Conditions vulnerability identification of natural and technical objects based on linear spline interpolation of interface traffic intensity

A.V. Skatkov, A.A. Bryukhovetskiy, I.А. Skatkov

Sevastopol State University, RF, Sevastopol, Universitetskaya St., 33

DOI: 10.33075/2220-5861-2021-4-143-151

UDC 004.56 


   The method of application of spline interpolation in solving the problems of identification of abnormal states (A-events) in information data flows and classification of the specified events in the control of natural and technical objects (NTO) is considered. The approach is based on the representation of the intensity of interface traffic by piecewise linear splines and implemented using a modeling stand. At the first stage, descriptions are generated and formed in the form of linear splines representing the states of controlled objects, one of which is subject to external disturbance. At the second stage, the generated descriptions of splines are used to assess discrepancies between the studied distributions and the influence of a number of factors on the reliability of decisions made using probabilistic modeling methods in the Anylogic environment.

   In the process of simulation modeling, it becomes possible to determine and evaluate the totality of the following characteristics: parametrically adjustable threshold values of critical regions; correspondence of the theoretical and empirical distribution of a random variable; areas of reliable recognition of the state of NTO; areas of hypothesis acceptance.

   Depending on the purpose of the model, the level of criticality of the objects of control, the expert has the right to set the necessary threshold values of the tuning parameters of the model, for which, on the one hand, high reliability of the controlled values of the characteristics of the objects will be ensured, on the other hand, an acceptable number of errors of the first and second kind is achieved, which means that the risks of making erroneous decisions will be reduced.

   The obtained results of the study confirm the stability and sensitivity of the method when choosing threshold values of the intervals that determine the state of NTO.

Keywords: spline interpolation, identification of A-events, probabilistic model, statistical estimates, nonparametric criterion.

To quote:

Full text in PDF(RUS)


  1. Gaisky V.A. and Gaisky P.V. Mnogomernyj garmonicheskij analiz pri izmerenijah polej morskoj sredy (Multidimensional harmonic analysis for measurements of marine environment). Sistemy kontrolja okruzhajushhej sredy, 2019, No. 4 (38), pp. 33–42.
  2. Chan P.K. and Mahoney M.V. Modeling multiple time series for anomaly detection. In Proceedings of the Fifth IEEE International Conference on Data Mining. IEEE Computer Society, Washington, USA, 2005, pp. 90–97.
  3. Agarwal D. Detecting anomalies in cross-classified streams: a bayesian approach. Knowledge andInformation Systems. 2006, Vol. 11, No. 1. pp. 29–44.
  4. Stechkin S.B. and Subbotin Yu.N. Splayny v vychislitel’noy matematike (Splines in computational mathematics). Moscow: Nauka, 1976, 247 p.
  5. K. de Bohr. Prakticheskoye rukovodstvo po splaynam (A practical guide to splines). Moscow: Radio and communication, 1985, 303 p.
  6. Kanahen D., Mowler K., and Nash S. Chislennyye metody i programmnoye obespecheniye (Numerical methods and software). Moscow: Mir, 1998, 286 p.
  7. Alekseev E.R., Chesnokova O.V., and Rudchenko E.A. Scilab: Resheniye inzhenernykh i matematicheskikh zadach (Scilab: Solving engineering and mathematical problems). Moscow: ALT Linux: BINOM. Knowledge Laboratory, 2008, 269 p.
  8. Ilyin V.A., Sadovnichy V.A., and Sendov Bl.Kh. Matematicheskiy analiz. Prodolzheniye kursa (Mathematical analysis. Continuation of the course.) Moscow: Izd-vo MGU, 1987. 342 p.
  9. Alberg J., Nilsson E., and Walsh J. Teoriya splaynov i yeye prilozheniya (Theory of splines and its applications). Moscow: Mir, 1972, 319 p.
  10. Skatkov A.V., Bryukhovetskiy A.A., Moiseev D.V., and Shevchenko V.I. Adaptivnyy metod obnaruzheniya uyazvimostey interfeysov bespilotnykh transportnykh sredstv v infrastrukture umnogo goroda (An adaptive method for detecting vulnerabilities in the interfaces of unmanned vehicles in the infrastructure of a smart city). Infokommunikatsionnyye tekhnologii, 2020,Vol. 18, No. 1, pp. 45–50.