Hybrid optimization for k-means clustering learning enhancement

In recent years, combinational optimization issues are introduced as critical problems in clustering algorithms to partition data in a way that optimizes the performance of clustering. K-means algorithm is one of the famous and more popular clustering algorithms which can be simply implemented and it can easily solve the optimization issue with less extra information. But the problems associated with Kmeans algorithm are high error rate, high intra cluster distance and low accuracy. In this regard, researchers have worked to improve the problems computationally, creating efficient solutions that lead to better data analysis through the K-means clustering algorithm. The aim of this study is to improve the accuracy of the Kmeans algorithm using hybrid and meta-heuristic methods. To this end, a metaheuristic approach was proposed for the hybridization of K-means algorithm scheme. It obtained better results by developing a hybrid Genetic Algorithm-K-means (GAK- means) and a hybrid Partial Swarm Optimization-K-means (PSO-K-means) method. Finally, the meta-heuristic of Genetic Algorithm-Partial Swarm Optimization (GAPSO) and Partial Swarm Optimization-Genetic Algorithm (PSOGA) through the K-means algorithm were proposed. The study adopted a methodological approach to achieve the goal in three phases. First, it developed a hybrid GA-based K-means algorithm through a new crossover algorithm based on the range of attributes in order to decrease the number of errors and increase the accuracy rate. Then, a hybrid PSO-based K-means algorithm was mooted by a new calculation function based on the range of domain for decreasing intra-cluster distance and increasing the accuracy rate. Eventually, two meta-heuristic algorithms namely GAPSO-K-means and PSOGA-K-means algorithms were introduced by combining the proposed algorithms to increase the number of correct answers and improve the accuracy rate. The approach was evaluated using six integer standard data sets provided by the University of California Irvine (UCI). Findings confirmed that the hybrid optimization approach enhanced the performance of K-means clustering algorithm. Although both GA-K-means and PSO-K-means improved the result of K-means algorithm, GAPSO-K-means and PSOGA-K-means meta-heuristic algorithms outperformed the hybrid approaches. PSOGA-K-means resulted in 5%- 10% more accuracy for all data sets in comparison with other methods. The approach adopted in this study successfully increased the accuracy rate of the clustering analysis and decreased its error rate and intra-cluster distance

Characterization of edge-contact influence on tridimensional elastohydrodynamic film shape, pressure, stress and temperature distributions

This doctoral project investigates edge contact influence on pressure, lubricant film thickness, temperature, and stress distribution of finite line contacts under an elastohydrodynamic lubrication (EHL) regime. This type of contact represents a common source of problems in engineering structures such as gears, cams and roller bearings, since non-conforming contact surfaces in such structures undergo intense stresses while transferring loads through relatively small contact areas. Additionally, they induce stressconcentration zones at their extremities; as a result, profile modification becomes necessary. The present study investigates influence of free edges on EHL characteristics of finite line contacts. The initial stage of the research develops a 3D numerical model for the thermal, non-Newtonian EHL of general contact problems. A semi-analytical method (SAM), based on the Boussinesq half-space theory, is combined with a free boundary correction process to provide a fast and precise description of edge contact conditions. A modified finite difference expansion of the Couette term of the Reynolds equation guarantees computational stability, while the Carreau expression defines the shear-thinning response of the lubricant. Free boundary impact on tridimensional stress distribution is also investigated by extending the free-edge correction procedure to evaluate the levels of surface and subsurface stresses using SAM. The stress distribution data derived from this procedure are then contrasted with Finite Element Method (FEM) results using a two-level factorial comparison. Three dimensionless factors — contact slenderness, contact length ratio, and load — are examined. The comparison shows that the new model developed in this thesis provides a high level of precision in the evaluation of stress distributions, while computing more than 125 times faster than FEM simulations. This powerful model is then used to investigate and establish the influence of different roller profile modifications on EHL film shape, pressure and temperature distributions. Based on a series of detailed analyses of different roller profile corrections, it is found that a large radius crowning combined with rounding corners provides the most effective profile adjustment. In the last step of this study, this newly developed model is combined with a multi-objective particle swarm optimization (PSO) to arrive at formulas establishing crowning and corner rounding radii, which can be applied to the rapid design of optimal rollers. The formulas take into account three dimensionless factors — slenderness, load, and lubricant viscosity — and coefficients for the formulas are derived from the PSO results using a five-level factorial design. By concurrently optimizing three objective functions — contact pressure uniformity, film thickness stability, and maximum load capacity — the predictions of these formulas guarantee optimal profile modifications. This study contributes to the understanding of edge influence on EHL characteristics of finite line contacts, while offering a robust model for axial profile corrections of lubricated contact problems