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1、4 基于支持向量机的干散货航运市场运价预警杨华龙 东方（大连海事大学 交通运输管理学院，辽宁 大连 116026)摘要：为分析预测干散货航运市场运价波动的警情，建立基于支持向量机的运价预警模型，并构造相应的算法. 选择BCI、BPI、BSI、BHSI等四个干散货运价指数作为警兆指标，结合航运专家知识经验，确定干散货航运市场运价的实际警度. 依据训练样本数据，利用支持向量机的学习功能，通过编制MATLAB软件程序，获得市场运价警度的分类超平面及预测警度区间，并进行内插和外推检验. 检验结果表明此方法对于干散货航运市场运价预警有很好的适用性.关键词：干散货航运市场；运价；预警；支持向量机中图法分类
2、号：TP691.2，F550.5 文献标识码：APre-warning of freight rate in dry bulk shipping market based on support vector machineYANG Hualong, DONG Fang(Transportation Management College, Dalian Maritime Univ., Dalian 116026, China)Abstract: A pre-warning model of freight rate was established based on support vector
3、machine and its algorithm was developed in order to analyze and forecast the alarm of freight rate fluctuation of dry bulk in shipping market. In accordance with shipping experts knowledge and experiences, the actual alarm degrees of freight rate within the sample interval of dry bulk in shipping ma
4、rket were determined by BCI, BPI, BSI and BHSI, which were selected as alarm criteria. The classification supper planes and forecasting intervals of freight rate alarm degree of dry bulk in shipping market were obtained by making use of the learning function of support vector machine and programming
5、 the MATLAB software based on the training sample data. And then the interpolation and extrapolation examines were carried on. The examination results show that this methodology has a very good serviceability with regard to the pre-warning of freight rate for dry bulk in shipping market. Key words:
6、dry bulk shipping market; freight rate; pre-warning; support vector machine.引 言收稿日期：2008-9-1基金项目：国家社会科学基金项目（05BJY076）, 辽宁省科技计划资助项目（2005401005）。作者简介：杨华龙(1964), 男, 辽宁人, 博士, 教授, 博导, 研究方向为交通运输规划与管理。Email:yang_；东方（1980），女，辽宁大连人，博士生，研究方向为交通运输现代化管理, Email: 运价是反映干散货航运供求关系的“晴雨表”，是调节干散货航运市场运力的有效杠杆。由于干散货航运市场运价
7、系统具有非线性和不确定性等特点，作为价格指数的种，运价指数是分析干散货航运市场运价系统的一种重要方法1，在航运市场运价分析中已得到广泛应用。研究运价指数的波动规律，探讨其发展变化趋势已经日益为人们所重视2。Byington3对进出口航运运价指数的弹性进行了计量经济分析，Parsons4，曾庆成5采用神经网络方法预测了运价指数的走势。上述方法主要是通过运价指数信息对航运市场运价的变化趋势作出一定程度的评估和预测，但尚无法对航运市场运价警情做出准确的预判。人们一般考虑航运市场变化大都参考波罗的海BDI指数，而BDI的指数计算方法是将BPI、BCI、BSI相加，取平均数，然后乘以一个固定的换算系数0
8、.998007990得出的。其中，BPI反映巴拿马型船舶市场的运价指数，由3条程租和4条期租典型航线根据各自的权重加权而成；BCI反映好望角型船舶市场的运价指数，由7条程租和4条期租典型航线根据各自的权重加权而成；BSI反映了超级大灵便型船（52454载重吨/10年或以下船龄/4x30吨吊杆）的市场租金变化情况，由5条航线据各自的权重加权而成。2007年伊始，波罗的海交易所为更全面反映灵便型船市场行情变化，在继续发布BSI同时，又推出新的灵便型船运价指BHSI。本文采用支持向量机(Support Vector Machine，简称SVM)方法，考虑到此方法使用多个因素进行分析效果较好的特点，将
9、BDI综合指数分解为BPI、BCI、BSI的同时，并补充加上了BHSI来考虑干散货航运市场的预警问题，从而为航运界提供了一条可行有效的运价预警途径，以便从容地应对干散货航运市场运价出现“过冷”或“过热”的现象，保证干散货航运市场平稳健康的发展。1 运价预警与机器学习问题干散货航运市场运价预警是在对干散货航运市场运价运行状况进行客观描绘的基础上，分析干散货航运市场的警情。合理解决干散货航运市场运价的非线性问题，正确分析影响干散货航运市场运价变化的不确定因素，并结合航运专家的经验，这些是做好干散货航运市场运价预警的关键。SVM方法是在统计学习理论基础上发展起来的一种新的通用机器学习问题。它以VC维
10、(Vapnik-Chervonenkis Dimension)理论和结构风险最小化原理为基础，根据有限的样本信息在模型的复杂性和学习能力之间寻找最佳折衷，以期获得最好的推广能力6-8。该方法兼顾训练误差和泛化能力，能够根据有限的样本信息在航运市场运价的复杂性与航运专家经验之间寻求最佳折衷。机器学习问题是从20世纪60年代由Vapnik等人开始研究的，到90年代中，机器学习问题已经逐渐成熟9。机器学习问题的基本模型如图1所示：系统S学习机LM输入 输出预输出 图1 机器学习的基本模型其中，系统S是我们研究的对象，它在一定的输入下得到一定的输出，LM是我们所求的学习机，预输出为。机器学习是根据已知
11、的训练样本求取对系统输入输出之间依赖关系的估计，使它对未知输出作出尽可能准确的预测。运价预警根据警兆变动来分析航运运价处于何种状态。设向量表示警兆变量，的分量为各项警兆指标，表示警度状态，干散货航运市场运价预警环节中预报警度的过程即寻找与之间的依赖关系，并根据这个依赖关系给定输入的值时能预测的值。由于干散货航运市场的复杂性，与之间的依赖关系不明确，我们只能通过对历史数据的学习来估计这个依赖关系。因此，干散货航运市场运价预警问题可看作一个基于经验数据的机器学习问题。利用支持向量机建立航运市场运价预警系统，首先要对干散货航运市场历史运价警情进行评判，得到系统训练样本，并在数据真实准确的基础上，选择
12、合理的警兆指标体系，同时，利用MATLAB软件编写支持向量机学习程序；其次，进行系统仿真，利用支持向量机算法程序对训练样本数据进行学习，得到警度分类超平面，并进行模型的内插、外推检验；最后，对仿真结果进行评判，得出适用性结论。2 航运市场运价预警模型及其求解近年来，世界航运市场供求关系变化速度惊人，使得运价指数波动剧烈。在今年5月份，航运市场达到旺季，各航线货量都呈现出强劲的增长势头，BDI在该月曾创过11793点最高；然而短短几个月， BDI指数回到了6年前，而航运股也正在面临历史上最为严峻的寒冬。美国金融危机引发的全球经济增长放缓，导致全球大宗原材料的海运需求下降，使得干散货海运贸易大受影
13、响，船只停港，大型散装船每天租价已从市场高峰时23.4万美元下降至目前的0.28万美元，给航运业拉响了“空袭警报”。航运市场运价变动的不确定性，对市场心理造成极大冲击，因此，对于航运市场预警问题的研究就显得十分重要，也迫在眉睫。而采用支持向量机建立预警模型，通过训练估计输入输出依赖关系，能够较好地分析出航运市场的警情，消除不确定性。2.1预警模型干散货航运市场运价警情可按严重程度的大小顺序有序排列，分为无警、轻警、中警、重警和巨警五种类型。在机器学习问题中即表示输出对应的是多类有序集。设为训练样本集（即已知警情的警兆指标样本集），其中上标j =1, k表示样本所属警情类别，此问题中k=5，其中
14、，j =1表示无警，j =2表示轻警，j =3表示中警，j =4表示重警，j =5表示巨警；下标i =1,，表示样本中属于第j类的数目，为训练样本总数目， 1, ,k是类别标号，表示实际警度，训练样本集按一定的度量大小顺序排列。定义个（即4个）线性分类函数把训练样本点分为k类（即5类），其几何解释就是寻找个平行的分类超平面。若输入的向量x（即航运市场运价警兆指标变量）满足，则x属于第j类警情的预警模型为： （1）其中，分类超平面的方向向量，为分类超平面的位置偏移量。2.2预警模型的求解支持向量机方法是求解学习机问题的最优分类面，它不但能将样本无错误的分开，而且使分类的间隔最大化，即推广性的界的
15、置信范围最小。k类顺序回归问题有k-1处分类间隔，把相邻两类中靠得最紧的那一对分类间隔最大化。假设w, 是划分靠得最紧的那一对分类超平面，将其边界点与分类面的距离归一化,即第j类和j+1类的间隔等于，间隔最大等价于或最小化，而要求分类面对所有样本分类正确，就是要求它满足: （2）若训练样本点是线性不可分的情况，可在约束条件中加一个松弛项，问题（1）便转化成下面的二次优化问题：s.t. （3）定义拉格朗日函数： （4）其中：C为大于零的常数，它是控制对错分样本惩罚的程度，,均为非负拉格朗日乘子。分别对上式中求偏导，并令之等0得 （5）为了表述方便，引进如下记述符号：是由第j类样本点组成的矩阵；是
16、由所有样本点组成的矩阵；是以拉格朗日乘子为分量的向量；是以拉格朗日乘子为分量的向量；是以拉格朗日乘子为分量的向量；是以拉格朗日乘子为分量组成的向量；是包含所有这些拉格朗日乘子和的向量；是的前半部分；是的后半部分。则问题（1）可进一步转化为问题（3）的对偶问题： j=1,k-1 （6） i=1,N解（6）可得，再由可求得这一组平行分类超平面的方向向量，位置偏移量可通过（3）求得。3实证分析3.1样本数据的选取为了准确地反映干散货航运市场的变化情况，本文选取四种干散货运价指数作为警兆指标，分别是BCI()、BPI()、BSI()、BHSI()。本文采集了干散货航运市场2007年1月到2008年10
17、月共22个月的数据。其中， BCI、BPI、BSI和BHSI各488个观测值（数据统计截止到2008年10月31日），对原始数据进行处理后，得到干散货航运市场运价指标数据，见表1。表1 干散货航运市场运价预警指标数据时间BCIBPIBSIBHSI时间BCIBPIBSIBHSIJan-076225.55 4285.59 2958.55 1494.41 Dec-0714634.19 9395.25 6024.52995.88 Feb-076338.61 4242.22 2807.17 1379.17 Jan-089668.55 6953.55 4850.55 2574.68 Mar-077236.
18、86 4988.95 3290.32 1665.91 Feb-089779.62 6742.81 4436.67 2096.38 Apr-078362.95 5389.79 36861854.32 Mar-0811251.68 8149.05 5167.53 2473.47 May-079192.24 6016.10 41792085.19 Apr-0812065.58330.41 4929.14 2468.32 Jun-077597.655776.94034.21925.65May-0816808.110144.356195.453221.2Jul-078471.24 7109.71 437
19、1.05 2148.67 Jun-0815815.33 9324.38 6222.43 2999.24 Aug-079736.09 7162.68 4786.09 2447.5Jul-0813221.26 8715.43 5398.57 2634.61 Sep-0711855.78827.655433.82639.65Aug-0811665.056470.154402.652289.8Oct-0714855.39 10631.22 6449.43 3031.91 Sep-086740.734942.913238.681763.45Nov-0715171.32 10616.32 6531.77
20、3040.36 Oct-082489.911416.521394.96760.873.2警度评估及预警度区间为将航运经济专家多年积累的经验有机地融入进来，本文采用专家调查评估的方法确定航运市场运价的实际警度。通过咨询专家，我们赋予BCI、BPI、BSI和BHSI的权重分别为=0.33，=0.33，=1.67，=1.67。对表1中的数据进行标准化处理： （7）其中：表示第项第月份运价指数； 表示第项运价指数的最大值；表示第项运价指数的最小值。则第月份航运市场运价的实际警度为 （8）航运运价第t份警度用表示。 为巨警；为重警；为中警；为轻警；为无警。由此可得各月运价警度评估值见表2：表2 航运市场
21、运价警度表Jan-07Feb-07Mar-07Apr-07May-07Jun-07Jul-07Aug-07Sep-07Oct-07Nov-070.710.720.640.600.500.560.460.400.260.060.05重警重警重警重警中警中警中警轻警轻警无警无警Dec-07Jan-08Feb-08Mar-08Apr-08May-08Jun-08Jul-08Aug-08Sep-08Oct-080.130.400.450.310.300.030.100.230.400.651.00轻警中警中警中警中警无警轻警轻警中警重警巨警本文通过编制MATLAB软件程序，首先选取Feb-07，May
22、-07，Sep-07，Dec-08，Jun-08和Oct-08等具有不同警度的几个月度数据作为外推实验点，其它的月度数据作训练样本点。利用上述预警模型，对训练样本进行学习，得到分类超平面的方向向量和4个位置偏移量分别为： = (-0.0006, 0.0004, -0.0011, 0.0075) = (5.4185, 7.6946, 9.8243, 10.7188)令g(x)=-0.0006x1+0.0004x2-0.0011x3+0.0075x4 （9）则训练样本可将这些运价的预警度分成以下五个区间：(b0, b1)=(-, 5.4185)巨警区间(b1, b2)=( 5.4185, 7.69
23、46) 重警区间(b2,b3)=( 7.6946, 9.8243)中警区间(b3, b4)=( 9.8243, 10.7188)轻警区间(b4, b5)=( 10.7188, +)无警区间3.3内插与外推检验通过预警模型计算得到g(x)的值落入的区间即是干散货航运市场运价对应的预测警度。对训练样本的月度数据作内插检验，即将训练样本点数据代入式（9）中进行检验，正确率93.75%，结果如表3：表3 航运市场运价预警模型内插检验结果时间g(x)预测警度实际警度时间g(x)预测警度实际警度Jan-075.932576重警重警Jan-0810.95479无警中警Mar-076.528437重警重警Fe
24、b-087.671865中警中警Apr-076.990946重警重警Mar-089.375354中警中警Jun-077.756925中警中警Apr-089.18321中警中警Jul-079.06801中警中警May-0811.31689无警无警Aug-0710.11497轻警轻警Jul-089.874564轻警轻警Oct-0710.98421无警无警Aug-087.919615中警中警Nov-0710.76149无警无警Sep-087.596053重警重警再用式（9）对Feb-07，May-07，Sep-07，Dec-08，Jun-08和Oct-08六个数据作外推检验，正确率83%，结果如表4
25、。表4 航运市场运价预警模型外推检验结果时间g(x)预测警度实际警度Feb-075.14961巨警重警May-077.933121中警中警Sep-0710.23784轻警轻警Dec-0710.81974无警无警Jun-089.890181轻警轻警Oct-083.244731巨警巨警4结论本文通过对干散货航运市场运价预警问题进行描述，利用支持向量机方法建立了干散货航运市场运价的预警模型，得出了干散货运价的预警度区间，并通过内插、外推方法的检验，证明了预警的精确度较高，此方法具有较好的适用性。SVM能够较为准确地预测干散货航运市场警情，为干散货航运市场运价的预警提供一条可行、有效的新途径。本文今后
26、的研究方向是将支持向量机方法与其他科学预测方法（如人工神经网络）相结合，建立干散货航运市场运价预警模型，通过加大样本数据的容量，进一步优化预警模型，并使问题的应用得到推广。参考文献：1 Albert W. Veenstra. The term structure of ocean freight rates. Maritime Policy & ManagementJ, 1999, Vol. 26, No. 3, 279-293.2 Alexandros M. Goulielmos, Mariniki Psifia. A study of trip and time charter freig
27、ht rate indices: 1968-2003. Maritime Policy & ManagementJ, 2007, Vol. 34, No. 1, 55-67.3 Russell Byington, Gary Olin. An econometric analysis of freight rate disparities in US liner trades. Applied EconomicsJ, 1983, Vol. 15, No. 3, 403-4074 Michael G. Parsons. Forecasting tanker freight rate using n
28、eural networks. Maritime Policy & ManagementJ, 1997, Vol. 24, No. 1, 9-30.5 曾庆成. 神经网络在波罗的海运价指数预测中的应用研究.大连海事大学学报I, 2004年, 第30卷, 第3期, 45-47.Zeng Qingcheng. Application of neural networks in forecasting BFI. Journal of Dalian Maritime UniversityJ, 2004, Vol. 30, No. 3, 45-47. 6 Cristianini N, Shawe-Tay
29、lor J. Introduction to Support Vector Machines. Cambridge: Cambridge University Press, Cambridge, UK, 2000: 52-76.7 Scholkopf S, Burges C J C, Smola A J. Advances in kernel Methods: Support Vector Learning. Cambridge: M IT Press, 1999, 43-45.8 Platt J. Fast Training of Support Vector Machine Using S
30、equential Minimal OptimizationA. Schokopf B, Burges C J C, Smola A J. Advances in Kernel Methods-Support Vector LearningC, Canbridge: MIT Press, 1999. 185-208. 9 王建成,王静,胡上序.基于概率模式分类识别方法的宏观经济预警系统设计J.系统工程理论与实践,1998,18(8): 6-10.Editors note: Judson Jones is a meteorologist, journalist and photographer.
31、 He has freelanced with CNN for four years, covering severe weather from tornadoes to typhoons. Follow him on Twitter: jnjonesjr (CNN) - I 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 satel
32、lite - Sputnik. I also missed watching Neil Armstrong step foot on the moon and the first space shuttle take off for the stars. Those events 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 th
33、e privatized space race has renewed my childhood dreams to reach for the stars.As a meteorologist, Ive still seen many important weather and 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 hang
34、ing 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 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,
35、 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 sky 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
36、 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 uncharted 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
37、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 our 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 groun
38、ded supersonic skydiverWith each twist, you could see the wrinkles of disappointment on the face of the current record holder and capcom (capsule communications), Col. Joe Kittinger. He hung his head low in mission control as he told Baumgartner the disappointing news: Mission aborted.The supersonic
39、 descent could happen as early as Sunday.The weather plays an important role in this mission. Starting at the ground, conditions have to be 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 le
40、vel 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/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
41、 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 feet (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 resem
42、bling an Olympic diving platform.Below, the Earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. 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 e
43、nd.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 seconds. 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 completel
44、y.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 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 thi
45、s 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 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, an
46、d 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