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首页> 外文期刊>Mechanical systems and signal processing >Influence of Polynomial Chaos expansion order on an uncertain asymmetric rotor system response
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Influence of Polynomial Chaos expansion order on an uncertain asymmetric rotor system response

机译：多项式混沌展开阶对不确定的不对称转子系统响应的影响

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摘要

A stochastic harmonic balance method with a recursive procedure is developed to evaluate the steady-state response of a rotor system with uncertain stiffness and asymmetric coupling that involves time-dependent terms. The Polynomial Chaos (PC) expansion is proposed to evaluate the mean and the standard deviation of the responses and the harmonic amplitudes of orders 1-4 involving 288 degrees-of-freedom. To determine the coefficients of the expansion requires to solve a large system of equations. To achieve this and to avoid numerical problems related to the size of the system, the first contribution of the study consists of a recursive evaluation of the Polynomial Chaos coefficients to be able to estimate the stochastic response for a high order of the Polynomial Chaos expansion. From the methodology implemented, the steady-state responses and n× harmonic components (for n=1, 2, 3 and 4 in the present study) of the asymmetric rotor with uncertainty are evaluated for several PC orders. Then, the second main contribution focuses on a clarification and analysis of the use of Polynomial Chaos expansion around the critical speeds. First, it is observed that the convergence is slow: the response obtained with 30 PCs is twice the one obtained with 200 PCs. Second, it is noted that the parity of the PC order has a strong influence on the response level: whereas two responses obtained with two consecutive even PC orders (or two consecutive odd PC orders) are almost the same for a given rotation speed, the ratio of the responses evaluated with two consecutive PC orders (one even order and one odd order) may be large (e.g. oscillations between two consecutive PC orders greater than 10 are noticeable if the PC order is about 30).
机译：开发了一种具有递归过程的随机谐波平衡方法，以评估具有不确定刚度和不对称耦合（涉及时间相关项）的转子系统的稳态响应。提出了多项式混沌（PC）展开法，以评估响应的平均值和标准偏差以及涉及288个自由度的1-4阶谐波幅度。要确定膨胀系数，需要解决一个大型方程组。为了实现这一目标并避免与系统规模有关的数值问题，该研究的第一贡献是对多项式混沌系数进行递归评估，以便能够估计高阶多项式混沌展开式的随机响应。从实施的方法学出发，对具有几个不确定度的不对称转子的稳态响应和nx谐波分量（在本研究中，n = 1、2、3和4）进行了评估。然后，第二个主要贡献集中于对临界速度附近的多项式混沌展开的使用的澄清和分析。首先，观察到收敛很慢：30台PC获得的响应是​​200台PC获得的响应的两倍。其次，要注意的是，PC顺序的奇偶性对响应级别有很大影响：而对于给定的旋转速度，两个连续的偶数PC顺序（或两个连续的奇数PC顺序）获得的两个响应几乎相同，用两个连续PC阶次（一个偶数阶和一个奇数阶）评估的响应之比可能很大（例如，如果PC阶数约为30，则两个连续PC阶次之间的振荡大于10会很明显）。

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