Roll-induced bifurcation in ship maneuvering under model uncertainty

• Published in: Journal of marine science and technology Vol. 21; no. 4; pp. 689 - 708
• Main Authors: Dash, Anil Kumar, Chandran, Praveen Perumpulissery, Khan, Mohammed Kareem, Nagarajan, Vishwanath, Sha, Om Prakash
• Format: Journal Article
• Language: English
• Published: Tokyo Springer Japan 01.12.2016; Springer; Springer Nature B.V
• Subjects: Analysis; Automotive Engineering; Bifurcations; Computer simulation; Curve fitting; Engineering; Engineering Design; Engineering Fluid Dynamics; Fluid mechanics; Marine; Mathematical models; Mechanical Engineering; Monte Carlo method; Monte Carlo simulation; Naval engineering; Offshore Engineering; Original Article; Polynomials; Probability distribution; Propellers; Rolling motion; Ships; Uncertainty; Warships; PMM; Wind; Twin-propeller twin-rudder; Roll motion coupling; Bifurcations; Uncertainty assessment and propagation; Ship maneuvering
• ISSN: 0948-4280; 1437-8213
• DOI: 10.1007/s00773-016-0382-1

In this paper, a mathematical model is developed for the maneuvering motion of a naval ship and bifurcations of its equilibrium are identified in roll-coupled motion. The subject ship is a high-speed surface combatant with twin-propeller twin-rudder system. Captive model tests are conducted for the ship using planar motion mechanism. Maneuvering coefficients are calculated by polynomial curve fitting of the test data. Uncertainty distribution in the coefficients is assumed same as that of the curve fitting errors. Uncertainty in the model coefficients is propagated to full-scale simulation results by the stochastic response surface method (SRSM). This method is computationally efficient as compared to standard Monte Carlo simulation technique. The SRSM uses polynomial chaos expansion of orthogonal to fit any probability distribution. Bifurcation analysis of the mathematical model is performed by varying the vertical center of gravity as the bifurcation parameter. Hopf bifurcation is identified. It is found that the bifurcations occur due to the coupling of roll motion with sway, yaw motion and rudder angle. In the presence of wind, roll angle response in bifurcation diagram is discussed.