A new nonlinear risk assessment model based on an improved projection pursuit

  • Longxia Qian
  • Ren Zhang
  • Taiping Hou
  • Hongrui Wang
Original Paper


Experience has shown that researchers and engineers are unable to construct ideal models for risk assessment and make optimal decisions in situations with insufficient data. A nonlinear risk assessment model is therefore proposed in this study based on an improved projection pursuit model (IPPM) for use in situations where insufficient data are available. A new projection index is initially proposed based on the maximum entropy principle in order to extract more information from original multidimensional data before a nonlinear risk assessment function is constructed using differential equation modeling. This function can be applied to all risk assessment problems after performing standardization and dimension reduction for the indicators. Five marine environmental risk assessment experiments for naval activity are then performed to train and validate the IPPM, as well as a traditional projection pursuit model using different numbers of training samples. The results of this analysis show that the IPPM is reliable, robust, and consistent, and can improve risk assessments by between 4.3 and 43.7% depending on performance criteria. Satisfactory results are obtained from the IPPM using just 12 training samples, and an acceptable result is still obtained if this number is reduced to just ten. Application of an IPPM therefore represents a valuable tool for risk assessment in situations where data is insufficient.


Insufficient data Improved projection pursuit Maximum entropy principle Projection index Differential equation model 



The study was supported by National Natural Science Foundation of China (Grant Nos. 51609254, 51279006, 51479003) and National Key R&D Program of China (Grant No. 2016YFC0402409). The authors would like to thank the Associate Editor and all the anonymous reviewers for their valuable comments and constructive suggestions, which led to an improvement in the presentation of this paper.


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Copyright information

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

Authors and Affiliations

  • Longxia Qian
    • 1
  • Ren Zhang
    • 1
  • Taiping Hou
    • 1
  • Hongrui Wang
    • 2
  1. 1.Institute of Meteorology and OceanographyNational University of Defense TechnologyNanjingChina
  2. 2.College of Water Sciences, Key Laboratory for Water and Sediment Sciences, Ministry of EducationBeijing Normal UniversityBeijingChina

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