Optimising Yacht Routes under Uncertainty
Optimising Yacht Routes under Uncertainty
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不确定性下优化游艇路线
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
A. Philpott
中科院分区：
文献类型：
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作者：
A. Philpott
帆船航线的规划受到天气的不确定性的影响。这在游艇比赛中尤为重要，因为天气预报的准确性可以决定比赛的结果。有了完美的天气预报，就可以使用给定游艇的极坐标表来计算最小化到达目的地时间的路线。为赛车游艇做这件事的软件现在是大多数商业仪器包的标准组成部分。由于天气信息的不确定性，路由问题变得更加困难。我们审查两个模型优化游艇航线的不确定性下的天气。第一种是适合短距离比赛。它将风视为一个马尔可夫过程，并根据观测的风向，它计算在每个点的过程中，以尽量减少在下一个标记的预期到达时间的跟踪和航向决策。第二个模型是针对海洋竞赛的，它使用集合预报而不是马尔可夫过程来模拟天气。在这两种模型中，都可以代表规避风险和寻求风险的行为。符号x穿过路线的距离y路线上的距离x（x，y）路线起点位置x起点终点位置x终点位置），（t W x时间t时位置x处的真实风速），（t x θ t τ时刻位置x处的真实风向航向时间损失（i，j，k）cn航行时间））（），（（n y i x to））1（），（（+ n y j x）在风角k（）k i fn，* 从该位置出发航行至终点的最短时间））（），（（n y i x在风角k。）（x r）位置x之前的位置集合。引言在本文中，我们考虑的问题，找到一条路线，最大限度地减少时间航行在海洋上的两个点之间的不确定的天气条件下。目前，许多竞赛游艇船长使用确定性游艇路由软件包来帮助他们的路线规划决策。该软件执行我们所说的确定性天气路由，因为它只考虑天气的一种可能性，并基于预测天气将完全按照预测发生的假设产生最佳路线。然而，以任何精度预测风是一个困难的问题，因此基于单一预测的方法可能产生在真实的天气条件下实施时表现不佳的解决方案。在这项工作中，我们考虑了未来不同天气条件演变的可能性，并生成在所有天气条件下都表现良好的路线。这需要解决一个随机天气路由问题。我们讨论了两种模型，适用于不同的情况。第一个模型适用于短距离比赛，其中，相对于在比赛期间随机波动的预期风向来设置路线。在这个模型中，抢风会导致速度损失，因此，主要关注的因素是观测到的未来风向。我们研究的第二个模型侧重于长距离海上游艇比赛，例如BT挑战赛或沃尔沃“环球”比赛。在这里，比赛过程中天气条件的变化更大，风向的短期随机波动不如大规模气象影响重要。在这两个模型中，我们需要能够计算游艇在帆的任何一点的速度。游艇的速度由许多因素决定，包括风力强度，真实风向角，电流，波浪和帆设置。这些因素可以分为环境因素，如风速和风向，海况和电流，以及可控因素，如帆的选择和纵倾。假设对于任何给定的环境条件，可控因素将被设置为使游艇的速度最大化。在这种假设下，游艇航行的速度取决于风力和船相对于风的航向。在给定的真实风角和真实风速下，游艇可以航行的最大速度由数值速度预测程序（VPP）和水上测量产生，并采用离散的三元组的形式，给出真实风角，真实风速和船速。已知值之间的插值给出了任何真实风角和真实风速的预测最大速度。图1是显示这些数据的典型“极坐标图”。
The planning of routes for sailing vessels is subject to uncertainty from the weather. This is particularly important in yacht racing where the accuracy of a weather prediction can determine the outcome of a race. With a perfect weather forecast it is possible to use the polar tables of a given yacht to compute a route that minimises its arrival time at its destination. Software that does this for racing yachts is now a standard part of most commercial instrumentation packages. With uncertain weather information the routing problem becomes more difficult. We review two models for optimising yacht routes under uncertainty about the weather. The first of these is suitable for short course racing. It treats the wind as a Markov process, and based on observations of the wind ditrection, it computes tacking and heading decisions at each point of the course so as to minimise the expected arrival time at the next mark. The second model, which is intended for ocean races, models the weather using ensemble forecasts rather than a Markov process. In both models it is possible to represent risk-averse and risk-seeking behaviour. NOTATION x distance across course y distance up the course x (x,y) location on course start x Location of start finish x Location of finish ) , ( t W x True wind speed at location x at time t ) , ( t x θ True wind direction at location x at time t τ Loss of time in a tack (i,j,k) cn Time to sail from )) ( ), ( ( n y i x to )) 1 ( ), ( ( + n y j x ) on tack k ( ) k i fn , * minimum time to sail to the finish departing from the location )) ( ), ( ( n y i x on tack k. ) (x Γ set of locations preceding location x . INTRODUCTION In this paper we consider the problem of finding a route that minimises the time to sail between two points on the ocean under uncertain weather conditions. Many racing yacht skippers currently use deterministic yacht routing software packages to help with their route planning decisions. This software performs what we refer to as deterministic weather routing in that it only considers one possibility for the weather and produces an optimal route based on the assumption that the predicted weather will occur exactly as forecast. However, it is a difficult problem to predict the wind with any accuracy, so an approach based on a single prediction can yield solutions that perform badly when implemented under real weather conditions. In this work, we consider the possibility of different weather conditions evolving in the future, and produce routes that perform well under all of them. This requires solving a stochastic weather routing problem. We discuss two models that are applicable in different situations. The first model is appropriate for short course racing, in which a course is set with respect to an expected wind direction that fluctuates randomly over the period of the race. In this model, tacking incurs a speed loss and because of this the major factor of interest is the observed future wind direction. The second model we examine focuses on long, offshore yacht races, such as the BT Challenge or the Volvo “Round The World” race. Here the variation in weather conditions over the course of a race is greater, and short-term random fluctuations in wind direction are less important than large-scale meteorological effects. In both models we need to be able to compute the velocity of the yacht at any point of sail. The speed of a yacht is determined by many factors, including wind strength, true wind angle, current, waves, and sail settings. These can be broken down into environmental factors, such as wind speed and direction, sea-state, and current, and controllable factors, such as sail choice and trim. It is assumed that, for any given environmental conditions, the controllable factors will be set so as to maximise the speed of the yacht. Given this assumption, the speed at which a yacht sails is dependent upon the wind strength and the boat’s heading relative to the wind. The maximum speed at which a yacht can sail for a given true wind angle and true wind speed is generated by numerical velocity prediction programs (VPPs) and on-the-water measurements and takes the form of a discrete set of triples giving true wind angle, true wind speed, and boat speed. Interpolating between known values gives predicted maximum speeds for any true wind angle and true wind speed. Figure 1 is a typical ‘polar plot’ showing these data.