Probabilistic simulation of offshore collisions

Collisions between tankers and offshore structures may result in serious problems such as oil pollution. It is therefore of interest to estimate the probability of a collision. This is done here by means of a simulation model using the GASP IV simulation program. The new method is based on a statistical prediction of the ship's path after some kind of critical failure affecting the manoeuvrability of the tanker has taken place.     

Collision Avoidance by a Ship with a Moving Obstacle: Computation of Feasible Command Strategies

A ship moving from a point A to a point B detects a moving small obstacle at close range. Hence, the ship has to perform a maneuver to avoid collision with the moving obstacle. Using a realistic model of a tanker ship, a method is proposed for computing feasible rudder command strategies for performing the collision-avoidance maneuver.     

Optimal Control of a Ship for Course Change and Sidestep Maneuvers

We consider a ship subject to kinematic, dynamic, and moment equations and steered via rudder under the assumptions that the rudder angle and rudder angle time rate are subject to upper and lower bounds. We formulate and solve four Mayer problems of optimal control, the optimization criterion being the minimum time.Problems P1 and P2 deal with course change maneuvers. In Problem P1, a ship initially in quasi-steady state must reach the final point with a given yaw angle and zero yaw angle time rate. Problem P2 differs from Problem P1 in that the additional requirement of quasi-steady state is imposed at the final point.Problems P3 and P4 deal with sidestep maneuvers. In Problem P3, a ship initially in quasi-steady state must reach the final point with a given lateral distance, zero yaw angle, and zero yaw angle time rate. Problem P4 differs from Problem P3 in that the additional requirement of quasi-steady state is imposed at the final point.The above Mayer problems are solved via the sequential gradient-restoration algorithm in conjunction with a new singularity avoiding transformation which accounts automatically for the bounds on rudder angle and rudder angle time rate.The optimal control histories involve multiple subarcs along which either the rudder angle is kept at one of the extreme positions or the rudder angle time rate is held at one of the extreme values. In problems where quasi-steady state is imposed at the final point, there is a higher number of subarcs than in problems where quasi-steady state is not imposed; the higher number of subarcs is due to the additional requirement that the lateral velocity and rudder angle vanish at the final point.     

Experimental and numerical analysis of self-excited friction oscillator

A self-excited friction oscillator has been designed and manufactured to carry out experimental analysis of dry friction phenomenon. A mathematical model of this oscillator has been formulated. The influence of the different types of classical friction characteristics on the dynamical behaviour of the model is investigated by way of numerical analysis. A comparison with dynamics of real oscillator is presented and some reasons of observed differences are explained. A particular analysis of experimental data leads to the confirmation of non-reversible friction characteristics and allows to formulate a hypothesis that a course of such characteristics also depends on value (not only on the sign) of acceleration.     

Optimal Control of a Ship for Collision Avoidance Maneuvers

We consider a ship subject to kinematic, dynamic, and moment equations and steered via rudder under the assumptions that the rudder angle and rudder angle time rate are subject to upper and lower bounds. We formulate and solve four Chebyshev problems of optimal control, the optimization criterion being the maximization with respect to the state and control history of the minimum value with respect to time of the distance between two identical ships, one maneuvering and one moving in a predetermined way.Problems P1 and P2 deal with collision avoidance maneuvers without cooperation, while Problems P3 and P4 deal with collision avoidance maneuvers with cooperation. In Problems P1 and P3, the maneuvering ship must reach the final point with a given lateral distance, zero yaw angle, and zero yaw angle time rate. In Problems P2 and P4, the additional requirement of quasi-steady state is imposed at the final point.The above Chebyshev problems, transformed into Bolza problems via suitable transformations, are solved via the sequential gradient-restoration algorithm in conjunction with a new singularity avoiding transformation which accounts automatically for the bounds on rudder angle and rudder angle time rate.The optimal control histories involve multiple subarcs along which either the rudder angle is kept at one of the extreme positions or the rudder angle time rate is held at one of the extreme values. In problems where quasi-steady state is imposed at the final point, there is a higher number of subarcs than in problems where quasi-steady state is not imposed; the higher number of subarcs is due to the additional requirement that the lateral velocity and rudder angle vanish at the final point.     

Maritime crude oil transportation - A split pickup and split delivery problem

The maritime oil tanker routing and scheduling problem is known to the literature since before 1950. In the presented problem, oil tankers transport crude oil from supply points to demand locations around the globe. The objective is to find ship routes, load sizes, as well as port arrival and departure times, in a way that minimizes transportation costs. We introduce a path flow model where paths are ship routes. Continuous variables distribute the cargo between the different routes. Multiple products are transported by a heterogeneous fleet of tankers. Pickup and delivery requirements are not paired to cargos beforehand and arbitrary split of amounts is allowed. Small realistic test instances can be solved with route pre-generation for this model. The results indicate possible simplifications and stimulate further research.     

A decision aid for milk tanker run allocation

This paper reports on a decision aid that recommends solutions to a particular vehicle allocation problem occurring in the New Zealand dairy industry. The decision aid has been developed for use by New Zealand milk tanker schedulers. It is designed to aid them in the allocation of tankers to milk collection routes in order to alleviate pumping bay congestion, which occurs when the tankers return to unload milk at a processing plant. It enables its users to remain in control of the tanker allocation process, while using their own experience and preferences. The paper describes the issues involved and the type of help that the schedulers need. It introduces a typical allocation problem and describes some heuristics for its solution, which are incorporated in the decision aid.     

A network solution to a general vehicle scheduling problem

Dantzig and Fulkerson and later Bellmore et al. have shown that certain vehicle (tanker) scheduling problems can be formulated as minimum cost flow problems on a network. In this paper, the results of Dantzig and Fulkerson are extended to the case where more than one type of vehicle can be used in the determination of an optimal fleet. (In tanker scheduling terminology; how many small, medium and large tankers would form an optical fleet.) It is seen how the problem can be formulated as a modified transportation problem where flow in some arcs is conditioned to there being flow on certain other arcs. These “conditional” transportation problems were solved directly as linear programs and showed the peculiarity of terminating all integer in spite of having a constraint matrix, which does not satisfy the well known sufficient conditions for urimodularity. We discuss the implementation of the model and its empirical results.     

An oil outflow model for tanker collisions and groundings

In this paper we have developed an oil outflow model for collision and grounding accidents of tankers. The collision model explicitly links input variables such as tanker hull design (single or double), displacement and speed, striking vessel displacement and speed, and the interaction angle of both vessels to output variables: longitudinal and transversal damage extents of the tanker. Overlaying these damage extents on the tank vessel’s design yields an oil outflow volume totaling the capacity of the damaged tank compartments. A similar model is developed for grounding accidents. A total of 80,000 simulation accident scenarios described in the National Research Council SR259 report published in 2001 served as the joint data set of input and output variables used in this “linking” process. The oil outflow model herein was designed keeping computational efficiency in mind to allow for its integration with a maritime transportation system (MTS) simulation. We shall demonstrate the use of the oil outflow model as a final analysis layer to evaluate double-hull effectiveness in a geographic context of an MTS simulation model developed for the oil transportation routes traversing the environmentally sensitive San Juan Islands area in Washington State.     

中缅原油管道贯通对进口原油海上运输成本的影响分析

研究了中缅原油管道贯通对我国进口原油海上运输成本的影响.首先分析了我国的主要原油进口地、进口量和海上运输航线等信息,然后选择了三种不同型号油轮,并调查了其载重量、航速、日租金等数据.以不同型号油轮的运输航次及各条航线上的实际运输量为决策变量,总租金(总运输成本)最小化为目标函数,分别建立了中缅原油管道贯通前后我国进口原油海上运输问题的数学模型,并分别给出了求解方法.最后,根据实际统计数据进行计算,分别求出了中缅原油管道贯通前后我国原油海上运输的总成本,结果显示,中缅原油管道贯通后我国进口原油的海上运输成本将降低4.95%.     

2010年全国研究生数模竞赛D题的评阅综述

2010年全国研究生数学建模竞赛D题的素材取自一项科研项目.将本题建为何种模型取决于建模人的数学基础和对本题描述运动过程的认识深度.评述介绍了三种建模思路:刚体平面运动模型,最优控制模型和微分方程模型,其中微分方程模型是在阅卷过程中从考生答卷中发现的,从答卷中发现了不少有共性的毛病,反应出国内大学和研究生数学教育中的弊病,值得有识之士们重视.     

A review of hydrodynamical models for semiconductors: Asymptotic behavior

We review recent results on the hydrodynamical model for semiconductors. The derivation of the mathematical model from the semi-classical Boltzmann equation in terms of the moment method is performed, and the mathematical analysis of the asymptotic behavior of both classical solutions and entropy weak solutions is given on spatially bounded domain or whole space.Dedicated to Constantine Dafermos on his 60^th birthday     

Mathematical Theory of Fluids in Motion

The goal of this paper is to present the recent development of mathematical fluid dynamics in the framework of classical continuum mechanics phenomenological models. In particular, we discuss the Navier–Stokes (viscous) and the Euler (inviscid) systems modeling the motion of a compressible fluid. The theory is developed from fundamental physical principles, the necessary mathematical tools introduced at the moment when needed. In particular, we discuss various concepts of solutions and their relevance in applications. Particular interest is devoted to well-posedness of the initial-value problems and their approximations including possibly certain numerical schemes.     

Optimal Control of a Ship for a Course-Changing Maneuver

The steering control of a ship during a course-changing maneuver is formulated as a Bolza optimal control problem, which is solved via the sequential gradient-restoration algorithm (SGRA). Nonlinear differential equations describing the yaw dynamics of a steering ship are employed as the differential constraints, and both amplitude and slew rate limits on the rudder are imposed. Two performance indices are minimized: one measures the time integral of the squared course deviation between the actual ship course and a target course; the other measures the time integral of the absolute course deviation. Numerical results indicate that a smooth transition from the initial set course to the target course is achievable, with a trade-off between the speed of response and the amount of course angle overshoot.     

Mathematical model for the bending of plastically anisotropic beams

A mathematical model for the bending of a plastically anisotropic beam simply supported at both ends and subjected to a constant moment is considered. A differential equation with variable coefficients is derived for the beam curvature. The yield points of the beam material under tension and compression are assumed to be known. The elastoplastic bending of the beam with allowance for the strength-different (SD) effect is considered. The classical Bernoulli–Euler beam theory and the ideal plasticity model are used construct the mathematical model, and the problem is solved analytically. The solutions obtained for a classical isotropic beam and an SD beam are compared, and the contribution of the SD effect is analyzed. The problem is solved completely, and its results can be used to study bending under different loading.     

基于复合控制的电液负载模拟器多余力抑制研究

针对电液负载模拟系统存在多余力且该多余力严重影响系统加载精度与控制性能的问题,建立了系统各部分以及整个系统的数学模型.通过对数学模型的研究,分析了系统多余力的产生机理,并建立了系统多余力的传递函数.提出了前馈PID复合控制的方法,并对该方法进行了仿真分析和实验研究.在仿真分析中,通过对多余力消扰前、引入前馈控制消扰后及引入复合控制消扰后3种情况的比较,说明前馈PID复合控制能够有效抑制系统多余力.实验结果进一步验证了前馈PID复合控制的有效性,同时实验结果显示在运动换向时系统多余力将出现突变,为下一步的研究指明了方向.     

Petrol delivery tanker assignment and routing: a case study in Hong Kong

In this paper, we present a case study on a tanker assignment and routing problem for petrol products in Hong Kong. A fleet of heterogeneous dangerous goods vehicles has been assigned to deliver several types of petroleum products to petrol stations with different tank capacities. Under the vendor-managed inventory system, the delivery company is responsible for controlling the station's inventory and replenishment. The operational characteristics and challenges such as geographic zoning, size of petrol stations, routing restrictions and so on are unique and have been described in this paper. A decision support system (DSS) combining heuristic clustering and optimal routing is employed to find the optimal fleet assignment and routing. Multiple objectives are considered simultaneously such that the number of tankers used could be minimized, the number of drops in trips is minimized, profit in terms of total products delivered is maximized and utilization of resources is maximized. The case illustrates the benefit and advantages of using the proposed DSS.     

Optimum three-dimensional flight of a supersonic aircraft

Optimum three-dimensional flight of supersonic aircraft is considered, particularly the minimization of flight time, which is important in the climbing and turning performance of a supersonic fighter. General properties of optimum three-dimensional flight are presented, and the maximum principle is used. Optimal control is obtained by a geometrical method using the domain of manoeuvrability.     

The Cauchy Problem for the Average Field Equation Describing a Model of a Magnetic Solid

We study a model of a magnetic solid treated as a system of particles with mechanical moment $\vec s,\vec s \in S^2$ , and magnetic moment $\vec \mu ,\vec \mu = \vec s$ , interacting with one another via the magnetic field, which determines variations in the mechanical moment of each particle. We study the system of integro-differential equations describing the evolution of the one-particle distribution function for this system of particles. We prove existence and uniqueness theorems for the generalized and the classical solution of the Cauchy problem for this system of equations. We also prove that the generalized solution continuously depends on the initial conditions.