A high-precision probabilistic uncertainty propagation method for problems involving multimodal distributions

Zhang, Z.; Jiang, Chao; Han, Xue; Ruan, Xiang

doi:10.1016/j.ymssp.2019.01.031

Cited by 34 publications

(6 citation statements)

References 57 publications

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“…However, in many instances, although the samples for establishing an ellipsoid convex model would be pretty limited, their distributions may have multiple distinct separate or intersecting multimodal. The multimodal situation is similar to the multi-peak situation of PDF in the probability theory (Zhang et al 2019;. Obviously, the traditional single ellipsoid model is not suitable for practically descript the multimodal of samples.…”

Section: Introductionmentioning

confidence: 94%

Multimodal ellipsoid model for non-probabilistic structural uncertainty quantification and propagation

Liu

Zhang

et al. 2021

Int J Mech Mater Des

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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.

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Section: Introductionmentioning

confidence: 94%

Multimodal ellipsoid model for non-probabilistic structural uncertainty quantification and propagation

Liu

Zhang

et al. 2021

Int J Mech Mater Des

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“…This example is modified from [48]. The dome truss system consists of 52 bars with 21 nodes, as shown in Fig.…”

Section: A Truss Systemmentioning

confidence: 99%

High-Dimensional Reliability Method Accounting for Important and Unimportant Input Variables

Yin

2021

Journal of Mechanical Design

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Reliability analysis is usually a core element in engineering design and can be performed with physical models (limit-state functions). Reliability analysis becomes computationally expensive when the dimensionality of input random variables is high. This work develops a high dimensional reliability analysis method by a new dimension reduction strategy so that the contributions of unimportant input variables are also accommodated by the dimension reduction. The dimension reduction is performed with the first iteration of the first order reliability method (FORM), which identifies important and unimportant input variables. Then a higher order reliability analysis is performed in the reduced space of only important input variables. The reliability obtained in the reduced space is then integrated with the contributions of unimportant input variables, resulting in the final reliability prediction that accounts for both types of input variables. Consequently, the new reliability method is more accurate than the traditional method, which fixes unimportant input variables at their means. The accuracy is demonstrated by three examples.

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“…(Most Probable Point, MPP), 对于常见的多峰随机变量上述标准化过程通常会引入较大的计算误差 [23] ; 传统的基于矩的不确定性传播方法通常仅计算响应函数的前四阶矩便可以很好地拟合单峰响应的概率密度函数. 然而, 如果响应概率密度函数是多峰分布则需要高阶矩才能较好地拟合, 而高阶矩的计算效率和精度存在较大挑战 [24] . 为此, 国内外学者针对多峰随机分布中的上述问题进行研究并取得了一定的成果. Hu 和 Du [23] 提出了一种针对双峰分布的均值鞍点…”

Section: 引言不确定性广泛存在于工程问题中例如非均匀材unclassified

“…Zhang 等 [24] 提出了一种针对多峰分布的单变降维法 (univariate dimension reduction method, UDRM) 并通过最大熵方法拟合出了响应的概率密度函数. Meng 等 [25] 提出了一种新型混合模型并使用混沌多项式方…”

Section: 引言不确定性广泛存在于工程问题中例如非均匀材unclassified

An uncertainty propagation analysis method considering multimodal random distribution

Xie¹,

Zhang²,

Jiang³

2021

Sci. Sin.-Tech.

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A high-precision probabilistic uncertainty propagation method for problems involving multimodal distributions

Cited by 34 publications

References 57 publications

Multimodal ellipsoid model for non-probabilistic structural uncertainty quantification and propagation

Multimodal ellipsoid model for non-probabilistic structural uncertainty quantification and propagation

High-Dimensional Reliability Method Accounting for Important and Unimportant Input Variables

An uncertainty propagation analysis method considering multimodal random distribution

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