Uncertainty analysis method for mechanical system based on multi-cluster ellipsoidal model

doi:10.3785/j.issn.1006-754X.2025.04.168

Chinese Journal of Engineering Design

2025, Vol. 32

Issue (2): 141-150 DOI: 10.3785/j.issn.1006-754X.2025.04.168

Theory and Method of Mechanical Design

Uncertainty analysis method for mechanical system based on multi-cluster ellipsoidal model

Zhengyan MA^1,²(

),Heng OUYANG^1,²(

),Zhijie HAO^1,²,Shuo GAO^1,²,Baohui LIU^1,²

^1.School of Mechanical Engineering, Hebei University of Technology, Tianjin 300401, China
^2.State Key Laboratory of Intelligent Power Distribution Equipment and System, Hebei University of Technology, Tianjin 300401, China

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Abstract

Multi-source uncertainties, such as random loads, manufacturing errors, and installation inaccuracies, influence mechanical system during the service processes, resulting in the deviation of system response, which seriously affects the operation stability and system reliability. In practical engineering, it is very difficult to collect high-quality data of complex mechanical systems on a large scale. For this reason, the sample size of the obtained data is usually small, and its uncertainty is difficult to quantify using probability models. Furthermore, when mechanical systems operate under certain specific conditions, the data may cluster in certain areas, exhibiting distinct clustering characteristics, which leads to challenges for the uncertainty analysis and measurement of mechanical system under these conditions. To address the above issues, an uncertainty analysis method for mechanical systems based on a multi-cluster ellipsoidal model was proposed to accurately quantify the uncertainties of system parameters with clustering characteristics, so as to achieve the rapid evaluation of system response uncertainty. In order to accurately quantify the small sample data with clustering characteristics, the multi-cluster ellipsoidal model was employed for uncertainty modeling. Based on the parameter interval information, the sensitivity analysis of the mechanical system was conducted to determine the main parameters that affected the performance of the mechanical system. The upper and lower boundaries of the mechanical system response were obtained by using multi-cluster ellipsoidal model and the sequential quadratic programming algorithm to achieve the uncertainty propagation of system parameters. The accuracy and effectiveness of the proposed method were verified through three numerical examples and one radar system engineering example. The research results indicate that the hyper-ellipsoidal clustering method has high computational efficiency and accuracy when addressing the uncertainty of mechanical system performance under limited samples.

Key words： uncertainty propagation multi-cluster ellipsoidal model performance measure approach sensitivity analysis

Received: 04 September 2024 Published: 06 May 2025

CLC:

TB 114.3

Corresponding Authors: Heng OUYANG E-mail: 202221202078@stu.hebut.edu.cn;ouyangheng@hebut.edu.cn

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Cite this article:

Zhengyan MA,Heng OUYANG,Zhijie HAO,Shuo GAO,Baohui LIU. Uncertainty analysis method for mechanical system based on multi-cluster ellipsoidal model. Chinese Journal of Engineering Design, 2025, 32(2): 141-150.

URL:

https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2025.04.168 OR https://www.zjujournals.com/gcsjxb/Y2025/V32/I2/141

基于聚类椭球模型的机械系统不确定性分析方法

机械系统在服役过程中受到随机载荷、制造误差、安装误差等多源不确定性因素影响，导致系统响应常产生偏差，严重影响其运行稳定性与系统可靠性。在实际工程中，大规模、高质量采集复杂机械系统的数据非常困难，获取的数据样本量通常较小，难以通过概率模型描述其不确定性。此外，当机械系统在某些特定条件下运行时，数据可能集中在某些区域，呈现一定的聚类特征，导致该条件下机械系统的不确定性分析与度量存在挑战。为此，提出了一种基于聚类椭球模型的机械系统不确定性分析方法，来准确度量具有聚类特征系统参数的不确定性，实现系统响应不确定性的快速评估。为了准确量化具有聚类特性的小样本数据，采用聚类椭球模型对其进行不确定性建模；根据参数区间信息，开展机械系统敏感性分析，确定了影响机械系统性能的主要参数；结合聚类椭球模型和序列二次规划算法获取机械系统响应的上、下边界，实现了系统参数不确定性传播；通过3个数值算例和1个雷达系统工程算例验证了所提方法的准确性和有效性。研究结果表明，在处理小样本条件下机械系统性能不确定性问题时，超椭球聚类方法具有较高的计算效率和精度。

关键词： 不确定性传播, 聚类椭球模型, 功能度量法, 敏感性分析

Fig.1 Total volume variation of ellipsoidal model

Fig.2 Schematic diagram of standardization transformation of ellipsoidal model

Fig.3 Comparison of ellipsoidal models under different thresholds in example 4.1

聚类数量/个	椭球模型总面积	$δ 1$	$δ 2$
1	3.586 1
2	0.817 6	3.39
3	0.594 7	0.37	12.42
4	0.496 9	0.20	2.28
5	0.449 0	0.11	2.04
6	0.374 0	0.20	0.64

Table 1 Total area variation of ellipsoidal model under different numbers of cluster in example 4.1

Fig.4 Scatter plot of sample distribution of uncertain variables in example 4.2

Fig.5 Comparison of ellipsoid models constructed by different methods in example 4.2

Table 2 Total area of ellipsoidal model in example 4.2

Fig.6 Uncertainty propagation results in example 4.2

Table 3 Total volume of ellipsoidal model in example 4.3

Table 4 Uncertainty propagation results in example 4.3

Table 5 Numerical range of radar parameters

Table 6 Sensitivity analysis results of maximum detection distance of radar

Fig.7 Radar system ellipsoidal models

Table 7 Uncertain propagation results of radar system


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