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首页> 外文期刊>International journal of mechanics and materials in design >Multimodal ellipsoid model for non-probabilistic structural uncertainty quantification and propagation
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Multimodal ellipsoid model for non-probabilistic structural uncertainty quantification and propagation

机译：非概率结构不确定性量化和传播的多模式椭球模型

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摘要

The traditional ellipsoid convex set is a kind of basic non-probabilistic model to measure uncertainties. However, it is difficult or inaccurate to quantify the uncertainties of variables with multimodal distributed samples. In this paper, a more generalized non-probabilistic ellipsoid model named multimodal ellipsoid model is proposed to effectively deal with the multimodal distributed samples. The samples with one or more similar properties are clustered together, and the principal directions of the samples and characteristic matrix are appropriately found through the Gaussian mixture model. Then, the multimodal ellipsoid model can be constructed by using the elliptical contour features of the Gaussian model to measure the uncertainties of variables. The proposed multimodal ellipsoid model can not only establish traditional ellipsoid model, but also establish multi-ellipsoid model for uncertain variables with multimodal samples. Furthermore, combining with the multimodal ellipsoid model and performance measure approach, the uncertain propagation results of system are obtained accurately. Three numerical examples and one engineering application are provided to demonstrate the effectiveness and accuracy of the proposed multimodal ellipsoid model.
机译：传统的椭圆形凸套是一种衡量不确定性的基本非概率模型。然而，难以或不准确地量化多模式分布式样品的变量的不确定性。本文提出了一种更广泛的非概率椭球模型，称为多模式椭球模型，以有效地处理多峰分布式样品。具有一个或多个相似性质的样品聚集在一起，并且通过高斯混合模型适当地发现样品和特征基质的主要方向。然后，可以通过使用高斯模型的椭圆形轮廓特征来构造多模式椭圆形模型来测量变量的不确定性。所提出的多模式椭球模型不仅可以建立传统的椭球模型，而且建立多椭粒模型，用于多峰样的不确定变量。此外，与多模式椭球模型和性能测量方法相结合，精确地获得了系统的不确定传播结果。提供了三个数值示例和一种工程应用，以证明所提出的多峰椭球模型的有效性和准确性。

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