臺灣博碩士論文加值系統

在磨潤領域中許多流體薄膜潤滑分析是需要大量計算時間的工作，這些分析工作往往無法在可接受的運算時間內，以單一核心處理器的電腦取得令人滿意的結果。雷諾方程式是描述流體薄膜潤滑的式子，為潤滑計算工作的瓶頸之一，而潤滑薄膜的黏度變化、流體的可壓縮性、軸承材料的彈性變形或可能有的非牛頓潤滑劑等情形，使得以數值方法求解潤滑薄膜壓力分佈更加耗時。本研究使用指令精簡且相容於序列計算的OpenMP語法和Cluster OpenMP軟體，進行流體薄膜潤滑分析與其相關最佳化設計的平行計算研究，並與openMosix平行計算模式比較。
本研究在有限差分法的序列程式中加入OpenMP的語法，進行氣體潤滑和熱液動壓潤滑軸承分析，當在計算中使用兩個執行緒時，分別可以獲得1.53和1.66的加速率。另外，在16個計算節點的openMosix環境下採用晶格搜尋法和區間分割法，進行氣體和熱液動壓潤滑軸承的最佳化設計，加速率分別為2.54 和6.56，代表計算資源使用率的平行效率分別為15.9%和41%，顯示計算資源閒置的情況嚴重。如果改採窘迫式平行區間分割法，閒置的計算資源可以被用來執行全域和局部的參數搜尋，更進一步的降低搜尋次數和計算時間，可獲得65.9%的平行效率。本研究採用的方法和步驟可以縮短潤滑分析與軸承最佳化的時間，並應用於複雜且需要計算資源的流體薄膜潤滑分析，或其它耗費時間的工程計算工作。

In the field of Tribology fluid-film lubrication analysis is usually a hard computing problem which can not be satisfactorily solved within a reasonable time when sequential computation is used. When fluid viscosity and density variation, bearing surface elasticity or/and non-Newtonianity are taken into account in lubrication analysis, the task of solving Reynolds equation for film pressure distribution is not only complicated but also time consuming. In this study of parallel computing for the lubrication analysis the models of air-lubricated and THD (Thermohydrodynamic) bearings were used. The Straightforward OpenMP paradigm for SMP (Shared-Memory Processing) parallelism and its extension to a cluster, Cluster OpenMP, were examined. And an open source software, openMosix, which is designed for automatic load balancing in a cluster was also compared for its performance in parallel computing.
In this study, the sequential programs for bearing analysis are easily transformed to parallel ones by adding some OpenMP directives. Then, the programs can be compiled and executed as multithreaded applications. When the two processor cores are used for the air bearing and THD analyses the resulted speedups are 1.53 and 1.66, respectively. The corresponding parallel efficiencies are 15.9% and 41%. In the case of parallel optimization of bearings, an openMosix cluster of 16 computing nodes was used. A speedup of 2.54 (15.9%) was obtained when the lattice search was used in the air bearing optimization. While in the THD lubrication model the DIRECT (DIviding RECTangles) algorithm was used as the optimization tool, a speedup of 6.65 (41%) was obtained in the same cluster. However, the standard DIRECT algorithm can be easily modified to explore the computing resources in a parallel environment to create the so-called embarrassingly parallel DIRECT algorithm. The results of speedup of 10.54 or parallel efficiency of 65.9% were can be achieved.
It is noted that the straightforward OpenMP and openMosix parallel programming models can help to minimize the computing time in solving lubrication problems and implementing optimum design for bearings. The procedure laid out in this study can be applied to other complex lubrication analyses or many computationally expensive applications in engineering.

目 錄

中文摘要 v
英文摘要(Abstract) vi
第一章 前 言 1
1.1 研究背景與動機 1
1.2 研究目的 2
1.3 研究規劃 3
第二章 文獻回顧 4
2.1 流體薄膜潤滑 4
2.2 平行計算技術 6
2.3 應用平行計算技術的潤滑研究 10
第三章 潤滑模型 13
3.1 液動壓潤滑模型 13
3.2 氣體潤滑多孔洞平面軸承模型 14
3.3 熱液動壓潤滑滑塊軸承模型 16
第四章 平行計算 19
4.1 平行計算系統環境 19
4.1.1 分散記憶體架構與共享記憶體架構 19
4.1.2 單一系統鏡像叢集 23
4.1.3 電腦叢集軟體 24
4.2 可平行性分析 26
4.3 計算工作平行化方式 28
4.3.1 高階/低階平行化 28
4.3.2 資料/任務型平行化方式 29
4.3.3 工作分割量平行化方式 30
4.3.4 遮蔽效應及負載平衡機制 30
4.4 平行計算的性能評估指標 32
第五章 結果與討論 33
5.1 平行計算系統環境的參數研究 34
5.1.1 openMosix叢集系統 35
5.1.2 OpenMP共享記憶體架構 39
5.1.3 Cluster OpenMP叢集系統 44
5.2 液動壓潤滑之滑塊軸承性能分析 50
5.3 氣體潤滑軸承 56
5.3.1 軸承性能分析 57
5.3.2 最佳化參數分析 60
5.4 熱液動壓潤滑軸承 64
5.4.1 軸承性能分析 65
5.4.2 最佳化參數分析 69
第六章 結 論 79
參考文獻 81
附錄A 平行計算通用標準 86
附錄B 作業系統核心延伸套件 93
附錄C 平行計算的系統環境 96
附錄D 最佳化演算法 99
附錄E 程式碼 103

圖目錄

圖2-1 序列程式-正弦與餘弦的計算 7
圖2-2 OpenMP平行程式-正弦與餘弦的計算 8
圖2-3 MPI平行程式-正弦與餘弦的計算 8
圖3-1 液動壓潤滑方形滑塊軸承的示意圖 13
圖3-2 氣體潤滑多孔洞平面軸承的示意圖 14
圖3-3 熱液動壓潤滑滑塊軸承的示意圖 16
圖4-1 固定花費發生於多核心叢集系統的位置 23
圖4-2 沒有相依性的程式-計算0°至360°餘弦值 26
圖4-3 具有相依性的計算工作 27
圖4-4 說明高階/低階平行化的波傳程式碼 29
圖5-1 便利使用的程式開發環境 34
圖5-2 叢集系統C和X的固定花費測試程式 36
圖5-3 子運算任務數量與平行計算效率的關係 39
圖5-4 子運算任務數量與平行計算效率的關係(關閉HT功能) 39
圖5-5 測試共享記憶體運算的OpenMP程式碼 40
圖5-6 超執行緒功能對於OpenMP平行程式的影響 41
圖5-7 雙執行緒於OpenMP平行程式的影響(關閉HT功能) 42
圖5-8 執行緒展開匯集操作的示意圖 43
圖5-9 控制CLOMP平行計算模式的設定檔 45
圖5-10 測試用CLOMP平行計算模式固定花費時間的程式碼 47
圖5-11 叢集系統Qib的固定花費時間測試結果 49
圖5-12 有限差分法離散的液膜壓力分佈 52
圖5-13 沿x方向分割壓力分佈網格的示意圖 53
圖5-14 液動壓潤滑分析平行計算的結果(CLOMP功能) 56
圖5-15 氣體潤滑多孔洞平面軸承性能分析的流程 58
圖5-16 氣體軸承設計參數收斂過程(晶格搜尋法) 61
圖5-17 氣體軸承最佳化設計之目標函數收斂過程 62
圖5-18 氣體軸承最佳化設計參數的收斂過程 62
圖5-19 目標函數計算數量的變化(晶格搜尋法) 63
圖5-20 熱液動壓潤滑軸承性能分析的流程 66
圖5-21 陣列讀取順序對於計算效率的影響分析 67
圖5-22 紅黑排序法於SOR方法的影響性分析 68
圖5-23 計算負載量對加速率的影響分析 69
圖5-24 熱液動壓潤滑軸承的負載能力(N)分佈圖 70
圖5-25 熱液動壓軸承最佳化設計前四步驟(DIRECT演算法) 72
圖5-26 熱液動壓軸承最佳化參數的搜尋結果 73
圖5-27 液動壓軸承目標函數的收斂過程 73
圖5-28 目標函數計算數量的變化歷程 74
圖5-29 窘迫式平行DIRECT演算法的前四個步驟 76
圖5-30 窘迫式DIRECT演算法的最佳參數搜尋結果 77
圖5-31 標準和窘迫式DIRECT演算法的垂直浪費比較 77
圖5-32 標準和窘迫式DIRECT演算法的收斂過程比較 78
圖A-1 訊息傳遞(MPI)平行計算過程的示意圖 87
圖A-2 多執行緒(OpenMP)平行計算過程的示意圖 90
圖C-1 長庚大學磨潤實驗室高效能計算之電腦機房 97
圖D-1 晶格搜尋法的流程圖 99
圖D-2 區間分割法(DIRECT)的最佳設計參數搜尋流程 101
圖D-3 具有最佳值潛力區域的辨識圖範例 101
圖E-1 液動壓潤滑分析的序列程式 103
圖E-2 液動壓潤滑分析的OpenMP平行程式 104
圖E-3 氣體軸承性能分析的序列程式 106
圖E-4 氣體軸承性能分析的OpenMP平行程式 108
圖E-5 晶格搜尋法的序列程式 108
圖E-6 晶格搜尋法的openMosix平行程式 109
圖E-7 流體速度場的積分係數計算程式碼(IJK排列) 110
圖E-8 流體速度場的積分係數計算程式碼(KJI排列) 110
圖E-9 熱液動壓液膜壓力分佈計算的程式碼 110
圖E-10 流體薄膜壓力分佈計算的序列程式(紅黑排序法) 111

表目錄

表3-1 液動壓潤滑軸承的幾何尺寸和潤滑數據 14
表3-2 熱液動壓潤滑軸承的潤滑數據和初始條件 18
表5-1 平行計算模式的固定花費類別 35
表5-2 固定花費的測試結果(openMosix叢集系統) 38
表5-3 共享記憶體運算的固定花費測試結果 44
表5-4 分散式共享記憶體運算的環境參數 46
表5-5 液動壓潤滑OpenMP平行程式的效率(X叢集) 54
表5-6 液動壓潤滑OpenMP平行程式的效率(Qib叢集) 54
表5-7 分散式共享記憶體運算於液動壓潤滑分析的計算效率 56
表5-8 氣體軸承的規格和潤滑數據 57
表5-9 氣體潤滑OpenMP平行程式的效率 59
表5-10 液動壓潤滑OpenMP平行程式的效率 69
表A-1 平行計算標準的特性比較 91
表A-2 平行計算標準的優缺點比較 92
表C-1 平行計算環境之硬體規格概要 96
表C-2 叢集系統C之軟、硬體資訊 97
表C-3 叢集系統X之軟、硬體資訊 98
表C-4 叢集系統Qib之軟、硬體資訊 98

[1] Reynolds, O., "On the Theory of Lubrication and its Application to Mr. Beauchamp Tower's Experiments, including an Experimental Determination of the Viscosity of Olive Oil," Philosophical Transactions of the Royal Society of London, pp. 157-234, 1886.
[2] Harrison, W. J., "The Hydrodynamical Theory of Lubrication with Special Reference to Air as a Lubricant," Transactions of Cambridge Philosophical Society, 22, pp. 6-54, 1913.
[3] Fogg, A., "Fluid Film Lubrication of Parallel Thrust Surfaces," in Proceedings of the Institution of Mechanical Engineers, London, UK, 1946.
[4] Dowson, D., "A Generalized Reynolds Equation for Fluid-Film Lubrication," International Journal of Mechanical Sciences, 4, pp. 159-164, 1962.
[5] Ezzat, H. A., and Rhode, S. M., "A Study of Thermohydrodynamic Performance of Finite Slider Bearings," ASME Journal of Lubrication Technology, 95, pp. 298-307, 1973.
[6] Wang, N., and Seireg, A. A., "Thermohydrodynamic Analysis Incorporating Thermal Expansion across the Film," ASME Journal of Tribology, 116, pp. 681-689, 1994.
[7] Bhushan, B., Introduction to Tribology, John Wiley & Sons, New York, USA, 2002.
[8] Wang, J., Qu, S., and Yang, P., "Simplified Multigrid Technique for the Numerical Solution to the Steady-state and Transient EHL Line Contacts and the Arbitrary Entrainment EHL Point Contacts," Tribology International, 34, pp. 191-202, 2001.
[9] Hamrock, B. J., Fundamentals of Fluid Film Lubrication, McGraw-Hill, New York, USA, 1994.
[10] Mongkolwongrojn, M., Aiumpornsin, C., and Thammakosol, K., "Theoretical Investigation in Thermoelastohydrodynamic Lubrication with Non-Newtonian Lubricants under Sudden Load Change," Journal of Tribology, 128, pp. 771-777, 2006.
[11] Wang, J., Kaneta, M., and Yang, P., "Numerical Analysis of TEHL Line Contact Problem under Reciprocating Motion," Tribology International, 38, pp. 165-178, 2005.
[12] 蔡智明，<液膜潤滑數值模型之平行化分析>，長庚大學，碩士論文，2003。
[13] Kennedy, F. E., Citters, D. W. V., Wongseedakaew, K., and Mongkolwongrojn, M., "Lubrication and Wear of Artificial Knee Joint Materials in a Rolling/Sliding Tribotester," Journal of Tribology, 129, pp. 326-335, 2007.
[14] Dobrica, M. B., and Fillon, M., "Thermohydrodynamic Behavior of a Slider Pocket Bearing," Journal of Tribology, 128, pp. 312-318, 2006.
[15] Wang, N., and Chang, C.-Y., "An Application of Newton's Method to the Lubrication Analysis of Air-Lubricated Bearings," Tribology Transactions, 42, pp. 419-424, 1999.
[16] "Message Passing Interface Forum," http://www.mpi-forum.org.
[17] "The OpenMP API Specification for Parallel Computing," http://www.openmp.org.
[18] Suzuki, M., Okuda, H., and Yagawa, G., "MPI/OpenMP Hybrid Parallel Molecular Dynamics Simulation of a Protein Structure on SMP Cluster Architecture," in Proceedings of 2nd MIT Conference on Computational Fluid and Solid Mechanics, pp. 1826-1828, 2003.
[19] Larson, D. J., and Nasstrom, J. S., "Shared- and Distributed- memory Parallelization of a Lagrangian Atmospheric Dispersion Model," Atmospheric Environment, 36, pp. 1559-1564, 2002.
[20] Hoeflinger, J., Alavilli, P., Jackson, T., and Kuhn, B., "Producing Scalable Performance with OpenMP: Experiments with two CFD Applications," Parallel Computing, 27, pp. 391-413, 2001.
[21] Smith, L., and Bull, M., "Development of Mixed Mode MPI/OpenMP Applications," Scientific Programming, 9, pp. 83-98, 2001.
[22] Hammonds, J. S., Saied, F., and Shannon, M. A., "Solving Coupled 3-D Paraxial Wave and Thermal Diffusion Equations with Mixed-mode Parallel Computations," Parallel Computing, 33, pp. 43-53, 2006.
[23] Blikberg, R., and Sørevik, T., "Load Balancing and OpenMP Implementation of Nested Parallelism," Parallel Computing, 31, pp. 984-998, 2005.
[24] Tian, X., Hoeflinger, J. P., Haab, G., Chen, Y.-K., Girkar, M., and Shah, S., "A Compiler for Exploiting Nested Parallelism in OpenMP Programs," Parallel Computing, 31, pp. 960-983, 2005.
[25] Aversa, R., Martino, B. D., Rak, M., Venticinque, S., and Villano, U., "Performance Prediction through Simulation of a Hybrid MPI/OpenMP Application," Parallel Computing, 31, pp. 1013-1033, 2005.
[26] Hadjidoukas, P. E., and Papatheodorou, T. S., "OpenMP Extensions for Master-Slave Message Passing Computing," Parallel Computing, 31, pp. 1155-1167, 2005.
[27] Huang, L., Chapman, B., and Liu, Z., "Towards a More Efficient Implementation of OpenMP for Clusters via Translation to Global Arrays," Parallel Computing, 31, pp. 1114-1139, 2005.
[28] Nakajima, K., "Parallel Iterative Solvers for Finite-Element Methods Using an OpenMP/MPI Hybrid Programming Model on the Earth Simulator," Parallel Computing, 31, pp. 1048-1065, 2005.
[29] Park, I., and Kim, S. W., "Study of OpenMP Applications on the InfiniBand-Based Software Distributed Shared-Memory System," Parallel Computing, 31, pp. 1099-1113, 2005.
[30] "TOP500 Project," http://www.top500.org.
[31] Meuer, H. W., "The TOP500 Project: Looking Back over 15 Years of Supercomputing Experience," University of Mannheim & Prometeus GmbH, Germany, pp. 1-14, 2008.
[32] Strohmaier, E., Dongarra, J. J., Meuer, H. W., and Simon, H. D., "Recent Trends in the Marketplace of High Performance Computing," Parallel Computing, 31, pp. 261-273, 2005.
[33] Intel, "Cluster OpenMP* User's Guide." vol. 9.1: http://developer.intel.com/.
[34] Wang, N., Chan, C.-W., and Tsai, C.-M., "Performance Evaluation of a Cluster OpenMP Computing System in a Multi-objective Optimization of Air Bearing," in 2008 STLE 63rd Annual Meeting and Exhibition, Cleveland, Ohio, USA, 2008.
[35] "Lahey Computer Systems," http://www.lahey.com.
[36] "MOSIX," http://www.mosix.com.
[37] Olsson, D. M., and Nelson, L. S., "The Nelder-Mead Simplex Procedure for Function Minimization," Technometrics, 17, pp. 45-51, 1975.
[38] Wang, N., and Chang, Y.-Z., "A Hybrid Search Algorithm for Porous Air Bearings Optimization," Tribology Transactions, 45, pp. 471-477, 2002.
[39] "The openMosix Project," http://openmosix.sourceforge.net/.
[40] Wang, N., and Chen, L.-W., "A Divide-and-Conquer Parallel Computing Scheme for the Optimization Analysis of Tribological Systems," Tribology Transactions, 47, pp. 313-320, 2004.
[41] 陳立偉，<電腦叢集應用於多孔洞氣靜壓軸承之最佳化設計>，長庚大學，碩士論文，2003。
[42] Wang, N., and Yen, M.-L., "A Parametric Study of an Open-Source Distributed Computing Environment for Tribological Studies," Tribology Transactions, 48, pp. 1-8, 2005.
[43] 葉明隴，<液膜潤滑平行計算效率之參數研究>，長庚大學，碩士論文，2004。
[44] Wang, N., "A Parallel Computing Application of the Genetic Algorithm for Lubrication Optimization," Tribology Letters, 18, pp. 105-112, 2005.
[45] Wang, N., and Tsai, C.-M., "Application of Thread-Level Parallel Programming to Thermohydrodynamic Lubrication Computation," Tribology Transactions, 49, pp. 473-481, 2006.
[46] Huebner, K. H., "Application of Finite Element Methods to Thermohydrodynamic Lubrication," International Journal for Numerical Methods in Engineering, 8, pp. 139-165, 1974.
[47] Almasi, G. S., and Gottlieb, A., Highly Parallel Computing, Benjamin-Cummings publishers, Redwood City, CA, USA, 1989.
[48] Sloan, J. D., High Performance Linux Clusters with OSCAR, Rocks, openMosix & MPI, 1st Ed., O'Reilly Media, Sebastopol, CA, USA, 2004.
[49] Intel, "Extending OpenMP* to Clusters, White Paper," http://www.intel.com/.
[50] Wilkinson, B., and Allen, M., Parallel Programming: Techniques and Applications Using Networked Workstations and Parallel computers, Prentice-Hall, New Jersey, USA, 1999.
[51] Bernstei, A. J., "Analysis of Programs for Parallel Processing," IEEE Transactions on Electronic Computers, 15, pp. 757-762, 1996.
[52] Gropp, W., Lusk, E., and Thakur, R., Using MPI-2: Advanced Features of the Message Passing Interface, MIT Press, Cambridge, Massachusetts, USA, 1999.
[53] Wallin, D., Löf, H., Hagersten, E., and Holmgren, S., "Multigrid and Gauss-Seidel Smoothers Revisited: Parallelization on Chip Multiprocessors," in Proceedings of the 20th Annual International Conference on Supercomputing, 2006.
[54] Chaudhary, V., Hase, W. L., Jiang, H., Sun, L., and Thaker, D., "Experiments with Parallelizing Tribology Simulations," The Journal of Supercomputing, 28, pp. 323-343, 2004.
[55] Wang, N., Chang, Y.-Z., and Tsai, C.-M., "The Application of Nearly Embarrassingly Parallel Computation in the Optimization of Fluid-Film Lubrication," Tribology Transactions, 47, pp. 34-42, 2004.
[56] "National Center for High-Performance Computing," http://www.nchc.org.tw.
[57] Gerald, C. F., and Wheatley, P. O., Applied Numerical Analysis, Addison Wesley Publishing Company, San Luis Obispo, USA, 1998.
[58] Chandra, R., Dagum, L., Kohr, D., Maydan, D., McDonald, J., and Menon, R., Parallel Programming in OpenMP, 1st Ed., Morgan Kaufmann, San Francisco, CA, USA, 2000.
[59] Press, W., Teukolsky, S., Vetterling, W., and Flannery, B., Numerical Recipes in Fortran, Cambridge University Press, New York, USA, 1992.
[60] Jones, D. R., Perttunen, C. D., and Stuckman, B. E., "Lipschitzian Optimization without the Lipschitz Constant," Journal of Optimization Theory and Applications, 79, pp. 157-181, 1993.
[61] Zhu, H., and Bogy, D. B., "DIRECT Algorithm and Its Application to Slider Air-Bearing Surface Optimization," IEEE Transactions on Magnetics, 38, pp. 2168-2170, 2002.
[62] Gropp, W., Lusk, E., and Skjellum, A., Using MPI: Portable Parallel Programming with the Message-Passing Interface, 2nd Ed., MIT Press, Cambridge, Massachusetts, USA, 1999.