Arabian Journal for Science and Engineering

, Volume 43, Issue 10, pp 5541–5549 | Cite as

Study on the Robust Regression of the Prediction of Vibration Velocity in Underwater Drilling and Blasting

  • Yaxiong Peng
  • Li Wu
  • Chunhui Chen
  • Binbin Zhu
  • Qinji Jia
Research Article - Civil Engineering


In underwater drilling and blasting engineering, the altitude effect must be reflected in predicting vibration velocity due to the complex water medium conditions and monitoring environment. In this paper, the similar law of explosion was employed and the elevation difference factor \(\beta \) was introduced to embody the impact altitude had on vibration velocity, and the prediction formula which embodied the altitude effect was presented. On account of the weakness of the regression analysis of OLS method, the robust regression was proposed to predict vibration velocity, which enhanced the robustness of the prediction formula. Based on the shallow blasting engineering of Guoyuan Port in Chongqing, China, the method above was, respectively, adopted to fit vibration velocity, and three groups of underwater drilling and blasting tests in the same field conditions were conducted to certify the fitting results. Result shows that the optimized formula is more accurate than Sadove Formula. Besides, the weighted calculation can remarkably improve the robustness of the prediction formula, and the robust regression is more suitable for predicting vibration velocity in underwater drilling and blasting.


Underwater drilling and blasting Vibration velocity Altitude effect Robust regression Ordinary least squares 


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The research described in this paper was financially supported by National Natural Science Foundation of China (Grant no. 41672260) and the technology plan program of HuBei province (Grant no. 2013CFA110).


  1. 1.
    Monjezi, M.; Bahrami, A.; Yazdian, A.: Simultaneous prediction of fragmentation and flyrock in blasting operation using artificial neural networks. Int. J. Rock Mech. Min. Sci. 47, 476–480 (2009)CrossRefGoogle Scholar
  2. 2.
    Ak, H.; Konuk, A.: The effect of discontinuity frequency on ground vibrations produced from bench blasting: a case study. Soil Dyn. Earthq. Eng. 28, 686–694 (2008)CrossRefGoogle Scholar
  3. 3.
    Peng, Y.X.; Wu, L.; Su, Y.; Chen, C.H.: Study on the effect of elevation on the prediction of underwater drill and blasting vibration frequency. Geosyst. Eng. 19, 170–176 (2016)CrossRefGoogle Scholar
  4. 4.
    Gao, F.Q.; Hou, A.J.; Yang, X.L.; Yang, J.: Analysis of blasting vibration duration based on dimension theory. Mental Mine. 41, 143–145 (2010)Google Scholar
  5. 5.
    Hajihassani, M.; Armaghani, D.J.; Marto, A.; Mohamad, E.T.: Ground vibration prediction in quarry blasting through an artificial neural network optimized by imperialist competitive algorithm. Bull. Eng. Geol. Environ. 74(3), 873–886 (2015)CrossRefGoogle Scholar
  6. 6.
    Shi, X.Z.; Chen, X.; Shi, C.X.; Liu, B.; Zhang, X.: Prediction model for blasting vibration peak speed based on GEP. J. Vib. Shock 34(10), 95–99 (2015)Google Scholar
  7. 7.
    Khandelwal, M.; Singh, T.N.: Prediction of blast induced ground vibrations and frequency in opencast mine: a neural network approach. J. Sound Vib. 289(4), 711–725 (2006)CrossRefGoogle Scholar
  8. 8.
    Khandelwal, M.; Singh, T.N.: Prediction of blast-induced ground vibration using artificial neural network. Int. J. Rock Mech. Min. Sci. 46(7), 1214–1222 (2009)CrossRefGoogle Scholar
  9. 9.
    Shi, X.Z.; Dong, K.C.; Qiu, X.Y.; Chen, X.K.: Analysis of the PPV prediction of blasting vibration based on support vector machine regression. Eng. Blast. 15(3), 28–30 (2009)Google Scholar
  10. 10.
    Khandelwal, M.; Kankar, P.K.; Harsha, S.P.: Evaluation and prediction of blast induced ground vibration using support vector machine. Int. J. Min. Sci. Technol. 47(1), 509–516 (2010)Google Scholar
  11. 11.
    Langefors, U.; Kihlstrom, B.: The Modern Technique of Rock Blasting. Wiley, New York (1963)Google Scholar
  12. 12.
    Ambraseys, N.R.; Hendron, A.J.: Dynamic Behavior of Rock Masses: Rock Mechanics in Engineering Practices. Wiley, London (1968)Google Scholar
  13. 13.
    Holmberg, R.; Persson, P.A.: Design of tunnel perimeter blasthole patterns to prevent rock damage. In: Proceedings of IMM Tunneling ’79 Conference. London, pp. 280-283 (1979)Google Scholar
  14. 14.
    Lu, W.B.; Hustrulid, W.: An improvement to the equation for the attenuation of the peak particle velocity. Eng. Blast. 8(3), 1–4 (2002)Google Scholar
  15. 15.
    Khandelwal, M.; Saadat, M.: A dimensional analysis approach to study blast-induced ground vibration. Rock Mech. Rock Eng. 48, 727–735 (2015)CrossRefGoogle Scholar
  16. 16.
    Moore, A.J.; Richards, A.B.; Gad E.: Structural response of brick veneer houses to blast vibration. In: Proceedings of the 29th Annual Conference on Explosives and Blasting Technique, USA (2003)Google Scholar
  17. 17.
    Wu, L.; Yan, T.J.; Zhou, C.B.: Blasting Engineering of the Rock Drilling. China University of Geosciences Press, Wuhan (2004)Google Scholar
  18. 18.
    Yang, G.L.; Rocque, P.; Katsabanis, P.; Bawden, W.F.: Measurement and analysis of near-field blast vibration and damage. Geotech. Geol. Eng. 12(2), 169–182 (1994)CrossRefGoogle Scholar
  19. 19.
    Li, C.J.; Wu, L.; Fu, H.T.; Peng, Y.X.; Li, H.Y.; Su, L.: Design optimization of underwater drilling and blasting based on AHP-Fuzzy method. Explos. Mater. 15(4), 45–50 (2015)Google Scholar
  20. 20.
    Wu, L.; Chen, J.P.; Su, J.H.: Seismic effect by blasting. Explos. Mater. (23)04, 24–27 (1999)Google Scholar
  21. 21.
    Gu, R.G.; Zhou, C.B.: The influential factors of blasting vibration underwater by grey correlation analysis. Blasting 18(4), 15–17 (2001)Google Scholar
  22. 22.
    Liu, Y.Q.; Li, H.B.; Pei, Q.T.; Zhang, W.: Prediction of peak particle velocity induced by underwater blasting based on the combination of grey relational analysis and genetic neural network. Rock Soil Mech. 34(s1), 260–264 (2013)Google Scholar
  23. 23.
    Lu, T.; Shi, Q.; Huang, C.; Li, J.R.: Study on attenuation parameters of blasting vibration by nonlinear regression analysis. Rock Soil Mech. 28(9), 1871–1878 (2007)Google Scholar
  24. 24.
    Peng, Y.X.; Wu, L.; Su, Y.; Li, H.Y.; Li, C.J.: Study on the fitting model of underwater drilling and blasting vibration attenuation considering the effect of elevation. J. Vib. Shock 35(13), 174–178 (2016)Google Scholar
  25. 25.
    Tang, H.; Shi, Y.Q.; Li, H.B.; Li, J.R.; Wang, X.W.; Jiang, P.C.: Prediction of peak particle velocity of blasting vibration by neural network. Rock Mech. Eng. 26(S1), 3533–3539 (2007)Google Scholar
  26. 26.
    Zhang, Y.P.; Cao, P.; Dong, L.J.: A robust regression model and its application in calculating shear strength of rock. Sci. Technol. Rev. 28(7), 91–95 (2010)Google Scholar
  27. 27.
    Huber, P.J.: Robust regression: asymptotics, conjectures and Monte Carlo. Ann. Stat. 1, 799–821 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Huber, P.J.: Robust Statistics. Wiley, Hoboken, NJ (2004)Google Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  • Yaxiong Peng
    • 1
  • Li Wu
    • 1
  • Chunhui Chen
    • 1
  • Binbin Zhu
    • 1
  • Qinji Jia
    • 1
  1. 1.Faculty of EngineeringChina University of GeosciencesWuhanChina

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