Preview

Research Bulletin by Russian Maritime Register of Shipping

Advanced search

Construction of a spatial approximation of a set of diagrams of static stability of an autonomous ship

EDN: FOJTIH

Abstract

The relevance of the chosen research topic is explained by the active development of autonomous navigation and the need to solve tasks arising during the operation of marine autonomous surface ships. The mathematical model developed as a part of the research for the operational assessment of ship motion characteristics in irregular seas suggests a method for calculating the righting arm depending on the angle of roll and draft. In this paper, mathematical methods of surface approximation are considered, applicable for processing nonuniformly distributed data; approximations of the surface formed by a set of static stability diagrams corresponding to different cases of vessel mass loading are constructed, and the results obtained are compared. It is concluded that the methods based on cubic and biharmonic splines have the best approximation capabilities for this task.

About the Authors

S. V. Shults
St. Petersburg State Marine Technical University
Russian Federation

PhD student

190121, St. Petersburg, Lotsmanskaya ul., 3



М. А. Kuteynikov
Russian Maritime Register of Shipping
Russian Federation

DSc

191186, St. Petersburg, Millionnaya ul., 7A 



V. Yu. Shults
St. Petersburg State Marine Technical University
Russian Federation

PhD

190121, St. Petersburg, Lotsmanskaya ul., 3



References

1. Kasyk L., Wolnowska A.E., Pleskacz K., Kapuściński T. The analysis of social and situational systems as components of human errors resulting in navigational accidents. Applied Sciences. 2023. Vol. 13, Issue 11. P. 6780. DOI 10.3390/app13116780.

2. Gomzyakov M.V. Overview of maritime transport casualties in the Far East. Research Bulletin by Russian Maritime Register of Shipping. 2020. No. 58/59. P. 4 — 10. (In Russ.)

3. Kuteinikov M.A., Samoilov V.R. Criteria of risk of stability loss under dead ship condition. Research Bulletin by Russian Maritime Register of Shipping. 2019. No. 56/57. P. 40 — 50. (In Russ.)

4. Shults S.V., Kuteinikov М.А., Shults V.Yu. An overview of application of artificial neural networks in modeling motions of autonomous ship. Research Bulletin by Russian Maritime Register of Shipping. 2025. No. 78. P. 44 — 50. EDN UFKSYW. (In Russ.)

5. Jimenez-Fernandez V.M., Vazquez-Leal H., Filobello-Nino U.A., Jimenez-Fernandez M. et al. Exploring the use of two-dimensional piecewise-linear functions as an alternative model for representing and processing grayscale-images. Journal of Applied Research and Technology. 2016. Vol. 14, No. 5. DOI 10.1016/j.jart.2016.09.001.

6. Jimenez-Fernandez V.M., Cerecedo-Nunez H.H., Vazquez-Leal H., Beltran-Parrazal L. et al. A parametric piecewise-linear approach to laser projection. Computational and Applied Mathematics. 2014. Vol. 33, Issue 3. P. 841 — 858.

7. Jimenez-Fernandez V.M., Vazquez-Leal H., Filobello-Nino U., Cerecedo-Nunez H.H. et al. A comparative study between piecewise-linear and point-based methodologies for galvanometer mirror systems. Revista Facultad de Ingeniería Universidad de Antioquia. 2014. Vol. 73. P. 124 — 133.

8. Zhang Z.G., Chan S.C., Zhang X., Lam E.Y. et al. High-resolution reconstruction of human brain MRI image based on local polynomial regression. 4th International IEEE/EMBS conference on neural engineering. 2009. P. 245 — 248.

9. Zhang Z.G., Chan S.C., Zhu Z.Y. A new two-stage method for restoration of images corrupted by Gaussian and impulse noises using local polynomial regression and edge preserving regularization. IEEE international symposium on circuits and systems. 2009. P. 948 — 951.

10. Karim S.A.A., Rosli M.A.M., Mustafa M.I.M. Cubic spline interpolation for petroleum engineering data. Applied Mathematical Sciences. 2014. Vol. 8. P. 5083 — 5098.

11. Karim S.A.A., Yahya N. Seabed loging data curve fitting using cubic splines. Applied Mathematical Sciences. 2013. Vol. 7, No. 81. P. 4015 — 4026.

12. Ross A., Dass S., Jain A. A deformable model for fingerprint matching. Pattern Recognition. 2005. Vol. 38. P. 95 — 103. DOI 10.1016/j.patcog.2003.12.021.

13. Bikeev E.V., Kalabegashvili G.I. Primenenie metodiki approksimatsii splainom tipa «tonkikh plastin» dlya opredeleniya deformatsii krupnogabaritnogo rеflektora [Application of the thin-plate spline approximation technique to determine the deformations of a large-sized reflector]. Nauka i obrazovanie segodnya [Science and Education Today]. 2017. No. 2 (13). P. 6 — 8.

14. Douglas B.C., Agreen R.W. The sea state correction for GEOS 3 and SEASAT satellite altimeter data. Journal of Geophysical Research. 1983. Vol. 88 (C3). P. 1655 — 1661. DOI 10.1029/JC088iC03p01655.

15. Munchow A. Detiding three-dimensional velocity survey data in coastal waters. Journal of Atmospheric and Oceanic Technology. 2000. Vol. 17, Issue 5. P. 736 — 748.

16. Feliciano L., Ortiz-Rivera E. Biharmonic spline interpolation for solar radiation mapping using Puerto Rico as a case of study. Conference Record of the IEEE Photovoltaic Specialists Conference. 2012. P. 002913 — 002915. DOI 10.1109/PVSC.2012.6318196.

17. Debrin A.S., Semenov A.F., Bastron A.V., Kuzmin P.N. Development of software products for modeling the characteristics of photovoltaic modules to increase the FSES operation efficiency of autonomous consumers. Izvestia. Orenburg State Agrarian University. 2020. No. 3 (83). P. 222 — 225. (In Russ.)

18. Amidror I. Scattered data interpolation methods for electronic imaging systems: a survey. Journal of Electronic Imaging. 2002. Vol. 11, No. 2. P. 157 — 176.

19. Ambrosius F. Interpolation of 3D surfaces for contact modeling. University of Twente Tech. Rep. March 2005. 51 p. 20. Boor C. de. Bicubic spline interpolation. Journal of Mathematics and Physics. 1962. Vol. 41, No. 4. P. 212 — 218. DOI 10.1002/sapm1962411212.

20. Bhattacharyya B.K. Bicubic spline interpolation as a method for treatment of potential field data. Geophysics. 1969. Vol. 34. P. 402 — 423. DOI 10.1190/1.1440019.

21. Briggs I.C. Machine contouring using minimum curvature. Geophysics. 1974. Vol. 39, No. 1. P. 39 — 48. DOI 10.1190/1.1440410.

22. Turley, R. Steven. Cubic interpolation with irregularly-spaced points in Julia 1.4 / Brigham Young University. Faculty Publications. 2018. 2177.

23. Jain R., Kasturi R., Schunck B. Machine Vision. McGraw-Hill, 1995. 549 p.

24. Han X., Han J. Representation of piecewise biharmonic surfaces using biquadratic B-Splines. Journal of Computational and Applied Mathematics. 2015. Vol. 290. P. 403 — 411. DOI 10.1016/j.cam.2015.05.025.


Review

For citations:


Shults S.V., Kuteynikov М.А., Shults V.Yu. Construction of a spatial approximation of a set of diagrams of static stability of an autonomous ship. Research Bulletin by Russian Maritime Register of Shipping. 2025;1(80):82-93. (In Russ.) EDN: FOJTIH

Views: 33


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 2223-7097 (Print)