Estimating the travel time and the most likely path from the Global Drifter Program

<p>We provide a novel method and tool for computing the most likely path taken by drifters between arbitrary fixed locations in the ocean. In addition to this we provide an estimate of the travel time associated with the path. Lagrangian pathways and travel times are of practical value not just in understanding surface currents, but also in modelling the transport of ocean-borne species such as planktonic organisms, and floating debris such as plastics. To demonstrate the capabilities of this method we show emperical results derived from the Global Drifter Program data. We use the drifter data to construct Markov transition matrices and apply Dijkstra's algorithm to find the most likely paths. The novelty is that we apply hexagonal tessellation of the ocean using Uber's H3 index (which we show is far superior to the standard practice of rectangular or lat-lon gridding). Furthermore, we provide techniques for measuring uncertainty by bootstrapping and applying rotations to the hexagonal grid. The methodology is purely data-driven, and requires no simulations of drifter trajectories. The method scales globally and is computationally efficient.</p>

Multi-Robot Adversarial Patrolling Strategies via Lattice Paths

In full-knowledge multi-robot adversarial patrolling, a group of robots have to detect an adversary who knows the robots' strategy. The adversary can easily take advantage of any deterministic patrolling strategy, which necessitates the employment of a randomised strategy. While the Markov decision process has been the dominant methodology in computing the penetration detection probabilities, we apply enumerative combinatorics to characterise the penetration detection probabilities. It allows us to provide the closed formulae of these probabilities and facilitates characterising optimal random defence strategies. Comparing to iteratively updating the Markov transition matrices, our methods significantly reduces the time and space complexity of solving the problem. We use this method to tackle four penetration configurations.

Modeling a random sequence of extremes of loads for fatigue tests under irregular loading

Methods and approaches to tests under random loading are considered, their role is characterized. To ensure the random nature of loading, a modeling method based on Markov transition matrices and real processes recorded in operation is proposed. Keywords: random loading process, Markov repetition matrices, resource estimation, corrected linear hypothesis, parameter of completeness of the loading spectrum. [email protected]

Optimizing maintenance decisions in railway wheelsets: A Markov decision process approach

This article models the decision problem of maintaining railway wheelsets as a Markov decision process, with the aim to provide a way to support condition-based maintenance for railway wheelsets. A discussion on the role of the railway wheelsets is provided, as well as some background on the technical standards that guide maintenance decisions. A practical example is explored with the estimation of Markov transition matrices for different condition states that depend on the wheelset diameter, its mileage since last turning action (or renewal) and the damage occurrence. Bearing in mind all the possible maintenance actions, an optimal strategy is achieved, providing a map of best actions depending on the current state of the wheelset.

An Estimation of Thailand's Hourly Solar Radiation Using Markov Transition Matrix Method

To estimate global solar radiation from easy available weather forecast data (sky condition), Markov model is used for this estimation. The five-year (1996-2000) global radiation data that are taken at an hour intervals from Nakhon Pathom station, Thailand (latitude 13.81ºN and longitude 100.04ºE) are used to construct the Markov transition matrices. The global radiation sequences in 2000 will be generated by based on the characteristic probability of moving global radiation values which were observed from the obtained data during 1996-1999. The autocorrelation function is used for checking the order of probability of moving obtained data. In this study, the five first and five second-order Markov transition matrices (MTMs), which are selected from the autocorrelation functions, are constructed, each MTMs will be used for generating global radiation values in each day with different sky conditions (clear, partly cloudy, mostly cloudy, cloudy and overcast). From the results of comparison between the statistical characteristics of observed and two synthetic generated data, global radiation data behavior slightly improved by the second order Markov model.