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工程设计学报
Chinese Journal of Engineering Design  2026, Vol. 33 Issue (2): 147-158    DOI: 10.3785/j.issn.1006-754X.2026.05.213
Theory and Method of Mechanical Design     
Uncertainty analysis of high-dimensional full-field structural response based on evidence theory
Yue ZHAO1(),Jinhe ZHANG2,3,Jinning ZHI1
1.School of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China
2.College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China
3.State Key Laboratory of Advanced Design and Manufacturing Technology for Vehicle, Hunan University, Changsha 410082, China
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Abstract  

The propagation analysis of high-dimensional structural responses under complex uncertain variables is prone to problems such as low modeling efficiency and poor analytical accuracy. To address this issue, a rapid analysis method for high-dimensional structural response uncertainty based on evidence theory was proposed. Firstly, the basic probability assignment of evidence variables was utilized to generate sample sets efficiently via optimal Latin hypercube sampling.Secondly, principal component analysis was applied to reduce the dimensionality of the high-dimensional structural responses, extracting low-dimensional features and eigenvectors to decrease modeling complexity. Finally, an extreme learning machine was employed to construct the mapping relationship between the uncertainty parameters and the low-dimensional features, enabling the prediction of uncertainty propagation at any position of the high-dimensional responses with respect to the input variables. Validation through the examples demonstrated that the proposed method could effectively quantify the uncertainty distribution at arbitrary positions of both high-dimensional time-domain and spatial responses, achieving high accuracy with relatively high modeling efficiency. The proposed method can significantly reduce the complexity of uncertainty analysis for high-dimensional full-field responses and serve as an effective tool for uncertainty propagation analysis of complex engineering structures.

Key words： structural uncertainty      evidence theory      extreme learning machine      uncertainty propagation     
Received: 30 September 2025      Published: 28 April 2026
CLC:  TH 122  
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Yue ZHAO
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Cite this article:

Yue ZHAO,Jinhe ZHANG,Jinning ZHI. Uncertainty analysis of high-dimensional full-field structural response based on evidence theory. Chinese Journal of Engineering Design, 2026, 33(2): 147-158.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2026.05.213     OR     https://www.zjujournals.com/gcsjxb/Y2026/V33/I2/147


基于证据理论的结构高维全场响应不确定性分析

当结构存在复杂不确定性变量时，开展高维响应传播分析可能面临建模效率低与分析精度差等问题。基于此，提出了一种基于证据理论的结构高维响应不确定性快速分析方法。首先，依据证据变量的基本可信度分配，结合最优拉丁超立方采样技术，高效生成样本集；其次，采用主成分分析技术对结构高维全场响应进行降维处理，提取低维特征与特征向量，以降低建模复杂度；最后，利用极限学习机构建不确定性参数与低维特征之间的映射关系，进而预测输入变量对结构高维响应任意位置的不确定性传播结果。算例验证表明，对于高维时域响应与空间响应，所提出的方法均能有效量化结构响应中任意位置的不确定性分布，并在保证较高建模效率的同时实现高精度求解。所提出的方法能够显著降低高维全场响应不确定性分析的复杂度，为复杂工程结构的不确定性传播分析提供了一种有效的工具。


关键词： 结构不确定性,  证据理论,  极限学习机,  不确定性传播 
Fig.1 Flowchart of HDUP algorithm
Fig.2 Truss structure
EtDtAt
焦元/1011PaBPA焦元/(103kg/m3)BPA焦元/cm2BPA
[1.82, 1.83]0.10[7.85, 7.90]0.05[1.60, 1.61]0.25
[1.83, 1.84]0.25[7.90, 7.95]0.20[1.61, 1.62]0.40
[1.84, 1.85]0.40[7.95, 8.00]0.40[1.62, 1.63]0.20
[1.85, 1.86]0.20[8.00, 8.05]0.25[1.63, 1.64]0.10
[1.86, 1.87]0.05[8.05, 8.10]0.10[1.64, 1.65]0.05
Table 1 Quantitative forms of uncertainty parameters in truss structure
Fig.3 Feature truncation and response result convergence of truss structure
Fig.4 Mean of time-domain response of truss structure
Fig.5 Standard deviation of time-domain response of truss structure
Fig.6 Response of truss structure at specific time nodes
Fig.7 Joint of robot
Erνrpr1pr2
焦元/1011PaBPA焦元BPA焦元/103PaBPA焦元/103PaBPA
[1.96, 1.97]0.10[0.25, 0.26]0.05[40, 41]0.10[18.0， 18.5]0.05
[1.97, 1.98]0.20[0.26, 0.27]0.20[41, 42]0.20[18.5, 19.0]0.10
[1.98, 1.99]0.30[0.27, 0.28]0.40[42, 43]0.30[19.0, 19.5]0.15
[1.99, 2.00]0.25[0.28, 0.29]0.25[43, 44]0.25[19.5, 20.0]0.25
[2.00, 2.01]0.10[0.29, 0.30]0.10[44, 45]0.10[20.0， 20.5]0.35
[2.01, 2.02]0.05[45, 46]0.05[20.5, 21.0]0.10
Table 2 Quantitative forms of uncertainty parameters in robot joint structure
Fig.8 Feature truncation and response result convergence of robot joint structure
Fig.9 Mean of displacement response of robot joint
Fig.10 Standard deviation of displacement response of robot joint
Fig.11 Response of robot joint structure at specific spatial nodes
Fig.12 Turbine blade of jet engine
Ebνbpb1
焦元/1011PaBPA焦元BPA焦元/105PaBPA
[1.98, 1.99]0.05[0.290, 0.295]0.15[4.7, 4.8]0.10
[1.99, 2.00]0.15[0.295, 0.300]0.20[4.8, 4.9]0.20
[2.00, 2.01]0.35[0.300, 0.305]0.40[4.9, 5.0]0.40
[2.01, 2.02]0.25[0.305, 0.310]0.20[5.0, 5.1]0.20
[2.02, 2.03]0.15[0.310, 0.315]0.05[5.1, 5.2]0.10
[2.03, 2.04]0.05
pb2αbK
焦元/105PaBPA焦元/(1/K)BPA焦元/［W/(m·K)］BPA
[4.7, 4.8]0.10[11.85, 11.90]0.10[11.0, 11.2]0.05
[4.8, 4.9]0.20[11.90, 11.95]0.20[11.2, 11.4]0.15
[4.9, 5.0]0.40[11.95, 12.00]0.30[11.4, 11.6]0.30
[5.0, 5.1]0.20[12.00, 12.05]0.25[11.6, 11.8]0.20
[5.1, 5.2]0.10[12.05, 12.10]0.10[11.8, 12.0]0.15
[12.10, 12.15]0.05[12.0, 12.2]0.10
[12.2, 12.4]0.05
KcKstcto
焦元/［W/(m2·℃)］BPA焦元/［W/(m2·℃)］BPA焦元/102℃BPA焦元/102℃BPA
[34.0, 34.2]0.05[44.0, 44.2]0.05[1.2, 1.3]0.1[8.0, 8.5]0.1
[34.2, 34.4]0.10[44.2, 44.4]0.15[1.3, 1.4]0.2[8.5, 9.0]0.3
[34.4, 34.6]0.15[44.4, 44.6]0.30[1.4, 1.5]0.4[9.0, 9.5]0.4
[34.6, 34.8]0.20[44.6, 44.8]0.20[1.5, 1.6]0.3[9.5, 10.0]0.2
[34.8, 35.0]0.30[44.8, 45.0]0.15
[35.0, 35.2]0.15[45.0, 45.2]0.10
[35.2, 35.4]0.05[45.2, 45.4]0.05
Table 3 Quantitative forms of uncertainty parameters in turbine blade structure
Fig.13 Feature truncation and response result convergence of turbine blade structure
Fig.14 Mean of stress response of turbine blade
Fig.15 Standard deviation of stress response of turbine blade
Fig.16 Response of turbine blade structure at specific spatial nodes
 
 
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