Structural and Multidisciplinary Optimization

, Volume 58, Issue 5, pp 1947–1960 | Cite as

Nonparametric uncertainty representation method with different insufficient data from two sources

  • Xiang Peng
  • Zhenyu Liu
  • Xiaoqing Xu
  • Jiquan Li
  • Chan Qiu
  • Shaofei Jiang


The uncertainty information of design variables is included in the available representation data, and there are differences among representation data from different sources. Therefore, the paper proposes a nonparametric uncertainty representation method of design variables with different insufficient data from two sources. The Gaussian interpolation model for sparse sampling points and/or sparse sampling intervals from a single source is constructed through maximizing the logarithmic likelihood estimation function of insufficient data. The weight ratios of probability density values at sampling points are optimized through minimizing the total deviation of the fusion model, and the fusion Gaussian model is constructed based on the weight sum of the optimum probability density values of sampling points for Source 1 and Source 2. The methodology is extended to five different fusion conditions, which contain the fusion of uncertain distribution parameters, the fusion of insufficient data and interval data, etc. Five application examples are illustrated to verify the effectiveness of the proposed methodology.


Uncertainty representation Insufficient data Data fusion Maximum likelihood estimation 



This work was supported by the National Natural Science Foundation of China under grant [numbers 51505421, 51490663, U1610112]; the Zhejiang Provincial Natural Science Foundation of China under grant [number: LY18E050020]; the National Key Research and Development Program of China under grant [number: 2017YFB0603704].


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Xiang Peng
    • 1
    • 2
  • Zhenyu Liu
    • 2
  • Xiaoqing Xu
    • 1
  • Jiquan Li
    • 1
  • Chan Qiu
    • 2
  • Shaofei Jiang
    • 1
  1. 1.Key Laboratory of E&MZhejiang University of TechnologyHangzhouChina
  2. 2.State Key of CAD&CGZhejiang UniversityHangzhouChina

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