On the Possibility of Using the Method of Sign-Perturbed Sums for the Processing of Dynamic Test Data

  • M. V. VolkovaEmail author
  • O. N. Granichin
  • G. A. Volkov
  • Yu. V. Petrov


At the present time, the methods for the measurement and prediction of the dynamic strength of materials are complicated and unstandardized. An experimental data processing method based on the incubation time criterion is considered. Only a finite number of measurements containing random errors and limited statistical information are usually available in practice, since dynamic tests are laborious, and every individual test requires a lot of time. This strongly restricts the number of applicable data processing methods unless we are satisfied with approximate and heuristic solutions. The method of sign-perturbed sums (SPS) is used for the estimation of finite-sample confidence regions with a specified confidence probability under the assumption of noise symmetries. It is shown that several experimental points are sufficient to determine the strength parameter with an accuracy acceptable for engineering calculations. The applicability of the proposed method is demonstrated in the processing of a number of experiments on the dynamic fracture of rocks.


sign-perturbed sums dynamic fracture incubation time 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. D. Campbell and W. G. Ferguson, “The temperature and strain-rate dependence of shear strength of mild steel,” Philos. Mag. 21, 63–82 (1970).CrossRefGoogle Scholar
  2. 2.
    A. J. Rosakis, J. Duffy, and L. B. Freund, “The determination of dynamic fracture toughness of alsi 4340 steel by the shadow spot method,” J. Mech. Phys. Solids 32, 443–460 (1984).CrossRefGoogle Scholar
  3. 3.
    D. A. Shockey, L. Seaman, and D. R. Curran, Material Behavior under High Stress and Ultrahigh Loading Rates (Springer-Verlag, New York, 1983).Google Scholar
  4. 4.
    G. R. Johnson and W. H. Cook, “Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures,” Eng. Fract. Mech. 21, 31–48 (1985).CrossRefGoogle Scholar
  5. 5.
    V. S. Nikiforovsky and E. I. Shemyakin, Dynamic Fracture of Solids (Nauka, Novosibirsk, 1979) [in Russian].Google Scholar
  6. 6.
    K. Ravi-Chandar, “Experimental challenges in the investigation of dynamic fracture of brittle materials,” in Physical Aspects of Fracture (Kluwer, Dordrecht, 2001), in Ser.: NATO Science Series, Series II: Mathematics, Physics and Chemistry, Vol. 32, pp. 323–342.CrossRefGoogle Scholar
  7. 7.
    J. F. Kalthoff and S. Winkler, “Failure mode transition at high rates of shear loading,” in Proc. Int. Conf. on Impact Loading and Dynamic Behavior of Materials, Bremen, 1987 (DGM-Informationsgesellschaft, Oberursel, 1988), pp. 161–176.Google Scholar
  8. 8.
    G. I. Kanel, S. V. Razorenov, K. Baumung, and J. Singer, “Dynamic yield and tensile strength of aluminum single crystals at temperatures up to the melting point,” J. Appl. Phys. 90, 136–143 (2001).CrossRefGoogle Scholar
  9. 9.
    Y. V. Petrov and A. A. Utkin, “Dependence of the dynamic strength on loading rate,” Mater. Sci. 25, 153–156 (1989).CrossRefGoogle Scholar
  10. 10.
    Y. V. Petrov, “Incubation time criterion and the pulsed strength of continua: Fracture, cavitation, and electrical breakdown,” Dokl. Phys. 49, 246–249 (2004).CrossRefGoogle Scholar
  11. 11.
    A. A. Gruzdkov and Y. V. Petrov, “Cavitation breakup of low-and high-viscosity liquids,” Tech. Phys. 53, 291–295 (2008).CrossRefGoogle Scholar
  12. 12.
    N. M. Pugno, “Dynamic quantized fracture mechanics,” Int. J. Fracture 140, 159–168 (2006).CrossRefzbMATHGoogle Scholar
  13. 13.
    Q. Z. Wang, S. Zhang, and H. P. Xie, “Rock dynamic fracture toughness tested with holed-cracked flattened Brazilian discs diametrically impacted by SHPB and its size effect,” Exp. Mech. 50, 877–885 (2010).CrossRefGoogle Scholar
  14. 14.
    L. Ljung, System Identification: Theory for the User (Prentice Hall, Englewood Cliffs, NJ, 1999).zbMATHGoogle Scholar
  15. 15.
    E.-W. Bai, K. M. Nagpal, and R. Tempo, “Bounded-error parameter estimation: Noise models and recursive algorithms,” Automatica 32, 985–999 (1996).MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    F. Blanchini and M. Sznaier, “A convex optimization approach to synthesizing bounded complexity HINF filters,” IEEE Trans. Autom. Control 57, 219–224 (2012).zbMATHGoogle Scholar
  17. 17.
    B. Csaji, M. C. Campi, and E. Weyer, “Sign-perturbed sums: A new system identification approach for constructing exact non-asymptotic confidence regions in linear regression models,” IEEE Trans. Signal Process. 63, 169–181 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    S. H. Cho, Y. Ogata, and K. Kaneko, “Strain-rate dependency of the dynamic tensile strength of rock,” Int. J. Rock Mech. Min. Sci. 40, 763–777 (2003).CrossRefGoogle Scholar
  19. 19.
    M. Volkova, G. Volkov, O. Granichin, and Y. Petrov, “Sign-perturbed sums approach for data treatment of dynamic fracture tests,” in Proc. 56th IEEE Conf. on Decision and Control (CDC), Melbourne, Australia, Dec. 12–15, 2017 (IEEE, Piscataway, NJ, 2018), pp. 1652–1656. ## Scholar
  20. 20.
    A. Senov, K. Amelin, N. Amelina, and O. Granichin, “Exact confidence regions for linear regression parameter under external arbitrary noise,” in Proc. 2014 American Control Conference (ACC 2014), Portland, OR, June 4–6, 2014 (IEEE, Piscataway, NJ, 2014), pp. 5097–5102.Google Scholar
  21. 21.
    A. A. Senov and O. N. Granichin, “Identification of linear regression parameters for arbitrary external noise in observations,” in Proc. 12th All-Russ. Meeting on Control Problems (VSPU-2014), Moscow, June 16–19, 2014 (Inst. Probl. Upr. im. V.A. Trapeznikova, Moscow, 2014), pp. 2708–2719.Google Scholar
  22. 22.
    K. Amelin and O. N. Granichin, “Randomized control strategies under arbitrary external noise,” IEEE Trans. Autom. Control 61, 1328–1333 (2016).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • M. V. Volkova
    • 1
    Email author
  • O. N. Granichin
    • 1
  • G. A. Volkov
    • 1
  • Yu. V. Petrov
    • 1
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

Personalised recommendations