系统的响应。所提出的 SGS-IRAPC 保留了传统任意多项式混沌方法的准确性和简单性，同时避免了其低效率。在 SGS-IRAPC 中，响应由基于矩的任意多项式混沌展开近似，展开系数由最小二乘近似法确定。一种新的稀疏采样方案将稀疏网格方案与顺序采样方案相结合，利用顺序采样方案生成用于计算扩展系数的采样点，以降低计算成本。使用典型的数学问题和工程应用证明了所提出的替代方法的效率。