A parallel computing application of the genetic algorithm for lubrication optimization

This study investigated the performance of parallel optimization by means of a genetic algorithm (GA) for lubrication analysis. An air-bearing design was used as the illustrated example and the parallel computation was conducted in a single system image (SSI) cluster, a system of loosely network-connected desktop computers. The main advantages of using GAs as optimization tools are for multi-objective optimization, and high probability of achieving global optimum in a complex problem. To prevent a premature convergence in the early stage of evolution for multi-objective optimization, the Pareto optimality was used as an effective criterion in offspring selections. Since the execution of the genetic algorithm (GA) in search of optimum is population-based, the computations can be performed in parallel. In the cases of uneven computational loads a simple dynamic load-balancing scheme is proposed for optimizing the parallel efficiency. It is demonstrated that the huge amount of computing demand of the GA for complex multi-objective optimization problems can be effectively dealt with by parallel computing in an SSI cluster.     

An Application of Newton's Method to the Lubrication Analysis of Air-Lubricated Bearings

This study deals with the development of a computational procedure for solving the isothermal compressible Reynolds equation as the governing equation of air-bearing analysis. Newton's method is used to linearize Reynolds equation and an iterative successive relaxation process is adopted to solve for the air film pressure. The optimal value of relaxation factor for the cases studied is suggested in this report for numerical stability and computational efficiency. The model is verified numerically by examining the conservation of mass flow of the lubricant. The dimensional analysis of the governing equation permits the model to be readily applied to any given film geometry.

The computer model developed can evaluate the air film pressure distribution, load capacity, frictional force, and mass flow of an air bearing. The proposed computational scheme efficiently analyzes the performance of air-lubricated journal bearings at large eccentricity ratios. A similar procedure can be employed to investigate the performance of highspeed noncircular air bearing or gas-lubrication film under slip-flow conditions. This study gives an analytical basis for the design of orifice-compensated externally pressurized air-lubricated bearing.     

Application of the Genetic Algorithm to the Multi-Objective Optimization of Air Bearings

A feasible solution must be obtained in a reasonable time with high probability of global optimum for a complex tribological design problem. To meet this decisive requirement in a multi-objective optimization problem, the popular and powerful genetic algorithms (GAs) are adopted in an illustrated air bearing design. In this study, the goal of multi-objective optimization is achieved by incorporating the criterion of Pareto optimality in the selection of mating groups in the GAs. In the illustrated example the diversity of group members in the evolution process is much better maintained by using Pareto ranking method than that with the roulette wheel selection scheme. The final selection of the optimal point of the points satisfied the Pareto optimality is based on the minimum–maximum objective deviation criterion. It is shown that the application of the GA with the Pareto ranking is especially useful in dealing with multi-objective optimizations. A hybrid selection scheme combining the Pareto ranking and roulette wheel selections is also presented to deal with a problem with a combined single objective. With the early generations running the Pareto ranking criterion, the resultant divergence preserved in the population benefits the overall GA's performance. The presented procedure is readily adoptable for parallel computing, which deserves further study in tribological designs to improve the computational efficiency.     

A Hybrid Search Algorithm for Porous Air Bearings Optimization

The study deals with the development of a hybrid search algorithm for efficient optimization of porous air bearings. Both the compressible Reynolds equation and Darcy's law are linearized and solved iteratively by a successive-over-relaxation method for modeling parallel-surface porous bearings. Three factors affecting the computational efficiency of the numerical model are highlighted and discussed. The hybrid optimization is performed by adopting genetic algorithm (GA) for initial search and accelerated by simplex method (SM) for refined solution. A simple and useful variable transformation is presented and used to convert the unconstrained SM to a constrained method. In this study, the hybrid search algorithm for a multi-variable design exhibits better efficiency compared with the search efficiency by using the SM. The proposed hybrid method also eliminates the need of several trials with random initial guesses to ensure high probability of global optimization. This study presents a new approach for optimizing the performance of porous air bearings and other tribological components.     

Stopping Criterion in Iterative Solution Methods for Reynolds Equations

Iterative solution methods are usually used for solving a variety of Reynolds equations in lubrication analysis due to their simplicity and effectiveness. The objective of this study is to present a robust stopping criterion for iterative methods, by which the iterative process of the methods can be terminated for high execution efficiency without sacrificing the solution accuracy. In this study, the compressible and incompressible fluid Reynolds equations are solved by popular relaxation methods. A very efficient preconditioned conjugate gradient method is also applied in a case for verification. The proposed stopping criterion for iterative methods is based on a coarse-grid truncation error analysis. Three different gridwork groups are required for estimating the truncation errors, which involves only a small amount of additional execution time. In the numerical models examined, the amount of truncation error in a model is insensitive to the gridwork used. It is also found that in a calculation the best prediction of truncation error for terminating the iteration is obtained by using the average fluid film pressure. It is shown that for all the cases tested the proposed stopping criterion can meet the objective stated. The stopping criterion can also be applied when the efficiency of iterative methods is to be compared in solving Reynolds equations.     

A Simulated Air Bearing Analysis by Design of Experiments and Its Applications in Optimization

This study presents an air-bearing design procedure by using Taguchi's Design of Experiments (TDE) to simulate the analysis of systems without adequate models. Instead of taking data from experiments, the performance of air bearings is obtained by an empirical verified numerical model. This arrangement eliminates the errors inevitably introduced in tests. When comparing with full factorial analysis, the number of tests is significantly reduced by using TDE in the demonstrated study. The optimum set of the variables predicted by TDE is numerically verified in the cases investigated. The analysis of orthogonal arrays consisting of three levels shows better performance prediction than the two levels analysis. The straightforward and easy to use procedure can be applied conjunction with numerical optimization technique to give an excellent start-point to minimize search time in a multi-variable design as illustrated in this report.     

Optimum design of externally pressurized air bearing using Cluster OpenMP

This study presents a performance evaluation of a new portable parallel programming paradigm, the Cluster OpenMP (CLOMP) for distributed computing, in conducting an optimum design of air bearings. The multi-objective optimization was carried out by using a genetic algorithm (GA) incorporating Pareto optimality criterion. Since the GA is natural parallel evolution algorithm, the computation of the search was carried out in parallel by using the CLOMP. In this study, the performance of a CLOMP cluster of four dual-core computers for the air bearing optimization was compared with a shared-memory processing (SMP) computer equipped with two quad-core processors. To examine the parallel efficiency of the CLOMP in the GA optimization, several multithread applications of various task sizes were tested. It is shown that the air bearing optimization can be effectively dealt with by the CLOMP (parallel efficiency of 96.2-98.8%) as well as the SMP computing (93.1-99.4%) in the studied cases. The CLOMP retains the characteristics of directive-based OpenMP, such as incremental programming and serial-coding compatibility. The verified high parallel efficiency of the CLOMP cluster demonstrates its potential applications of the scalable computing in many tribological optimizations.     

Comparative study of initial stages of copper immersion deposition on bulk and porous silicon

Initial stages of Cu immersion deposition in the presence of hydrofluoric acid on bulk and porous silicon were studied. Cu was found to deposit both on bulk and porous silicon as a layer of nanoparticles which grew according to the Volmer-Weber mechanism. It was revealed that at the initial stages of immersion deposition, Cu nanoparticles consisted of crystals with a maximum size of 10 nm and inherited the orientation of the original silicon substrate. Deposited Cu nanoparticles were found to be partially oxidized to Cu₂O while CuO was not detected for all samples. In contrast to porous silicon, the crystal orientation of the original silicon substrate significantly affected the sizes, density, and oxidation level of Cu nanoparticles deposited on bulk silicon.     

Nanostructures formed by displacement of porous silicon with copper: from nanoparticles to porous membranes

ABSTRACT: The application of porous silicon as a template for the fabrication of nanosized copper objects is reported. Three different types of nanostructures were formed by displacement deposition of copper on porous silicon from hydrofluoric acid-based solutions of copper sulphate: (1) copper nanoparticles, (2) quasi-continuous copper films, and (3) free porous copper membranes. Managing the parameters of porous silicon (pore sizes, porosity), deposition time, and wettability of the copper sulphate solution has allowed to achieve such variety of the copper structures. Elemental and structural analyses of the obtained structures are presented. Young modulus measurements of the porous copper membrane have been carried out and its modest activity in surface enhanced Raman spectroscopy is declared.     

An efficient global optimization algorithm for multifactor dynamic systems

Abstract

In this study we present an efficient global optimization method, DIviding RECTangle (DIRECT) algorithm, for parametric analysis of dynamic systems. In a bounded constrained problem the DIRECT algorithm explores multiple potentially optimal subspaces in one search. The algorithm also eliminates the need for derivative calculations which are required in some efficient gradient‐based methods. In this study the first optimization example is to find the dynamic parameters of a tennis racket. The second example is a biomechanical parametric study of a heel‐toe running model governed by six factors. The effectiveness of the DIRECT algorithm is compared with a genetic algorithm in an analysis of heel‐toe running. The result shows that the DIRECT algorithm obtains an improved result in 83% less execution time. It is demonstrated that the straightforward DIRECT algorithm provides a general procedure for solving global optimization problems efficiently and confidently.