Yeni köşe sayma algoritmaları ve makine mühendisliğindeki uygulamaları

This thesis presents the development of three novel vertex enumeration algorithms and their engineering applications. The first algorithm, named the Corridor Method, is introduced as an efficient geometric method for vertex enumeration in simple linear regression problems with bounded error. The method uses bijective maps between lines in measurement space and points in parameter space and shows significantly better performance compared to well-known algorithms in all simulations. The Corridor Method is then extended to cover generic linear optimization problems with two variables, resulting in the Modified Corridor Method. Additionally, a third algorithm, the Edge Tracking Algorithm (ETA), is developed to be used in multidimensional linear problems. ETA tracks the edges of the solution polytope starting from a given vertex to explore the adjacent vertices of the given vertex and shows better performance than well-known algorithms for some of the problems. The thesis then demonstrates the use of these algorithms in mechanical engineering applications. In the regression application, a new regression tool based on the solution polytope obtained by the algorithms is proposed . This tool is compared to other regression techniques, and found to be superior in all experiments by large margins. In the second application, the resulting polytope of the algorithms is used to investigate the feasibility of the assembly. Also, the expected and maximum possible misalignment concepts are discussed based on the resulting polytopes using Monte Carlo simulations.