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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Unified polynomial expansion for interval and random response analysis of uncertain structure-acoustic system with arbitrary probability distribution
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Unified polynomial expansion for interval and random response analysis of uncertain structure-acoustic system with arbitrary probability distribution

机译：具有任意概率分布的不确定结构-声学系统的区间统一多项式展开和随机响应分析

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摘要

For structure-acoustic system with uncertainties, the interval model, the random model and the hybrid uncertain model have been introduced. In the interval model and the random model, the uncertain parameters are described as either the random variable with well defined probability density function (PDF) or the interval variable without any probability information, whereas in the hybrid uncertain model both interval variable and random variable exist simultaneously. For response analysis of these three uncertain models of structure-acoustic problem involving arbitrary PDFs, a unified polynomial expansion method named as the Interval and Random Arbitrary Polynomial Chaos method (IRAPCM) is proposed. In IRAPCM, the response of the structureacoustic system is approximated by APC expansion in a unified form. Particularly, only the weight function of polynomial basis is required to be changed to construct the APC expansion for the response of different uncertain models. Through the unified APC expansion, the uncertain properties of the response of three uncertain models can be efficiently obtained. As the APC expansion can provide a free choice of the polynomial basis, the optimal polynomial basis for the random variable with arbitrary PDFs can be obtained by using the proposed IRAPCM. The IRAPCM has been employed to solve a mathematical problem and a structure-acoustic problem, and the effectiveness of the unified IRAPCM for response analysis of three uncertain models is demonstrated by fully comparing it with the hybrid first-order perturbation method and several existing polynomial chaos methods. 2018 Elsevier B.V. All rights reserved.
机译：对于具有不确定性的结构声学系统，引入了区间模型，随机模型和混合不确定模型。在区间模型和随机模型中，不确定参数被描述为具有明确定义的概率密度函数（PDF）的随机变量或没有任何概率信息的区间变量，而在混合不确定模型中，区间变量和随机变量都存在同时。为了对涉及任意PDF的这三种不确定的结构声学问题的响应模型进行响应分析，提出了一种称为区间和随机任意多项式混沌方法（IRAPCM）的统一多项式展开方法。在IRAPCM中，通过APC扩展以统一形式近似结构声学系统的响应。特别是，只需要改变多项式的权函数就可以构造APC扩展来响应不同的不确定模型。通过统一的APC展开，可以有效地获得三个不确定模型响应的不确定属性。由于APC扩展可以自由选择多项式基础，因此可以通过使用建议的IRAPCM获得具有任意PDF的随机变量的最佳多项式基础。将IRAPCM用于解决一个数学问题和一个结构声学问题，并且通过与混合一阶微扰法和几种现有的多项式混沌方法进行充分比较，证明了统一的IRAPCM对三种不确定模型的响应分析的有效性。方法。 2018 Elsevier B.V.保留所有权利。

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