摘要
在热物性反问题中,温度对参数的敏感度(简称敏感度)是一个重要的并行计算算法研究的内容。对“敏感度”进行理论分析和计算,进而开发高效并行算法是作者所在课题组多年并行算法研究的深入工作。
论文叙述了“敏感度”的研究现状和研究进展,研究了非均匀网格下虚边界预测(VBF)的并行算法,讨论了基于两重网格的非均匀网格VBF并行算法以及非均匀变步长并行计算方法,给出了热物性反问题中温度对参数的敏感度的初边值问题,以及多个参数表达的热物性系数对应的敏感度初边值问题,计算结果表明:对不同的参数,敏感度的函数值大小不同。由此建立了基于敏感度的非均匀网格虚边界预测反问题高效并行算法。
本文用8个节点处理器进行了并行计算,并行计算效率为85%。
本文的主要创新点是:
(1)研究了基于两重网格非均匀步长的虚边界预测的并行算法。
在粗细两重网格上,取步长不同的非均匀网格,在子区域虚拟边界上,建立边界函数值预测方法,算例表明该算法比直接对各子区域进行迭代求解的方法有更高的求解效率,计算时间大约为直接迭代求解的2/3左右。
(2)建立了热物性反问题中温度对参数的敏感度的初边值问题及并行计算数学模型。
根据温度对参数的敏感度的定义,建立了敏感度的初边值问题,构造了区域分裂并行计算模型,对单参数和多参数的热物性反问题参数的敏感度进行了并行计算,得到敏感度随时间和空间变化的数据。
(3)构造了基于温度对参数敏感度的两重网格变步长虚边界预测的反问题高效并行算法。
对敏感度计算数据进行分析,发现参数不同,温度的敏感度也不同。因而,提出了根据不同的参数,选取不同计算步长的并行算法。算例表明,在相同的精确度下,该算法比等步长算法减少40-65%的计算量。
本文得到国家自然科学基金项目(项目编号:60173046,69773021)、中科院软件所计算机科学国家重点实验室开放课题基金(批准号:SYSKF1009)、湖北省自然科学基金面上项目(2005ABA227)的资助。
The Temperature Sensitivity of Parameter (TSP) is an important science research project in the invert heat conduct research to find new efficient parallel algorithms. And for develop efficient parallel algorithm is the depth of the authors' research group for many years.
This research describes the progress of the temperature sensitivity, studies non-uniform grid virtual boundary prediction on parallel algorithm, parallel computing based on two-level non-uniform grid VBF parallel algorithm. The Thermal parameters sensitivity analysis of initial boundary value problems sensitive initial boundary value problem is taking into account, Considered the expression of multiple parameters corresponding to the parallel computing method of sensitivity initial boundary value problems, the calculation results show that:for different parameters, calculation of sensitivity values are not the same. The efficient parallel algorithm of temperature parameter sensitivity is build. Finally,this article used8node processors for parallel computing, and the efficiency of parallel computing is85%.
The main innovation points of this dissertation are:
(1) The parallel algorithm with virtual boundary forecast based on two-grid non-uniform grids.
On the double grid, the different steps of the non-uniform grid are given. On the region of virtual boundary value, establish forecast method of boundary function, the results of this algorithm show higher efficiency than the method of solving the direct iterative method that used to solve the sub-region, the computing time is about direct iterative method is about2/3.
(2) Inverse heat conduction problem is used to establish the initial boundary value problem of temperature sensitivity parameter,and to cstablish the parallel computing model. According to the temperature on the sensitivity definition, establishes the initial boundary value problem of sensitivity, constructs the region splitting parallel computing model, for single and multiple parameters inverse heat conduction problem parameter sensitivity were calculated, be sensitive with the change of time and space data.
(3) The fast domain splitting varied step parallel algorithm based on temperature parameter sensitivity data. According to the data of the sensitivity for different parameters, this research find the temperature parameter sensitivity is different. Therefore, a different step length parallel algorithm is obtained based on the polynomial coefficients.
引文
[1]P.C.Sabatier.Inverse problems:an introduction,Inverse problems,1985(1):1-4.
[2]张宏.基于QPSO算法的二维热传导反问题的研究[D].无锡:江南大学2007.
[3]熊向团.抛物型偏微分方程中几类反问题的正则化理论及算法[D].兰州:兰州大学应用数学系,2007.
[4]陈艳.热传导反问题的高效分布式并行算法研究[D].武汉:武汉理工大学2007.
[5]杨维,李歧强.粒子群优化算法综述[J].中国工程科学.2003,6(5):86-94.
[6]蒋录全.地震数据反演中的Monte-Carlo算法、模拟退火算法(SA)及遗传算法(GA)[J].西南石油学院学报,1995,17(3):29-36.
[7]许小勇.热传导方程稳恒源项识别的模拟退火算法[J].海南大学学报自然科学版.2006,24(4):344-347.
[8]申鼎才.并行遗传算法在热传导反问题中的应用[D].武汉:武汉理工大学计算机学院,2005.
[9]Guo Qingping, Shen Dingcai, GuoYucheng, C.-H. Lai, Parallel Genetic Algorithms for the solution of Inverse Heat Conduction Problems [J]. International Journal of Computer Mathematics (IJCM), March 2007:1-9.
[10]杨海天,胡国俊.共轭梯度法求解多宗量稳态传热反问题[J].应用基础与工程科学学报,2002,10(2):174-180.
[11]Xie, Jianli, Zou Jun. An improved model function method for choosing regularization parameters in linear inverse problems [J]. Inverse Problems, June,2002,18(3):631-643.
[12]陈国良,孙广中,徐云等.并行计算的一体化研究现状与发展趋势[J].科学通报.2009,54(8):1043-1049.
[13]陈国良,孙广中,徐云等.并行算法研究方法学[J].2008,31(9):1493-1502.
[14]陈勇,陈国良,李春生,何家华.SMP机群混合编程模型研究[J].小型微型计算机系统,2004,25(10):1763-1767.
[15]Qingping Guo. Network Computing Performance Evaluation in Message Passing Environment [J].the Journal of Parallel Algorithms and Applications,2003,18(4):217-224.
[16]张武生,薛巍,李建江等.MPI并行程序设计实例教程.北京:清华大学出版社.2009.
[17]Qingping Guo,Yakup Paker,Shesheng Zhang,Dennis Parkinson and Jianing Wei.Optimum tactics of parallel multi-grid algorithm with virtual boundary forecast method running on a local network with the PVM platform[J].Journal of Computer Science and Technology,2000,15(4):355-359.
[18]Online Computer Library Center, Inc. The Message Passing Interface Standard [EB/OL].[2012-03-20].http://www.mcs.anl.gov/research/projects/mpi/.
[19]刘杰,肖金生,覃峰等.陶瓷/金属梯度热障涂层圆筒的传热与热应力有限差分分析[J].武汉理工大学学报,2002,26(3):379-382.
[20]朱宗柏,曾宪友,肖金生.陶瓷/金属梯度材料瞬态传热的有限差分分析[J].武汉理工大学学报,2001,23(6):18-20.
[21]陆金甫,关治.偏微分方程数值解法[M].北京:清华大学出版社,2004.
[22]John von Neumann.On Regular Rings[J].Proc Natl Acad Sci USA.1936,22(12):707-713.
[23]郭庆平,章社生,卫加宁.在多层网格区域分裂并行计算中虚拟边界条件预测算法[J].数值计算与计算机应用,2000,4:287-293.
[24]李庆扬,王能超,易大义.数值分析[M].北京:清华大学出版社,2001:233-243.
[25]Yimin Xuan,Qiang Li. Investigation on Convective Heat Transfer and Flow Features of Nanofluids[J].Journal of Heat Transfer,2003,125(1):151-156.
[26]Langton, C,GArtifical Life [M].Redwood:Addison-wesloy,1989,1-47.
[27]Reynolds. Flocks, herds, and schools. A distributed behavioral model [J]. Computer Graphic. 1987,21(4):25-34.
[28]E. O. Wilson Sociobiology:The New Synthesis [M]. Belknap Press of Harvard University Press.2000.
[29]Kennedy J, Eberhart R. Particle swarm optimization. Proceedings of IEEE International Conference on Neural Networks[C]. Piscataway:IEEE Service Center,1995:1942-1948.
[30]Eberhart, R. A new optimizer using particle swarm theory [A].Proceedings of the Sixth International Symposium on Micro Machine and Human Science[C].Piscataway NJ:IEEE Service Center,1995,39-43.
[31]Frans van den Bergh.Cooperative Learning in Neural Networks using Particle Swarm Optimizers[J].South African Computer Journal,2000(11):84-90.
[32]邹大力.基于计算智能的结构损伤识别研究[D].大连理工大学.2005博士论文.
[33]Shi Y, Eberhart R C.A modified Particle Swarm Optimizer. Proceedings of the IEEE International Conference on Evolutionary Computation [C]. IEEE Press, Piscataway, NJ, 1998:69-73.
[34]Shi Y, Eberhart R C. Empirical Study of Particle Swarm Optimization. Proceedings of the 1999 Congress on Evolutionary Computation [C]. Piscataway,NJ,IEEE Service Center, 2001.
[35]林川,冯全源.一种新的自适应粒子群优化算法[J].计算机工程,2008,34(7):181-183.
[36]吕振肃,侯志荣.自适应变异的粒子群优化算法[J].电子学报,2004,32(3):416-420.
[37]阳春华,谷丽姗.自适应变异的粒子群优化算[J].计算机工程,2008,34(16):188-190.
[38]谭爱国,琚长江.多自适应策略的粒子群优化算法及应用[J].计算机系统应用,2012,21,(2):163-166.
[39]Ananth Grama, Anshul Gupta, Goerge Karypis, Vipin Kumar.并行计算导论[M].张斌,毛国勇,程海英等译.北京:机械工业出版社,2005:63-103.
[40]张林波,迟学斌,莫则尧,李若.并行计算导论[M].北京:清华大学出版社,2006."325-351.
[41]李晓梅,吴建平.数值并行算法与软件[M].北京:科学出版社,2007"152-182.
[42]Michael J.Quinn. MPI与OpenMP并行程序设计[-M].陈文光,武永卫等译.北京:清华大学出版社,2004:128-141.
[43]Wen-Lih Chen, Yu-Ching Yang, Win-Jin Chang, Haw-Long Lee. Inverse problem of estimating transient heat transfer rate on external wall of forced convection pipe[J]. Energy Conversion and Management,49 2008:2117-2123.
[44]Xie,Jianli;Zou Jun.An improved model function method for choosing regularization parameters in linesr inverse problems.Inverse Problems,V18,N3,June,2002,p631-643.
[45]Nicholas Z., J. C. Liu, An analiysis of 2-D linear inverse heat transfer problem using an integral method[J], Numerical heat transfer,1988, Vo 113,527-533.
[46]Jingbo Wang and Nicholas Zabaras,Using Bayesian statistics in the estimation of heat source in radiation[J], International Journal of Heat and Mass Transfer, Vol 48, No.1,2005, 15-29.
[47]Johansson B. T.; Lesnic D.; Reeve T.,A method of fundamental solutions for the one-dimensional inverse Stefan problem [J], Appl. Math. Model,2011, Vol.35 No.9, 4367-4378.
[48]Tian Na; Sun Jun; Xu Wenbo, Estimation of unknown heat source function in inverse heat conduction problems using quantum-behaved particle swarm optimization[J], International Jour, of heat and mass transfer,2011,Vol.54, No.17-18,4110-4116.
[49]Adili A.; Hasni N.; Kerkeni C., An inverse problem based on genetic algorithm to estimate thermophysical properties of fouling[J], International J. of thermal science, 2010,Vol.49,No.6:889-900.
[50]于杰,陈敬超,洪振军,周晓龙,Cu-FeS复合材料导热性能的计算研究,[J],复合材料学报,2010(5),136-142.
[51]周静伟,毛谦敏.淬火测试探头表面冷却特性的反问题辨识[J].中国计量学报,1998(2):85-89.
[52]顾元宪,周业涛,陈飚松,林巍,基于灵敏度的热传导辨识问题求解方法[J],土木工程学报,2002(3),94-98。
[53]薛齐文,非线性热传导反问题数值求解,宁夏大学学报,2010(4),40-48.
[54]赵莉,程荣.一种并行BP神经网络的动态负载平衡方案[J],计算机技术与发展,2006,16(7):67-69.
[55]N. Zabaras,et.An Analysis of Inverse Heat Transfer Problems With Phase Changes Using an Integral Method[J], J. Heat Transfer,1988,Vol 110, No.3,554-561.1988.
[56]J.Maria,et. Filter digital form of two future temperature methods for the inverse heat conduction:A spectral comparison[J], Numerical Methods in Biomedical Engineering, Vo126, No.5,554-573, May 2010.
[57]林建生.粒子群算法及神经网络算法在热传导反问题求解中的应用研究[D].武汉:武汉理工大学计算机学院,2010.
[58]李灿,高彦栋等.热传导问题的MATLAB数值计算.华中科技大学学报(自然科学版),2002,9.
[59]Deng,S;Hwang,Y.Applying neural networks to solution of forward and inverse heat conduction problems, International Journal of Heat and Mass Transfer,V49,n25-26, December 2006,p 4732-4750.
[60]Piatkowski Grzegorz, Ziemiandski Leonard,The solution of an inverse problem in plates by means of artificial neural networks, Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science), v 3070, Artificial Intelligent and Soft Computing-ICAISC 2004,2004, p 1087-1092.
[61]王秀春,智会强等.多宗量导热反问题求解的神经网络法[J].航空动力学报,2004,19(4):525-529.
[62]Guo Qingping, Shen Dingcai.The Application of Parallel Genetic Algorithm On Heat Conduction Inverse Problem, DCABES and ICPACE Joint Conference on Distributed Algorithms for Science and Engineering Proceedings, London, UK,2005,8.
[63]Wang, Ruili; Wu, Jiansheng; Kemp, Ray. A Genetic-Algorithm-based Neural Network Approach for Short-term Traffic Flow Forecasting[C]. Second International Symposium on Neural Network. Proceedings,2005,3498(3):965-970.
[64]Hong,lu;Mu Zhichun. Application of immune genetic algorithm in BP neural networks. Beijing Keji Daxue Xuebao/Journal of University of Science and Technology Beijing, v28,October,2006, p 997-1000.
[65]Lin Shih-Ming, A sequential algorithm and error sensitivity analysis for the inverse heat conduction problems with multiple heat sources[J], Appl. Math. Modelling,2011,Vol 35 No.6页:2607-2617.
[66]熊盛武,卢孝强.偏微分方程参数识别问题的遗传程序设计方法.武汉理工大学学报(信息与管理工程版),2003,6.
[67]王万斌,闵涛等.一维抛物型方程参数识别反问题的数值解法.西安理工大学学报,2003,19.
[68]韩莉芬.基于神经网络的薄板冲压成形中的反演问题研究[D].湖南大学.2006博士论文.
[69]Comparison of various methods for simultaneous retrieval of surface emissivities and gas properties in gray participating media. Deiveegan, M. (Heat Transfer and Thermal Power Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Madras); Balaji, C.; Venkateshan, S.P. Source:Journal of Heat Transfer, v 128, n 8,2006, p 829-837. DOI:10.1115/1.2227037. Database:Compendex. (AN 065210336568).
[70]韩光明.基于机群计算的热传导反问题高效分布式并行算法设计[D].武汉理工大学.2005硕士论文.(指导老师:郭庆平)
[71]申鼎才.并行遗传算法在热传导反问题中的应用[D].武汉理工大学.2004硕士论文.(指导老师:郭庆平)
[72]杨磊.基于PC机群环境MPI的多重网格并行算法研究[D].武汉理工大学.2003硕士论文.(指导老师:郭庆平)
[73]Parallel programming characteristics of a DSP-based parallel system. Gao, Shu (School of Computer Science, Wuhan University of Technology); Guo, Qing-Ping. Source:Journal of Zhejiang University:Science, v 7, n 10, October,2006, p 1669-1675. DOI: 10.1631/jzus.2006.A1669. Database:Compendex. (AN 064510226394).
[74]Hwang, Y., Deng, S. Applying neural networks to the solution of forward and inverse heat conduction problems. International Journal of Heat and Mass Transfer vol.49, no.25-26: 4732-50 Dec.2006. INSPEC:9313831. (AN 9313831).
[75]Jung, BS, Author, Reprint Author Jung Bup Sung Jung, Bup Sung, Kim, SK, et al. Inverse estimation of surface temperature in nanoscale using the artificial neural network. HT2005: PROCEEDINGS OF THE ASME SUMMER HEAT TRANSFER CONFERENCE 2005, VOL 1,403-410.2005. ISTP:000243378100052. (GA BFN92).
[76]Wu, Jianhua; Li, Na; Li, Jinghui; Chen, Lanfeng. Genetic algorithm and neural network design for face classifier.Yi Qi Yi Biao Xue Bao/Chinese Journal of Scientific Instrument, v 27, n SUPPL., June,2006, p 2230-2231
[77]Yinghua, Lu; Jialing, Han; Jun, Kong; Yulong, Yang; Gang, Hou. A novel color image watermarking method based on genetic algorithm and hybrid neural networks。Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), v 4259 LNAI, Rough Sets and Current Trends in Computing-5th International Conference, RSCTC 2006, Proceedings,2006, p 806-814.
[78]Hong,lu;Mu Zhichun. Application of immune genetic algorithm in BP neural networks. Beijing Keji Daxue Xuebao/Journal of University of Science and Technology Beijing, v28,October,2006, p 997-1000.
[79]Sampath, Suresh; Singh, Riti. An integrated fault diagnostics model using genetic algorithm and neural networksJournal of Engineering for Gas Turbines and Power,Volume 128,January 2006,p 49-56.
[80]陈艳,郭庆平.并行遗传算法在导热反问题中的应用[J],计算机与数字工程,ISSN: 1672-9722.0.2007-03-005
[81]N.Drosinos,N.Koziris.Performance Comparison of pure MPI vs Hybrid MPI-OpenMP Parallelization Models on SMP Clusters,in:Proceedings of the 18th International Parallel and Distributed Processing Symposium 2004(IPDPS 2004),Santa Fe,New Mexico,April 2004.
[82]M.D.Jones,R.Yao,Parallel OSEM Reconstruction speed with MPI,OpenMP,and Hybrid MPI-OpenMP Programming Models,in:In IEEE Nuclear Science Symposium and Medical Imaging Conference Record,Rome,Italy,October 2004.
[83]OpenMP,The OpenMP ARB.http://www.openmp.org/.
[84]Message Passing Interface Forum.MPI-2:A message passing interface standard.High
[85]David R.Butenhof.Programming with POSIX Threads.Addison Wesley,1997.
[86]Quinn M J,Parallel Programming in C with MPI and OpenMP[M].McGraw-Hill Companies,Inc,2004.
[87]刘衍民,赵庆祯,牛奔.基于自适应动态邻居和广义学习的改进粒子群算法[J].计算机应用,2010,(10).
[88]刘衍民;隋常玲;牛奔;解决约束优化问题的改进粒子群算法.2011.
[89]Guo Qingping(郭庆平), Shen Dingcai (申鼎才), GuoYucheng (郭羽成), C.-H. Lai, Parallel Genetic Algorithms for the solution of Inverse Heat Conduction Problems. International Journal of Computer Mathematics (IJCM), March 2007, p1-9.
[90]刘祥港;在Linux平台下基于MPI的并行PC集群搭建的实现[J].Computer Knowledge and Technology 2011.
[91]王勇超,张璟,王新卫,马静.基于MPICH2的高性能计算集群系统研究[J].计算机技术与发展,2008,(09).
[92]葛美宝;徐定华;一类热传导方程逆时反问题的数值解法Journal of Zhejiang Normal University(Natural Sciences).2011.
[93]Xiang-Tuan Xiong,Chu-Li Fu,Zhi Qian. Two numerical methods for solving a backward heat conduction problem[J].Applied Mathe-matics and Computation.2006,179:370-377.
[94]王长有.椭圆型边值问题的比较方法及解的存在性[J].安徽大学学报(自然科学版),2006,(03).
[95]Jin Yixiong,Cheng Haozhong,Yan Jianyong,et al. New discrete method for particle swarm optimization and its application in transmission network expansion plan-ning[J].Electric Power Systems Research,2007,77 (3/4):227-233.
[96]Qun Niu,Bin Jiao,Xingsheng Gu. Particle swarm optimization combined with genetic operators for job shop scheduling problem with fuzzy processing time[J].Applied Mathematics and Computation,2008, (205):148-158.
[97]Mohammed El-Abd,Hassan Hassan,Mohab Anis,et al. Discrete cooperative particle swarm optimization for FPGAplacement[J].Applied soft computing,2010, (10):284-295.
[98]王巍,赵国杰.粒子群优化在资源受限工程调度问题中的应用[J].哈尔滨工业大学学报,2007,(04).
[99]郑超,高连生.蚁群算法在资源受限项目调度问题中的应用[J].计算机工程与应用,2005,(27).
[100]Kolisch R,Hartmann S. Experimental investigation of heuristics for resource-constrained project scheduling:An update.European Journal of Operational Research,2006,174 (1):23-37.
[101]Gregorio Toscano Pulido,Carlos A Coello. A constraint-handlingmechanism for particle swarm optimization[C].2004 Congress onEvolutionary Computation(CEC'2004)June 2004.Portland,Oregon:IEEE,2004,1:1396-1403.
[102]Coath G,Halgamuge S K. A comparison of constraint-handlingmethods for the application of particle swarm optimization to con-strained nonlinear optimization problems[C]. Proceedings of the Congress on Evolutionary Computation 2003(CEC'2003), December2003.
[103]Piscat-away,New Jersey. Canberra,Australia:IEEE Service Center,2003,4:2419-2425.
[104]HuX,Eberhart R C,Shi Y. Engineering optimization with particleswarm[C].Proceedings ofthe 2003 IEEE Swarm IntelligenceSymposium. Indianapolis,Indiana,USA:IEEEService Center,2003,:53-57.
[105]郭庆军,李慧民,赛云秀.非线性约束优化的算法分析[J].计算机工程与应用,2009,(19).
[106]严阳,周育人.解非线性约束规划问题的分组粒子群算法[J].电脑与信息技术,2009,(04).
[107]Lin Jiansheng, Guo Qingping, Qi Jingjing. A Back Propagation Neural Network Parallel Algorithm for Inverse Heat Conduction Problems. DCABES 2009 PROCEEDINGS [C], Wuhan,2009:38-42.
[108]ZhouMing,GuoQingPing.An Improved Elitist Strategy Fighting Premature Convergence. DCABES 2009 PROCEEDINGS [C], Wuhan,2009:73-75.
[109]Wei-min ZHONG, Shao-jun LI, Feng QIAN.θ-PSO:a new strategy of particle swarm optimization. Journal of Zhejiang University SCIENCE A [J].2008,9(6):786-790.
[110]Qi Jingjing, Guo Qingping, Lin Jiansheng, Zhou Ming, Zhang Shesheng. Parallel Particle Swarm Optimization Algorithm of Inverse Heat Conduction Problem. DCABES 2010 PROCEEDINGS [C], Hong Ko ng,2010:5-9.