Orthogonal spline expansions for uncertainty quantification in linear dynamical systems
Orthogonal spline expansions for uncertainty quantification in linear dynamical systems
复制标题
DOI：
10.1016/j.jsv.2021.116366
复制
发表时间：
2021-07
影响因子：
4.7
通讯作者：
S. Rahman;Ramin Jahanbin
中科院分区：
文献类型：
--
作者：
S. Rahman;Ramin Jahanbin
本文利用正交化样条法的最新进展来解决线性结构动力学中的不确定性量化问题。该方法基于样条型混沌展开(SCE)和样条维分解(SDD)，对输入随机变量中的量测一致的正交化基样条构造了感兴趣的动力系统响应的类傅立叶展开，并用标准最小二乘回归估计展开系数。在随机动力响应中，SCE和SDD方法能够捕捉到高度的非线性和非光滑性，明显优于多项式混沌展开(PCE)方法。然而，由于张量积结构的影响，SCE和PCE一样，也受到维度诅咒的影响。相比之下，SDD配备了理想的输入变量维度层次结构，在很大程度上减少了维度的诅咒。两自由度动力系统频率响应分析的数值结果表明，在估计响应统计量时，基函数较少的低阶SCE可以消除或显著减小高阶PCE产生的虚假振荡。最后，对包含110个随机变量的战斗机进行了高维模态分析，验证了SDD方法解决大规模UQ问题的能力。
This paper leverages recent progress on orthonormal splines for solving uncertainty quantification (UQ) problems from linear structural dynamics. The resulting methods, premised on spline chaos expansion (SCE) and spline dimensional decomposition (SDD), both construe Fourier-like expansion of a dynamic system response of interest with respect to measure-consistent orthonormalized basis splines in input random variables and standard least-squares regression for estimating the expansion coefficients. The SCE and SDD methods are capable of capturing high nonlinearity and non-smoothness, if they exist, in a stochastic dynamic response markedly better than the polynomial chaos expansion (PCE) method. However, due to the tensor-product structure, SCE, like PCE, also suffers from the curse of dimensionality. In contrast, SDD, equipped with a desirable dimensional hierarchy of input variables, deflates the curse of dimensionality to a great extent. Numerical results from frequency response analysis of a two-degree-of-freedom dynamic system indicate that a low-order SCE with fewer basis functions removes or markedly reduces the spurious oscillations generated by high-order PCE in estimating the response statistics. Finally, a high-dimensional modal analysis of a fighter jet comprising 110 random variables was conducted, demonstrating the ability of SDD in solving large-scale UQ problems.