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1、基于粒子群优化算法下的灰色系统船闸货运量预测基金项目：国家自然科学基金资助项目（50479032）作者简介：杨星(1978-)，男，湖北人，博士研究生，主要从事交通、海洋方面的研究。杨星1 王娅娜2（1中山大学河口海岸研究所，广州 510275；2 河海大学交通与海洋学院，南京 210098）摘 要：采用灰色系统理论，建立了基于GM(1,1)的船闸货运量预测模型，模型参数计算分别采用粒子群优化算法和最小二乘法，两者进行对比发现，两者预测误差相当，但是粒子群优化算法可以避免繁琐的矩阵运算而优于最小二乘法，文章最后应用基于粒子群优化算法的灰色系统模型进行了船闸货运量的预测。可以认为，基于粒子群优化
2、算法的灰色系统船闸货运量预测方法值得在水运界进行推广和探讨。关键词：粒子群优化；灰色理论；船闸；货运量；预测模型中图分类号：F502 文献标识码：A 文章编号：Forecast of the Lock Freight VolumeBased on Grey System Theory and Particle Swarm OptimizationYang xing1 Wang ya-na2(1. Institute of Estuarine and Coastal Studies, Sun Yat-sen University, Guangzhou 510275 ; 2.College of
3、Traffic , Hohai University , Nanjing 210098 )Abstract :Based on the grey system theory , the GM ( 1,1 ) forecast model of the lock freight volume is established . The particle swarm optimization and the least square method are adopted respectively to compute the model parameters. Consequent results
4、are analyzed and compared , which shows the particle swarm optimization is better than the least square method. The future lock freight volume is predicted by using the model and the grey forecast method based particle swarm optimization is recommended to be used in the waterway engineering . Key wo
5、rds: particle swarm optimization ;grey theory ; lock; freight volume ; forecast model引言航道货运量预测是制定有关政策、编制运输发展规划和运输企业经营决策、日常管理的依据1,也是进行航运规划, 确定各枢纽的通航建筑物规模最直接和最重要的基础性工作。目前常用的某些预测方法（回归分析、神经网络法25、移动平均法、指数平滑法等），若样本较小，常造成较大误差 ，使预测目标失效。若样本较大，则计算复杂，不易应用。灰色系统理论是研究解决灰色系统分析、建模、预测、决策和控制的理论。灰色预测的模型所需建模信息少，运算方便，建模
6、的精度高，在各种预测领域都有着广泛的应用67。近年来，在交通流量的预测中，应用灰色理论获得了较好的效果813。但在内河运量的预测却是从2000开始才陆续有学者进行研究1415，这些研究主要集中在中短期预测领域，对于长期预测尚有待于时间的检验和进一步的探讨论证。本文拟将灰色系统理论应用于淮阴船闸的货物运输量预测上，首先建立基于GM (1,1 )的船闸货运量预测模型，GM(1,1)模型是应用最广的一类模型，是由一个只包含两个参数变量的一阶微分方程构成的模型。计算时需要将模型微分方程转化为矩阵形式，由于参数变量只有两个，而方程数却有多个，当矩阵的秩大于2时，方程组无解，传统的做法是用最小二乘法得到最
7、小二乘解。本文通过粒子优化算法可以避免矩阵运算，降低运算难度。文章最后通过与实测结果的对比分析与验证，分析研究基于粒子优化算法灰色系统模型预测船闸货运量时的精度，并比较了基于粒子优化算法和基于最小二乘法灰色系统预测法的预测精度。1 基于粒子群优化算法下的灰色预测模型GM (1,1 ) 的建立GM (1,1 ) 模型是灰色系统理论中最简单常用的预测模型，也是其余灰色预测法建模的基础。GM (1,1 ) 表示一阶的、具有两个参数变量的微分方程，在实际应用中，它不是连续的，而是经数据系列处理过的离散方程。1.1 模型的建立GM (1,1)表示一阶的、具有两个参数变量（a,b）的微分方程模型，具体形式
8、如下： （1）设有数列共有n个观测值，表示为：， （2）对做一阶累加，生成新的序列： （3） 令为的均值序列 （4） 则GM(1,1)的定义型，即GM(1,1)的灰微分方程模型为 （5）以代入上式，有 （6）对上述离散方程组，用随机粒子群优化算法求解，可得。把所求得的系数代入到公式，然后求解微分方程，得到GM (1,1)预测模型为： (7)累减后得到原始数据序列的预测公式：，并且规定。以上所述的即是GM (1,1)的建模过程，也是建立船闸货运量灰色预测模型的基础。1.2 粒子群优化算法（PSO）粒子群优化算法由Kennedy和Eberhart在1995年提出，该算法模拟鸟集群飞行觅食的行为。设
9、想一群鸟在随机搜寻食物，这个区域里只有一块食物，所有的鸟知道食物在哪里，但他们知道目前距离食物还有多远，那么找到食物的最简单的方法就是找寻距离食物最近的鸟的周围区域，及根据自身飞经验判断食物的所在。每个寻优的问题解被想像成一只鸟或者称为粒子。所有的粒子有一个目标函数以判断该粒子目前位置的好坏，每一个粒子必须具有记忆性，能记得所搜寻到的最佳位置。每一個粒子还有一个速以决定飞行的距离和方向。粒子群优化算法流程如下：（1）初始化：将族群做初始化，以随机的方式求出每一个粒子（鸟）的初始位置与速；（2）评估：依据目标函数计算出其目标值以作为判断每一个粒子所处位置的好坏；（3）查找个体极值：找出每一个粒子
10、到目前为止搜寻过程中的最佳解，这个最佳解称为个体极值；（4）查找全局极值：找出所有粒子到目前为止所搜寻到的整体最佳解，这个最佳解称为全局极值；（5）更新粒子速度和位置：假设搜索空间为D维，粒子群中第i个粒子的两个状态量位置和速度分别用和表示，该粒子迄今为止搜索到的最好位置（即历史最优值）记为，所有粒子迄今为止搜索到的最好位置记为。那么该粒子的速度和位置更新等式（第d维）可表示为: （8）式中：Vid表示每一个粒子在第d维的速度；i表示粒子的编号，粒子数一般取50，对于比较难的问题或者特定类别的问题,粒子数可以取超过100的数；d表示维；w表示惯性权重，常数，用来控制粒子的历史速度对当前速度的影
11、响程度，一个较大的w 值能加速粒子搜索新的区域，因此，选取适当的w值能平衡PSO算法的全局和局部搜索能力，从而得到更好的解。本文取为0.8；c1、c2表示学习常数，本文取2；Rand()表示在范围0,1内取值的随机函数；Pid表示每一个粒子到目前为止，所出现的最佳位置；Pgd表示所有粒子到目前为止，所出现的最佳位置；Vmax和Vmin是常数，决定粒子在一个循环中最大的速度,人为设定。式（8）中第1部分为粒子先前的速度，它使粒子有在搜索空间中扩张的趋势，从而使算法具有全局搜索的能力；第2部分为“认知”部分，表示粒子吸取自身经验知识的过程；第3部分为“社会”部分，表示粒子学习其它粒子经验的过程，表
12、现了粒子间信息的共享与社会协作。1.3粒子群优化算法求解灰色系统预测模型参数变量a,b参照公式(6),本文取船闸货运量问题的目标函数为： （9）其中，F表示为： （10）具体计算步骤如下：(1) 初始化粒子群:由于公式（9）中只存在两个变量（a，b），搜索空间为2维。取粒子数=50、c1=2、c2=2、w=0.8、最大迭代数=1000；(2) 假设a的取值范围为a1，a2，b的取值范围为b1，b2,则第一维和第二维50个粒子初始位置可以分别设置为： (11)式中：a和b的取值范围可以先取大，先在一个较大的范围内进行搜索，然后根据结果逐步缩小搜索范围，直到最优解满足要求为止；(3)第一维和第二维
13、50个粒子的初始速度可以分别设置为： (12)式中：和代表第一维的速度最大和最小值，和代表第二维的速度最大和最小值；(4) 用目标函数评价所有粒子；(5) 将初始评价值作为个体历史最优解Pid,并寻找群体内最优解Pgd。重复执行以下步骤,直到满足终止条件或达到最大迭代次数，其中注意事项包括：(1) 对每一个粒子,按式(8)计算和。当、超过其范围时,按边界取值；(2) 用式(9) 评价所有粒子，评价值为；(3) 若某个粒子的当前评价值优于其历史最优评价值,则记当前评价值为该历史最优评价值,同时记当前位置为该粒子历史最优位置,更新Pid；(4) 寻找当前群体内最优解,若优于历史最优解,则更新Pgd
14、。最终计算结果为： （13）式中：被用于估计计算误差，数值越小时计算结果越优。2 基于GM (1,1)模型的船闸货运量预测建模数据采用19962005年淮阴船闸的货物运输量（见表1）,该数据为原始数据序列。表1淮阴船闸近年货物运输量(单位：万t)Table 1 Huaiyin lock freight volume in 1996-2000年份1996199719981999200020012002200320042005货运量3457341336163731414246735122527569667053数据来源：19902005 年苏北航务管理处船闸通过量统计表。按照GM (1,1 )建模
15、机理,首先对做一次累加生成计算得(i=1,2,3)：然后根据公式(4)计算得(i=2,3)：依据粒子群优化算法求解参数a=-0.10247136829，b=2552.30379746835。另外，参照文献15中介绍的最小二乘法计算得出a=-0.10151357546，b= 2627.58197816314。分别代入GM (1,1)模型, 则船闸货运量预测模型为： （14）累减还原得到： （15）应用该模型对19962005年淮阴船闸货运量进行计算，并进行模型精度的比较(见表2)。比较结果粒子群优化法平均相对误差为3.81%，最小二乘法平均相对误差为3.79%，两者均小于10%，预测模型精度较好
16、。最小二乘法需要求解矩阵（一般为奇异矩阵），其求解过程繁琐且不易获得近似解，所以本文进行了一些改进，用粒子群算法代替最小二乘法进行参数计算。两者求解数据的本质都一样，都是寻求经验公式并使其最大限度的拟合到观测数据，其结果也是相近的。最小二乘法出现较早，粒子群算法出现较晚。如果把最小二乘法看做是一种理论解，粒子群算法则更像是数值解，所以后者适应面更广，不需要烦琐的矩阵运算，所以算法上优于最小二乘法。表219962005 年淮阴船闸货运量模型预测值及误差值Table 2 Prediction and prediction accuracy of Huaiyin lock freight volum
17、e in 1996-2005待添加的隐藏文字内容3年份计算值原始值绝对误差相对误差PSOLSPSOLSPSOLS19963457345734570000199730613135341325227810.318.1519983391347036162251466.224.041999375738413731261100.692.942000416242514142201090.492.63200146114705467362321.320.69200251095208512213860.251.6820035660576452753854897.309.282004627163806966695
18、5869.988.41200569487062705310591.490.13PSO：粒子优化算法；LS：最小二乘算法应用基于粒子群优化算法的灰色系统船闸货物运输量模型，进行远景预测(见表3)，20062010年淮阴船闸累计货运量预测值分别为7697万t，8528万t，9448万t，10468万t，11597万t。表320062010年淮阴船闸货物运输量预测值(单位:万t)Table 3 Prediction of Huaiyin lock freight volume in 2006-2010年份20062007200820092010货运量76978528944810468115973 结
19、论1) 相对于其他传统的预测方法，灰色GM(1,1)模型法由于具有所需数据少、计算量小的优点。2) 基于粒子优化算法建立的船闸货运量灰色预测模型，方法简便易行，结果合理可信，预测精度较高，在算法上优于基于最小二乘算法建立的船闸货运量灰色预测模型。3) 灰色预测法在中短期预测( n5) 上具有优势，应用于船闸货运量的长期预测，尚有待于时间的检验和进一步的探讨论证。参考文献：1 蒋惠园, 杨大鸣. 货运量预测方法的比较J. 运筹与管理,2002,11 (3) :74-79.J IAN G Hui2yuan ,YAN G Da2ming. the Forecast Methods of Volume
20、 of Water Freight for ComparisionJ. OPERATIONS RESEARCH AND MANAGEMENT SCIENCE,2002,11(3):74-79. (in Chinese)2 周伯荣,张丙伟. 基于改进BP算法的中频淬火工艺参数预测J. 江苏大学学报(自然科学版),2007,28(6):495-499.ZHOU Bo-rong1, ZHANG Bing-wei. Prediction on medium-frequency induction quenching of steel based on improved BP network algor
21、ithmJ. Journal of Jiangsu University(Natural Science Edition),2007,28(6):495-499. (in Chinese)3 郁飞,罗春潮,许勃.基于模糊神经网络的柴油机排气噪声预测J.华东船舶工业学院学报(自然科学版),2001,15(6):54-57YU Fei, LUO Chun chao, XU Bo. Forecast of Exhaust Noise for Diesel Engines Based on FNN J. Journal of East China Shipbuilding Institute (Nat
22、ural Science Edition),2001,15(6): 54-57. (in Chinese)4 Yin Hongbin , Wong S C , Xu Jianmin , et al. Urban traffic flow prediction using a fuzzy-neural approach J .Transportation Research Part C , 2002 (10) :85- 98.5 Kalogqirou S A ,Pantelious S. Thermosiphon solar domestic water heating systems : lo
23、ng - term performance prediction using artificial neural networks J . Solar Energy ,2000 ,69(2) :163 - 165.6 Wang M H,Hung C P. Novel Grey Model for the Prediction of Trend of Dissolved Gases in Oil-Filled Power ApparatusJ . Electric Power Systems Research ,2003 ,67 (1) :53 - 58.7 Wang M H. Grey-Ext
24、ension Method for Incipient Fault Forecasting of Oil-Immersed Power Transformer J . Electric Power Components and Systems , 2004 , 32 (10) : 959 - 975.8 Chen Shuyan , Qu Gaofeng , Wang Xinghe , et al. Traffic flow forecas ting based on grey neural network model A . In :Proceedings of the Second Inte
25、rnational Conference on Machine Learning and Cybernetics C . Xipan , 2003: 2-5 ,11.9张新天, 罗晓辉. 灰色理论与模型在交通量预测中的应用J. 公路,2001,8:47.Zhang Xintian ,Luo Xiaohui. Application of grey system and its model in traffic flow predict J . Highway , 2001 (8) :4-7. (in Chinese)10 Li Qingfu,Hu Qunfang,Zhang Peng. App
26、lication of Grey-Markov model in predicting traffic volumeJ. Proceedings of 2007 IEEE International Conference on Grey Systems and Intelligent Services, 2007:707-711.11 S.J. Huang, C.L. Huang. Control of an inverted pendulum using grey prediction model. IEEE Transaction on Industrial Application, 20
27、00, 36(2): 452-458.12 Chen Shuyan , Qu Gaofeng , Wang Xinghe , et al. Traffic flow forecasting based on grey neural network model J .Proceedings of the Second International Conference on Machine Learning and Cybernetics, 2003: 2-5.13张海东, 毕效辉. 灰色残差GM (1,1 ) 模型在道路交通量预测中的应用J. 西南科技大学学报,2002,17 (3) :912.
28、Zhang Haidong,Bi Xiaohui. The application of grey residual GM(1,1) on transport volume forecastJ. Journal of Southwest University of Science and Technology,2007,17(3):912. (in Chinese)14 朱俊,张玮,钟春欣等. 航道货运量预测方法及其应用J. 中国港湾建设,2008,156(4):1416.ZHU Jun, ZHANG Wei, ZHONG Chun- xin, et al. Application of Ge
29、netic Programming to Forecast Waterway FreightJ. China Harbour Engineering,2008,156(4):1416. (in Chinese)15 冯宏琳,张玮,廖鹏. 基于灰色系统理论的船闸货运量预测J. 武汉理工大学学报（交通科学与工程版），2006,30(1):810814Feng Honglin ,Zhang Wei,Liao Peng. Forecast of the Lock Freight Volume Based on Grey System TheoryJ. Journal of Wuhan Universi
30、ty of Technology (Transportation Science & Engineering),2006,30(1):810814. (in Chinese)Editors note: Judson Jones is a meteorologist, journalist and photographer. He has freelanced with CNN for four years, covering severe weather from tornadoes to typhoons. Follow him on Twitter: jnjonesjr (CNN) - I
31、 will always wonder what it was like to huddle around a shortwave radio and through the crackling static from space hear the faint beeps of the worlds first satellite - Sputnik. I also missed watching Neil Armstrong step foot on the moon and the first space shuttle take off for the stars. Those even
32、ts were way before my time.As a kid, I was fascinated with what goes on in the sky, and when NASA pulled the plug on the shuttle program I was heartbroken. Yet the privatized space race has renewed my childhood dreams to reach for the stars.As a meteorologist, Ive still seen many important weather a
33、nd space events, but right now, if you were sitting next to me, youd hear my foot tapping rapidly under my desk. Im anxious for the next one: a space capsule hanging from a crane in the New Mexico desert.Its like the set for a George Lucas movie floating to the edge of space.You and I will have the
34、chance to watch a man take a leap into an unimaginable free fall from the edge of space - live.The (lack of) air up there Watch man jump from 96,000 feet Tuesday, I sat at work glued to the live stream of the Red Bull Stratos Mission. I watched the balloons positioned at different altitudes in the s
35、ky to test the winds, knowing that if they would just line up in a vertical straight line we would be go for launch.I feel this mission was created for me because I am also a journalist and a photographer, but above all I live for taking a leap of faith - the feeling of pushing the envelope into unc
36、harted territory.The guy who is going to do this, Felix Baumgartner, must have that same feeling, at a level I will never reach. However, it did not stop me from feeling his pain when a gust of swirling wind kicked up and twisted the partially filled balloon that would take him to the upper end of o
37、ur atmosphere. As soon as the 40-acre balloon, with skin no thicker than a dry cleaning bag, scraped the ground I knew it was over.How claustrophobia almost grounded supersonic skydiverWith each twist, you could see the wrinkles of disappointment on the face of the current record holder and capcom (
38、capsule communications), Col. Joe Kittinger. He hung his head low in mission control as he told Baumgartner the disappointing news: Mission aborted.The supersonic descent could happen as early as Sunday.The weather plays an important role in this mission. Starting at the ground, conditions have to b
39、e very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/
40、8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause), he can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 f
41、eet (22.7 miles/36.53 kilometers). Here, Fearless Felix will unclip. He will roll back the door.Then, I would assume, he will slowly step out onto something resembling an Olympic diving platform.Below, the Earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too har
42、d. Still, hell be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. It will be like he is diving into the shallow end.Skydiver preps for the big jumpWhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 second
43、s. Like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to Earth. But this will not be enough to stop him completely.If he goes too fast or spins out of control, he has a stabilization parachute that can be deployed to slow him down. His team hopes its
44、not needed. Instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).In order to deploy this chute successfully, he will have to slow to 172 mph (277 kph). He will have a reserve parachute that will open automatically if he loses
45、 consciousness at mach speeds.Even if everything goes as planned, it wont. Baumgartner still will free fall at a speed that would cause you and me to pass out, and no parachute is guaranteed to work higher than 25,000 feet (7,620 meters).It might not be the moon, but Kittinger free fell from 102,800 feet in 1960 - at the dawn of an infamous space race that captured the hearts of many. Baumgartner will attempt to break that record, a feat that boggles the mind. This is one of those monumental moments I will always remember, because there is no way Id miss this.