Extending the scope of wavelet regression methods by coefficient-dependent thresholding

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非线性动力学入门-西安交通大学教师个人主页

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另一方面梁的轴向应变的表达式也会因变形大小的不同而采用不同的表达式比如小变形时应变而当考虑大变形时可能采用的应变表达式就是进而得到的梁的振动方程将会是一个含有高度非线性项的偏微分方程组
非线性动力学入门
张新华
西安交通大学工程力学系 2011 年 07 月
前言
─1687 年，牛顿(Isaac Newton, 1643 ～ 1727)发表了《自然哲学之数学原理》(Mathematical Principles of Natural Philosophy)，标志着经典力学(亦即牛顿力学)的正式诞生。牛顿力学主要研究自由质点系的宏观运动规律。 ─1788 年，拉格朗日(Joseph Louis Lagrange, 1736 ～ 1813)发表了分析力学教程(Analytical Mechanics)，标志着拉格朗日力学的诞生。Lagrange 力学属于分析力学的主要内容之一，在位形空间中研究带有约束的质点系动力学。 ─1833 年，哈密尔顿(William Rowen Hamilton, 1805 ～ 1865)对 Lagrange 力学进行了改造，引进了相空间(2n 维空间)，对系统内在的对称性(辛对称， Symplectic)进行了刻画。狭义上的哈密尔顿力学只适用于保守系统，而广义的哈密尔顿力学在适用于非保守系统。哈密尔顿力学也属于分析力学的主要组成部分。在此后发展起来的量子力学中 Hamilton 力学发挥着巨大的作用。目前在天体力学、计算 Hamilton 力学，量子力学，甚至弹性力学(即所谓的辛弹性力学)中哈密尔顿力学依然发挥着重要作用。 ─1927 年，Birkhoff(George David Birkhoff, 1844 ～ 1944)发表了“动力系统”(Dynamical Systems)，标志着 Birkhoff 动力学的正式问世。Birkhoff 动力学建立了研究非完整力学的框架。 ─1892 ～ 1899，彭加莱(Henri Poincaré, 1854 ～ 1912)发表了三卷本的“天体力学中的新方法”(New Methods of Celestial Mechanics)，系统性地提出了研究动力学系统的定性方法，即几何方法。经典力学的目标之一就是设法求得系统的解析解，而 Poincaré意识到对于大多数非线性系统而言，求其解析解是不可能的，而必须发展新的研究方法。他超越了他的时代，极富远见地预测到了非线性系统混沌现象(系统的解对初始条件具有极端敏感依赖性)的存在。更为重要的是，Poincaré开创了研究非线性动力系统的几何方法，当之无愧地被誉为非线性科学之父，其影响是划时代的。 ─1892 年，李亚普诺夫(Aleksandr Mikhailovich Lyapunov, 1857 ～ 1918)在他的博士论文“运动稳定性的一般问题”(General problem of the stability of motion )中，系统地探讨了非线性动力学系统的稳定性问题。他提出了两种研究稳定性的方法：李亚普诺夫第一方法(间接方法)和李亚普诺夫第二方法(直接方法)。他从代数角度出发，对动力学系统的研究开创了一个崭新的领域。彭加莱与李亚普诺夫，前者从几何角度，后者从代数角度，开拓了非线性科学的研究疆域和研究手段。 ─1963 年，Lorenz(Edward Norton Lorenz, 1917 ～ 2008)发表了“确定性非周期流”(Deterministic Nonperiodic Flow)的论文，认为大气系统的性态对初值极为敏感，从而导致准确的长期天气预报是不可能的。该文标志着人类首次借助于计算机发现了混沌(Chaos)现象的存在。 ─1757 年，欧拉(Leonhard Euler, 1707 ～ 1783)发表了压杆稳定性的论文，首次探讨了力学系统的分岔现象。作为分岔理论重要分支的突变理论(Catastrophe Theory)则主要由法国数学家托姆(René Thom, 1923 ～ 2002)于上个世纪 60 年代创立，由齐曼(Christopher Zeeman，1925 ～)在 70 年代大力推广普及。 ─1834 年，英国的罗素(John Scott Russell, 1808 ～ 1882)骑着马在 Union 运河上散步时，发现了现在称之为孤立波(又称作孤波，Solitary wave)的 i

人工智能英文参考文献(最新120个)

人工智能是一门新兴的具有挑战力的学科。

自人工智能诞生以来,发展迅速,产生了许多分支。

诸如强化学习、模拟环境、智能硬件、机器学习等。

但是,在当前人工智能技术迅猛发展,为人们的生活带来许多便利。

下面是搜索整理的人工智能英文参考文献的分享，供大家借鉴参考。

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Forecasting the urban power load in China based on the risk analysis of land-use change and loaddensityY.X.He ⇑,J.X.Zhang,Y.Xu,Y.Gao,T.Xia,H.Y.HeSchool of Economics and Management,North China Electric Power University,Zhu Xin Zhuang,Bei Nong Lu No.2,Changping District,Beijing,Chinaa r t i c l e i n f o Article history:Received 5November 2013Received in revised form 9February 2015Accepted 19March 2015Keywords:UrbanPower load forecasting RiskCellular automata Land-use change Load densitya b s t r a c tAlong with the increasing development of the urban society and economy,urban power is facing an increasing number of risk factors.The conventional load forecasting methods cannot guarantee the accu-racy of the prediction;however,scientiﬁc urban load forecasting has a greatly signiﬁcant meaning to urban power planning and supply.This paper ﬁrstly analyzes the risk factors that affect the ﬂuctuation of the power load.From the perspective of the spatial load,the factors inﬂuencing the ﬂuctuation of the urban power load are mainly determined by the change in land use and load density per unit area.Secondly,based on the basic principle of cellular automata,the rules and model of land-use change are established by considering the risk factors.From the aspect of land-use change,the cellular change rules of the land use with the risk factors are proposed and the methods of land classiﬁcation change are presented by combining them with geographic information system (GIS)technology.Meanwhile,after comprehensively considering the effect of the risk factors on the load density ﬂuctuations,the power load forecasting model is established based on the risk analysis of the land-use change and load density.Finally,taking a speciﬁc city as an example,the case study results show that this model is scientiﬁc.Ó2015Elsevier Ltd.All rights reserved.IntroductionElectric power is a powerful driving force of the economic and social development,which is the material guarantee of economic and social modernization.Carrying out scientiﬁc,rational and prac-tical power development planning plays a signiﬁcant role in the entire power industry,the whole national economy and the improvement of social modernization.In addition,with the con-tinuous development of China’s urban economy,the risk factors that affect the urban power load are increasing.How to forecast the urban power load scientiﬁcally and conduct urban power grid development planning has become an urgent problem.The methods of load forecasting have been studied in depth by scholars.Many models have been used to forecast the power load,such as support vector regression model [1],the neural networks model [2],the two-dimensional wavelet based state dependent parameter model [3],the nonparametric regression techniques [4],and the dynamic simulation theory [5].In addition,some combination forecasting methods have also been widely applied,such as the wavelet transform and artiﬁcial neural network [6],methods of artiﬁcial and wavelet neural networks [7],fuzzy neural networks and simulated annealing [8],support vector machines and ant colony optimization [9],chaotic theory and ant swarm optimization [10],support vector machines and genetic algorithms [11],and rough sets and cellular automata theory [12].However,the methods above paid more attention to ﬁtting the load data from the past year.Although the accuracy of the ﬁtting results was improved,the risk factors that affect urban development and the electricity demand were considered less and this would inﬂu-ence the accuracy of the ﬁnal forecasting results.The methods of load forecasting have also been researched from the aspect of the change of spatial load,namely,based on the per-spective of land-use change,the load change has been further ana-lyzed.The land-use change during 1982to 2004in Thailand was analyzed by using GIS,and the land tenure and resource utilization were the main factors that affect the land-use change [13].In [14],the relationship between the land-use change and the population density was researched based on data collected from six national-level districts during 1950to 1990in Israel.In [15],a method of land-use change from the aspect of evaluating socioeco-nomic and environmental impacts was established.Forecasting scenarios were developed in the future land-use model by means of land-use trends data and statistical,theoretical and deter-ministic modeling techniques [16].In addition,the relationships between factors inﬂuencing the land-use change and the ﬁnal/10.1016/j.ijepes.2015.03.0180142-0615/Ó2015Elsevier Ltd.All rights reserved.⇑Corresponding author.Tel.:+8601061773113;fax:+8601061773311.E-mail address:heyongxiu@ (Y.X.He).change results were analyzed by using logistic regression.A map of land-use/cover change was generated by using GIS technology and calculated the rates of conversion[17].The reference above ana-lyzed the factors that affect the land-use change and simulated the change process through GIS technology.However,methods combining land-use change with load forecasting have also been analyzed by some scholars.The power load was forecasted based on an analysis of the land-use change[18].And a model through the cellular automata theory and GIS technology was introduced to forecast the load[19].In[20],the measurement model was applied to analyze the land-use changes,risk factors,rates of con-version and so on.A new cellular automata model was established for simulating the change in urban development[21,22].According to most of the researchers mentioned above,these methods fail to consider comprehensively the risk factors that affect the land-use change.In addition,the rules of land-use change were relatively simple.At present,the cellular automata theory is widely applied in load forecasting,and it is suitable for forecasting the spatial load.Based on the cellular automata theory and combined with the advantage of GIS technology in simulating the situation of land-use change,the risk factors that affect the land-use change are simulated and the urban load is forecasted in this paper.This paper is organized as follows:Section‘Analysis of the risk factors of China’s urban power load’analyzes the risk factors that affect China’s urban power load.Section‘Analysis of the risk factors lead-ing to the land-use change’further analyzes the risk factors that affect land-use change.Section‘Risk forecasting model of urban land-use change based on the cellular automata theory’presents the risk forecasting model of urban land-use change based on the cellular automata theory.Section‘Risk analysis and modeling of the load density’analyzes the risk factors of the load density. Section‘Urban load forecasting model based on analysis of the risk factors of land-use change’proposes a model for China’s urban load forecasting by considering the risk factors’change.Section‘Case study’takes a speciﬁc city as an example for a further analysis. Finally the conclusions are proposed in Section‘Conclusion’. Analysis of the risk factors of China’s urban power loadThe risk factors that affect China’s urban power load,if divided according to the source of the risk factors,include policy,the eco-nomic circumstance,the electricity price,important activities,etc. If divided according to the nature of the power consumption and mainly considering the inﬂuence of the electricity demand of the primary industry,secondary industry,tertiary industry and resi-dential living,the main risk factors are as follows:r the structure and the change of land use function;s the load density per unit area inﬂuenced by social and economic development;t the elec-tricity demand of the secondary industry;u the electricity demand of the tertiary industry,v the electricity demand of resi-dential living;w the policy of energy conservation and consump-tion reduction;x the adjustment of the industrial structure;y the change in the energy consumption structure;z the demand-side management; 10the proportion of high power-consuming sectors in the industrial system; 11the power consumption per GDP; 12the policy of direct power purchase for the large users; 13the international economic situation; 14the development speed of the urban economy; 15the periodicﬂuctuation in allthe industries; 16the policy for electricity prices; 17the favorable policy for electricity prices made by local government; 18other energy prices; 19important activity; 20the climate and tempera-ture;the urban population;the level of residential income; the electricity demand of the primary industry;the possessive quantity of household appliances,etc.However,the land-use function change and the load density are the main risk factors that lead to a change in the urban power load. Along with the change in land function,the demand for electricity of each type land is different;therefore,it can bring about various risks for urban electricity consumption.With the urban social and economic development,the load density per unit also changes. Then,it becomes the key risk source that causes the change in the urban load.Analysis of the risk factors leading to the land-use change The risk factors that lead to land-use change are as follows:the natural environment,land-use management,economic develop-ment,population,urban policies,etc.The risk of the natural environmentAs a result of the different urban geographical positions,the natural environment also differs.For example,commercial land occupies a large amount of space in coastal cities;industrial land occupies a large amount of space in cities that own rich minerals, etc.However,the natural environment can change as time passes. For example,with the rapid development of the economy,many mineral deposits are being reduced quickly,and have even become insufﬁcient.Hence,under this critical circumstance,the exploita-tion of minerals must be reduced by considering urban strategic planning.At the same time,the land-use situation is also adjusted. The risk of land-use managementIt is necessary for decision makers to implement macro man-agement in order to make full use of the land.From the perspective of environmental protection,the proportions of landscaping have been stipulated in all cities.From the aspect of the economy,the demand and the yield of land need to be analyzed in order to work out proper planning for land use.Through a proper plan,the maxi-mum land proﬁts under various constraints can be obtained as fully as possible,whereas different management methods can bring about different risks due to the land-use change.The risk of economic developmentBased on a certain amount of input,the factors of economic development include land,capital,material,technique and labor. Economic development necessarily generates a change in land input.In addition,an obvious consistency exists between economic development and urban geographic expansion,namely,the greater the speed of economic development,the greater the speed of urban expansion.Economic development has a relationship with the land-use situation,and the economic added values that are created by dif-ferent kinds of land are also different.Therefore,except for the construction of the urban land,the land with greater added value per unit area has a higher possibility for land-use change.The risk of population changeThe population and the land are closely related,namely,the growing population is associated with the urban expansion.With the increasing growth of the population,the situation of land use and exploitation is enlarged and enhanced.Especially,residential land is increasing.On the other hand,with the development of society and the economy and the improvement of the level of mate-rial and cultural life,it is necessary to exploit more and more land in order to meet the increasing demands of material and cultural life.72Y.X.He et al./Electrical Power and Energy Systems73(2015)71–79The risk of the urban policyIn order to implement urban strategic planning effectively,many policies are established by the government,such as the national policies of population migration,the policies of industrial structure adjustment,the estate exploitation policies,the urban development policies,and the investment policies.As the result of the above policies,the properties of urban land use may change with the policies’adjustment.Risk forecasting model of urban land-use change based on the cellular automata theoryCellular automata (CA)are a dynamic system in which time and space are discrete.Each cell distributed across the lattice grid has a limited discrete state,abides by the same rules and is updated syn-chronously with certain partial rules.The structure of each cell evolves in the dynamic system by simple interaction.The CA are structured by a series of model rules;all the models adhering to these rules are considered as cellular automata.The position of all the cells in n-dimensional space could be determined by an n variables integer matrix.CA is composed of cells and states,cellular lattice,neighbors,transition rules and time,which are shown in Fig.1.When the simulation of the land-use change starts,the model domain is divided into identical panes.Each pane represents a cell.The cell is analyzed using the change rules,and the neighboring cells (eight cells)are also analyzed.Determination of the rules of land-use changeAccording to the analysis of the risk factors inﬂuencing the land-use change,the following rules of land-use change are developed.The change rules used for judging the cellular life value of the land Based on the cellular automata theory,each cell can be endowed with the characteristic of life.In addition,the develop-ment trend of the land can be described by its life value.Hence,the cellular life value of the land can be used to determine whether the land type of the cell changes at time t þ1.The classiﬁcation of the life value is divided into three parts in this paper:young,mid-dle and old.Cell at young age:The life value of the cell is smaller.The land type of the cell generally belongs to residential areas,commercialoutlets or industrial parks,etc.In addition,considering the inﬂu-ence of construction costs,investment recycling,personnel ﬂow and other factors,the land type of the cell may change.At the same time,the increasing trend of the power load is rapid.Thus,the change risk of the cell is relatively higher.Cell at middle age:The life value of the cell is relatively longer.Generally,the land type of the cell can change during the planning years,but if signiﬁcant historical events happen,the land type of the cell will change.At the same time the increasing trend of the power load is slow.Thus,the change risk of the cell is high.Cell at old age:The cell has reached a certain service life.Regardless of residential areas,commercial outlets or industrial parks,the land is facing the problem of recession or reconstruction.In addition,the corresponding return of the initial construction investment has been obtained.Thus,the change risk of the cell is relatively lower during the planning years.For the given age interval,time can be deﬁned,and the cellular life value of the land can be obtained from Eq.(1).L t ðx ;y Þ¼L y ðx ;y Þ06L t ðx ;y Þ6Tm L m ðx ;y ÞT m <L t ðx ;y Þ6T nL o ðx ;y ÞL t ðx ;y Þ>T n8><>:ð1Þwhere L t ðx ;y Þis the life value of the cell ðx ;y Þat time t ;x ;y are the values of cellular coordinates,respectively;L y ðx ;y Þrepresents the cell at young age;L m ðx ;y Þrepresents the cell at middle age;L o ðx ;y Þrepresents the cell at old age;T m is the upper limit of the life value of the cell at young age;T n is the upper limit of the life value of the cell at middle age.The change rule used for considering the urban land-use planning It is very important that the land type of each cell at time t þ1is in accord with the urban development planning.Hence,before applying other change rules,the land type of each cell at time t þ1should be analyzed through the requirements of development planning.The change rule applied to judge the attractive force of the center The attractive force of the center is the effect of large urban facilities,leading industries,commercial center and other impor-tant industries in the neighboring cells.The smaller the distance between the cell and the center is,the greater the inﬂuence or attractive force is,then the faster the change speed of land-use is.Hence,the negative power function can be applied in quantify-ing the attractive force of the center.The formulas are expressed asfollows:Y.X.He et al./Electrical Power and Energy Systems 73(2015)71–7973C ðx ;y Þ¼exp fÀl 1Âd ðx ;y Þ=d max g ð2Þd ðx ;y Þ¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃðx Àx 0Þ2þðy Ày 0Þ2q ð3Þwhere ðx ;y Þis the position coordinate of the cell;C ðx ;y Þis the attractive force of the center;l 1is the rate parameter of the attrac-tive force and the interval is set between 0and 1;the larger the scale of the central cell ðx 0;y 0Þis,the bigger the rate parameter is,then the greater the attractive force is;d ðx ;y Þis the distance between the cell ðx ;y Þand the central cell;d max is the distance between the edge of the planned area and the central cell;the shorter the distance is,the greater the attractive force is.For the medium-sized and small city,the position of the central cell can be deﬁned as the urban center.The change rule applied to judge the inﬂuence force of the neighboring cellsEach cell has neighboring cells,which may belong to different land types.Meanwhile,the neighboring cells can cause the land-use change of the cell,namely,inﬂuence force.This can be expressed as follows:d l ¼n lnð4Þwhere d l is the inﬂuence force of the neighboring cells whose land type is l ;n is the total number of neighboring cells;n l is the numbers of neighboring cells whose land type is l .The change rule used for judging the effect of road trafﬁc on each cell Based on the construction of road trafﬁc,the trafﬁc conditions along the road are changed,trafﬁc speed is enhanced and trafﬁc time is saved.From the perspective of urban development,the land that is near to the important road trafﬁc and subject to trafﬁc inﬂu-ence not only has a higher market value,but also faces a change in the land type and the attractive force.In addition,the land type may change because of the trend of the market value in different areas.Then,with the increasing development of land around the road trafﬁc,different land types around the road need to be redis-tributed,ultimately leading to continuous adjustment of the land-use change.tr ðx ;y Þ¼exp ÀXtm m ¼1x m Âﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃðx Àx m Þ2þðy Ày m Þ2q!ð5Þwhere tr ðx ;y Þis the effect of the important road trafﬁc on the cell ðx ;y Þ;x m ;y m are the central coordinates of the important road m ,respectively;x m is the weight reﬂecting the signiﬁcance of road m ;tm is the total number of important trafﬁc roads.The change rule used for judging the topographical advantageThe study,which is about the effect of the topography on the spatial distribution of land-use change,actually means the analysis of land-use change at different levels of topography.The number and the proportion of land-use types are the most common indica-tors.The formula is expressed as follows:F ij ¼S ij S j ÂS iSð6Þwhere,i is the land type i :j is the level j of the topography;F ij is the advantage index of topographical distribution of the land type i at the topographical level j ;S ij is the area of the land type i at the topographical level j ;S i is the total area of the land type i in the research region;S j is the total area of the topographical level j in the research region;S is the total area of the research region.The change rule applied to judge the highest proﬁt of land-use change Basic types of land-use change can be divided into parts,such as:residential land,commercial land,industrial land,warehouse space,land for roads and squares,municipal facilities land,public green land,special land,unutilized land and external trafﬁc land.It is assumed that the land type changes among the types above,and i is the number of the land type before the land type of the cell changes;j is the number of the land type after the land type of the cell changes;E ði ;j Þis the proﬁt value per unit area while the land type of the cell changes from type i to type j .E ði ;j Þ¼E j ÀE i ÀC ði ;j Þð7Þwhere E j is the proﬁt value per unit area of land type j ;E i is the proﬁt value per unit area of land type i ;C ði ;j Þis the change cost when the land type of the cell changes from type i to type j .Risk model of the cellular change rulesIn this analysis of the risk of the cellular change,this paper fol-lows some steps which are shown in Fig.2.(1)Based on the analysis of the risk factors inﬂuencing the land-use change in Section ‘Analysis of the risk factors leading to the land-use change’,the risk can be divided into 5parts which includes the natural environment risk,the land-use management risk,the economic development risk,the popu-lation change risk and the urban policy risk.Different risks have different probability distribution functions,this paper lists some typical probability distribution functions as follows:r The binomial distribution,and it can be expressed as Eq.(8).p ðe ¼k Þ¼C k n p kð1Àp Þn Àk ð8Þs The Poisson distribution,and it can be expressed as Eq.(9).p f x ¼k g ¼k k e Àkk !;k >0;k ¼0;1;2; (9)where X follows the Poisson distribution and the parameter is k .t The normal distribution,and it can be expressed as Eq.(10).F ðX 6x Þ¼1ﬃﬃﬃﬃﬃﬃﬃ2p p rZxÀ1eÀðy Àl Þ22dy ð10Þwhere,l is the mean value,r is the standard deviation and X is obtained from À1to þ1.u The 0–1distribution,and it can be expressed as Eq.(11).p ¼f x ¼k g ¼ð1Àp Þk p ð1Àk Þ;ðk ¼0;1Þð11Þ(2)According to the cellular development mode,the changesteps are established as follows based on comprehensive consideration and gradual perfection.Firstly,judge whether the attribute values of each cell meet the change rules’constraint.Rule 1:S 1ðx ;y Þis the judgment value of the service life of the cell.Based on the formula (1),if the cellular service life value belongs to the young age cell,the value of S 1ðx ;y Þis zero;if the cellular service life value belongs to the middle or old age cell,the value of S 1ðx ;y Þis one.Rule 2:It is assumed that S 2ðx ;y Þis the judgment value that is used to judge whether the cell meets the urban construction planning constraint.If the cell meet the constraint,the value of S 2ðx ;y Þis one;else the value of S 2ðx ;y Þis zero.Rule 3:S 3ðx ;y Þis the judgment value that reﬂects the attractive force of the central cell.Based on formula (2),if C ðx ;y ÞP a ,the74Y.X.He et al./Electrical Power and Energy Systems 73(2015)71–79value of S3ðx;yÞis one;else the value of S3ðx;yÞis zero.(The cri-tical value is a.)Rule4:S4ðx;yÞis the judgment value that reﬂects the inﬂuence force of the neighboring cell.Based on formula(4),if d j>h,the value of S4ðx;yÞis one;else the value of S4ðx;yÞis zero.(The cri-tical value is h.)Rule5:S5ðx;yÞreﬂects the inﬂuence level of the important road trafﬁc.Based on formula(5),if the distance between the road trafﬁc and the cell is more than the critical value,that is,trðx;yÞP d l,the value of S5ðx;yÞis one;else the value of S5ðx;yÞis zero.(The critical value is d l.)Rule6:S6ðx;yÞreﬂects the inﬂuence level of the advantage of topographical distribution.Based on formula(6),if F ij P e,the distribution of land type of the cell on level j belongs to the pre-dominant distribution,then the value of S6ðx;yÞis one;else the value of S6ðx;yÞis zero,namely,the distribution on level j belongs to the disadvantage distribution,and the land type of the cell is not suitable for further development.(The critical value is e.)(3)Based on analyzing the probability distributions of the riskfactors inﬂuencing the land-use change and applying Monte Carlo simulation,the distributions of the rules above can be obtained.It is assumed that the distributions of the change risk in rule1,rule2,rule3and rule6follow the bino-mial distribution,and the formula is as follows: pðe¼kÞ¼C k n p kð1ÀpÞnÀkð12ÞIt is assumed that the distributions of the change risk in rule4 and rule5follow the Poisson distribution,and the formula is as follows:P f X¼k g k k eÀkk!;k>0;k¼0;1;2; (13)where X follows the Poisson distribution and the parameter is k.(4)Determination of the risk value R m reﬂecting the effect of therisk factors on the change rule of the land use.R m¼Zþ1À1gmðxÞf mðxÞdxð14Þwhere R m is the risk value and it reﬂects the effect of the risk factorson the change rule m,gmðxÞis the probability density function of therule m and fmðxÞis the inﬂuence function that represents the effect of the risk factors on the rule m of the land-use change.If the attribute values of the cell meet the constraint of thechange rules1–6and R m<bm,the value of S mðx;yÞis one (m¼1;2;...;6).In this case,theﬁnal cellular type can be deter-mined by using rule7.While the risk value is less than the given critical value b m,it can be concluded that the judgment of the change rule is credible and accurate and the rule is suitable for jud-ging the situation of the land-use change.Rule7:S7ðx;yÞis the judgment value that reﬂects theﬁnal cel-lular type.Based on the proﬁt level of the land-use change brought by the risk value,the model can be expressed as Eqs.(15)and(16).Eði;kÞ¼max f Eði;jÞg;j¼1;2;...;nð15ÞS7ðx;yÞ¼kð16Þwhere S7ðx;yÞis theﬁnal land type of cellðx;yÞand it owns the highest proﬁt level Eði;kÞin the process of land-type change.After the rules above have been followed,the ultimate land type and area of each cell can be obtained at time t.Based on the fore-casting result of each cell,the electricity consumption canﬁnally be calculated.Risk analysis and modeling of the load density(1)The residential load density is inﬂuenced by the urban pop-ulation,residential income level,living space per person, household appliances’capacity,etc.(2)The commercial load density is inﬂuenced by the urban GDP,international economic situation,speed of urban economic development,commercial cyclicalﬂuctuation,etc.(3)The industrial load density is inﬂuenced by technical pro-gress,energy saving policy,etc.(4)The agricultural load density is inﬂuenced by farmland area,technical progress,etc.The probability distributions of different types of load density are analyzed as follows.Based onﬁtting the data from the past years,the more suitable probability distribution of the residential and agricultural load density is the normal distribution,and the formula can be expressed as Eq.(10).In addition,through application in the same way,the more suit-able probability distribution of the commercial and industrial load density is the exponential distribution,and the formula can be expressed as follows.FðxÞ¼1ÀeÀh x;x>00;x60ð17Þwhere random variable X follows the exponential distribution and the parameter is h.Y.X.He et al./Electrical Power and Energy Systems73(2015)71–7975。

基于多核最小二乘支持向量回归的TDOA-DOA映射方法

基于多核最小二乘支持向量回归的TDOA-DOA映射方法张峰;陈华伟;李妍文【摘要】基于到达时间差(Time difference of arrival,TDOA)估计的方法是声源波达方向(Direction of arrival,DOA)估计中的一类重要方法.其中由TDOA到DOA的映射是该类方法的关键步骤.本文提出了一种基于多核聚类最小二乘支持向量回归(Least-squares support vector regression,L&SVR)的TDOA-DOA映射方法,并且分析了其稀疏化处理后的性能.为了提高混响噪声环境下的TDOA-DOA 映射性能,本文还给出了一种基于归一化中值滤波的TDOA估计离群值消除方法.仿真结果表明,本文提出的方法要优于现有的最小二乘方法以及单核LS-SVR方法.%In sound source direction of arrival (DOA) estimation,one of the typical methods is based on the time difference of arrival (TDOA).For the TDOA-based sound source DOA estimation,the TDOADOA mapping is a crucial step.Here,we propose a TDOA-DOA mapping approach based on the multikernel least-squares support vector regression (LS-SVR),and also analyze its performance with sparsification.In addition,we present an outlier detection method based on the normalized median filtering to post-process the TDOA estimation for improving the performance of TDOA-DOA mapping in noisy reverberant environments.Simulation results show that the proposed method is superior to its counterparts,such as LS and single-kernel LS-SVR methods.【期刊名称】《数据采集与处理》【年(卷),期】2017(032)003【总页数】10页(P540-549)【关键词】声源波达方向估计;到达时间差估计;最小二乘支持向量回归;多核学习【作者】张峰;陈华伟;李妍文【作者单位】南京航空航天大学电子信息工程学院,南京,210016;南京航空航天大学电子信息工程学院,南京,210016;南京航空航天大学电子信息工程学院,南京,210016【正文语种】中文【中图分类】TN911.7声源波达方向(Direction of arrival, DOA)估计是音频与语音信号处理领域的一个重要研究方向，在视频会议系统[1]、机器人听觉[2]和说话人识别系统[3]等诸多领域具有广泛应用。

新型滑动最小二乘技术的实现及其在无网格法中应用

2 滑动最小二乘(MLS)近似
B. Nayroles 等[2]提出的 DEM 和 T. Belytschko 等[3]的 EFGM 都以 MLS 近似为基础。在边界为Γ 的域Ω 中，函数 u(x)可拟出插值 u ( x) ：
h
n I m j
将基函数正交化，得
u h = ∑∑ p j ( x)( A −1 ( x) B( x)) jI u I
第 25 卷
增 1
2006 年 2 月
岩石力学与工程学报 Chinese Journal of Rock Mechanics and Engineering
Vol.25 Supp.1 Feb.， 2006
新型滑动最小二乘技术的实现及其在无网格法中应用
张延军 1，王恩志 2
(1. 吉林大学建设工程学院，吉林长春 130026；2. 清华大学水利水电工程系，北京 100084)
2D
• 3005 •
d=
i =1，n − 2 j =i +1，n−1 k ≠ j，n
∑ ∑ ∑ w w w (Θ
( xi，x j，xk )) 2
(8)
权函数，在节点处的计算点取一微位移 ε = 10−3 ，其余按常规 MLS 近似求解，可计算得到基函数 α 1 ，
Θ 2 D ( xi，x j，xk ) = − x j yi + xk yi + xi y j − xk y j − xi yk − x j yk
Sp (i ) ( x) ， α i ( x) 为正规方程的系数。上述公式中，
当包含奇异权函数 w( x，xk ) 的函数奇异性发生时，
可通过取极限方法避免奇异性的发生[6
3.2 Breitkopf 给出的公式求解法

面板数据stata处理步骤介绍

xA6_Panel_Data - Printed on 2011-11-25 10:43:02 149 reg y x dum1 dum2 dum3, nocons 150 est store m_pooldum3 151 152 *-M2：放入两个虚拟变量，三家公司有一个公共的截距项 153 reg y x dum2 dum3 154 est store m_pooldum2 155 156id t 158 xtreg y x, fe 159 est store m_fe 160 est table m_*, b(%6.3f) star(0.1 0.05 0.01) 161 162 163 *-6.1.4.3 stata的估计方法解析 164 165 * 目的：如果截面的个数非常多，那么采用虚拟变量的方式运算量过大 166 * 因此，要寻求合理的方式去除掉个体效应 167 * 因为，我们关注的是 x 的系数，而非每个截面的截距项 168 * 处理方法： 169 * 170 * y_it = u_i + x_it*b + e_it (1) 171 * ym_i = u_i + xm_i*b + em_i (2) 组内平均 172 * ym = um + xm*b + em (3) 样本平均 173 * (1) - (2), 可得： 174 * (y_it - ym_i) = (x_it - xm_i)*b + (e_it - em_i) （4）//within估计 175 * (4)+(3), 可得： 176 * (y_it-ym_i+ym) = um + (x_it-xm_i+xm)*b + (e_it-em_i+em) 177 * 可重新表示为： 178 * Y_it = a_0 + X_it*b + E_it 179 * 对该模型执行 OLS 估计，即可得到 b 的无偏估计量 180 181 egen y_meanw = mean(y), by(id) /*公司内部平均*/ 182 egen y_mean = mean(y) /*样本平均*/ 183 egen x_meanw = mean(x), by(id) 184 egen x_mean = mean(x) 185 gen dy = y - y_meanw + y_mean 186 gen dx = x - x_meanw + x_mean 187 reg dy dx 188 est store m_stata 189 190 est table m_*, b(%6.3f) star(0.1 0.05 0.01) 191 192 193 *-6.1.4.4 解读 xtreg,fe 的估计结果 194 195 use invest2.dta, clear 196 tsset id t 197 edit 198 xtreg market invest stock, fe 199 200 *-- R^2 201 * y_it = a_0 + x_it*b_o + e_it (1) pooled OLS 202 * y_it = u_i + x_it*b_w + e_it (2) within estimator 203 * ym_i = a_0 + xm_i*b_b + em_i (3) between estimator 204 * 205 * -> R-sq: within 模型(2)对应的R2，是一个真正意义上的R2 206 * -> R-sq: between corr{xm_i*b_w,ym_i}^2 207 * -> R-sq: overall corr{x_it*b_w,y_it}^2 208 209 *-- F(2,93) = 33.23 检验除常数项外其他解释变量的联合显著性 210 * 93 = 100-2-5 211 212 *-- corr(u_i, Xb) = 0.5256 213 214 *-- sigma_u, sigma_e, rho 215 * rho = sigma_u^2 / (sigma_u^2 + sigma_e^2) 216 dis e(sigma_u)^2 / (e(sigma_u)^2 + e(sigma_e)^2) 217 dis 1023.5914^2 / (1023.5914^2 + 370.9569^2) 218 219 *-- 个体效应是否显著？（假设检验） 220 * F(4, 93) = 97.68 H0: a1 = a2 = a3 = a4 = 0 221 * Prob > F = 0.0000 表明，固定效应高度显著 222 Page 3

求解线性方程组稀疏解的稀疏贪婪随机Kaczmarz算法

大小 k̂ 。②输出 xj。③初始化 S = {1，…，n}，x0 = 0，
j = 0。④当 j ≤ M 时，置 j = j + 1。⑤选择行向量
ai，i ∈
{
1，…，n
}，每一行对应的概率为
‖a‖i
2 2
‖A‖
2 F
。
⑥
( | ) 确定估计的支持集 S，S = supp xj-1 max { k̂，n-j+1 } 。
行从而达到加快算法收敛速度的目的。算法 3 给出
稀疏贪婪随机 Kaczmarz 算法。
算法 3 稀疏贪婪随机 Kaczmarz 算法。①输入
A∈ Rm×n，b ∈ Rm，最大迭代数 M 和估计的支持集的
大小 k̂ 。 ② 输出 xk。 ③ 初始化 S = {1，…，n}，x0 =
x
* 0
=
0。④
置
k
=
0
时，当
k
≤
M
-
1
时。⑤计算
( {| | } ϵk=
1 2
‖b
1 - Ax‖k 22
max
1≤ ik ≤ m
bik - aik xk 2
‖a
‖ ik
2 2
+
)1
‖A‖
2 F
（2）
⑥决定正整数指标集
{ | | } Uk =
ik|
bik - aik xk
2
≥
ϵ‖k b
-
Ax‖k
‖22 a
‖ ik
2 2
ï í
1
ï î
j
l∈S l ∈ Sc
其中，j 为迭代步数。当 j → ∞ 时，wj⊙ai → aiS，因此

经验模态与小波分解在光学遥感内波参数提取中的应用

经验模态与小波分解在光学遥感内波参数提取中的应用叶海彬;杨顶田;杨超宇【摘要】内波遥感参数提取是利用遥感影像研究海洋内波的重要手段,通过提取内波的基本参数可以对海洋内波的生成与传播机制进行进一步的研究.提出了利用经验模态分解、小波分解与高阶多项式拟合从光学影像中提取内波半波宽度的方法.经验模态分解与小波分解对内波剖面数据进行尺度分解,根据归一化方差最大来提取内波分量；多项式拟合基于内波剖面的亮暗条纹变化完全由内波调制的假设,对数据进行拟合,并根据一阶导数来提取半波宽度.用南海北部东沙岛附近2004年7月10日的中-巴资源卫星(China-Brazil Earth Resources Satellite,CBERS)影像对方法进行了验证.结果表明,3种方法能较好地提取所需参数,获取的内波半波宽度具有较好的一致性；上述方法在处理非平稳及非线性遥感数据上,具有非常明显的优势.基于一维非线性内波理论,通过提取的内波半波宽度,辅以水深和混合层深度数据,反演了内波的振幅.%Retrieving internal wave parameters from remote sensing data plays an important role in internal wave research. The generation and propagation mechanisms of such waves can be studied using the parameters extracted from remote sensing data. The authors use empirical mode decomposition, wavelet decomposition and high-order polynomial fitting in extracting internal waves' (IWs) half-wave width from optical remote sensing images. With the method of Empirical mode decomposition and wavelet decomposition the remote sensing data is decomposed and the signal of IWs is extracted by the normalized variance of IWs. Polynomial fitting is based on the assumptions that bright and dark stripes completely change within the wave modulation and that the firstderivative the half-wave width can be extracted. The three methods have been verified by the image of China-Brazil Earth Resources Satellite (CBERS), which was imaging the northern South China Sea near Dongsha Atoll on July 10th, 2004. Results show that the three methods can effectively extract the needed parameters with all the results of half-wave width being in good agreement with each other. The above methods have obvious advantages in dealing with non-stationary and nonlinear remote sensing data. Using the extracted half-wave width data and other related data (water depth and mixed layer depth), the authors retrieve IWs' amplitude base on the nonlinear internal wave theory.【期刊名称】《热带海洋学报》【年(卷),期】2012(031)002【总页数】8页(P47-54)【关键词】经验模态分解;小波分解;多项式拟合;光学遥感;内波;半波宽度【作者】叶海彬;杨顶田;杨超宇【作者单位】热带海洋环境国家重点实验室(中国科学院南海海洋研究所),广东广州510301;中国科学院研究生院,北京100049;热带海洋环境国家重点实验室(中国科学院南海海洋研究所),广东广州510301;热带海洋环境国家重点实验室(中国科学院南海海洋研究所),广东广州510301;中国科学院研究生院,北京100049【正文语种】中文【中图分类】P237;P733.3遥感影像能够观测到内波, 但由于海洋现象十分复杂, 遥感影像上信息含量非常丰富, 加上成像过程中各种斑点噪声的影响, 要从图像中提取与内波有关的信息较为困难。

一类动力学方程及流体力学方程解的Gevrey类正则性

Boltzmann 方程 . . . . . . . . . . . . . . . . . . . . . . . . 碰撞算子 Q(f, f ) 的基本性质 . . . . . . . . . . . . . . . . . Fokker-Planck 方程、Landau 方程以及 Boltzmann 方程线性化模型 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Navier-Stokes 方程 . . . . . . . . . . . . . . . . . . . . . . . Gevrey 函数空间 . . . . . . . . . . . . . . . . . . . . . . . .
研究现状及本文主要结果 . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 1.2.2 1.2.3 1.2.4 存在性及唯一性 . . . . . . . . . . . . . . . . . . . . . . . . . 动力学方程的正则性理论: 空间齐次情形 . . . . . . . . . . . 动力学方程的正则性理论: 空间非齐次情形 . . . . . . . . . . Navier-Stokes 方程的正则性理论 . . . . . . . . . . . . . . .
第二章预备知识 2.1 2.2 2.3 基本记号
Fourier 变换 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 基本函数空间及常用不等式 . . . . . . . . . . . . . . . . . . . . . . 2.3.1 2.3.2 Lp 空间及其性质 . . . . . . . . . . . . . . . . . . . . . . . . Sobolev 空间及其性质 . . . . . . . . . . . . . . . . . . . . .

系统辨识_6_多新息辨识理论与方法_丁锋

的最小二乘辨识算法或随机梯度等辨识算法有下列形式： ^ （ t） = θ ^ （ t － 1 ） + L （ t ） e（ t ）， θ e（ t）： = 其中 L（ t） ∈R 为算法增益向量（ gain vector）， T ^ （ t － 1 ） ∈R 为标量新息（ scalar innovay （ t）－ φ （ t ） θ tion），即单新息（ single innovation）．这个算法可以这样描述： t 时刻的参数估计向量 ^ （ t）是用增益向量 L （ t）与标量新息 e （ t ）的乘积， θ 对 ^ （ t － 1 ）进行修正， ^ （ t） t － 1 时刻参数估计向量 θ 即θ ^ （ t － 1 ）的基础上加上增益向量 L （ t ）与新息是在 θ e（ t）的乘积．这种方法也称为新息修正辨识方法或新息辨识方法．上述算法中新息 e （ t ）是标量，我们把这个标量 in新息加以推广，就导出了多新息辨识方法（ multinovation identification method ）［24］．多新息辨识理论（ multiinnovation identification theory ）就是将单新息从新息修正角度提出多新息修修正技术加以推广，正技术辨识的概念，建立多新息修正辨识方法，简称多新息辨识方法．顾名思义，多新息算法就是将新息加以推广．对将算法中的标量新息 e （ t ） ∈ R 推广标量系统而言， t ） ∈ Rp ， innova为新息向量 E （ p，即多新息（ multin tion），为使矩阵乘法维数兼容，增益向量 L （ t ） ∈ R t ） ∈R n × p ，须推广为增益矩阵（ gain matrix） Γ（ p，那么 n

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EXTENDINGTHESCOPEOFWAVELETREGRESSIONMETHODSBYCOEFFICIENT-DEPENDENTTHRESHOLDING

ARNEKOVAC,BERNARDW.SILVERMANABSTRACT.Variousaspectsofthewaveletapproachtononparametricregressionareconsid-ered,withtheoverallaimofextendingthescopeofwavelettechniques,toirregularly-spaceddata,toregularly-spaceddatasetsofarbitrarysize,toheteroscedasticandcorrelateddata,andtodatathatcontainoutliers.Thecoreofthemethodologyisanalgorithmforﬁndingallthevariancesandwithin-levelcovariancesinthewavelettableofasequencewithgivencovari-ancestructure.Iftheoriginalcovariancematrixisbandlimited,thenthealgorithmislinearinthelengthofthesequence.Thevariance-calculationalgorithmallowsdataonanysetofindependentvariablevaluestobetreated,byﬁrstinterpolatingtoaﬁneregulargridofsuitablelength,andthenconstructingawaveletexpansionofthegriddeddata.Variousthresholdingmethodsarediscussedandinvestigated.Exactriskformulaeforthemeansquareerrorofthemethodologyforgivendesignarederived.Goodperformanceisobtainedbynoise-proportionalthresholding,withthresholdssomewhatsmallerthantheclassicaluniversalthreshold.Outliersinthedatacanberemovedordownweighted,andaspectsofsuchrobusttech-niquesaredevelopedanddemonstratedinanexample.Anothernaturalapplicationistocor-relateddata,wherethecovarianceofthewaveletcoefﬁcientsisnotduetoaninitialgridtransformbutisanintrinsicfeature.Theuseofthemethodinthesecircumstancesisdemon-stratedbyanapplicationtodatasynthesizedinthestudyofionchannelgating.Thebasicapproachofthepaperhasmanyotherpotentialapplications,andsomeofthesearediscussedbrieﬂy.

ArneKovaciswissenschaftlicherMitarbeiter,Fachbereich6,MathematikundInformatik,Universit¨atGesamthochschuleEssen,45117Essen,Germany(E-mail:Arne.Kovac@uni-essen.de);andBernardW.Silver-manisProfessorofStatistics,SchoolofMathematics,UniversityofBristol,UniversityWalk,BristolBS81TW,UK.(E-mail:B.W.Silverman@bristol.ac.uk)ThisworkwasstartedwhenAKwasaresearchstudentattheUniversityofBristol,supportedbytheGermanAcademicExchangeServiceandwascontinuedwhileBWSwasaFellowattheCenterforAdvancedStudyintheBehavioralSciences,Stanford,supportedbyNSFgrantSBR-9601236.TheauthorsgratefullythankGuyNason,MartinL¨owendickandtherefereesfortheirhelpfulcomments.12ARNEKOVAC,BERNARDW.SILVERMAN1.INTRODUCTION

1.1.Backgroundandmainresult.Instatistics,waveletmethodshavebeenmostwidelystudiedinthenon-parametricregressionproblemofestimatingafunctiononthebasisofobservationsattimepoints,modelledas(1)

wherearenoise.Withsomenotableexceptions,thecurrentliteraturemainlydealswithapowerof2,independentandidenticallydistributederrors,andequallyspacedpoints.Ourmethod-ologyallowsalltheseassumptionstoberelaxed,butweshallespeciallybeconcernedwithnon-equallyspacedpointsandwithgeneralsamplesize,withrobustmethodsthatallowoutlierstobedownweightedintheﬁttingprocess,andwithcorrelatedandheteroscedasticerrors.

Mostwavelet-basedmethodsusethediscretewavelettransform(DWT)describedbyMal-lat(1989).Initsstandardform,thisprovidesamultiresolutionanalysisofavectorofvalues.Inthe‘classical’waveletregressionsetting,thesevaluesarethedatapoints,andthevariancematrixofisamultipleoftheidentitymatrix.BecausetheDWTisanorthogonaltransform,thewaveletcoefﬁcientsarealsouncorrelatedwithequalvariances.JohnstoneandSilverman(1997)haveconsideredthecaseofwaveletthresholdingwherethenoiseiscorre-latedbutstationary.Thevariancesofthewaveletcoefﬁcientsateachlevelarethenidentical,butdifferbetweenlevels,andsothecoefﬁcientscanbethresholdedlevelbylevel.Butwhatifhasmoregeneral,andnotnecessarilystationary,variancematrix?IngeneraltheDWTcoefﬁcientswillbeheteroscedasticandcorrelated.Wesetupanalgorithmyieldingallthevariancesandwithin-levelcovariancesoftheDWTforawiderangeofvari-ancematrices.Providedisband-limited,thealgorithmwillbelinearin.Thisalgorithmisthecoreofourmethodologyandhasverybroadpotentialuses.WepresentitanddiscussitscomplexitypropertiesinSection2,beforeapplyingitinspeciﬁcregressioncontexts,relaxingmanyoftheclassicalassumptions.COEFFICIENT-DEPENDENTTHRESHOLDINGINWAVELETREGRESSION30.00.20.40.60.81.01234Equivalence RatioNOx0.00.20.40.60.81.01234

Equivalence RatioNOx

0.00.20.40.60.81.01234Equivalence RatioNOx0.00.20.40.60.81.01234Equivalence RatioNOx

FIGURE1.Eighty-eightmeasurementsofexhaustfromburningethanolwiththreewaveletestimators.Awaveletbasiswithﬁvevanishingmomentswasused.Topright:dataregardedaslyingonaregulargrid,andstandarduni-versalthresholdingwaveletestimatorapplied.(Thedataisextendedtolength128byreﬂection.)Bottomleft:ourmethodforirregulardataassumingequalvariances.Bottomright:ourmethodforirregulardatawithlocalestimationofthevariance.Universalthresholdsareusedineachcase;forthebottomﬁguresthesearenoise-proportional.