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

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

Abstract

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.

Keywords

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

Notes

Acknowledgements

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.

References

  1. Aven T (2010) On how to define, understand and describe risk. Reliab Eng Syst Saf 95:623–631CrossRefGoogle Scholar
  2. Bai CZ, Hong M, Wang D, Zhang R, Qian LX (2014) Evolving an information diffusion model using a genetic algorithm for monthly river discharge time series interpolation and forecasting. J Hydrometeorol 15(6):2236–2249CrossRefGoogle Scholar
  3. Bai CZ, Zhang R, Hong M, Qian LX, Wang ZX (2015) A new information diffusion modelling technique based on vibrating string equation and its application in natural disaster risk assessment. Int J Gen Syst 44(5):601–614CrossRefGoogle Scholar
  4. Datta D, Chutia R (2016) Probability–credibility health risk assessment under uncertain environment. Stoch Env Res Risk Assess 31(2):449–460Google Scholar
  5. Friedman JH, Tukey JW (1974) A projection pursuit algorithm for exploratory data analysis. IEEE Trans Comput 23(9):881–890CrossRefGoogle Scholar
  6. Ge Y, Dou W, Gu ZH et al (2013) Assessment of social vulnerability to natural hazards in the Yangtze River Delta, China. Stoch Env Res Risk Assess 27(8):1899–1908CrossRefGoogle Scholar
  7. Gentile M, Rogers WJ, Mannan MS (2003) Development of an inherent safety index based on fuzzy logic. AIChE J 49(4):959–968CrossRefGoogle Scholar
  8. Haimes YY (2009) On the complex definition of risk: a systems-based approach. Risk Anal 29(12):1647–1654CrossRefGoogle Scholar
  9. Hu TS, Lam KC, Ng ST (2001) River flow time series prediction with a range-dependent neural network. Hydrol Sci J 46:729–745CrossRefGoogle Scholar
  10. Huang CF (1996) Fuzzy risk assessment of urban natural hazards. Fuzzy Set Syst 83:271–282CrossRefGoogle Scholar
  11. Huang CF (1997) Principle of information diffusion. Fuzzy Sets Syst 91(1):69–90CrossRefGoogle Scholar
  12. Jia XL, Li CH, Cai YP, Wang X, Sun L (2015) An improved method for integrated water security assessment in the Yellow River basin, China. Stoch Env Res Risk Assess 29(8):2213–2227CrossRefGoogle Scholar
  13. Jin JL, Zhang XL, Ding J (2002) Projection pursuit model for evaluating grade of flood disaster loss. Syst Eng Theory Pract 22(2):140–144 (in Chinese) Google Scholar
  14. Jones GA, Jones JM (2000) Information and coding theory. Springer, LondonCrossRefGoogle Scholar
  15. Khuri AI (2003) Advanced calculus with applications in statistics. Wiley, HobokenGoogle Scholar
  16. Li J, Huang GH, Zeng G, Maqsood I, Huang Y (2007) An integrated fuzzy-stochastic modeling approach for risk assessment of groundwater contamination. J Environ Manag 82(2):173–188CrossRefGoogle Scholar
  17. Liang XS (2014) Unraveling the cause-effect relation between time series. Phys Rev E 90:052150CrossRefGoogle Scholar
  18. Liang XS (2015) Normalizing the causality between time series. Phys Rev E 92:022126CrossRefGoogle Scholar
  19. Liu KFR, Ko CY, Fan C, Chen CW (2013) Incorporating the LCIA concept into fuzzy risk assessment as a tool for environmental impact assessment. Stoch Env Res Risk Assess 27(4):849–866CrossRefGoogle Scholar
  20. Nayak PC, Sudhheer KP, Rangan DM, Ramasastri KS (2004) A neuro-fuzzy computing technique for modeling hydrological time series. J Hydrol 291:52–66CrossRefGoogle Scholar
  21. Plummer R, de Loë R, Armitage D (2012) A systematic review of water vulnerability assessment tools. Water Resour Manag 26:4327–4346CrossRefGoogle Scholar
  22. Qian LX, Wang HR, Zhang KN (2014) Evaluation criteria and model for risk between water supply and water demand and its application in Beijing. Water Resour Manag 28(13):4433–4447CrossRefGoogle Scholar
  23. Qian LX, Zhang R, Hong M, Wang HR, Yang LZ (2015) A new multiple integral model for water shortage risk assessment and its application in Beijing, China. Nat Hazards 80(1):43–67CrossRefGoogle Scholar
  24. Tidwell VC, Arlin Cooper J, Silva Consuelo J (2005) Threat assessment of water supply systems using markov latent effects modeling. J Water Resour Plan Manag 131(3):218–227CrossRefGoogle Scholar
  25. Wang SH (1998) Differential equation model and chaos. Publication of University of Science and Technology of China, Hefei (in Chinese) Google Scholar
  26. Wang ZH, Chao F (2015) Sources of production inefficiency and productivity growth in China: a global data envelopment analysis. Energy Econ 49:380–389CrossRefGoogle Scholar
  27. Wang JW, Ni CJ (2008) Application of projection pursuit dynamic cluster model in regional partition of water resources in China. Water Resour Manag 22:1421–1429CrossRefGoogle Scholar
  28. Wang WC, Chau KW, Cheng CT, Qiu L (2009) A comparison of performance of several artificial intelligence methods for forecasting monthly discharge time series. J Hydrol 374:294–306CrossRefGoogle Scholar
  29. Wu WY, Yin SY, Liu HL, Chen HH (2014) Groundwater vulnerability assessment and feasibility mapping under reclaimed water irrigation by a modified DRASTIC model. Water Resour Manag 28(5):1219–1234CrossRefGoogle Scholar
  30. Xiao XP, Wen JH, Xie M (2010) Grey relational analysis and forecast of demand for scrap steel. J Grey Syst 22(1):73–80Google Scholar
  31. Xie YL, Xia DH, Huang GH, Li W, Xu Y (2017) A multistage stochastic robust optimization model with fuzzy probability distribution for water supply management under uncertainty. Stoch Env Res Risk Assess 31(1):125–143CrossRefGoogle Scholar
  32. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353CrossRefGoogle Scholar
  33. Zhang R (2012) Characteristic diagnosis of marine environmental factors and risk assessment of oceanic military activity. Beijing Normal University Press, Beijng (in Chinese) Google Scholar
  34. Zhang Q, Zhang JQ, Yan DH, Bao YL (2013a) Dynamic risk prediction based on discriminant analysis for maize drought disaster. Nat Hazards 65:1275–1284CrossRefGoogle Scholar
  35. Zhang R, Peng P, Xu Z, Li J, Niu S (2013b) A risk assessment modeling technique based on knowledge extraction and information diffusion with support specification. Int J Gen Syst 42(8):807–819CrossRefGoogle Scholar
  36. Zhao J, Jin JL, Guo QZ et al (2014) Dynamic risk assessment model for flood disaster on a projection pursuit cluster and its application. Stoch Env Res Risk Assess 28(8):2175–2183CrossRefGoogle Scholar

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

Personalised recommendations