scholarly journals Multi-Criteria Optimisation of Multi-Stage Positional Game of Vessels

2020 ◽  
Vol 27 (1) ◽  
pp. 46-52
Author(s):  
Józef Lisowski
Keyword(s):  
Mathematical Model ◽  
State Constraints ◽  
Control Algorithms ◽  
State Variables ◽  
The North ◽  
Positional Games ◽  
Multi Stage ◽  
The North Sea ◽  
Safe Control ◽  
Control State

AbstractThe paper presents a mathematical model of a positional game of the safe control of a vessel in collision situations at sea, containing a description of control, state variables and state constraints as well as sets of acceptable ship strategies, as a multi-criteria optimisation task. The three possible tasks of multi-criteria optimisation were formulated in the form of non-cooperative and cooperative multi-stage positional games as well as optimal non-game controls. The multi-criteria control algorithms corresponding to these tasks were subjected to computer simulation in Matlab/Simulink software based on the example of the real navigational situation of the passing of one’s own vessel with eighteen objects encountered in the North Sea.

scholarly journals A predictive model for the wettability of chalk

2020 ◽  
Vol 2 (10) ◽  
Author(s):  
Meysam Nourani ◽  
Niels Hemmingsen Schovsbo ◽  
Ashkan Jahanbani Ghahfarokhi ◽  
Carsten Møller Nielsen ◽  
Lykourgos Sigalas ◽  
...  
Keyword(s):  
Mathematical Model ◽  
North Sea ◽  
Analytical Method ◽  
Oil Fields ◽  
Laboratory Measurements ◽  
The North ◽  
Water Wettability ◽  
The North Sea ◽  
Capillary Pressure Curves ◽  
The U.S

Abstract Wettability is usually measured in special core analyses of limited plug samples according to typically costly and time-consuming procedures. For comparative purposes, wettability is considered an index. The two most frequently used wettability indices are the Amott–Harvey wettability index and the U.S. Bureau of Mines (USBM) index. The Amott–Harvey wettability index is linked to imbibition characteristics and the USBM index is associated with the area under capillary pressure curves. To provide a fast analytical method, a mathematical model for predicting the wettability of chalk is presented. The model is calibrated using experimental wettability data and subsequently applied to two wells in Danish chalk oil fields in the North Sea and to outcrop chalk samples. The model supplements traditional labor-intensive laboratory measurements and predicts water wettability variations with depth by modeling both depth and porosity dependencies; in addition, it provides estimates of the effects of the aging time and displacement temperature of chalk wettability measurements in the laboratory.

A mathematical model of a river—shallow sea system used to investigate tide, surge and their interaction in the Thames—southern North Sea region

1974 ◽  
Vol 275 (1255) ◽  
pp. 567-609 ◽  
Keyword(s):  
Mathematical Model ◽  
Sea Level ◽  
North Sea ◽  
Southern Bight ◽  
The North ◽  
Open Sea ◽  
The North Sea ◽  
Good Potential ◽  
Tidal Oscillation ◽  
The One

A mathematical model is used to reproduce tidal and surge motion in the Thames Estuary and the Southern Bight of the North Sea. The model is based on a numerical finite-difference solution of the nonlinear hydrodynamical equations representing motion in the area. The equations are nonlinear in so far as they include quadratic bottom friction and allow for time variations in the total depth of water; the inclusion of advective terms is limited to the river. Solution of the one-dimensional equations for the river and the two-dimensional equations for the sea takes place within a single computational array. The scheme for calculating motion in the sea is similar to that developed by Heaps (1969), and the scheme for the river was developed by Rossiter & Lennon (1965). Tidal and surge motion within the model are reproduced by specifying the initial tidal contours of the sea, the external influences of surge and tidal oscillation along the open sea boundaries, and wind stresses over the sea surface. Computations have been concerned with generating lunar tidal oscillations for the construction of an M2 co-tidal chart, and investigating the interaction between tides and surges, in this region of shallow waters. The investigation of interaction involved calculating the sea’s response to the separate and combined effects of tidal and meteorological forces, whence the effects of a tide on a surge were deduced, possibly for the first time at offshore locations. Computed interaction phenomena for the period of a severe storm surge, 15 to 17 February 1962, were found to accord with the results of Proudman (19550, b, J957) and Rossiter (1961). Agreement between computed sea-level disturbances and actually recorded disturbances for this surge period revealed that the model has good potential for simulating sea level disturbances which occur in nature.

Partial validation of a numerical model for tidal motion in the Tay Estuary

1987 ◽  
Vol 92 (3-4) ◽  
pp. 275-283
Author(s):  
D. J. Gunn ◽  
J. McManus ◽  
O. Yenigun
Keyword(s):  
Mathematical Model ◽  
Numerical Model ◽  
Boundary Conditions ◽  
North Sea ◽  
Integral Method ◽  
The Road ◽  
Tidal Motion ◽  
The North ◽  
Open Sea ◽  
The North Sea

SynopsisIn a mathematical model of the Tay (Gunn & Yenigun 1987) based upon the Local Integral Method (Gunn & Yenigun 1985), tidal levels at the seaward boundaries and velocities at landward boundaries are used in setting boundary conditions, so that validation studies are mainly based upon changes in internal tidal levels, and comparison between computed and measured velocities within the modelled region. The comparisons of tidal levels within this estuary over a 5.0 m tide showed agreement with overall values from Buddon Ness to the rail bridge, but within the overall agreement there were significant differences in the immediate vicinity of the road bridge. Velocities predicted within the estuary have been compared with measurements provided by a number of surveys in the period from 1972-78. The agreement between experiment and prediction was good in the central and western regions of the model, but the comparison between measurement and prediction was less good near the eastern boundaries. The principal reason for poorer agreement in the east was the difficulty in setting boundary conditions at the open sea extremes of the model. The most satisfactory way of improving the model near the open sea boundaries would be to link the model for the Tay with a model for velocity and level in the North Sea.

scholarly journals Comparison of Dynamic Games in Application to Safe Ship Control

2014 ◽  
Vol 21 (3) ◽  
pp. 3-12 ◽  
Author(s):  
Józef Lisowski
Keyword(s):  
Dynamic Games ◽  
State Constraints ◽  
Goal Function ◽  
Control Algorithms ◽  
Optimum Control ◽  
State Equations ◽  
Multi Stage ◽  
Control Goal ◽  
Ship Control ◽  
Marine Navigation

Abstract The paper introduces methods of dynamic games for automation of ship control in the collision situation, the game control processes in marine navigation and the fundamental mathematical model of the game ship control. First, state equations, control and state constraints and then control goal function in the form of payments: the integral payment and the final one, have been defined. Multi-stage positional, and multi-step matrix, non-cooperative and cooperative, game and optimum control algorithms for a collision situation, have been presented. Te considerations have been illustrated with an exemplary computer simulation of algorithms to determine a safe own ship's trajectory in the process of passing the ships encountered in Kattegat Strait.

scholarly journals Game control methods in avoidance of ships collisions

2012 ◽  
Vol 19 (Special) ◽  
pp. 3-10 ◽  
Author(s):  
Józef Lisowski
Keyword(s):  
Goal Function ◽  
Control Algorithms ◽  
Control Methods ◽  
State Equations ◽  
Multi Stage ◽  
Optimal Control Algorithms ◽  
Control Goal ◽  
Ship Control ◽  
Marine Navigation ◽  
Control State

ABSTRACT The paper introduces application of selected methods of a game theory for automation of the processes of moving marine objects, the game control processes in marine navigation and the base mathematical model of game ship control. State equations, control and state constraints have been defined first and then control goal function in the form of payments - the integral payment and the final one. Multi-stage positional and multi-step matrix, non-cooperative and cooperative, game and optimal control algorithms in a collision situation has been presented. The considerations have been illustrated as an examples of a computer simulations mspg.12 and msmg.12 algorithms to determine a safe own ship’s trajectory in the process of passing ships encountered in Kattegat Strait.

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