Optimiranje smjera jedrenja

scientific master's theses

• Title (english): Optimization of the sailing route
• Author: Dino Mandić
• Mentor: Dragutin Ščap (mentor)
• Committee member: Izvor Grubišić (predsjednik povjerenstva)
• Committee member: Dragutin Ščap (član povjerenstva)
• Committee member: Krešimir Matković (član povjerenstva)
• Granter: University of Zagreb; Faculty of Mechanical Engineering and Naval Architecture; Zagreb
• Defense date and country: 2008-12-11, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Mechanical Engineering
• Universal decimal classification (UDC): 796/799 - Sport; 51 - Mathematics

Abstract

U ovom radu opisan je postupak za određivanje optimalne rute za jedrenje u kojem se koriste dvije metode za optimizaciju: - genetski algoritam - Nelder-Mead metoda. Određivanje optimalne rute za jedrenje je od posebnog značenja za jedrenje na dužim rutama, gdje se vremenske prilike mijenjaju u vremenu i prostoru, dok se kod kraćih relacija može pretpostaviti da je vjetar nepromjenjiv. Optimalna ruta za jedrenje se računa pomoću prognoze vjetra za određeno područje i polarnog dijagrama jedrilice. U polarnom dijagramu je definirana ovisnost brzine jedrilice o brzini i smjeru vjetra u odnosu na pramac, a prognozom vjetra je definiran smjer i brzina vjetra u prostoru i vremenu. Poznavajući prognozu vjetra i polarni dijagram, potrebno je zadati polaznu i krajnju točku za jedrenje, te vrijeme polaska kako bi se moglo točno definirati polje vjetra na promatranom području u prostoru i vremenu. Iz zadanih podataka o vjetru i brodu je moguće za svaki smjer jedrenja u određenom trenutku odrediti brzinu jedrilice, te se na taj način izračuna vrijeme potrebno za jedrenje na određenoj ruti. Za određivanje optimalne rute za jedrenje potrebno je u obzir uzeti što je moguće više mogućnosti, jer na otvorenom moru teoretski postoji neograničeni broj mogućnosti za odabir rute. Iz tog razloga je odabran genetski algoritam kojim se vrlo brzo pronalazi globalni optimum, a za dodatno poboljšanje rezultata je odabrana Nelder-Meadova metoda koja brzo izračunava lokalni optimum oko početnog vektora. Kao početni vektor se koristi rezultat dobiven genetskim algoritmom, pa se na taj način koriste dobre strane obiju metoda u svrhu brzog i preciznog izračunavanja globalnog optimuma. Za matematički model računanja vremena za jedrenje, kod manjih udaljenosti se pretpostavlja jedrenje po ravnoj plohi, dok se dok većih udaljenosti uvažava zakrivljenost Zemlje, te se duljina ruta između dviju točki računa po loksodromi.

Abstract (english)

In this work is described the procedure for determining the optimal route for sailing in which two methods for optimization are used: - Genetic algorithm - Nelder-Mead method. To determine the optimal route for sailing is of special significance for sailing on the longer routes, where the weather conditions change in time and location, while at the short distance can assume that the wind is unalterable. The optimal route for sailing is calculated relative to the weather forecast and sailing boat polar diagram data. In the polar diagram is defined dependence speed sailing boats on the speed and direction of wind on the bow, and by the wether forecast is defined direction and speed of wind in the specific area and time. Beside the weather forecast and sailing boat polar diagram, it is required to specify the departure and arrival points as well as the departure time in order to define wind on the specific area relative to the location and time. From the all specifed data about the wind and the boat it is possible for each direction of sailing at a time to determine the sailing boat speed and thus to calculate the time required for sailing on a particular route. To determine the optimal route at offshore sailing, it is necessary to take into account as much as possible opportunities because there is theoretically unlimited number of possibilities for the optimal sailing route. For this reason it was selected genetic algorithm that quickly finds global optimum, and for the further improvement of results is selected Nelder-Mead method, which quickly calculates the optimum from the initial state. As the initial vector is the result obtained using genetic algorithm, this approach enables the exploitation of the good side of both methods for the purpose of quick and precise calculation of global optimum. At mathematical model for calculation of the sailing time at smaller distances is assumed sailing at plane, while at the larger distances curvature of Earth is taken into account. Due to this, the distance between two points on Earth is calulated as Rhumb line instead of straight line.

• Keywords: optimizacija; genetski algoritam; Nelder-Mead metoda; jedrenje; optimalna ruta; loksodroma; ortodroma
• Keywords (english): optimization; genetic algorithm; Nelder-Mead method; sailing; optimal sailing route; Rhumb line; Orthodrome
• Language: croatian
• URN:NBN: urn:nbn:hr:235:799896
• Study programme: Title: Mechanical Engineering - mr.sc.; Study programme type: university; Study level: postgraduate; Academic / professional title: magistar znanosti (magistar znanosti)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-12-21 23:26:01