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Polynomial chaos expansion for permutation and cyclic permutation invariant systems: aApplication to mistuned bladed disks
Journal of Sound and Vibration ( IF 4.3 ) Pub Date : 2021-03-23 , DOI: 10.1016/j.jsv.2021.116103
Juliette Dréau , Benoit Magnain , Florence Nyssen , Alain Batailly

This article deals with the stochastic modeling of industrial mistuned bladed disks. More specifically, a cost-efficient implementation of polynomial chaos expansion is proposed, it is dedicated to mathematical systems exhibiting permutation invariance or cyclic permutation invariance of their random variables. Significant gains are obtained in comparison to the classical implementation of polynomial chaos expansion since potentially costly evaluations of the investigated deterministic system are only required over a small subspace of the random space. The proposed methodology is detailed and validated on analytical test cases before it is applied to two mistuned bladed disks models. First, computations carried out with a simplified bladed disk model allow an in-depth comparison between Monte Carlo simulations, previously published results with a standard polynomial chaos expansion and the proposed methodology. The latter is then employed to assess the influence of mistuning on the eigenfrequencies and amplification magnification of an industrial compressor stage. It is evidenced that in comparison to the standard polynomial chaos expansion, the proposed methodology yields computational gains of the same order of magnitude as the ones obtained going from Monte Carlo simulations to polynomial chaos expansion. Alternately, the proposed methodology may be employed to significantly increase the accuracy of the standard polynomial chaos expansion while featuring an identical computational cost.



中文翻译:

置换和循环置换不变系统的多项式混沌展开

本文涉及工业雾化刀片式磁盘的随机建模。更具体地说,提出了一种经济高效的多项式混沌扩展实施方案,它专用于表现出其随机变量的置换不变性或循环置换不变性的数学系统。与多项式混沌展开的经典实现相比,获得了显着收益,因为仅在随机空间的一小部分子空间上才需要对所研究的确定性系统进行潜在的昂贵评估。在将其应用于两个误解的刀片式磁盘模型之前,对所提出的方法进行了详细分析并通过了分析测试案例进行了验证。首先,使用简化的刀片式磁盘模型进行的计算可以在蒙特卡洛模拟之间进行深入的比较,以前发布的结果,其中包含标准多项式混沌扩展和建议的方法。然后将后者用于评估雾化对工业压缩机级的本征频率和放大倍数的影响。有证据表明,与标准多项式混沌扩展相比,所提出的方法所产生的计算增益与从蒙特卡洛模拟到多项式混沌扩展所获得的计算增益相同。或者,可以采用提出的方法来显着提高标准多项式混沌扩展的精度,同时具有相同的计算成本。然后将后者用于评估雾化对工业压缩机级的本征频率和放大倍数的影响。有证据表明,与标准多项式混沌扩展相比,所提出的方法所产生的计算增益与从蒙特卡洛模拟到多项式混沌扩展所获得的计算增益相同。或者,可以采用提出的方法来显着提高标准多项式混沌扩展的精度,同时具有相同的计算成本。然后将后者用于评估雾化对工业压缩机级的本征频率和放大倍数的影响。有证据表明,与标准多项式混沌扩展相比,所提出的方法所产生的计算增益与从蒙特卡洛模拟到多项式混沌扩展所获得的计算增益相同。或者,可以采用提出的方法来显着提高标准多项式混沌扩展的精度,同时具有相同的计算成本。所提出的方法所产生的计算增益与从蒙特卡洛模拟到多项式混沌展开所获得的计算增益相同。或者,可以采用提出的方法来显着提高标准多项式混沌扩展的精度,同时具有相同的计算成本。所提出的方法所产生的计算增益与从蒙特卡洛模拟到多项式混沌展开所获得的计算增益相同。或者,可以采用提出的方法来显着提高标准多项式混沌扩展的精度,同时具有相同的计算成本。

更新日期:2021-04-05
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