Mining Subsidence Paper_Ren_Li_Buckeridge_rev4_Jan2010

格式：pdf
大小：965.16 KB
文档页数：19

下载文档原格式

A_review_on_time_series_data_mining

A review on time series data miningTak-chung FuDepartment of Computing,Hong Kong Polytechnic University,Hunghom,Kowloon,Hong Konga r t i c l e i n f oArticle history:Received19February2008Received in revised form14March2010Accepted4September2010Keywords:Time series data miningRepresentationSimilarity measureSegmentationVisualizationa b s t r a c tTime series is an important class of temporal data objects and it can be easily obtained from scientiﬁcandﬁnancial applications.A time series is a collection of observations made chronologically.The natureof time series data includes:large in data size,high dimensionality and necessary to updatecontinuously.Moreover time series data,which is characterized by its numerical and continuousnature,is always considered as a whole instead of individual numericalﬁeld.The increasing use of timeseries data has initiated a great deal of research and development attempts in theﬁeld of data mining.The abundant research on time series data mining in the last decade could hamper the entry ofinterested researchers,due to its complexity.In this paper,a comprehensive revision on the existingtime series data mining researchis given.They are generally categorized into representation andindexing,similarity measure,segmentation,visualization and mining.Moreover state-of-the-artresearch issues are also highlighted.The primary objective of this paper is to serve as a glossary forinterested researchers to have an overall picture on the current time series data mining developmentand identify their potential research direction to further investigation.&2010Elsevier Ltd.All rights reserved.1.IntroductionRecently,the increasing use of temporal data,in particulartime series data,has initiated various research and developmentattempts in theﬁeld of data mining.Time series is an importantclass of temporal data objects,and it can be easily obtained fromscientiﬁc andﬁnancial applications(e.g.electrocardiogram(ECG),daily temperature,weekly sales totals,and prices of mutual fundsand stocks).A time series is a collection of observations madechronologically.The nature of time series data includes:large indata size,high dimensionality and update continuously.Moreovertime series data,which is characterized by its numerical andcontinuous nature,is always considered as a whole instead ofindividual numericalﬁeld.Therefore,unlike traditional databaseswhere similarity search is exact match based,similarity search intime series data is typically carried out in an approximatemanner.There are various kinds of time series data related research,forexample,ﬁnding similar time series(Agrawal et al.,1993a;Berndtand Clifford,1996;Chan and Fu,1999),subsequence searching intime series(Faloutsos et al.,1994),dimensionality reduction(Keogh,1997b;Keogh et al.,2000)and segmentation(Abonyiet al.,2005).Those researches have been studied in considerabledetail by both database and pattern recognition communities fordifferent domains of time series data(Keogh and Kasetty,2002).In the context of time series data mining,the fundamentalproblem is how to represent the time series data.One of thecommon approaches is transforming the time series to anotherdomain for dimensionality reduction followed by an indexingmechanism.Moreover similarity measure between time series ortime series subsequences and segmentation are two core tasksfor various time series mining tasks.Based on the time seriesrepresentation,different mining tasks can be found in theliterature and they can be roughly classiﬁed into fourﬁelds:pattern discovery and clustering,classiﬁcation,rule discovery andsummarization.Some of the research concentrates on one of theseﬁelds,while the others may focus on more than one of the aboveprocesses.In this paper,a comprehensive review on the existingtime series data mining research is given.Three state-of-the-arttime series data mining issues,streaming,multi-attribute timeseries data and privacy are also brieﬂy introduced.The remaining part of this paper is organized as follows:Section2contains a discussion of time series representation andindexing.The concept of similarity measure,which includes bothwhole time series and subsequence matching,based on the rawtime series data or the transformed domain will be reviewed inSection3.The research work on time series segmentation andvisualization will be discussed in Sections4and5,respectively.InSection6,vary time series data mining tasks and recent timeseries data mining directions will be reviewed,whereas theconclusion will be made in Section7.2.Time series representation and indexingOne of the major reasons for time series representation is toreduce the dimension(i.e.the number of data point)of theContents lists available at ScienceDirectjournal homepage:/locate/engappaiEngineering Applications of Artiﬁcial Intelligence0952-1976/$-see front matter&2010Elsevier Ltd.All rights reserved.doi:10.1016/j.engappai.2010.09.007E-mail addresses:cstcfu@.hk,cstcfu@Engineering Applications of Artiﬁcial Intelligence24(2011)164–181original data.The simplest method perhaps is sampling(Astrom, 1969).In this method,a rate of m/n is used,where m is the length of a time series P and n is the dimension after dimensionality reduction(Fig.1).However,the sampling method has the drawback of distorting the shape of sampled/compressed time series,if the sampling rate is too low.An enhanced method is to use the average(mean)value of each segment to represent the corresponding set of data points. Again,with time series P¼ðp1,...,p mÞand n is the dimension after dimensionality reduction,the‘‘compressed’’time series ^P¼ð^p1,...,^p nÞcan be obtained by^p k ¼1k kX e ki¼s kp ið1Þwhere s k and e k denote the starting and ending data points of the k th segment in the time series P,respectively(Fig.2).That is, using the segmented means to represent the time series(Yi and Faloutsos,2000).This method is also called piecewise aggregate approximation(PAA)by Keogh et al.(2000).1Keogh et al.(2001a) propose an extended version called an adaptive piecewise constant approximation(APCA),in which the length of each segment is notﬁxed,but adaptive to the shape of the series.A signature technique is proposed by Faloutsos et al.(1997)with similar ideas.Besides using the mean to represent each segment, other methods are proposed.For example,Lee et al.(2003) propose to use the segmented sum of variation(SSV)to represent each segment of the time series.Furthermore,a bit level approximation is proposed by Ratanamahatana et al.(2005)and Bagnall et al.(2006),which uses a bit to represent each data point.To reduce the dimension of time series data,another approach is to approximate a time series with straight lines.Two major categories are involved.Theﬁrst one is linear interpolation.A common method is using piecewise linear representation(PLR)2 (Keogh,1997b;Keogh and Smyth,1997;Smyth and Keogh,1997). The approximating line for the subsequence P(p i,y,p j)is simply the line connecting the data points p i and p j.It tends to closely align the endpoint of consecutive segments,giving the piecewise approximation with connected lines.PLR is a bottom-up algo-rithm.It begins with creating aﬁne approximation of the time series,so that m/2segments are used to approximate the m length time series and iteratively merges the lowest cost pair of segments,until it meets the required number of segment.When the pair of adjacent segments S i and S i+1are merged,the cost of merging the new segment with its right neighbor and the cost of merging the S i+1segment with its new larger neighbor is calculated.Ge(1998)extends PLR to hierarchical structure. Furthermore,Keogh and Pazzani enhance PLR by considering weights of the segments(Keogh and Pazzani,1998)and relevance feedback from the user(Keogh and Pazzani,1999).The second approach is linear regression,which represents the subsequences with the bestﬁtting lines(Shatkay and Zdonik,1996).Furthermore,reducing the dimension by preserving the salient points is a promising method.These points are called as perceptually important points(PIP).The PIP identiﬁcation process isﬁrst introduced by Chung et al.(2001)and used for pattern matching of technical(analysis)patterns inﬁnancial applications. With the time series P,there are n data points:P1,P2y,P n.All the data points in P can be reordered by its importance by going through the PIP identiﬁcation process.Theﬁrst data point P1and the last data point P n in the time series are theﬁrst and two PIPs, respectively.The next PIP that is found will be the point in P with maximum distance to theﬁrst two PIPs.The fourth PIP that is found will be the point in P with maximum vertical distance to the line joining its two adjacent PIPs,either in between theﬁrst and second PIPs or in between the second and the last PIPs.The PIP location process continues until all the points in P are attached to a reordered list L or the required number of PIPs is reached(i.e. reduced to the required dimension).Seven PIPs are identiﬁed in from the sample time series in Fig.3.Detailed treatment can be found in Fu et al.(2008c).The idea is similar to a technique proposed about30years ago for reducing the number of points required to represent a line by Douglas and Peucker(1973)(see also Hershberger and Snoeyink, 1992).Perng et al.(2000)use a landmark model to identify the important points in the time series for similarity measure.Man and Wong(2001)propose a lattice structure to represent the identiﬁed peaks and troughs(called control points)in the time series.Pratt and Fink(2002)and Fink et al.(2003)deﬁne extrema as minima and maxima in a time series and compress thetime Fig.1.Time series dimensionality reduction by sampling.The time series on the left is sampled regularly(denoted by dotted lines)and displayed on the right with a largedistortion.Fig.2.Time series dimensionality reduction by PAA.The horizontal dotted lines show the mean of each segment.1This method is called piecewise constant approximation originally(Keoghand Pazzani,2000a).2It is also called piecewise linear approximation(PLA).Tak-chung Fu/Engineering Applications of Artiﬁcial Intelligence24(2011)164–181165series by selecting only certain important extrema and dropping the other points.The idea is to discard minor ﬂuctuations and keep major minima and maxima.The compression is controlled by the compression ratio with parameter R ,which is always greater than one;an increase of R leads to the selection of fewer points.That is,given indices i and j ,where i r x r j ,a point p x of a series P is an important minimum if p x is the minimum among p i ,y ,p j ,and p i /p x Z R and p j /p x Z R .Similarly,p x is an important maximum if p x is the maximum among p i ,y ,p j and p x /p i Z R and p x /p j Z R .This algorithm takes linear time and constant memory.It outputs the values and indices of all important points,as well as the ﬁrst and last point of the series.This algorithm can also process new points as they arrive,without storing the original series.It identiﬁes important points based on local information of each segment (subsequence)of time series.Recently,a critical point model (CPM)(Bao,2008)and a high-level representation based on a sequence of critical points (Bao and Yang,2008)are proposed for ﬁnancial data analysis.On the other hand,special points are introduced to restrict the error on PLR (Jia et al.,2008).Key points are suggested to represent time series in (Leng et al.,2009)for an anomaly detection.Another common family of time series representation approaches converts the numeric time series to symbolic form.That is,ﬁrst discretizing the time series into segments,then converting each segment into a symbol (Yang and Zhao,1998;Yang et al.,1999;Motoyoshi et al.,2002;Aref et al.,2004).Lin et al.(2003;2007)propose a method called symbolic aggregate approximation (SAX)to convert the result from PAA to symbol string.The distribution space (y -axis)is divided into equiprobable regions.Each region is represented by a symbol and each segment can then be mapped into a symbol corresponding to the region inwhich it resides.The transformed time series ^Pusing PAA is ﬁnally converted to a symbol string SS (s 1,y ,s W ).In between,two parameters must be speciﬁed for the conversion.They are the length of subsequence w and alphabet size A (number of symbols used).Besides using the means of the segments to build the alphabets,another method uses the volatility change to build the alphabets.Jonsson and Badal (1997)use the ‘‘Shape Description Alphabet (SDA)’’.Example symbols like highly increasing transi-tion,stable transition,and slightly decreasing transition are adopted.Qu et al.(1998)use gradient alphabets like upward,ﬂat and download as symbols.Huang and Yu (1999)suggest transforming the time series to symbol string,using change ratio between contiguous data points.Megalooikonomou et al.(2004)propose to represent each segment by a codeword from a codebook of key-sequences.This work has extended to multi-resolution consideration (Megalooi-konomou et al.,2005).Morchen and Ultsch (2005)propose an unsupervised discretization process based on quality score and persisting states.Instead of ignoring the temporal order of values like many other methods,the Persist algorithm incorporates temporal information.Furthermore,subsequence clustering is a common method to generate the symbols (Das et al.,1998;Li et al.,2000a;Hugueney and Meunier,2001;Hebrail and Hugueney,2001).A multiple abstraction level mining (MALM)approach is proposed by Li et al.(1998),which is based on the symbolic form of the time series.The symbols in this paper are determined by clustering the features of each segment,such as regression coefﬁcients,mean square error and higher order statistics based on the histogram of the regression residuals.Most of the methods described so far are representing time series in time domain directly.Representing time series in the transformation domain is another large family of approaches.One of the popular transformation techniques in time series data mining is the discrete Fourier transforms (DFT),since ﬁrst being proposed for use in this context by Agrawal et al.(1993a).Raﬁei and Mendelzon (2000)develop similarity-based queries,using DFT.Janacek et al.(2005)propose to use likelihood ratio statistics to test the hypothesis of difference between series instead of an Euclidean distance in the transformed domain.Recent research uses wavelet transform to represent time series (Struzik and Siebes,1998).In between,the discrete wavelet transform (DWT)has been found to be effective in replacing DFT (Chan and Fu,1999)and the Haar transform is always selected (Struzik and Siebes,1999;Wang and Wang,2000).The Haar transform is a series of averaging and differencing operations on a time series (Chan and Fu,1999).The average and difference between every two adjacent data points are computed.For example,given a time series P ¼(1,3,7,5),dimension of 4data points is the full resolution (i.e.original time series);in dimension of two coefﬁcients,the averages are (26)with the coefﬁcients (À11)and in dimension of 1coefﬁcient,the average is 4with coefﬁcient (À2).A multi-level representation of the wavelet transform is proposed by Shahabi et al.(2000).Popivanov and Miller (2002)show that a large class of wavelet transformations can be used for time series representation.Dasha et al.(2007)compare different wavelet feature vectors.On the other hand,comparison between DFT and DWT can be found in Wu et al.(2000b)and Morchen (2003)and a combination use of Fourier and wavelet transforms are presented in Kawagoe and Ueda (2002).An ensemble-index,is proposed by Keogh et al.(2001b)and Vlachos et al.(2006),which ensembles two or more representations for indexing.Principal component analysis (PCA)is a popular multivariate technique used for developing multivariate statistical process monitoring methods (Yang and Shahabi,2005b;Yoon et al.,2005)and it is applied to analyze ﬁnancial time series by Lesch et al.(1999).In most of the related works,PCA is used to eliminate the less signiﬁcant components or sensors and reduce the data representation only to the most signiﬁcant ones and to plot the data in two dimensions.The PCA model deﬁnes linear hyperplane,it can be considered as the multivariate extension of the PLR.PCA maps the multivariate data into a lower dimensional space,which is useful in the analysis and visualization of correlated high-dimensional data.Singular value decomposition (SVD)(Korn et al.,1997)is another transformation-based approach.Other time series representation methods include modeling time series using hidden markov models (HMMs)(Azzouzi and Nabney,1998)and a compression technique for multiple stream is proposed by Deligiannakis et al.(2004).It is based onbaseFig.3.Time series compression by data point importance.The time series on the left is represented by seven PIPs on the right.Tak-chung Fu /Engineering Applications of Artiﬁcial Intelligence 24(2011)164–181166signal,which encodes piecewise linear correlations among the collected data values.In addition,a recent biased dimension reduction technique is proposed by Zhao and Zhang(2006)and Zhao et al.(2006).Moreover many of the representation schemes described above are incorporated with different indexing methods.A common approach is adopted to an existing multidimensional indexing structure(e.g.R-tree proposed by Guttman(1984))for the representation.Agrawal et al.(1993a)propose an F-index, which adopts the R*-tree(Beckmann et al.,1990)to index theﬁrst few DFT coefﬁcients.An ST-index is further proposed by (Faloutsos et al.(1994),which extends the previous work for subsequence handling.Agrawal et al.(1995a)adopt both the R*-and R+-tree(Sellis et al.,1987)as the indexing structures.A multi-level distance based index structure is proposed(Yang and Shahabi,2005a),which for indexing time series represented by PCA.Vlachos et al.(2005a)propose a Multi-Metric(MM)tree, which is a hybrid indexing structure on Euclidean and periodic spaces.Minimum bounding rectangle(MBR)is also a common technique for time series indexing(Chu and Wong,1999;Vlachos et al.,2003).An MBR is adopted in(Raﬁei,1999)which an MT-index is developed based on the Fourier transform and in(Kahveci and Singh,2004)which a multi-resolution index is proposed based on the wavelet transform.Chen et al.(2007a)propose an indexing mechanism for PLR representation.On the other hand, Kim et al.(1996)propose an index structure called TIP-index (TIme series Pattern index)for manipulating time series pattern databases.The TIP-index is developed by improving the extended multidimensional dynamic indexﬁle(EMDF)(Kim et al.,1994). An iSAX(Shieh and Keogh,2009)is proposed to index massive time series,which is developed based on an SAX.A multi-resolution indexing structure is proposed by Li et al.(2004),which can be adapted to different representations.To sum up,for a given index structure,the efﬁciency of indexing depends only on the precision of the approximation in the reduced dimensionality space.However in choosing a dimensionality reduction technique,we cannot simply choose an arbitrary compression algorithm.It requires a technique that produces an indexable representation.For example,many time series can be efﬁciently compressed by delta encoding,but this representation does not lend itself to indexing.In contrast,SVD, DFT,DWT and PAA all lend themselves naturally to indexing,with each eigenwave,Fourier coefﬁcient,wavelet coefﬁcient or aggregate segment map onto one dimension of an index tree. Post-processing is then performed by computing the actual distance between sequences in the time domain and discarding any false matches.3.Similarity measureSimilarity measure is of fundamental importance for a variety of time series analysis and data mining tasks.Most of the representation approaches discussed in Section2also propose the similarity measure method on the transformed representation scheme.In traditional databases,similarity measure is exact match based.However in time series data,which is characterized by its numerical and continuous nature,similarity measure is typically carried out in an approximate manner.Consider the stock time series,one may expect having queries like: Query1:ﬁnd all stocks which behave‘‘similar’’to stock A.Query2:ﬁnd all‘‘head and shoulders’’patterns last for a month in the closing prices of all high-tech stocks.The query results are expected to provide useful information for different stock analysis activities.Queries like Query2in fact is tightly coupled with the patterns frequently used in technical analysis, e.g.double top/bottom,ascending triangle,ﬂag and rounded top/bottom.In time series domain,devising an appropriate similarity function is by no means trivial.There are essentially two ways the data that might be organized and processed(Agrawal et al., 1993a).In whole sequence matching,the whole length of all time series is considered during the similarity search.It requires comparing the query sequence to each candidate series by evaluating the distance function and keeping track of the sequence with the smallest distance.In subsequence matching, where a query sequence Q and a longer sequence P are given,the task is toﬁnd the subsequences in P,which matches Q. Subsequence matching requires that the query sequence Q be placed at every possible offset within the longer sequence P.With respect to Query1and Query2above,they can be considered as a whole sequence matching and a subsequence matching,respec-tively.Gavrilov et al.(2000)study the usefulness of different similarity measures for clustering similar stock time series.3.1.Whole sequence matchingTo measure the similarity/dissimilarity between two time series,the most popular approach is to evaluate the Euclidean distance on the transformed representation like the DFT coefﬁ-cients(Agrawal et al.,1993a)and the DWT coefﬁcients(Chan and Fu,1999).Although most of these approaches guarantee that a lower bound of the Euclidean distance to the original data, Euclidean distance is not always being the suitable distance function in speciﬁed domains(Keogh,1997a;Perng et al.,2000; Megalooikonomou et al.,2005).For example,stock time series has its own characteristics over other time series data(e.g.data from scientiﬁc areas like ECG),in which the salient points are important.Besides Euclidean-based distance measures,other distance measures can easily be found in the literature.A constraint-based similarity query is proposed by Goldin and Kanellakis(1995), which extended the work of(Agrawal et al.,1993a).Das et al. (1997)apply computational geometry methods for similarity measure.Bozkaya et al.(1997)use a modiﬁed edit distance function for time series matching and retrieval.Chu et al.(1998) propose to measure the distance based on the slopes of the segments for handling amplitude and time scaling problems.A projection algorithm is proposed by Lam and Wong(1998).A pattern recognition method is proposed by Morrill(1998),which is based on the building blocks of the primitives of the time series. Ruspini and Zwir(1999)devote an automated identiﬁcation of signiﬁcant qualitative features of complex objects.They propose the process of discovery and representation of interesting relations between those features,the generation of structured indexes and textual annotations describing features and their relations.The discovery of knowledge by an analysis of collections of qualitative descriptions is then achieved.They focus on methods for the succinct description of interesting features lying in an effective frontier.Generalized clustering is used for extracting features,which interest domain experts.The general-ized Markov models are adopted for waveform matching in Ge and Smyth(2000).A content-based query-by-example retrieval model called FALCON is proposed by Wu et al.(2000a),which incorporates a feedback mechanism.Indeed,one of the most popular andﬁeld-tested similarity measures is called the‘‘time warping’’distance measure.Based on the dynamic time warping(DTW)technique,the proposed method in(Berndt and Clifford,1994)predeﬁnes some patterns to serve as templates for the purpose of pattern detection.To align two time series,P and Q,using DTW,an n-by-m matrix M isﬁrstTak-chung Fu/Engineering Applications of Artiﬁcial Intelligence24(2011)164–181167constructed.The(i th,j th)element of the matrix,m ij,contains the distance d(q i,p j)between the two points q i and p j and an Euclidean distance is typically used,i.e.d(q i,p j)¼(q iÀp j)2.It corresponds to the alignment between the points q i and p j.A warping path,W,is a contiguous set of matrix elements that deﬁnes a mapping between Q and P.Its k th element is deﬁned as w k¼(i k,j k)andW¼w1,w2,...,w k,...,w Kð2Þwhere maxðm,nÞr K o mþnÀ1.The warping path is typically subjected to the following constraints.They are boundary conditions,continuity and mono-tonicity.Boundary conditions are w1¼(1,1)and w K¼(m,n).This requires the warping path to start andﬁnish diagonally.Next constraint is continuity.Given w k¼(a,b),then w kÀ1¼(a0,b0), where aÀa u r1and bÀb u r1.This restricts the allowable steps in the warping path being the adjacent cells,including the diagonally adjacent cell.Also,the constraints aÀa uZ0and bÀb uZ0force the points in W to be monotonically spaced in time.There is an exponential number of warping paths satisfying the above conditions.However,only the path that minimizes the warping cost is of interest.This path can be efﬁciently found by using dynamic programming(Berndt and Clifford,1996)to evaluate the following recurrence equation that deﬁnes the cumulative distance gði,jÞas the distance dði,jÞfound in the current cell and the minimum of the cumulative distances of the adjacent elements,i.e.gði,jÞ¼dðq i,p jÞþmin f gðiÀ1,jÀ1Þ,gðiÀ1,jÞ,gði,jÀ1Þgð3ÞA warping path,W,such that‘‘distance’’between them is minimized,can be calculated by a simple methodDTWðQ,PÞ¼minWX Kk¼1dðw kÞ"#ð4Þwhere dðw kÞcan be deﬁned asdðw kÞ¼dðq ik ,p ikÞ¼ðq ikÀp ikÞ2ð5ÞDetailed treatment can be found in Kruskall and Liberman (1983).As DTW is computationally expensive,different methods are proposed to speedup the DTW matching process.Different constraint(banding)methods,which control the subset of matrix that the warping path is allowed to visit,are reviewed in Ratanamahatana and Keogh(2004).Yi et al.(1998)introduce a technique for an approximate indexing of DTW that utilizes a FastMap technique,whichﬁlters the non-qualifying series.Kim et al.(2001)propose an indexing approach under DTW similarity measure.Keogh and Pazzani(2000b)introduce a modiﬁcation of DTW,which integrates with PAA and operates on a higher level abstraction of the time series.An exact indexing approach,which is based on representing the time series by PAA for DTW similarity measure is further proposed by Keogh(2002).An iterative deepening dynamic time warping(IDDTW)is suggested by Chu et al.(2002),which is based on a probabilistic model of the approximate errors for all levels of approximation prior to the query process.Chan et al.(2003)propose aﬁltering process based on the Haar wavelet transformation from low resolution approx-imation of the real-time warping distance.Shou et al.(2005)use an APCA approximation to compute the lower bounds for DTW distance.They improve the global bound proposed by Kim et al. (2001),which can be used to index the segments and propose a multi-step query processing technique.A FastDTW is proposed by Salvador and Chan(2004).This method uses a multi-level approach that recursively projects a solution from a coarse resolution and reﬁnes the projected solution.Similarly,a fast DTW search method,an FTW is proposed by Sakurai et al.(2005) for efﬁciently pruning a signiﬁcant number of search candidates. Ratanamahatana and Keogh(2005)clariﬁed some points about DTW where are related to lower bound and speed.Euachongprasit and Ratanamahatana(2008)also focus on this problem.A sequentially indexed structure(SIS)is proposed by Ruengron-ghirunya et al.(2009)to balance the tradeoff between indexing efﬁciency and I/O cost during DTW similarity measure.A lower bounding function for group of time series,LBG,is adopted.On the other hand,Keogh and Pazzani(2001)point out the potential problems of DTW that it can lead to unintuitive alignments,where a single point on one time series maps onto a large subsection of another time series.Also,DTW may fail to ﬁnd obvious and natural alignments in two time series,because of a single feature(i.e.peak,valley,inﬂection point,plateau,etc.). One of the causes is due to the great difference between the lengths of the comparing series.Therefore,besides improving the performance of DTW,methods are also proposed to improve an accuracy of DTW.Keogh and Pazzani(2001)propose a modiﬁca-tion of DTW that considers the higher level feature of shape for better alignment.Ratanamahatana and Keogh(2004)propose to learn arbitrary constraints on the warping path.Regression time warping(RTW)is proposed by Lei and Govindaraju(2004)to address the challenges of shifting,scaling,robustness and tecki et al.(2005)propose a method called the minimal variance matching(MVM)for elastic matching.It determines a subsequence of the time series that best matches a query series byﬁnding the cheapest path in a directed acyclic graph.A segment-wise time warping distance(STW)is proposed by Zhou and Wong(2005)for time scaling search.Fu et al.(2008a) propose a scaled and warped matching(SWM)approach for handling both DTW and uniform scaling simultaneously.Different customized DTW techniques are applied to theﬁeld of music research for query by humming(Zhu and Shasha,2003;Arentz et al.,2005).Focusing on similar problems as DTW,the Longest Common Subsequence(LCSS)model(Vlachos et al.,2002)is proposed.The LCSS is a variation of the edit distance and the basic idea is to match two sequences by allowing them to stretch,without rearranging the sequence of the elements,but allowing some elements to be unmatched.One of the important advantages of an LCSS over DTW is the consideration on the outliers.Chen et al.(2005a)further introduce a distance function based on an edit distance on real sequence(EDR),which is robust against the data imperfection.Morse and Patel(2007)propose a Fast Time Series Evaluation(FTSE)method which can be used to evaluate the threshold value of these kinds of techniques in a faster way.Threshold-based distance functions are proposed by ABfalg et al. (2006).The proposed function considers intervals,during which the time series exceeds a certain threshold for comparing time series rather than using the exact time series values.A T-Time application is developed(ABfalg et al.,2008)to demonstrate the usage of it.Fu et al.(2007)further suggest to introduce rules to govern the pattern matching process,if a priori knowledge exists in the given domain.A parameter-light distance measure method based on Kolmo-gorov complexity theory is suggested in Keogh et al.(2007b). Compression-based dissimilarity measure(CDM)3is adopted in this paper.Chen et al.(2005b)present a histogram-based representation for similarity measure.Similarly,a histogram-based similarity measure,bag-of-patterns(BOP)is proposed by Lin and Li(2009).The frequency of occurrences of each pattern in 3CDM is proposed by Keogh et al.(2004),which is used to compare the co-compressibility between data sets.Tak-chung Fu/Engineering Applications of Artiﬁcial Intelligence24(2011)164–181 168。

back-matter

References1. D.L.Burkholder.Distribution function inequalities for martingales.Ann.Probability,1:19–42,1973.2. D.L.Burkholder and R.F.Gundy.Distribution function inequalities for thearea integral.Studia Math.,44:527–544,1972.3. D.L.Burkholder,R.F.Gundy,and M.L.Silverstein.A maximal functioncharacterization of the class H p.Trans.Amer.Math.Soc.,157:137–153,1971.4. A.P.Calder´o n.Intermediate spaces and interpolation,the complex method.Studia Math.,24:113–190,1964.5. A.P.Calder´o n.An atomic decomposition of distributions in parabolic H pspaces.Advances in Math.,25:216–225,1977.6. A.P.Calder´o n and A.Torchinsky.Parabolic maximal functions associated witha distribution,I.Advances in Math.,16:1–64,1975.7. A.P.Calder´o n and A.Torchinsky.Parabolic maximal functions associated witha distribution,II.Advances in Math.,24:101–171,1977.8. A.P.Calder´o n and A.Zygmund.On the existence of certain singular integrals.Acta.Math.,88:85–139,1952.9.S.Y.A.Chang and R.Feﬀerman.A continuous version of duality of H1andBMO on the bidisc.Ann.of Math.,112:179–201,1980.10.S.Y.A.Chang,J.M.Wilson,and T.H.Wolﬀ.Some weighted norm inequalitiesconcerning the Schroedinger m.Math.Helv.,60:217–246,1985.11.S.Chanillo and R.L.Wheeden.L p-estimates for fractional integrals and Sobolevinequalities with applications to Schroedinger operators.10:1077–1116,1985.12.S.Chanillo and R.L.Wheeden.Some weighted norm inequalities for the areaintegral.Indiana U.Math.Jour.,36:277–294,1987.13.R.Coifman and C.Feﬀerman.Weighted norm inequalities for maximal functionsand singular integrals.Studia Math.,51:269–274,1974.14. D.Cruz-Uribe and C.P´e rez.Two-weight extrapolation via the maximal oper-ator.J.Funct.Anal.,174:1–17,2000.15.I.Daubechies.Ten Lectures on Wavelets,volume61of CBMS-NSF RegionalConferences in Applied Mathematics.Society for Industrial and Applied Math-ematics,Philadelphia,1992.16.J.Duoandikoetxea.Fourier analysis.Number29in Graduate Studies in Math-ematics.American Mathematical Society,Providence,2001.220References17. C.Feﬀerman.The uncertainty principle.Bull.Amer.Math.Soc.(NS),9:129–206,1983.18. C.Feﬀerman and E.M.Stein.Some maximal inequalities.Amer.Jour.ofMath.,93:107–115,1971.19. C.Feﬀerman and E.M.Stein.H p spaces of several variables.Acta Math.,129:137–193,1972.20.R.Feﬀerman,R.F.Gundy,M.L.Silverstein,and E.M.Stein.Inequalitiesfor ratios of functionals of harmonic A, 79:7958–7960,1982.21.G.B.Folland.Real Analysis:Modern Techniques and Their Applications.WileyInterscience,New York,1999.22.M.Frazier,B.Jawerth,and G.Weiss.Littlewood-Paley Theory and the Studyof Function Spaces.Number79in CBMS Regional Conference Series in Math-ematics.American Mathematical Society,Providence,1991.23.J.Garcia-Cuerva.An extrapolation theorem in the theory of A p weights.Proc.Amer.Math.Soc.,87:422–426,1983.24.J.Garcia-Cuerva and J.L.Rubio de Francia.Weighted Norm Inequalities andRelated Topics.North-Holland,Amsterdam,1985.25.J.B.Garnett.Bounded Analytic Functions.Academic Press,New York,1981.26.R.F.Gundy and R.L.Wheeden.Weighted integral inequalities for the nontan-gential maximal function,Lusin area integral,and Walsh-Paley series.Studia Math.,49:107–124,1973/74.27. A.Haar.Zur Theorie der orthogonalen Funktionensysteme.Math.Ann.,69:331–371,1910.28.G.H.Hardy and J.E.Littlewood.A maximal theorem with function-theoreticapplications.Acta Math.,54:81–116,1930.29.L.Hormander.Estimates for translation invariant operators in L p spaces.ActaMath.,104:93–139,1960.30.R.A.Hunt,B.Muckenhoupt,and R.L.Wheeden.Weighted norm inequalitiesfor the conjugate function and Hilbert transform.Trans.Amer.Math.Soc., 176:227–251,1973.31.Y.Katznelson.An Introduction to Harmonic Analysis.Dover,New York,1976.32.R.Kerman and E.Sawyer.The trace inequality and eigenvalue estimates forSchroedinger operators.Annales de L’Institut Fourier,36:207–228,1986.33. A.Khinchin.Ueber dyadische Brueche.Math.Zeit.,18:109–116,1923.34.M.A.Krasnosel’skii and Ya.B.Rutickii.Convex functions and Orlicz spaces.P.Noordhoﬀ,Groningen,1961.35. D.S.Kurtz.Littlewood-Paley and multiplier theorems on weighted L p spaces.Trans.Amer.Math.Soc.,259:235–254,1980.36. D.S.Kurtz and R.L.Wheeden.Results on weighted norm inequalities formultipliers.Trans.Amer.Math.Soc.,255:343–362,1979.37.J.E.Littlewood and R.E.A.C.Paley.Theorems on Fourier series and powerseries,Part I.J.London Math.Soc.,6:230–233,1931.38.J.E.Littlewood and R.E.A.C.Paley.Theorems on Fourier series and powerseries,Part II.Proc.London Math.Soc.,42:52–89,1937.39.J.E.Littlewood and R.E.A.C.Paley.Theorems on Fourier series and powerseries,Part III.Proc.London Math.Soc.,43:105–126,1937.40.J.Marcinkiewicz.Sur l’interpolation d’op´e rations. C.R.Acad.Sci.Paris,208:1272–1273,1939.References221 41.S.G.Mihlin.On the multipliers of Fourier integrals.Dokl.Akad.Nauk.,109:701–703,1956.42. B.Muckenhoupt.Weighted norm inequalities for the Hardy maximal function.Trans.Amer.Math.Soc.,165:207–226,1972.43.T.Murai and A.Uchiyama.Good-λinequalities for the area integral and thenontangential maximal function.Studia Math.,83:251–262,1986.44. F.Nazarov.Private communication.45.R.O’Neill.Fractional integration in Orlicz spaces.Trans.Amer.Math.Soc.,115:300–328,1963.46. C.P´e rez.Weighted norm inequalities for singular integral operators.J.LondonMath.Soc.,49:296–308,1994.47. C.P´e rez.On suﬃcient conditions for the boundedness of the Hardy-Littlewoodmaximal operator between weighted L p spaces with diﬀerent weights.Proc.London Math.Soc.,71:135–157,1995.48. C.P´e rez.Sharp weighted L p weighted Sobolev inequalities.Annales deL’Institut Fourier,45:809–824,1995.49.J.L.Rubio de Francia.Factorization theory and A p weights.Amer.Jour.ofMath.,106:533–547,1984.50. C.Segovia and R.L.Wheeden.On weighted norm inequalities for the Lusinarea integral.Trans.Amer.Math.Soc.,176:103–123,1973.51. E.M.Stein.On the functions of Littlewood-Paley,Lusin,and Marcinkiewicz.Trans.Amer.Math.Soc.,88:430–466,1958.52. E.M.Stein.On some functions of Littlewood-Paley and Zygmund.Bull.Amer.Math.Soc.,67:99–101,1961.53. E.M.Stein.Singular Integrals and Diﬀerentiability Properties of Functions.Princeton University Press,Princeton,1970.54. E.M.Stein.The development of square functions in the work of A.Zygmund.Bull.Amer.Math.Soc.,7:359–376,1982.55.J.O.Stromberg and A.Torchinsky.Weighted Hardy Spaces,volume1381ofLecture Notes in Mathematics.Springer-Verlag,Berlin,1989.56. A.Torchinsky.Real-Variable Methods in Harmonic Analysis.Academic Press,New York,1986.57. A.Uchiyama.A constructive proof of the Feﬀerman-Stein decomposition ofBMO(R n).Acta Math.,148:215–241,1982.58.G.Weiss.A note on Orlicz spaces.Portugal Math.,15:35–47,1950.59.J.M.Wilson.The intrinsic square function.To appear in Revista MatematicaIberoamericana.60.J.M.Wilson.A sharp inequality for the square function.Duke Math.Jour.,55:879–888,1987.61.J.M.Wilson.Weighted inequalities for the dyadic square function withoutdyadic A∞.Duke Math.Jour.,55:19–49,1987.62.J.M.Wilson.Weighted norm inequalities for the continuous square function.Trans.Amer.Math.Soc.,314:661–692,1989.63.J.M.Wilson.Chanillo-Wheeden inequalities for0<p≤1.J.London Math.Soc.,41:283–294,1990.64.J.M.Wilson.Some two-parameter square function inequalities.Indiana U.Math.Jour.,40:419–442,1991.65.J.M.Wilson.Paraproducts and the exponential square class.Jour.of Math.Analy.and Applic.,271:374–382,2002.66. A.Zygmund.On certain integrals.Trans.Amer.Math.Soc.,55:170–204,1944.IndexY-functional,44,49,80adapted functionmultidimensional,81,90one-dimensional,69Calder´o n reproducing formula,85 Calder´o n-Zygmund operator,157, 158convergence,86,88,92–95,112,119in weighted L p,129limitations,97normalization,85redundancy,124Calder´o n-Zygmund decomposition,5 Calder´o n-Zygmund kernel,153Calder´o n-Zygmund operator,153 boundedness,154on test class,156,157Calder´o n reproducing formula,157, 158weighted norm inequalities,158,159 Carleson box,88top half,88Chanillo-Wheeden Inequality(Theorem3.10),60compact-measurable exhaustion,87 constantly changing constant,3Cruz-Uribe-P´e rez Theorem(Theorem10.9),181weighted norm inequalities,181,182, 184doubling weight,26dyadiccube,2,77interval,2maximal function,15square functionmultidimensional,77,78one-dimensional,13dyadic A∞,26dyadic doubling,26dyadic maximal function,15Hardy-Littlewood,15ﬁne structure,17 multidimensional,77one-dimensionalF-adapted,70exponential square class,39 multidimensional,80Fourier transform,1Free Lunch Lemma(Lemma6.2),114 functionalY-,44,49,80good and bad functions,6good family ofcubes,81,90intervals,69good-λinequalities,19goodbye to,189,190224IndexH¨o rmander-Mihlin Multiplier Theorem, 197Haar coeﬃcients,10and averages,12ﬁltering properties,10Haar functions,9multidimensional,77,82 Hamiltonian operator,145Hardy-Littlewood maximal function, 34,35dyadic,15Hardy-Littlewood Maximal Theorem, 34,35,37dyadic,15Hilbert transform,151harmonic conjugate,152 interpolation,17,32intrinsic square function,103,104,117, 118Khinchin’s Inequalities(Theorem14.1), 215maximal functiondyadic,15Hardy-Littlewood,34,35dyadic,15Orlicz space,167,168Rubio de Francia,27necessity of A∞,55Orlicz maximal functionintegrability,174,176Orlicz space,162dual,164examples,163H¨o lder inequality,166local,166maximal function,167,168P´e rez Maximal Theorem(Theorem10.4),168,185potential wells,147probability lemma,79Rademacher functions,214random variables,214independent,214Schr¨o dinger equation,145Schwartz class,2singular integral operator,151splitting of functions,5square functionclassical,113,120dyadicmultidimensional,77,78one-dimensional,13intrinsic,103,104,117,118dominates many others,117,118 one-dimensionalF-adapted,70real-variable,101semi-discretemultidimensional,90one-dimensional,71stopping-time argument,21,23,49 telescoping sum,52,64Uchiyama Decomposition Lemma(Lemma6.3),115uncertainty principle,147weak-type inequality,16weight,26A1,47A d∞,26,27,45,47 counterexample,217doubling,26draping,28inequalities,29counterexample,31,36,43,55,62,64,67Muckenhoupt A p condition,129connection with A∞,132,135,136extrapolation,131maximal functions,137,138singular integrals,159,160 weighted norm inequalitiesCalder´o n-Zygmund operator,158, 159Cruz-Uribe-P´e rez Theorem(Theorem10.9),184square function,181A p weights,130Young function,161approximate dual,172examples,173dual,164examples,165Lecture Notes in Mathematics For information about earlier volumesplease contact your bookseller or SpringerLNM Online archive:V ol.1732:K.Keller,Invariant Factors,Julia Equivalences and the(Abstract)Mandelbrot Set(2000)V ol.1733:K.Ritter,Average-Case Analysis of Numerical Problems(2000)V ol.1734:M.Espedal,A.Fasano,A.Mikeli´c,Filtration in Porous Media and Industrial Applications.Cetraro1998. Editor:A.Fasano.2000.V ol.1735:D.Yafaev,Scattering Theory:Some Old and New Problems(2000)V ol.1736:B.O.Turesson,Nonlinear Potential Theory and Weighted Sobolev Spaces(2000)V ol.1737:S.Wakabayashi,Classical Microlocal Analysis in the Space of Hyperfunctions(2000)V ol.1738:M.Émery,A.Nemirovski,D.V oiculescu, Lectures on Probability Theory and Statistics(2000)V ol.1739:R.Burkard,P.Deuﬂhard,A.Jameson,J.-L. Lions,G.Strang,Computational Mathematics Driven by Industrial Problems.Martina Franca,1999.Editors: V.Capasso,H.Engl,J.Periaux(2000)V ol.1740:B.Kawohl,O.Pironneau,L.Tartar,J.-P.Zole-sio,Optimal Shape Design.Tróia,Portugal1999.Editors: A.Cellina,A.Ornelas(2000)V ol.1741:E.Lombardi,Oscillatory Integrals and Phe-nomena Beyond all Algebraic Orders(2000)V ol.1742: A.Unterberger,Quantization and Non-holomorphic Modular Forms(2000)V ol.1743:L.Habermann,Riemannian Metrics of Con-stant Mass and Moduli Spaces of Conformal Structures (2000)V ol.1744:M.Kunze,Non-Smooth Dynamical Systems (2000)V ol.1745:man,G.Schechtman(Eds.),Geomet-ric Aspects of Functional Analysis.Israel Seminar1999-2000(2000)V ol.1746:A.Degtyarev,I.Itenberg,V.Kharlamov,Real Enriques Surfaces(2000)V ol.1747:L.W.Christensen,Gorenstein Dimensions (2000)V ol.1748:M.Ruzicka,Electrorheological Fluids:Model-ing and Mathematical Theory(2001)V ol.1749:M.Fuchs,G.Seregin,Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids(2001)V ol.1750:B.Conrad,Grothendieck Duality and Base Change(2001)V ol.1751:N.J.Cutland,Loeb Measures in Practice: Recent Advances(2001)V ol.1752:Y.V.Nesterenko,P.Philippon,Introduction to Algebraic Independence Theory(2001)V ol.1753:A.I.Bobenko,U.Eitner,PainlevéEquations in the Differential Geometry of Surfaces(2001)V ol.1754:W.Bertram,The Geometry of Jordan and Lie Structures(2001)V ol.1755:J.Azéma,M.Émery,M.Ledoux,M.Yor (Eds.),Séminaire de Probabilités XXXV(2001)V ol.1756:P.E.Zhidkov,Korteweg de Vries and Nonlin-ear Schrödinger Equations:Qualitative Theory(2001)V ol.1757:R.R.Phelps,Lectures on Choquet’s Theorem (2001)V ol.1758:N.Monod,Continuous Bounded Cohomology of Locally Compact Groups(2001)V ol.1759:Y.Abe,K.Kopfermann,Toroidal Groups (2001)V ol.1760:D.Filipovi´c,Consistency Problems for Heath-Jarrow-Morton Interest Rate Models(2001)V ol.1761:C.Adelmann,The Decomposition of Primes in Torsion Point Fields(2001)V ol.1762:S.Cerrai,Second Order PDE’s in Finite and Inﬁnite Dimension(2001)V ol.1763:J.-L.Loday,A.Frabetti,F.Chapoton,F.Goi-chot,Dialgebras and Related Operads(2001)V ol.1764:A.Cannas da Silva,Lectures on Symplectic Geometry(2001)V ol.1765:T.Kerler,V.V.Lyubashenko,Non-Semisimple Topological Quantum Field Theories for3-Manifolds with Corners(2001)V ol.1766:H.Hennion,L.Hervé,Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness(2001)V ol.1767:J.Xiao,Holomorphic Q Classes(2001)V ol.1768:M.J.Pﬂaum,Analytic and Geometric Study of Stratiﬁed Spaces(2001)V ol.1769:M.Alberich-Carramiñana,Geometry of the Plane Cremona Maps(2002)V ol.1770:H.Gluesing-Luerssen,Linear Delay-Differential Systems with Commensurate Delays:An Algebraic Approach(2002)V ol.1771:M.Émery,M.Yor(Eds.),Séminaire de Prob-abilités1967-1980.A Selection in Martingale Theory (2002)V ol.1772:F.Burstall,D.Ferus,K.Leschke,F.Pedit, U.Pinkall,Conformal Geometry of Surfaces in S4(2002) V ol.1773:Z.Arad,M.Muzychuk,Standard Integral Table Algebras Generated by a Non-real Element of Small Degree(2002)V ol.1774:V.Runde,Lectures on Amenability(2002)V ol.1775:W.H.Meeks,A.Ros,H.Rosenberg,The Global Theory of Minimal Surfaces in Flat Spaces. Martina Franca1999.Editor:G.P.Pirola(2002)V ol.1776:K.Behrend,C.Gomez,V.Tarasov,G.Tian, Quantum Comohology.Cetraro1997.Editors:P.de Bar-tolomeis,B.Dubrovin,C.Reina(2002)V ol.1777:E.García-Río,D.N.Kupeli,R.Vázquez-Lorenzo,Osserman Manifolds in Semi-Riemannian Geometry(2002)V ol.1778:H.Kiechle,Theory of K-Loops(2002)V ol.1779:I.Chueshov,Monotone Random Systems (2002)V ol.1780:J.H.Bruinier,Borcherds Products on O(2,1) and Chern Classes of Heegner Divisors(2002)V ol.1781:E.Bolthausen,E.Perkins,A.van der Vaart, Lectures on Probability Theory and Statistics.Ecole d’Etéde Probabilités de Saint-Flour XXIX-1999.Editor: P.Bernard(2002)V ol.1782:C.-H.Chu,u,Harmonic Functions on Groups and Fourier Algebras(2002)V ol.1783:L.Grüne,Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretiza-tion(2002)V ol.1784:L.H.Eliasson,S.B.Kuksin,S.Marmi,J.-C. Yoccoz,Dynamical Systems and Small Divisors.Cetraro, Italy1998.Editors:S.Marmi,J.-C.Yoccoz(2002)V ol.1785:J.Arias de Reyna,Pointwise Convergence of Fourier Series(2002)V ol.1786:S.D.Cutkosky,Monomialization of Mor-phisms from3-Folds to Surfaces(2002)V ol.1787:S.Caenepeel,itaru,S.Zhu,Frobenius and Separable Functors for Generalized Module Cate-gories and Nonlinear Equations(2002)V ol.1788:A.Vasil’ev,Moduli of Families of Curves for Conformal and Quasiconformal Mappings(2002)V ol.1789:Y.Sommerhäuser,Yetter-Drinfel’d Hopf alge-bras over groups of prime order(2002)V ol.1790:X.Zhan,Matrix Inequalities(2002)V ol.1791:M.Knebusch,D.Zhang,Manis Valuations and Prüfer Extensions I:A new Chapter in Commutative Algebra(2002)V ol.1792:D.D.Ang,R.Gorenﬂo,V.K.Le,D.D.Trong, Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction(2002)V ol.1793:J.Cortés Monforte,Geometric,Control and Numerical Aspects of Nonholonomic Systems(2002)V ol.1794:N.Pytheas Fogg,Substitution in Dynamics, Arithmetics and Combinatorics.Editors:V.Berthé,S.Fer-enczi,C.Mauduit,A.Siegel(2002)V ol.1795:H.Li,Filtered-Graded Transfer in Using Non-commutative Gröbner Bases(2002)V ol.1796:J.M.Melenk,hp-Finite Element Methods for Singular Perturbations(2002)V ol.1797:B.Schmidt,Characters and Cyclotomic Fields in Finite Geometry(2002)V ol.1798:W.M.Oliva,Geometric Mechanics(2002)V ol.1799:H.Pajot,Analytic Capacity,Rectiﬁability, Menger Curvature and the Cauchy Integral(2002)V ol.1800:O.Gabber,L.Ramero,Almost Ring Theory (2003)V ol.1801:J.Azéma,M.Émery,M.Ledoux,M.Yor (Eds.),Séminaire de Probabilités XXXVI(2003)V ol.1802:V.Capasso, E.Merzbach, B.G.Ivanoff, M.Dozzi,R.Dalang,T.Mountford,Topics in Spatial Stochastic Processes.Martina Franca,Italy2001.Editor: E.Merzbach(2003)V ol.1803:G.Dolzmann,Variational Methods for Crys-talline Microstructure–Analysis and Computation(2003) V ol.1804:I.Cherednik,Ya.Markov,R.Howe,G.Lusztig, Iwahori-Hecke Algebras and their Representation Theory. Martina Franca,Italy1999.Editors:V.Baldoni,D.Bar-basch(2003)V ol.1805:F.Cao,Geometric Curve Evolution and Image Processing(2003)V ol.1806:H.Broer,I.Hoveijn.G.Lunther,G.Vegter, Bifurcations in Hamiltonian puting Singu-larities by Gröbner Bases(2003)V ol.1807:man,G.Schechtman(Eds.),Geomet-ric Aspects of Functional Analysis.Israel Seminar2000-2002(2003)V ol.1808:W.Schindler,Measures with Symmetry Prop-erties(2003)V ol.1809:O.Steinbach,Stability Estimates for Hybrid Coupled Domain Decomposition Methods(2003)V ol.1810:J.Wengenroth,Derived Functors in Functional Analysis(2003)V ol.1811:J.Stevens,Deformations of Singularities (2003)V ol.1812:L.Ambrosio,K.Deckelnick,G.Dziuk, M.Mimura,V.A.Solonnikov,H.M.Soner,Mathematical Aspects of Evolving Interfaces.Madeira,Funchal,Portu-gal2000.Editors:P.Colli,J.F.Rodrigues(2003)V ol.1813:L.Ambrosio,L.A.Caffarelli,Y.Brenier, G.Buttazzo,C.Villani,Optimal Transportation and its Applications.Martina Franca,Italy2001.Editors:L.A. Caffarelli,S.Salsa(2003)V ol.1814:P.Bank, F.Baudoin,H.Föllmer,L.C.G. Rogers,M.Soner,N.Touzi,Paris-Princeton Lectures on Mathematical Finance2002(2003)V ol.1815: A.M.Vershik(Ed.),Asymptotic Com-binatorics with Applications to Mathematical Physics. St.Petersburg,Russia2001(2003)V ol.1816:S.Albeverio,W.Schachermayer,M.Tala-grand,Lectures on Probability Theory and Statistics. Ecole d’Etéde Probabilités de Saint-Flour XXX-2000. Editor:P.Bernard(2003)V ol.1817:E.Koelink,W.Van Assche(Eds.),Orthogonal Polynomials and Special Functions.Leuven2002(2003) V ol.1818:M.Bildhauer,Convex Variational Problems with Linear,nearly Linear and/or Anisotropic Growth Conditions(2003)V ol.1819:D.Masser,Yu.V.Nesterenko,H.P.Schlick-ewei,W.M.Schmidt,M.Waldschmidt,Diophantine Approximation.Cetraro,Italy2000.Editors:F.Amoroso, U.Zannier(2003)V ol.1820:F.Hiai,H.Kosaki,Means of Hilbert Space Operators(2003)V ol.1821:S.Teufel,Adiabatic Perturbation Theory in Quantum Dynamics(2003)V ol.1822:S.-N.Chow,R.Conti,R.Johnson,J.Mallet-Paret,R.Nussbaum,Dynamical Systems.Cetraro,Italy 2000.Editors:J.W.Macki,P.Zecca(2003)V ol.1823: A.M.Anile,W.Allegretto, C.Ring-hofer,Mathematical Problems in Semiconductor Physics. Cetraro,Italy1998.Editor:A.M.Anile(2003)V ol.1824:J.A.Navarro González,J.B.Sancho de Salas, C∞–Differentiable Spaces(2003)V ol.1825:J.H.Bramble,A.Cohen,W.Dahmen,Mul-tiscale Problems and Methods in Numerical Simulations, Martina Franca,Italy2001.Editor:C.Canuto(2003)V ol.1826:K.Dohmen,Improved Bonferroni Inequal-ities via Abstract Tubes.Inequalities and Identities of Inclusion-Exclusion Type.VIII,113p,2003.V ol.1827:K.M.Pilgrim,Combinations of Complex Dynamical Systems.IX,118p,2003.V ol.1828:D.J.Green,Gröbner Bases and the Computa-tion of Group Cohomology.XII,138p,2003.V ol.1829:E.Altman,B.Gaujal,A.Hordijk,Discrete-Event Control of Stochastic Networks:Multimodularity and Regularity.XIV,313p,2003.V ol.1830:M.I.Gil’,Operator Functions and Localization of Spectra.XIV,256p,2003.V ol.1831:A.Connes,J.Cuntz,E.Guentner,N.Hig-son,J.E.Kaminker,Noncommutative Geometry,Martina Franca,Italy2002.Editors:S.Doplicher,L.Longo(2004) V ol.1832:J.Azéma,M.Émery,M.Ledoux,M.Yor (Eds.),Séminaire de Probabilités XXXVII(2003)V ol.1833:D.-Q.Jiang,M.Qian,M.-P.Qian,Mathemati-cal Theory of Nonequilibrium Steady States.On the Fron-tier of Probability and Dynamical Systems.IX,280p, 2004.V ol.1834:Yo.Yomdin,te,Tame Geometry with Application in Smooth Analysis.VIII,186p,2004.V ol.1835:O.T.Izhboldin, B.Kahn,N.A.Karpenko, A.Vishik,Geometric Methods in the Algebraic Theory of Quadratic Forms.Summer School,Lens,2000.Editor: J.-P.Tignol(2004)V ol.1836:C.Nˇa stˇa sescu,F.Van Oystaeyen,Methods of Graded Rings.XIII,304p,2004.V ol.1837:S.Tavaré,O.Zeitouni,Lectures on Probabil-ity Theory and Statistics.Ecole d’Etéde Probabilités de Saint-Flour XXXI-2001.Editor:J.Picard(2004)V ol.1838:A.J.Ganesh,N.W.O’Connell,D.J.Wischik, Big Queues.XII,254p,2004.V ol.1839:R.Gohm,Noncommutative Stationary Processes.VIII,170p,2004.V ol.1840:B.Tsirelson,W.Werner,Lectures on Probabil-ity Theory and Statistics.Ecole d’Etéde Probabilités de Saint-Flour XXXII-2002.Editor:J.Picard(2004)V ol.1841:W.Reichel,Uniqueness Theorems for Vari-ational Problems by the Method of Transformation Groups(2004)V ol.1842:T.Johnsen,A.L.Knutsen,K3Projective Mod-els in Scrolls(2004)V ol.1843:B.Jefferies,Spectral Properties of Noncom-muting Operators(2004)V ol.1844:K.F.Siburg,The Principle of Least Action in Geometry and Dynamics(2004)V ol.1845:Min Ho Lee,Mixed Automorphic Forms,Torus Bundles,and Jacobi Forms(2004)V ol.1846:H.Ammari,H.Kang,Reconstruction of Small Inhomogeneities from Boundary Measurements(2004) V ol.1847:T.R.Bielecki,T.Björk,M.Jeanblanc,M. Rutkowski,J.A.Scheinkman,W.Xiong,Paris-Princeton Lectures on Mathematical Finance2003(2004)V ol.1848:M.Abate,J.E.Fornaess,X.Huang,J.P.Rosay, A.Tumanov,Real Methods in Complex and CR Geom-etry,Martina Franca,Italy2002.Editors:D.Zaitsev,G. Zampieri(2004)V ol.1849:Martin L.Brown,Heegner Modules and Ellip-tic Curves(2004)V ol.1850:man,G.Schechtman(Eds.),Geomet-ric Aspects of Functional Analysis.Israel Seminar2002-2003(2004)V ol.1851:O.Catoni,Statistical Learning Theory and Stochastic Optimization(2004)V ol.1852:A.S.Kechris,ler,Topics in Orbit Equivalence(2004)V ol.1853:Ch.Favre,M.Jonsson,The Valuative Tree (2004)V ol.1854:O.Saeki,Topology of Singular Fibers of Dif-ferential Maps(2004)V ol.1855:G.Da Prato,P.C.Kunstmann,siecka, A.Lunardi,R.Schnaubelt,L.Weis,Functional Analytic Methods for Evolution Equations.Editors:M.Iannelli, R.Nagel,S.Piazzera(2004)V ol.1856:K.Back,T.R.Bielecki,C.Hipp,S.Peng, W.Schachermayer,Stochastic Methods in Finance,Bres-sanone/Brixen,Italy,2003.Editors:M.Fritelli,W.Rung-galdier(2004)V ol.1857:M.Émery,M.Ledoux,M.Yor(Eds.),Sémi-naire de Probabilités XXXVIII(2005)V ol.1858:A.S.Cherny,H.-J.Engelbert,Singular Stochas-tic Differential Equations(2005)V ol.1859:E.Letellier,Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras(2005)V ol.1860:A.Borisyuk,G.B.Ermentrout,A.Friedman, D.Terman,Tutorials in Mathematical Biosciences I. Mathematical Neurosciences(2005)V ol.1861:G.Benettin,J.Henrard,S.Kuksin,Hamil-tonian Dynamics–Theory and Applications,Cetraro, Italy,1999.Editor:A.Giorgilli(2005)V ol.1862:B.Helffer,F.Nier,Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians(2005)V ol.1863:H.Führ,Abstract Harmonic Analysis of Con-tinuous Wavelet Transforms(2005)V ol.1864:K.Efstathiou,Metamorphoses of Hamiltonian Systems with Symmetries(2005)V ol.1865:D.Applebaum,B.V.R.Bhat,J.Kustermans, J.M.Lindsay,Quantum Independent Increment Processes I.From Classical Probability to Quantum Stochastic Cal-culus.Editors:M.Schürmann,U.Franz(2005)V ol.1866:O.E.Barndorff-Nielsen,U.Franz,R.Gohm, B.Kümmerer,S.Thorbjønsen,Quantum Independent Increment Processes II.Structure of Quantum Lévy Processes,Classical Probability,and Physics.Editors:M. Schürmann,U.Franz,(2005)V ol.1867:J.Sneyd(Ed.),Tutorials in Mathematical Bio-sciences II.Mathematical Modeling of Calcium Dynamics and Signal Transduction.(2005)V ol.1868:J.Jorgenson,ng,Pos n(R)and Eisenstein Series.(2005)V ol.1869:A.Dembo,T.Funaki,Lectures on Probabil-ity Theory and Statistics.Ecole d’Etéde Probabilités de Saint-Flour XXXIII-2003.Editor:J.Picard(2005)V ol.1870:V.I.Gurariy,W.Lusky,Geometry of Müntz Spaces and Related Questions.(2005)V ol.1871:P.Constantin,G.Gallavotti,A.V.Kazhikhov, Y.Meyer,ai,Mathematical Foundation of Turbu-lent Viscous Flows,Martina Franca,Italy,2003.Editors: M.Cannone,T.Miyakawa(2006)V ol.1872:A.Friedman(Ed.),Tutorials in Mathemati-cal Biosciences III.Cell Cycle,Proliferation,and Cancer (2006)V ol.1873:R.Mansuy,M.Yor,Random Times and En-largements of Filtrations in a Brownian Setting(2006)V ol.1874:M.Yor,M.Émery(Eds.),In Memoriam Paul-AndréMeyer-Séminaire de Probabilités XXXIX(2006) V ol.1875:J.Pitman,Combinatorial Stochastic Processes. Ecole d’Etéde Probabilités de Saint-Flour XXXII-2002. Editor:J.Picard(2006)V ol.1876:H.Herrlich,Axiom of Choice(2006)V ol.1877:J.Steuding,Value Distributions of L-Functions (2007)V ol.1878:R.Cerf,The Wulff Crystal in Ising and Percol-ation Models,Ecole d’Etéde Probabilités de Saint-Flour XXXIV-2004.Editor:Jean Picard(2006)V ol.1879:G.Slade,The Lace Expansion and its Applica-tions,Ecole d’Etéde Probabilités de Saint-Flour XXXIV-2004.Editor:Jean Picard(2006)V ol.1880:S.Attal,A.Joye,C.-A.Pillet,Open Quantum Systems I,The Hamiltonian Approach(2006)V ol.1881:S.Attal,A.Joye,C.-A.Pillet,Open Quantum Systems II,The Markovian Approach(2006)V ol.1882:S.Attal,A.Joye,C.-A.Pillet,Open Quantum Systems III,Recent Developments(2006)V ol.1883:W.Van Assche,F.Marcellàn(Eds.),Orthogo-nal Polynomials and Special Functions,Computation and Application(2006)V ol.1884:N.Hayashi, E.I.Kaikina,P.I.Naumkin, I.A.Shishmarev,Asymptotics for Dissipative Nonlinear Equations(2006)V ol.1885:A.Telcs,The Art of Random Walks(2006)V ol.1886:S.Takamura,Splitting Deformations of Dege-nerations of Complex Curves(2006)V ol.1887:K.Habermann,L.Habermann,Introduction to Symplectic Dirac Operators(2006)V ol.1888:J.van der Hoeven,Transseries and Real Differ-ential Algebra(2006)V ol.1889:G.Osipenko,Dynamical Systems,Graphs,and Algorithms(2006)V ol.1890:M.Bunge,J.Funk,Singular Coverings of Toposes(2006)V ol.1891:J.B.Friedlander, D.R.Heath-Brown, H.Iwaniec,J.Kaczorowski,Analytic Number Theory, Cetraro,Italy,2002.Editors:A.Perelli,C.Viola(2006) V ol.1892:A.Baddeley,I.Bárány,R.Schneider,W.Weil, Stochastic Geometry,Martina Franca,Italy,2004.Editor: W.Weil(2007)V ol.1893:H.Hanßmann,Local and Semi-Local Bifur-cations in Hamiltonian Dynamical Systems,Results and Examples(2007)V ol.1894:C.W.Groetsch,Stable Approximate Evaluation of Unbounded Operators(2007)V ol.1895:L.Molnár,Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces(2007)V ol.1896:P.Massart,Concentration Inequalities and Model Selection,Ecole d’Étéde Probabilités de Saint-Flour XXXIII-2003.Editor:J.Picard(2007)V ol.1897:R.Doney,Fluctuation Theory for Lévy Processes,Ecole d’Étéde Probabilités de Saint-Flour XXXV-2005.Editor:J.Picard(2007)V ol.1898:H.R.Beyer,Beyond Partial Differential Equa-tions,On linear and Quasi-Linear Abstract Hyperbolic Evolution Equations(2007)V ol.1899:Séminaire de Probabilités XL.Editors: C.Donati-Martin,M.Émery,A.Rouault,C.Stricker (2007)V ol.1900:E.Bolthausen,A.Bovier(Eds.),Spin Glasses (2007)V ol.1901:O.Wittenberg,Intersections de deux quadriques et pinceaux de courbes de genre1,Inter-sections of Two Quadrics and Pencils of Curves of Genus 1(2007)V ol.1902: A.Isaev,Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds(2007)V ol.1903:G.Kresin,V.Maz’ya,Sharp Real-Part Theo-rems(2007)V ol.1904:P.Giesl,Construction of Global Lyapunov Functions Using Radial Basis Functions(2007)V ol.1905:C.Prévˆo t,M.Röckner,A Concise Course on Stochastic Partial Differential Equations(2007)V ol.1906:T.Schuster,The Method of Approximate Inverse:Theory and Applications(2007)V ol.1907:M.Rasmussen,Attractivity and Bifurcation for Nonautonomous Dynamical Systems(2007)V ol.1908:T.J.Lyons,M.Caruana,T.Lévy,Differential Equations Driven by Rough Paths,Ecole d’Étéde Proba-bilités de Saint-Flour XXXIV-2004(2007)V ol.1909:H.Akiyoshi,M.Sakuma,M.Wada, Y.Yamashita,Punctured Torus Groups and2-Bridge Knot Groups(I)(2007)V ol.1910:man,G.Schechtman(Eds.),Geo-metric Aspects of Functional Analysis.Israel Seminar 2004-2005(2007)V ol.1911: A.Bressan, D.Serre,M.Williams, K.Zumbrun,Hyperbolic Systems of Balance Laws. Lectures given at the C.I.M.E.Summer School held in Cetraro,Italy,July14–21,2003.Editor:P.Marcati(2007) V ol.1912:V.Berinde,Iterative Approximation of Fixed Points(2007)V ol.1913:J.E.Marsden,G.Misiołek,J.-P.Ortega, M.Perlmutter,T.S.Ratiu,Hamiltonian Reduction by Stages(2007)V ol.1914:G.Kutyniok,Afﬁne Density in Wavelet Analysis(2007)V ol.1915:T.Bıyıkoˇg lu,J.Leydold,P.F.Stadler,Laplacian Eigenvectors of Graphs.Perron-Frobenius and Faber-Krahn Type Theorems(2007)V ol.1916:C.Villani,F.Rezakhanlou,Entropy Methods for the Boltzmann Equation.Editors:F.Golse,S.Olla (2008)V ol.1917:I.Veseli´c,Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger (2008)V ol.1918:B.Roberts,R.Schmidt,Local Newforms for GSp(4)(2007)V ol.1919:R.A.Carmona,I.Ekeland, A.Kohatsu-Higa,sry,P.-L.Lions,H.Pham, E.Taﬂin, Paris-Princeton Lectures on Mathematical Finance2004. Editors:R.A.Carmona,E.Çinlar,I.Ekeland,E.Jouini, J.A.Scheinkman,N.Touzi(2007)V ol.1920:S.N.Evans,Probability and Real Trees.Ecole d’Étéde Probabilités de Saint-Flour XXXV-2005(2008) V ol.1921:J.P.Tian,Evolution Algebras and their Appli-cations(2008)V ol.1922:A.Friedman(Ed.),Tutorials in Mathematical BioSciences IV.Evolution and Ecology(2008)V ol.1923:J.P.N.Bishwal,Parameter Estimation in Stochastic Differential Equations(2008)V ol.1924:M.Wilson,Weighted Littlewood-Paley Theory and Exponential-Square Integrability(2008)V ol.1925:M.du Sautoy,Zeta Functions of Groups and Rings(2008)V ol.1926:L.Barreira,V.Claudia,Stability of Nonauto-nomous Differential Equations(2008)Recent Reprints and New EditionsV ol.1618:G.Pisier,Similarity Problems and Completely Bounded Maps.1995–2nd exp.edition(2001)V ol.1629:J.D.Moore,Lectures on Seiberg-Witten Invariants.1997–2nd edition(2001)V ol.1638:P.Vanhaecke,Integrable Systems in the realm of Algebraic Geometry.1996–2nd edition(2001)V ol.1702:J.Ma,J.Yong,Forward-Backward Stochas-tic Differential Equations and their Applications.1999–Corr.3rd printing(2007)V ol.830:J.A.Green,Polynomial Representations of GL n,with an Appendix on Schensted Correspondence and Littelmann Paths by K.Erdmann,J.A.Green and M.Schocker1980–2nd corr.and augmented edition (2007)。

Data Mining：Concepts and Techniques

4
Types of Outliers (I)

Three kinds: global, contextual and collective outliers Global Outlier Global outlier (or point anomaly) Object is Og if it significantly deviates from the rest of the data set Ex. Intrusion detection in computer networks Issue: Find an appropriate measurement of deviation Contextual outlier (or conditional outlier) Object is Oc if it deviates significantly based on a selected context o Ex. 80 F in Urbana: outlier? (depending on summer or winter?) Attributes of data objects should be divided into two groups Contextual attributes: defines the context, e.g., time & location Behavioral attributes: characteristics of the object, used in outlier evaluation, e.g., temperature Can be viewed as a generalization of local outliers—whose density significantly deviates from its local area Issue: How to define or formulate meaningful context?

克劳德·麦凯《回到哈莱姆》中的跨国书写

克劳德•麦凯《回到哈莱姆》中的跨国书写舒进艳内容摘要：克劳德•麦凯的《回到哈莱姆》描摹了20世纪早期的黑人跨国体验。

学界主要阐释了作者个人的跨国经历与黑人国际主义思想对小说塑造主要人物的影响，而忽视了小说中副线主人公雷的国籍及其旅居哈莱姆的意义。

雷的跨国移民经历既再现了麦凯的复杂跨国情感与认同经历，又观照了哈莱姆作为流散非裔移居的理想家园与城市黑人社区所承载的空间意涵。

论文提出哈莱姆具有三个维度，作为移民唤起历史记忆的地理空间、建构跨国身份的政治空间及容纳差异的多元文化空间，并考察移民在跨国流动中历经的现代性体验，以此揭示他们通过改变既定身份与重新定义自我而竭力摆脱传统的民族、种族和阶级观念的束缚与身份认同的困惑，从而参与到美国城市的种族空间生产中。

关键词：克劳德•麦凯；《回到哈莱姆》；跨国书写基金项目：本文系国家社会科学重大项目“美国文学地理的文史考证与学科建构”（项目编号：16ZDA197）；天津市研究生科研创新项目“美国新现实主义小说的跨国空间研究”（项目编号：19YJSB039）的阶段性研究成果。

作者简介：舒进艳，南开大学外国语学院博士研究生、喀什大学外国语学院副教授，主要从事美国文学研究。

Title: Claude Mckay’s Transnational Writing in Home to HarlemAbstract: Claude McKay’s Home to Harlem depicts the black transnational experience of the early 20th century. Academics mainly studied the influence of McKay’s personal transnational experience and black internationalist thinking on his main character, but neglected the minor plot’s protagonist Ray and his nationality, and the significance of his sojourn in Harlem. Ray’s transnational migration experience not only embodies McKay’s complex transnational feeling and identity experience, but also reflects Harlem’s spatial significance as an ideal home for African diaspora and urban black community. The paper aims to examine Caribbean immigrants’ experience of modernity in Harlem which is interpreted as the geographic space for immigrants to evoke historical memories, the political space for constructing transnational identities and the multicultural space for accommodating differences. It is to prove that they manage to extricate themselves from the shackles of traditional concepts of nation, race and class and their confusion of identity by changing their established identity and redefining themselves, and thus participate in the production of racial space in American cities.60Foreign Language and Literature Research 2 (2021)外国语文研究2021年第2期Key words: Claude Mckay; Home to Harlem; transnational writingAuthor: Shu Jinyan is Ph. D. candidate at College of Foreign Languages, Nankai University (Tianjin, 300071, China), associate professor at School of Foreign Studies, Kashi University (Kashi 844000, China). Her major academic research interest includes American literature. E-mail: ******************1925年，阿伦•洛克在《新黑人》选集中将哈莱姆描述为一个国际化的文化之都，视其重要性堪比欧洲新兴民族国家的首都。

Archive of Applied Mechanics manuscript No. (will be inserted by the editor) Developments i

LEOPOLD-FRANZENS UNIVERSITYChair of Engineering Mechanicso.Univ.-Prof.Dr.-Ing.habil.G.I.Schu¨e ller,Ph.D.G.I.Schueller@uibk.ac.at Technikerstrasse13,A-6020Innsbruck,Austria,EU Tel.:+435125076841Fax.:+435125072905 mechanik@uibk.ac.at,http://mechanik.uibk.ac.atIfM-Publication2-407G.I.Schu¨e ller.Developments in stochastic structural mechanics.Archive of Applied Mechanics,published online,2006.Archive of Applied Mechanics manuscript No.(will be inserted by the editor)Developments in Stochastic Structural MechanicsG.I.Schu¨e llerInstitute of Engineering Mechanics,Leopold-Franzens University,Innsbruck,Aus-tria,EUReceived:date/Revised version:dateAbstract Uncertainties are a central element in structural analysis and design.But even today they are frequently dealt with in an intuitive or qualitative way only.However,as already suggested80years ago,these uncertainties may be quantiﬁed by statistical and stochastic procedures. In this contribution it is attempted to shed light on some of the recent advances in the now establishedﬁeld of stochastic structural mechanics and also solicit ideas on possible future developments.1IntroductionThe realistic modeling of structures and the expected loading conditions as well as the mechanisms of their possible deterioration with time are un-doubtedly one of the major goals of structural and engineering mechanics2G.I.Schu¨e ller respectively.It has been recognized that this should also include the quan-titative consideration of the statistical uncertainties of the models and the parameters involved[56].There is also a general agreement that probabilis-tic methods should be strongly rooted in the basic theories of structural en-gineering and engineering mechanics and hence represent the natural next step in the development of theseﬁelds.It is well known that modern methods leading to a quantiﬁcation of un-certainties of stochastic systems require computational procedures.The de-velopment of these procedures goes in line with the computational methods in current traditional(deterministic)analysis for the solution of problems required by the engineering practice,where certainly computational pro-cedures dominate.Hence,their further development within computational stochastic structural analysis is a most important requirement for dissemi-nation of stochastic concepts into engineering practice.Most naturally,pro-cedures to deal with stochastic systems are computationally considerably more involved than their deterministic counterparts,because the parameter set assumes a(ﬁnite or inﬁnite)number of values in contrast to a single point in the parameter space.Hence,in order to be competitive and tractable in practical applications,the computational eﬃciency of procedures utilized is a crucial issue.Its signiﬁcance should not be underestimated.Improvements on eﬃciency can be attributed to two main factors,i.e.by improved hard-ware in terms of ever faster computers and improved software,which means to improve the eﬃciency of computational algorithms,which also includesDevelopments in Stochastic Structural Mechanics3 utilizing parallel processing and computer farming respectively.For a con-tinuous increase of their eﬃciency by software developments,computational procedure of stochastic analysis should follow a similar way as it was gone in the seventieth and eighties developing the deterministic FE approach. One important aspect in this fast development was the focus on numerical methods adjusted to the strength and weakness of numerical computational algorithms.In other words,traditional ways of structural analysis devel-oped before the computer age have been dropped,redesigned and adjusted respectively to meet the new requirements posed by the computational fa-cilities.Two main streams of computational procedures in Stochastic Structural Analysis can be observed.Theﬁrst of this main class is the generation of sample functions by Monte Carlo simulation(MCS).These procedures might be categorized further according to their purpose:–Realizations of prescribed statistical information:samples must be com-patible with prescribed stochastic information such as spectral density, correlation,distribution,etc.,applications are:(1)Unconditional simula-tion of stochastic processes,ﬁelds and waves.(2)Conditional simulation compatible with observations and a priori statistical information.–Assessment of the stochastic response for a mathematical model with prescribed statistics(random loading/system parameters)of the param-eters,applications are:(1)Representative sample for the estimation of the overall distribution.4G.I.Schu¨e ller Indiscriminate(blind)generation of samples.Numerical integration of SDE’s.(2)Representative sample for the reliability assessment by gen-erating adverse rare events with positive probability,i.e.by:(a)variance reduction techniques controlling the realizations of RV’s,(b)controlling the evolution in time of sampling functions.The other main class provides numerical solutions to analytical proce-dures.Grouping again according to the respective purpose the following classiﬁcation can be made:Numerical solutions of Kolmogorov equations(Galerkin’s method,Finite El-ement method,Path Integral method),Moment Closure Schemes,Compu-tation of the Evolution of Moments,Maximum Entropy Procedures,Asymp-totic Stability of Diﬀusion Processes.In the following,some of the outlined topics will be addressed stressing new developments.These topics are described within the next six subject areas,each focusing on a diﬀerent issue,i.e.representation of stochastic processes andﬁelds,structural response,stochastic FE methods and parallel processing,structural reliability and optimization,and stochastic dynamics. In this context it should be mentioned that aside from the MIT-Conference series the USNCCM,ECCM and WCCM’s do have a larger part of sessions addressing computational stochastic issues.Developments in Stochastic Structural Mechanics5 2Representation of Stochastic ProcessesMany quantities involving randomﬂuctuations in time and space might be adequately described by stochastic processes,ﬁelds and waves.Typical ex-amples of engineering interest are earthquake ground motion,sea waves, wind turbulence,road roughness,imperfection of shells,ﬂuctuating prop-erties in random media,etc.For this setup,probabilistic characteristics of the process are known from various measurements and investigations in the past.In structural engineering,the available probabilistic characteristics of random quantities aﬀecting the loading or the mechanical system can be often not utilized directly to account for the randomness of the structural response due to its complexity.For example,in the common case of strong earthquake motion,the structural response will be in general non-linear and it might be too diﬃcult to compute the probabilistic characteristics of the response by other means than Monte Carlo simulation.For the purpose of Monte Carlo simulation sample functions of the involved stochastic pro-cess must be generated.These sample functions should represent accurately the characteristics of the underlying stochastic process orﬁelds and might be stationary and non-stationary,homogeneous or non-homogeneous,one-dimensional or multi-dimensional,uni-variate or multi-variate,Gaussian or non-Gaussian,depending very much on the requirements of accuracy of re-alistic representation of the physical behavior and on the available statistical data.6G.I.Schu¨e ller The main requirement on the sample function is its accurate represen-tation of the available stochastic information of the process.The associ-ated mathematical model can be selected in any convenient manner as long it reproduces the required stochastic properties.Therefore,quite diﬀerent representations have been developed and might be utilized for this purpose. The most common representations are e.g.:ARMA and AR models,Filtered White Noise(SDE),Shot Noise and Filtered Poisson White Noise,Covari-ance Decomposition,Karhunen-Lo`e ve and Polynomial Chaos Expansion, Spectral Representation,Wavelets Representation.Among the various methods listed above,the spectral representation methods appear to be most widely used(see e.g.[71,86]).According to this procedure,samples with speciﬁed power spectral density information are generated.For the stationary or homogeneous case the Fast Fourier Transform(FFT)techniques is utilized for a dramatic improvements of its computational eﬃciency(see e.g.[104,105]).Advances in thisﬁeld provide eﬃcient procedures for the generation of2D and3D homogeneous Gaus-sian stochasticﬁelds using the FFT technique(see e.g.[87]).The spectral representation method generates ergodic sample functions of which each ful-ﬁlls exactly the requirements of a target power spectrum.These procedures can be extended to the non-stationary case,to the generation of stochastic waves and to incorporate non-Gaussian stochasticﬁelds by a memoryless nonlinear transformation together with an iterative procedure to meet the target spectral density.Developments in Stochastic Structural Mechanics7 The above spectral representation procedures for an unconditional simula-tion of stochastic processes andﬁelds can also be extended for Conditional simulations techniques for Gaussianﬁelds(see e.g.[43,44])employing the conditional probability density method.The aim of this procedure is the generation of Gaussian random variates U n under the condition that(n−1) realizations u i of U i,i=1,2,...,(n−1)are speciﬁed and the a priori known covariances are satisﬁed.An alternative procedure is based on the so called Kriging method used in geostatistical application and applied also to con-ditional simulation problems in earthquake engineering(see e.g.[98]).The Kriging method has been improved signiﬁcantly(see e.g.[36])that has made this method theoretically clearer and computationally more eﬃcient.The diﬀerences and similarities of the conditional probability density methods and(modiﬁed)Kriging methods are discussed in[37]showing the equiva-lence of both procedures if the process is Gaussian with zero mean.A quite general spectral representation utilized for Gaussian random pro-cesses andﬁelds is the Karhunen-Lo`e ve expansion of the covariance function (see e.g.[54,33]).This representation is applicable for stationary(homoge-neous)as well as for non-stationary(inhomogeneous)stochastic processes (ﬁelds).The expansion of a stochastic process(ﬁeld)u(x,θ)takes the formu(x,θ)=¯u(x)+∞i=1ξ(θ) λiφi(x)(1)where the symbolθindicates the random nature of the corresponding quan-tity and where¯u(x)denotes the mean,φi(x)are the eigenfunctions andλi the eigenvalues of the covariance function.The set{ξi(θ)}forms a set of8G.I.Schu¨e ller orthogonal(uncorrelated)zero mean random variables with unit variance.The Karhunen-Lo`e ve expansion is mean square convergent irrespective of its probabilistic nature provided it possesses aﬁnite variance.For the im-portant special case of a Gaussian process orﬁeld the random variables{ξi(θ)}are independent standard normal random variables.In many prac-tical applications where the random quantities vary smoothly with respectto time or space,only few terms are necessary to capture the major part of the randomﬂuctuation of the process.Its major advantage is the reduction from a large number of correlated random variables to few most important uncorrelated ones.Hence this representation is especially suitable for band limited colored excitation and stochastic FE representation of random me-dia where random variables are usually strongly correlated.It might also be utilized to represent the correlated stochastic response of MDOF-systems by few most important variables and hence achieving a space reduction.A generalization of the above Karhunen-Lo`e ve expansion has been proposed for application where the covariance function is not known a priori(see[16, 33,32]).The stochastic process(ﬁeld)u(x,θ)takes the formu(x,θ)=a0(x)Γ0+∞i1=1a i1(x)Γ1(ξi1(θ))+∞i1=1i1i2=1a i1i2(x)Γ2(ξi1(θ),ξi2(θ))+ (2)which is denoted as the Polynomial Chaos Expansion.Introducing a one-to-one mapping to a set with ordered indices{Ψi(θ)}and truncating eqn.2Developments in Stochastic Structural Mechanics9 after the p th term,the above representations reads,u(x,θ)=pj=ou j(x)Ψj(θ)(3)where the symbolΓn(ξi1,...,ξin)denotes the Polynomial Chaos of order nin the independent standard normal random variables.These polynomialsare orthogonal so that the expectation(or inner product)<ΨiΨj>=δij beingδij the Kronecker symbol.For the special case of a Gaussian random process the above representation coincides with the Karhunen-Lo`e ve expan-sion.The Polynomial Chaos expansion is adjustable in two ways:Increasingthe number of random variables{ξi}results in a reﬁnement of the random ﬂuctuations,while an increase of the maximum order of the polynomialcaptures non-linear(non-Gaussian)behavior of the process.However,the relation between accuracy and numerical eﬀorts,still remains to be shown. The spectral representation by Fourier analysis is not well suited to describe local feature in the time or space domain.This disadvantage is overcome in wavelets analysis which provides an alternative of breaking a signal down into its constituent parts.For more details on this approach,it is referred to[24,60].In some cases of applications the physics or data might be inconsistent with the Gaussian distribution.For such cases,non-Gaussian models have been developed employing various concepts to meet the desired target dis-tribution as well as the target correlation structure(spectral density).Cer-tainly the most straight forward procedures is the above mentioned memo-ryless non-linear transformation of Gaussian processes utilizing the spectralrepresentation.An alternative approach utilizes linear and non-linearﬁl-ters to represent normal and non-Gaussian processes andﬁelds excited by Gaussian white noise.Linearﬁlters excited by polynomial forms of Poisson white noise have been developed in[59]and[34].These procedures allow the evaluation of moments of arbitrary order without having to resort to closure techniques. Non-linearﬁlters are utilized to generate a stationary non-Gaussian stochas-tic process in agreement with a givenﬁrst-order probability density function and the spectral density[48,15].In the Kontorovich-Lyandres procedure as used in[48],the drift and diﬀusion coeﬃcients are selected such that the solutionﬁts the target probability density,and the parameters in the solu-tion form are then adjusted to approximate the target spectral density.The approach by Cai and Lin[15]simpliﬁes this procedure by matching the spec-tral density by adjusting only the drift coeﬃcients,which is the followed by adjusting the diﬀusion coeﬃcient to approximate the distribution of the pro-cess.The latter approach is especially suitable and computationally highly eﬃcient for a long term simulation of stationary stochastic processes since the computational expense increases only linearly with the number n of dis-crete sample points while the spectral approach has a growth rate of n ln n when applying the eﬃcient FFT technique.For generating samples of the non-linearﬁlter represented by a stochastic diﬀerential equations(SDE), well developed numerical procedures are available(see e.g.[47]).3Response of Stochastic SystemsThe assessment of the stochastic response is the main theme in stochastic mechanics.Contrary to the representation of of stochastic processes and ﬁelds designed toﬁt available statistical data and information,the output of the mathematical model is not prescribed and needs to be determined in some stochastic sense.Hence the mathematical model can not be selected freely but is speciﬁed a priori.The model involves for stochastic systems ei-ther random system parameters or/and random loading.Please note,due to space limitations,the question of model validation cannot be treated here. For the characterization of available numerical procedures some classiﬁ-cations with regard to the structural model,loading and the description of the stochastic response is most instrumental.Concerning the structural model,a distinction between the properties,i.e.whether it is determinis-tic or stochastic,linear or non-linear,as well as the number of degrees of freedom(DOF)involved,is essential.As a criterion for the feasibility of a particular numerical procedure,the number of DOF’s of the structural system is one of the most crucial parameters.Therefore,a distinction be-tween dynamical-system-models and general FE-discretizations is suggested where dynamical systems are associated with a low state space dimension of the structural model.FE-discretization has no essential restriction re-garding its number of DOF’s.The stochastic loading can be grouped into static and dynamic loading.Stochastic dynamic loading might be charac-terized further by its distribution and correlation and its independence ordependence on the response,resulting in categorization such as Gaussian and non-Gaussian,stationary and non-stationary,white noise or colored, additive and multiplicative(parametric)excitation properties.Apart from the mathematical model,the required terms in which the stochastic re-sponse should be evaluated play an essential role ranging from assessing theﬁrst two moments of the response to reliability assessments and stabil-ity analysis.The large number of possibilities for evaluating the stochas-tic response as outlined above does not allow for a discussion of the en-tire subject.Therefore only some selected advances and new directions will be addressed.As already mentioned above,one could distinguish between two main categories of computational procedures treating the response of stochastic systems.Theﬁrst is based on Monte Carlo simulation and the second provides numerical solutions of analytical procedures for obtaining quantitative results.Regarding the numerical solutions of analytical proce-dures,a clear distinction between dynamical-system-models and FE-models should be made.Current research eﬀorts in stochastic dynamics focus to a large extent on dynamical-system-models while there are few new numerical approaches concerning the evaluation of the stochastic dynamic response of e.g.FE-models.Numerical solutions of the Kolmogorov equations are typical examples of belonging to dynamical-system-models where available approaches are computationally feasible only for state space dimensions one to three and in exceptional cases for dimension four.Galerkin’s,Finite El-ement(FE)and Path Integral methods respectively are generally used tosolve numerically the forward(Fokker-Planck)and backward Kolmogorov equations.For example,in[8,92]the FE approach is employed for stationary and transient solutions respectively of the mentioned forward and backward equations for second order systems.First passage probabilities have been ob-tained employing a Petrov-Galerkin FE method to solve the backward and the related Pontryagin-Vitt equations.An instructive comparison between the computational eﬀorts using Monte Carlo simulation and the FE-method is given e.g.in an earlier IASSAR report[85].The Path Integral method follows the evolution of the(transition)prob-ability function over short time intervals,exploiting the fact that short time transition probabilities for normal white noise excitations are locally Gaus-sian distributed.All existing path integration procedures utilize certain in-terpolation schemes where the probability density function(PDF)is rep-resented by values at discrete grid points.In a wider sense,cell mapping methods(see e.g.[38,39])can be regarded as special setups of the path integral procedure.As documented in[9],cumulant neglect closure described in section7.3 has been automated putational procedures for the automated generation and solutions of the closed set of moment equations have been developed.The method can be employed for an arbitrary number of states and closed at arbitrary levels.The approach,however,is limited by available computational resources,since the computational cost grows exponentially with respect to the number of states and the selected closurelevel.The above discussed developments of numerical procedures deal with low dimensional dynamical systems which are employed for investigating strong non-linear behavior subjected to(Gaussian)white noise excitation. Although dynamical system formulations are quite general and extendible to treat non-Gaussian and colored(ﬁltered)excitation of larger systems,the computational expense is growing exponentially rendering most numerical approaches unfeasible for larger systems.This so called”curse of dimen-sionality”is not overcome yet and it is questionable whether it ever will be, despite the fast developing computational possibilities.For this reason,the alternative approach based on Monte Carlo simu-lation(MCS)gains importance.Several aspects favor procedures based on MCS in engineering applications:(1)Considerably smaller growth rate of the computational eﬀort with dimensionality than analytical procedures.(2) Generally applicable,well suited for parallel processing(see section5.1)and computationally straight forward.(3)Non-linear complex behavior does not complicate the basic procedure.(4)Manageable for complex systems.Contrary to numerical solutions of analytical procedures,the employed structural model and the type of stochastic loading does for MCS not play a deceive role.For this reason,MCS procedures might be structured ac-cording to their purpose i.e.where sample functions are generated either for the estimation of the overall distribution or for generating rare adverse events for an eﬃcient reliability assessment.In the former case,the prob-ability space is covered uniformly by an indiscriminate(blind)generationof sample functions representing the random quantities.Basically,at set of random variables will be generated by a pseudo random number generator followed by a deterministic structural analysis.Based on generated random numbers realizations of random processes,ﬁelds and waves addressed in section2,are constructed and utilized without any further modiﬁcation in the following structural analysis.The situation may not be considered to be straight forward,however,in case of a discriminate MCS for the reliability estimation of structures,where rare events contributing considerably to the failure probability should be gener-ated.Since the eﬀectiveness of direct indiscriminate MCS is not satisfactory for producing a statistically relevant number of low probability realizations in the failure domain,the generation of samples is restricted or guided in some way.The most important class are the variance reduction techniques which operate on the probability of realizations of random variables.The most widely used representative of this class in structural reliability assess-ment is Importance Sampling where a suitable sampling distribution con-trols the generation of realizations in the probability space.The challenge in Importance Sampling is the construction of a suitable sampling distribu-tion which depends in general on the speciﬁc structural system and on the failure domain(see e.g.[84]).Hence,the generation of sample functions is no longer independent from the structural system and failure criterion as for indiscriminate direct MCS.Due to these dependencies,computational procedures for an automated establishment of sampling distributions areurgently needed.Adaptive numerical strategies utilizing Importance Direc-tional sampling(e.g.[11])are steps in this direction.The eﬀectiveness of the Importance sampling approach depends crucially on the complexity of the system response as well as an the number of random variables(see also section5.2).Static problems(linear and nonlinear)with few random vari-ables might be treated eﬀectively by this approach.Linear systems where the randomness is represented by a large number of RVs can also be treated eﬃciently employingﬁrst order reliability methods(see e.g.[27]).This ap-proach,however,is questionable for the case of non-linear stochastic dynam-ics involving a large set of random variables,where the computational eﬀort required for establishing a suitable sampling distribution might exceed the eﬀort needed for indiscriminate direct MCS.Instead of controlling the realization of random variables,alternatively the evolution of the generated sampling can be controlled[68].This ap-proach is limited to stochastic processes andﬁelds with Markovian prop-erties and utilizes an evolutionary programming technique for the genera-tion of more”important”realization in the low probability domain.This approach is especially suitable for white noise excitation and non-linear systems where Importance sampling is rather diﬃcult to apply.Although the approach cannot deal with spectral representations of the stochastic processes,it is capable to make use of linearly and non-linearlyﬁltered ex-citation.Again,this is just contrary to Importance sampling which can be applied to spectral representations but not to white noiseﬁltered excitation.4Stochastic Finite ElementsAs its name suggests,Stochastic Finite Elements are structural models rep-resented by Finite Elements the properties of which involve randomness.In static analysis,the stiﬀness matrix might be random due to unpredictable variation of some material properties,random coupling strength between structural components,uncertain boundary conditions,etc.For buckling analysis,shape imperfections of the structures have an additional impor-tant eﬀect on the buckling load[76].Considering structural dynamics,in addition to the stiﬀness matrix,the damping properties and sometimes also the mass matrix might not be predictable with certainty.Discussing numerical Stochastic Finite Elements procedures,two cat-egories should be distinguished clearly.Theﬁrst is the representation of Stochastic Finite Elements and their global assemblage as random structural matrices.The second category addresses the evaluation of the stochastic re-sponse of the FE-model due to its randomness.Focusingﬁrst on the Stochastic FE representation,several representa-tions such as the midpoint method[35],the interpolation method[53],the local average method[97],as well as the Weighted-Integral-Method[94,25, 26]have been developed to describe spatial randomﬂuctuations within the element.As a tendency,the midpoint methods leads to an overestimation of the variance of the response,the local average method to an underestima-tion and the Weighted-Integral-Method leads to the most accurate results. Moreover,the so called mesh-size problem can be resolved utilizing thisrepresentation.After assembling all Finite Elements,the random structural stiﬀness matrix K,taken as representative example,assumes the form,K(α)=¯K+ni=1K Iiαi+ni=1nj=1K IIijαiαj+ (4)where¯K is the mean of the matrix,K I i and K II ij denote the determinis-ticﬁrst and second rate of change with respect to the zero mean random variablesαi andαj and n is the total number of random variables.For normally distributed sets of random variables{α},the correlated set can be represented advantageously by the Karhunen-Lo`e ve expansion[33]and for non-Gaussian distributed random variables by its Polynomial chaos ex-pansion[32],K(θ)=¯K+Mi=0ˆKiΨi(θ)(5)where M denotes the total number of chaos polynomials,ˆK i the associated deterministicﬂuctuation of the matrix andΨi(θ)a polynomial of standard normal random variablesξj(θ)whereθindicates the random nature of the associated variable.In a second step,the random response of the stochastic structural system is determined.The most widely used procedure for evaluating the stochastic response is the well established perturbation approach(see e.g.[53]).It is well adapted to the FE-formulation and capable to evaluateﬁrst and second moment properties of the response in an eﬃcient manner.The approach, however,is justiﬁed only for small deviations from the center value.Since this assumption is satisﬁed in most practical applications,the obtainedﬁrst two moment properties are evaluated satisfactorily.However,the tails of the。

空场嗣后充填采矿法

空场嗣后充填采矿法英文回答：In-situ filling mining method is a mining techniquethat involves filling the mined-out areas with waste materials or backfill materials to support the surrounding rock and prevent collapse. This method is commonly used in underground mining operations where the extracted oreleaves voids behind.One advantage of the in-situ filling mining method is that it provides structural support to the underground mine, reducing the risk of cave-ins and ensuring the safety of miners. By filling the empty spaces with waste materials or backfill materials, the stability of the remaining rock is enhanced, making the mining operation safer and more efficient.Another benefit of this mining method is the environmental advantage it offers. Instead of leaving themined-out areas open and exposed, the in-situ filling mining method allows for the reclamation of the land. By filling the voids with waste materials, the land can be restored and used for other purposes such as agriculture or construction.Let me give you an example to illustrate how the in-situ filling mining method works. Imagine a scenario where a company is mining for gold in an underground mine. As the gold is extracted, voids are created in the mine. To prevent the collapse of the mine and ensure the safety of the miners, the company decides to use the in-situ filling mining method.They start by identifying suitable waste materials or backfill materials that can be used to fill the voids. These materials can be anything from sand and gravel to mine tailings or even cement. Once the materials are identified, they are transported to the mine and placedinto the voids using specialized equipment.As the voids are filled, the stability of the mineimproves, reducing the risk of cave-ins. The waste materials or backfill materials also provide support to the remaining rock, preventing it from collapsing. This allows the mining operation to continue safely and efficiently.中文回答：空场嗣后充填采矿法是一种采矿技术，其通过用废弃物或充填材料填充采空区域，以支撑周围的岩石并防止坍塌。

ZnS宽禁带半导体毕业设计

宽禁带半导体ZnS物性的第一性原理研究摘要硫化锌（ZnS）是一种新型的II-VI族宽禁带电子过剩本征半导体材料，其禁带宽度为3.67eV,具有良好的光致发光性能和电致发光性能。

在常温下禁带宽度是3.7eV，具有光传导性好，在可见光和红外范围分散度低等优点。

ZnS和基于ZnS的合金在半导体研究领域己经得到了越来越广泛的关注。

由于它们具有较宽的直接带隙和很大的激子结合能，在光电器件中具有很好的应用前景。

本文介绍了宽禁带半导体ZnS目前国内外的研究现状及其结构性质和技术上的应用。

阐述了密度泛函理论的基本原理，对第一性原理计算的理论基础作了详细的总结，并采用密度泛函理论的广义梯度近似（GGA）下的平面波贋势法，利用Castep软件计算了闪锌矿结构ZnS晶体的电子结构和光学性质。

电子结构如闪锌矿ZnS晶体的能带结构，态密度。

光学性质如反射率，吸收光谱，复数折射率，介电函数，光电导谱和损失函数谱。

通过对其能带及结构的研究，可知闪锌矿硫化锌为直接带隙半导体，通过一系列对光学图的分析，可以对闪锌矿ZnS的进一步研究做很好的预测。

关键词ZnS;宽禁带半导体；第一性原理；闪锌矿结构-I -First-principles Research on Physical Properties of Wide Bandgap Semiconductor ZnSAbstractZinc sulfide (ZnS) is a new family of ll-VI wide band gap electronic excess in tri nsic semic on ductor material with good photolu min esce nee properties and electroluminescent properties. At room temperature band gap is 3.7 eV, and there is good optical transmission in the visible and infrared range and low dispersi on. ZnS and Zn S-based alloy in the field of semic on ductor research has bee n paid more and more atte nti on. Because of their wide direct ban dgap and large excit on binding en ergy, the photovoltaic device has a good prospect.This thesis describes the current research status and structure of nature and tech ni cal applicati ons on wide band gap semic on ductor ZnS. Described the basic principles density functional theory, make a detailed summary for the basis of first principles theoretical calculations, using the density functional theory gen eralized gradie nt approximati on (GGA) un der the pla ne wave pseudopote ntial method, calculated using Castep software sphalerite ZnS crystal structure of electronic structure and optical properties. Electronic structures, such as sphalerite ZnS crystal band structure, density of states. Optical properties such as reflecta nee, absorpti on spectra, complex refractive in dex, dielectric function, optical conductivity spectrum and the loss function spectrum. Band and the structure through its research known as zin cble nde ZnS direct band gap semic on ductor,Through a series of optical map an alysis, can make a good predicti on for further study on zin cble nde ZnS.Keywords ZnS; Wide ban dgap semic on ductor; First-pri nciples; Zin cble nde structure-2-目录摘要 (I)Abstract (II)第1章绪论 ........................................................... 1..1.1 ZnS半导体材料的研究背景 ....................................... 1.1.2 ZnS的基本性质和应用........................................... 1.1.3 ZnS材料的研究方向和进展 (3)1.4 ZnS的晶体...................................................... 4.1.4.1 ZnS晶体结构 ............................................... 4.1.4.2 ZnS的能带结构............................................. 5.1.5 ZnS的发光机理................................................. 6.1.6研究目的和主要内容.............................................. 7.2.1相关理论......................................................... 9.2.1.1密度泛函理论 (9)2.1.2交换关联函数近似........................................... 1.12.2总能量的计算 (13)2.2.1势平面波方法 (14)2.2.2结构优化 (16)2.3 CASTEP软件包功能特点........................................ 1.8第3章ZnS晶体电子结构和光学性质.................................... 1.93.1闪锌矿结构ZnS的电子结构 (19)3.1.1晶格结构 (19)3.1.2能带结构 (20)3.1.3态密度 (21)3.2闪锌矿ZnS晶体的光学性质 (24)结论 (30)致谢 (31)参考文献 (32)附录A (33)附录B (45)-ill -第1章绪论1.1 ZnS半导体材料的研究背景Si是应用最为广泛的半导体材料，现代的大规模集成电路之所以成功推广应用，关键就在于Si半导体在电子器件方面的突破。

充填采矿法英文文献

0926-9851/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSD10926-985 1(95)00007-O
Also, the associated clean up and rock support costs, and lost production time due to rockbursts are immense. Although a variety of countermeasures are in use at the Lucky Friday and other burst-prone mines, no method has proven entirely reliable. Conventional rockburst countermeasures can be passive, e.g. observation of temporal/spatial sequences of rockmass failure using microseismic monitoring, or active, e.g. excavation sequencing, application of counter stresses through bolt installation, and/or destressing through a drill and blast sequence. Despite the use of these countermeasures, rockbursts continue, often with no microseismic precursors, (Blake and Cuvelier, 1990). As mining proceeds to greater depths, rockbursts will remain a persistent safety hazard and an impediment to production. Presently, there remains the need to develop a simple, rapid, and cost-effective tool for peri-

2024年云南省小学五年级上学期期中英语试卷及答案指导

2024年云南省英语小学五年级上学期期中复习试卷及答案指导一、听力部分（本大题有12小题，每小题2分，共24分）1、What is the weather like today?A. It’s sunny.B. It’s cloudy.C. It’s rainy.Answer: AExplanation: The question asks about the weather today. The correct answer is “It’s sunny,” which means option A.2、How do you spell “cat”?A. K-A-TB. C-A-TC. Q-A-TAnswer: BExplanation: The question asks how to spell the word “cat.” The correct answer is “C-A-T,” which means option B.3.Listen to the dialogue and answer the question.A. What is the weather like today?B. Where is Tom going?C. How is Tom feeling?Answer: A. What is the weather like today?Explanation: In the dialogue, the speaker mentions, “It’s a sunny day, isn’t it?” which indicates that they are discussing the weather. Ther efore, the correct answer is about the weather.4.Listen to the story and choose the correct option.A. The story is about a dog.B. The story is about a cat.C. The story is about a rabbit.Answer: B. The story is about a cat.Explanation: The story begin s with the line, “Once upon a time, there was a cat named Whiskers,” which clearly identifies the main character of the story. Thus, the correct answer is that the story is about a cat.5.What is the name of the capital city of France?A)LondonB)ParisC)RomeD)BerlinAnswer: B) ParisExplanation: The capital city of France is Paris, making option B the correct answer. London is the capital of the United Kingdom, Rome is the capital of Italy, and Berlin is the capital of Germany, which makes options A, C, and D incorrect.6.Listen to the following conversation between two students and choose the best answer to the question below.Student A: Hi, John. How was your science project?Student B: It was great! We learned about different layers of the Earth.Student A: That sounds interesting. What layer did you focus on?Student B: The crust. It’s the outermost layer of the Earth and varies in thickness.What did Student B focus on in their science project?A)The atmosphereB)The crustC)The oceanD)The coreAnswer: B) The crustExplanation: In the conversation, Student B mentions that they focused on the crust, which is the outermost layer of the Earth. Therefore, option B is the correct answer. The atmosphere refers to the layers of gases surrounding the Earth, the ocean is a body of saltwater, and the core is the innermost layer of the Earth, which are not mentioned in the conversation and thus make options A, C, and D incorrect.7.You will hear a conversation between a student and a teacher about a school project. Listen carefully and choose the correct answer.A. The project is about painting.B. The project is due next week.C. The project requires group work.Answer: B. The project is due next week.Explanation: The teacher mentions in the conversation that the project is due on Friday, which is next week.8.Listen to a short passage about different sports. Choose the sport that is mentioned in the passage.A. BasketballB. SwimmingC. TennisAnswer: C. TennisExplanation: The passage mentions that tennis is a popular sport for both adults and children. Basketball and swimming are not mentioned in the passage.9、You will hear a short conversation between two students about their weekend plans. Listen carefully and choose the best answer to the question.Question: What does the second student plan to do on Saturday afternoon?A)Go to the movies.B)Visit a museum.C)Go shopping.Answer: C) Go shopping.解析：In the conversation, the second student mentions, “I think I’ll go shopping on Saturday afternoon,” which indicates the correct answer.10、You will hear a short dialogue between a teacher and a student discussing the st udent’s homework. Listen carefully and answer the following question.Question: What is the main issue with the student’s homework?A)The student didn’t do it.B)The student turned it in late.C)The student didn’t follow the instructions.Answer: C) The student didn’t follow the instructions.解析：The teacher says, “Your homework seems to be missing some details. Did you not follow the instructions?” This indicates that the main issue is the student not following the given instructions for the homework.11、What is the weather like today?A. It’s sunny.B. It’s cloudy.C. It’s rainy.Answer: AExplanation: Listen to the question and choose the correct answer. The question asks about the weather today, and the correct answer is “It’s sunny.”12、Who is playing the piano in the music room?A. The teacher.B. The students.C. The principal.Answer: BExplanation: Listen to the question and choose the correct answer. The question is asking about who is playing the piano in the music room. The correct answer is “The students,” as it is common for students to play musical instrumentsin the music room.二、选择题（本大题有12小题，每小题2分，共24分）1、Choose the word that does not belong in the following group:A. appleB. bananaC. tomatoD. grape答案：C解析：The words “apple,” “banana,” and “grape”are all types of fruit. “Tomato,” on the other hand, is often considered a vegetable in culinary terms, so it does not belong in this group of fruits.2、Select the sentence that correctly uses the past tense:A. I watch television yesterday.B. She go to the park last week.C. We visited the museum last weekend.D. They were eating ice cream at the movie theater.答案：C解析：The correct past tense sentence is “We visited the museum last weekend.” The other options contain grammatical errors: “I watch televisio n yesterday” should be “I watched television yesterday,” “She go to the park last week” should be “She went to the park last week,” and “They were eatingice cream at the movie theater” is already in the correct past continuous tense form.3、Choose the correct word to complete the sentence.Tom is going to the beach with his family. He will need a _.A. hatB. penC. umbrellaD. shoeAnswer: AExplanation: The correct answer is “hat” because it is an item that is commonly used at the beach to protect from the sun. The other options (pen, umbrella, shoe) are not typically associated with beach activities.4、Select the sentence that correctly uses the past tense.A. She runs quickly.B. She is running quickly.C. She had run quickly.D. She will run quickly.Answer: CExplanation: The correct answer is “She had run quickly” as it is in the past perfect tense, indicating that the action of running quickly had already occurred before another past action. The other options are either in the present continuous tense (B) or future simple tense (D), which do not correctly conveythe past completion of the action. The present tense (A) is also incorrect as it does not indicate a past action.5、What is the capital city of France?A. LondonB. ParisC. RomeD. BerlinAnswer: BExplanation: The capital city of France is Paris. London is the capital of the United Kingdom, Rome is the capital of Italy, and Berlin is the capital of Germany.6、Which of the following is a planet in our solar system?A. VenusB. JupiterC. MoonD. SunAnswer: AExplanation: Venus is one of the eight planets in our solar system. Jupiter is also a planet, but the Moon is Earth’s only natural satellite, not a plane t. The Sun is the star at the center of our solar system, not a planet.7、What is the capital city of France?A. LondonB. ParisC. RomeD. MadridAnswer: BExplanation: The capital city of France is Paris. London is the capital of the United Kingdom, Rome is the capital of Italy, and Madrid is the capital of Spain.8、Which of the following is a compound word?A. AppleB. BananaC. SwimD. HappyAnswer: DExplanation: “Happy” is a compound word because it is formed by combining two words, “hap” and “py.” “Apple” and “banana” are single words, and “swim” is also a single word but can be a verb or a noun depending on the context.9.What is the main difference between a noun and a verb?A)Nouns are people, verbs are actions.B)Nouns are objects, verbs are subjects.C)Nouns are things, verbs show action or state.D)Nouns are feelings, verbs are thoughts.Answer: CExplanation: The main difference between a noun and a verb is that nouns are used to name people, places, things, and ideas, while verbs show action or state. Therefore, option C is the correct answer.10.Which sentence correctly uses the word “because” as a conjunction?A)The cat is sleeping, because it’s tired.B)The cat is sleeping; because it’s tired.C)The cat is sleeping, it’s tired.D)The cat is sleeping; it’s tired, because.Answer: AExplanation: The word “because” is a conjunction used to introduce a reason for something. In option A, “because” is correctly placed before the reason (“it’s tired”) to show thecause-and-effect relationship. Options B and D have incorrect punctuation, and option C does not use “because” as a conjunction.11.What is the capital city of France?A. New YorkB. LondonC. ParisD. TokyoAnswer: C. ParisExplanation: Paris is the capital city of France. New York is the capital city of the United States, London is the capital city of the United Kingdom, and Tokyo is the capital city of Japan.12.Which of the following is not a planet in our solar system?A. MercuryB. VenusC. EarthD. PlutoAnswer: D. PlutoExplanation: Pluto is no longer considered a planet in our solar system. It was reclassified as a dwarf planet in 2006. Mercury, Venus, and Earth are all major planets in our solar system.三、完型填空（10分）Task 3: Cloze TestRead the passage and choose the best word to fill in each blank from the options given.The story of “The Ugly Duckling” is a classic tale that teaches us about self-acceptance and the importance of being true to ourselves. One day, a mother duck had a special egg that was different from all the others. The egg was very large, and it took a long time for it to hatch. When the little duck finally came out, the other ducks were surprised to see it was ___________.1.A) beautiful2.B) cute3.C) unique4.D) uglyAfter hatching, the little duck felt___________because itwas___________compared to the other ducks. It had___________feathers and was not as fast as them. The other ducks would laugh at it and call it names.5.A) happy6.B) sad7.C) energetic8.D) curiousThe little duck tried to___________with the other ducks, but it was difficult. It spent many days feeling___________and wondering if it would ever ___________.9.A) blend in10.B) escape11.C) become friends12.D) find a homeOne day, the little duck saw a group of beautiful swans on a nearby lake. It was then that it realized that it was not as___________as it thought. The little duck finally ___________.13.A) realized its true beauty14.B) swam away15.C) hid from the other ducks16.D) lost hopeAnswer Key:1.D) ugly2.B) sad3.D) ugly4.C) unique5.B) sad6.B) sad7.A) blend in8.B) sad9.D) find a home10.B) sad11.A) realized its true beauty四、阅读理解（26分）Title: The Magic of BooksOnce upon a time, in a small village, there was a young boy named Tom. Tom was an avid reader and loved nothing more than escaping into the magical worlds of books. Every day after school, he would rush home to dive into another adventure. His favorite book series was about a group of friends who traveled through time and space, solving mysteries along the way.One day, Tom’s teacher, Mrs.Green, announced that the class was going to have a special project. They were asked to choose a book that they loved and write a report on it. Tom was excited about this project because he had juststarted reading a new book c alled “The Enchanted Forest.” This book was about a girl named Lily who discovers a hidden world behind her house and goes on a quest to save her village.Here is an excerpt from Tom’s report:“I recently read a captivating book called ‘The Enchanted Forest’ by Sarah Johnson. The story is about a young girl named Lily who discovers an enchanted forest behind her house. Lily’s world turns upside down when she learns that the forest is in danger of being destroyed. With the help of her friends, she embarks on a quest to save the forest and restore balance to her village.”Questions:1.What is the name of the young boy in the story?a) Lilyb) Tomc)Mrs.Greend)Sarah Johnson2.What is Tom’s favorite book series?a) “The Enchanted Forest”b) “Time and Space Mysteries”c) “Lily’s Quest”d) “Tom’s Adventures”3.What is the main goal of Lily in the story?a) To find her missing petb) To save her village from dangerc) To become the new queen of the enchanted forestd) To win a contestAnswers:1.b) Tom2.b) “Time and Space Mysteries”3.b) To save her village from danger五、写作题（16分）Title: Why Spring Is My Favorite SeasonSpring is my favorite season of the year. It’s the time when nature comes back to life after the cold winter months. The air becomes warmer, and everything starts to grow again. I love seeing the flowers bloom and the trees turn green. It’s also the perfect time for outdoor activities like picnics in the park or bike rides with friends.During spring, I enjoy spending more time outside playing sports and games with my family. The smell of fresh grass and blooming flowers fills my heart with joy. Spring gives me energy and hope, making every day feel new and exciting. When spring arrives, it feels like a fresh start, and that’s why it’s my most beloved season.Analysis:This essay meets the requirements by:•Sticking to the topic of a favorite season.•Providing specific reasons why spring is favored (nature coming back to life, outdoor activities).•Using descriptive language to convey personal feelings (flowers bloom, trees turn green, joy).•Keeping within the word limit while providing enough detail to paint a clear picture.•Expressing emotions and personal experiences associated with the season.The student demonstrates good writing skills by using varied vocabulary and sentence structures, making the essay engaging and coherent.。

稀有金属学报英文版关于残余应力的文章

稀有金属学报英文版关于残余应力的文章Title: Residual Stress Analysis in Advanced Materials: A ReviewResidual stress, a prevalent phenomenon in advanced materials, plays a crucial role in determining their mechanical properties and performance characteristics. Understanding and controlling residual stress have become imperative for optimizing the reliability and functionality of various engineering components. In this review, we delve into recent advancements in residual stress analysis methodologies, focusing on their applications in the field of rare metals.X-ray diffraction (XRD) techniques have emerged as powerful tools for quantifying residual stresses in metallic materials. By analyzing the diffraction patterns produced by X-rays interacting with the crystalline lattice, researcherscan accurately determine the magnitude and distribution of residual stresses within a material. Moreover, synchrotron X-ray sources have enabled high-resolution mapping of residual stresses in intricate microstructures, providing valuable insights for material design and process optimization.Neutron diffraction represents another indispensable technique for residual stress characterization, particularly in materials with large penetration depths or complex geometries. Neutrons, being highly penetrating and non-destructive, can interrogate bulk materials without significant sample preparation. Recent developments in neutron scattering instrumentation have facilitated in-situ stress monitoring during material processing, offering unprecedented opportunities for real-time quality control and defect detection.Furthermore, finite element analysis (FEA) has become indispensable for simulating and predicting residual stressdistributions in advanced materials. By discretizing the material domain into finite elements and solving the equilibrium equations iteratively, FEA can accurately model the thermo-mechanical processes involved in residual stress generation. Incorporating advanced material models and boundary conditions, researchers can simulate various manufacturing scenarios to optimize processing parameters and minimize residual stress-induced defects.In addition to experimental and numerical techniques, analytical models provide valuable insights into the underlying mechanisms governing residual stress formation. The superposition principle, plasticity theory, and phase transformation kinetics are commonly employed to formulate closed-form expressions for residual stress prediction in specific material systems. Although analytical models may lack the predictive accuracy of experimental and numerical methods, they offer valuable qualitative understanding and insights for guiding subsequent investigations.Moreover, advancements in material synthesis and processing techniques have enabled tailored manipulation of residual stresses in rare metal alloys. Additivemanufacturing processes, such as selective laser melting (SLM) and electron beam melting (EBM), offer unprecedented control over thermal gradients and cooling rates, thereby allowing precise adjustment of residual stress distributions within printed components. Furthermore, post-processing treatments, including shot peening and annealing, can alleviate residual stresses and enhance the mechanical properties of rare metal alloys.In conclusion, residual stress analysis remains acritical aspect of material characterization and process optimization in the field of rare metals. By leveraging advanced experimental techniques, numerical simulations, and analytical models, researchers can gain deeper insights into the origins and implications of residual stresses in advanced materials. Moreover, synergistic integration of materialsynthesis and processing techniques enables precise manipulation of residual stress distributions, thereby unlocking new opportunities for enhancing the performance and reliability of rare metal components in diverse engineering applications.。

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

Calculation of Mining Subsidence and Ground Principal Strains Using a Generalized Influence Function MethodG. Ren*, J. Li and J. BuckeridgeSchool of Civil, Environmental and Chemical Engineering, RMIT UniversityGPO Box 2476V, Melbourne 3001, Australia___________________________________________________________________________AbstractA generalized influence function method is introduced using tabulated influence weighting factors in subsidence calculation. Tabulated influence weighting factors have the advantage of being more flexible than having to find a mathematical influence function. The values of weighting factors can be readily adopted either using a local observational database if available, or a published data source. The flexibility and adoptability of the method is demonstrated through a case study with subsidence contours, movement vectors and principal strains. It is also demonstrated that the method is a valuable tool in assessing subsidence effects on surface structures and utilities.* Corresponding author : Tel.: 613 9925 2409 Fax: 613 9639 0138E-mail address: gang.ren@.au1. IntroductionThe accurate prediction of ground movements associated with underground mining is essential for assessing surface damage and effective damage prevention. Various methods can be used forpredicting mining subsidence and horizontal movements, including physical and numerical modeling methods, profile function and influence function methods [1]. Of these numerous prediction methods, the influence function method is increasingly favoured due to its flexibility andadoptability with computer programming [2]. Various mining configurations including irregularshaped panels, multiple extraction seams, inclined coal deposits and sloping ground can be taken into account using the influence function method [3 & 4]. The influence function method can be calibrated to suit local mining conditions to achieve better analytical results as demonstrated by Sheorey et al. [5]. Ren et al. [6] suggested that the angle of draw, inter alia , is influenced by the strength of the overburden strata. The angle of draw defines the extent of the underground extraction at the ground surface.In the application of the conventional influence function method, it is usually necessary to use a predefined influence function, which is a mathematical expression, to define the weighting factors. This paper presents a generalized influence function approach which makes use of influence factors in a tabular form for subsidence calculations.2. Mining Subsidence Prediction using Influence Function MethodThe influence function method used in subsidence prediction is based on the assumption that the effect of an underground extraction on the surface follows a prescribed mathematical expression, i.e. the influence function depends on the spatial relationship between the locations of the underground extraction and the surface point in question. This is illustrated in Figure 1, where an underground extraction element creates a subsidence trough at the surface. The profile for the subsidence trough can be prescribed by an influence function (Figure 2), which can be expressed mathematically. A general form of an influence function may be expressed as: )(x f k z =, where x can be either the zone angle θ or as the radial distance r from the centre of the subsidence trough (see Figure 2).A number of influence functions have been proposed by researchers, such as Bals, Sann, Ehrhardt and Sauer which were summarized by Kratzsch [7]:Bals’ influence function: θ2cos =z k (1)where θ is the zone angle (see Figures 2) Sann’s influence function: 241256.2r z e rk −= (2) Ehrhardt and Sauer’s influence function: 25.01392.0r z e k −= (3)where r is radial distance from centre of subsidence trough (see Figure 2). Influence functions are generally derived analytically from observations or based on assumptions. In general, these functions are mathematical expressions that are used to describe the effect of the removal of an underground element on the ground surface.A stochastic influence function that has been derived from statistical assumptions was adopted in computer programs for subsidence computation [3]. Application of this type of influence function assumes that the ground will achieve the most probable state of static equilibrium following theunderground extraction. Based on this probabilistic approach, the trough profile is assumed to follow the stochastic function (Whittaker and Reddish [2], p477): 2221R r z e R k ⋅−=π (4)where R is the radius of influence circle on surface (Figure 2).All influence functions, in essence, define the extent of influence of an underground extraction element on a surface point using a mathematical expression.Extensive studies have been conducted ([2], [3] & [4]) and the application of the stochastic influence function method to practical subsidence analysis has been well demonstrated in these literatures. In a relatively recent publication [5], Sheorey et al . proposed a new modified influence function based on the observational data obtained from a specific coal field in India: )cos 1(5352.02R rR k z ⋅+=π(5) This modified influence function gave generally much improved predictive results for the specific coal field in India [5].As noted, the influence function method used in mining subsidence prediction and analysis has become a powerful tool when it was programmed for personal computers. Complex extractiongeometries and topography can now be readily analysed and the output can be presented in graphical format [3 & 4].3.Generalized Influence Function Method 3.1 Subsidence Weighting FactorsThe conventional influence function method generally makes use of zone area or grid integration approach. Peng [1] has summarised the methodology of application of the influence function to subsidence calculation in detail. It is demonstrated that the influence function method is a flexible tool in subsidence analysis and prediction. However, all the presented influence function methods involve mathematical expressions to describe the effect of an underground extraction on the ground surface, such as the functions listed in Equations (1) to (5). Mathematical functions can be derived either from statistics or from curve fitting based on observation data obtained from specific coal fields. For example, if the influence area is evenly divided into 10 rings, the stochastic influence function at Equation (4) gives the following subsidence weighting factors (Table 1) [3]:Table 1: Weighting factors based on stochastic function Ring (i)* 1 2 3 4 5 6 7 8 9 10 ∑ Weight factorS(i)** 0.035 (0.031) 0.091 (0.087) 0.132 (0.128) 0.153 (0.149) 0.154 (0.149) 0.137 (0.133) 0.112 (0.108) 0.085 (0.081) 0.058 (0.055) 0.039 (0.035) 1 0.957 *Ring number counted from inter to outer** Values in brackets - weighting factors directly computed based on stochastic function without normalization The modified influence function (5) by Sheorey et al. gives the following weighting factors: Table 2: Weighting factors based on Equation (5) (after Sheorey, et al . [5])Ring (i) 1 2 3 4 5 6 7 8 9 10 ∑ Weight factor S(i) 0.030 0.085 0.131 0.161 0.171 0.160 0.129 0.086 0.040 0.007 1 Generally, in calculating the subsidence weighting factors, an infinitesimal extraction element dA will result in an amount of subsidence dS at the surface:dS = S 0 k z dA (6)where S 0 is the maximum possible subsidenceAn underground extraction panel of area “A ” will produce surface subsidence “S”, defined by:S = S 0dA k A z ∫∫(7)When the influence circle is divided into a number of rings (e.g. i=1 to n ), the subsidence weighting factors S(i) for an individual ring can be determined from:S(i) = S/S 0 = dA k A z ∫∫(8)For instance, if the stochastic influence function at (4) is used, we have:dA e R dA k i S A R r A z ∫∫∫∫⋅−==221)(π (9) Ren et al. [3] suggested the solving of the above intergration. After change to a polar system, the weighting factor for a specific ring can be calculated by: -2)(2)1()(R i r R i r e e i S ππ−−−−= (10)Where r i (i=1 to n ) is the radii of rings when the influence circle is devided into n number of rings. If the influence circle is evenly divided, i.e. ,00=r ,1011R r = ,1022R r =… R R r ==101010 (where R is the radius of influence circle), and S(i) values can be computed using Equation (10) for each of the 10 rings.Thus, S(1) = 0.031, S(2) = 0.087, … S(10) = 0.035. Table 1 lists the original weighting factor values as shown in brackets. We note the sum of the original S(i) does not equal to 1. This is because mathematically the weighting factor will never converge to nil even if the r i is outside the influence circle R. To ensure that the maximum subsidence is reached under total extraction condition, the following condition must be met [7]:1)(,1=∑=n i i S (11)This necessitates the requirement of a normalization process, where all weighting factor values (as shown in brackets in Table 1) were adjusted so that the sum of all weighting factors equals a unity. This normalization process involves spreading the difference between the original sum of S(i) and 1 to each individual rings. In this case, )957.01(101−× is added to each weighting factor, so that the sum of normalized S(i) equals 1 (see Table 1). It is noted that only fractional amount of adjustment is required in the case of stochastic influence function. Similar normalization process may be adopted for any other influence functions.From the above, it can be seen that the weighting factors S(i) can be mathematically calculated based on the influence function adopted. The disadvantage of this approach is the tedious mathematical procedure involved and its inability to be calibrated to suit a specific subsidence profile once an influence function is adopted.In fact, the calculation of weighting factors does not necessarily require a mathematical expression.A table listing the influence weighting factors will suffice to facilitate the calculation of subsidence and displacement. This leads to the assumption of the generalized influence function method as briefly described below.Instead of finding a mathematical expression for the weighting factor S(i), the values of S(i) can be expressed in a tabular form, as long as the condition at (11) is satisfied. The tabulated values can then be implemented in a computer program using the computational approach as outlined by Ren et al . [3]. It should be noted that the total sum of all weighting should equal to a unity for the case of a total extraction, i.e. all elements within the influence circle are extracted and the maximum possible subsidence value S 0 is reached.This generalized approach eliminates the need for having to find a mathematical function in order to work out the weighting factors in subsidence calculation. The weighting factor S(i) values that give reasonably good agreement with the observed data by a calibration process should be used. In practice, the calibration process would involve the following steps:(1)Use one of the influence functions (1) to (5) to establish initial base values for all weighting factors in Ring 1 to Ring 10; (2) Adjust the values of weighting factors, ensuring condition at (11), and observe thefollowing effects:(a) Increasing the weightings towards the centre of the influence zones and reducingthe weightings near the outer zones will result in a subsidence profile that is moreconcentrated in the centre of the trough.(b) Reducing the weightings in the centre of the influence zones and increasing theweightings near the outer zones will result in a flatter subsidence profile.(3) Repeat step (2) by trial and error until satisfactory results are obtained that fit wellwith the observed profile.Table 3 shows the weighting factors for the case study discussed in Section 4, where observedsubsidence profiles were available. In this case, the weighting factors were initially determined using the stochastic function as shown in Table1, and later were calibrated using the above mentioned steps to achieve better agreement with the measured profile.Table 3: Weighting factors for a case study Ring (i) 1 2 3 4 5 6 7 8 9 10 ∑ Weight factor S(i) 0.051 0.107 0.145 0.158 0.148 0.129 0.102 0.077 0.051 0.032 1 The weighting factor values for Tables 1, 2 and 3 are plotted in Figure 3 for comparison. Note that for the generalized approach, the influence of inner-rings is weighted more than outer rings. This will result in a “deep” and “narrow” subsidence profile as often observed in a typical longwall mining coal field.3.2 Effect of Angle of Draw in Influence Function MethodThe influence function method uses a number of important subsidence parameters such as the angle of draw ξ (Figure 2) in calculating subsidence values. The angle of draw determines the extent of influence of an underground extract element on the ground surface and demarcates the boundary of the influence circle [6]. The values of the angle of draw vary principally due to the geological settings, mass of overburden and mining configurations.For inclined extraction panels, the angle of draw is observed to have different characteristics between the rise-side of the panel and the low-side of the panel [2]. The angles at both sides determine the influence area on the surface.Direct application of the influence function method can give a subsidence value over the rib-side half of the maximum subsidence value produced by the whole extraction. Calibration is normally required to adjust this edge effect. The seam dip also has influence on the subsidence and train distribution. The method in which seam dip is accounted for in the influence function method was discussed by Ren et al.[4].3.3 Use of the Influence Function Method to Calculate Horizontal Movements and Strains Application of the influence function method will initially produce ground movement vectors which tend towards the extraction element (Figure 1), and this permits calculation of the magnitude of the vertical component V z . The horizontal component V h can then be calculated by expression: βtan z h V V = (12)Where β is the angle between the movement vector V at “Surface Point P” and the vertical in relation to the extraction element (see Figure 1).The relation between V h and V z at Equation (12) was established based on the assumption that the “Surface Point P” within the “Elementary Trough” (see Figure 1) would be displaced towards theextraction element. The vector of the movement is denoted by V in Figure 1, where V h = V sin β and V z = V cos β , hence Equation (12).Thus, by applying the principle of superposition [7], the overall influence of an extraction panel can be calculated for a surface point, including vertical and horizontal components.The computerized influence function method is able to perform calculations for series of surface points specified by grids at any specified intervals and the vertical components of subsidence can be presented with profiles and contours. The horizontal movements induced by underground mining are best presented using principal strains. The horizontal movements and vertical settlements are calculated for all surface points defined by the regular surface grids. Once the magnitudes of horizontal movements at four points on a grid are known, the following formulae can be used to calculate the principal strains and directions [8]:)2cos 11()2cos 11(213111A e A e E +++= (13)1312E e e E −+= (14) 231221223212sin )()cos sin (22tan v e e v e v e e A −−−= (15) Where e 1 and e 3 are strains along the two grid directions, the e 2 being the strain along the diagonal direction in the grid. The E 1 and E 2 are principal strains; A 1 is the angle of between E 1 and e 1 and v 2 is the angle between e 1 and e 2 (Figure 4).Equations (13) and (14) can be used to calculate the magnitudes of the principal strains over an extraction panel and Equation (15) can be used to define the orientations of the principal strains. Subsidence and principal strain calculations for each surface points specified by regular grids along with the subsidence contours can then be plotted as illustrated in the case study in Section 4.3.4 Presentation of Veridical Subsidence, Horizontal Movementsand Ground Strain PatternsWith the generalized influence function method discussed above, it is relatively straightforward to generate a series of grid data over the whole area affected by subsidence. Vertical subsidence values can be readily plotted as subsidence contours and presented by subsidence contours. The horizontal displacement vectors can be presented with a movement vector plot showing the magnitude and direction as shown in the case study in Section 4 (Figure 6). The principal strains induced by the subsidence at the surface can be plotted by a computer program using two vectors at 90° to each other to represent the magnitudes and directions (see Figures 7a & 7b). The advantage of this type of strain presentation is that it gives principal strain distribution patterns over the whole subsidence affected area with both magnitude and direction shown in a single plot. The tensile and compressive strains are also shown on the same plot. The potential subsidence effects on buildings, bridges,pipelines and transportation networks can be assessed from the principal strain plots as illustrated in the case study in Section 4 below.4 A Case Study using the Generalized Influence Function MethodThis case study involves an abandoned 1940 coal working that had been worked by the room-and-pillar method. Because the case may be sub judice, the location of the working can not be disclosed. As the condition of the supporting pillars gradually deteriorated over the years, signs of subsidence effect appeared at the surface with both vertical and horizontal movements observed. A number of residential buildings and public structures are adjacent to the old mine working (Figure 5). The relevant local authority sought prediction of the subsidence effects if the remaining mine pillars completely collapse.A subsidence analysis was performed using the generalized influence function method based on the assumption that the roof collapse would create a series of equivalent uniform extractions as shown in Figure 5. The mine working geometry was rather irregular and dipped at 25º towards the south. The average depth of the working was about 100 m and the seam thickness was 2 m. Earlier subsidence records and observational data were collected and the generalized influence function method was employed. The influence weighting factors in Table 3 were found to give reasonable concurrence with the observed data and were used for the subsidence calculations. Figure 6 shows the output of vertical subsidence represented by contours and horizontal displacement vectors over the mine workings. The general principal strain vectors are presented in Figure 7a, and Figure 7b shows the zoomed plot in the vicinity of the hospital building. The patterns and the magnitudes of the principal strain distributions are demonstrated in relation to the mining layout and the surface building. It is interesting to note that in Figure 7b, the hospital building would be subjected to mainly tensile strains, whilst near the corner of the mine working; the ground surface will be subjected to both tensile and compressive strains and within the mine working area the principal strains are mainly compressive in both directions.The surface subsidence (Figure 6) and ground strains (Figures 7a & 7b) associated with the old mine working represent the possible effect when the mine pillars completely collapse. A three-dimensional view of an exaggerated subsidence trough induced by the old mine is shown in Figure 8. Horizontal strains provide a good indicator for the effect of ground movement on surface structures.A demarcation line for a certain strain level can be manually plotted based on the principal strain plots (Figures 7a & 7b). In this case study, a demarcation line denoting 3mm/m principal strain (mainly tensile) was drawn around the underground extraction (Figure 7a). It can be seen that part of the hospital building falls within the 3 mm/m demarcation line, and would be affected by the ground movements should the mine pillars collapse. Furthermore, the subsidence effects in terms of ground strain and vertical settlement, spread significantly from the edge of the panel at the lower side of the seam due to the dip of the seam at 25 degrees.In the same case, the local transport authority was planning to construct a traffic road in the vicinity of the old mine (see Figure 7a). Technical advice was provided to the transport authority based on the findings of the subsidence analysis pertaining to the road alignment. It is deduced that if the road can not be designed to sustain 3 mm/m strain, it should be realigned away from the 3 mm/m strain demarcation line to avoid potential subsidence damages. In most cases, the 3 mm/m principal strain demarcation line can be used for preliminary assessment of the potential mining subsidence effects on surface structures. Any other values of strain demarcation lines can be produced for relevant analysis. Furthermore, it is demonstrated from Figure 7a that the pattern of principal strains induced by mining subsidence is rather complex. Depending on locations in relationship to the mine workings, the strains can be tensile in one direction and compressive in the perpendicular direction. Generally, within the mine working area the strains are predominantly compressive in both directions.It should be noted that the complete collapse of all mine pillars as illustrated in this study case may not necessarily represent the worst possible scenario in terms of subsidence effect on the surface structures. The pillars may fail randomly and create an irregular pattern of extraction which would give rise to strain concentrations at the surface. Therefore partial collapse of pillars with a resultant irregular pattern of subsidence may be more damaging to buildings, although it is difficult to quantify.5Discussion and ConclusionThe generalized influence function method is easy to use because it eliminates the need to find a mathematical expression for subsidence calculations. All subsidence weighting factors can be expressed in a tabulated form, which can be programmed in the subsidence calculations. In practice, it is not necessary to be bound to a mathematically defined function in order to establish the weighting factors. The generalized approach can be adopted to calibrate against observational data by assigning various values of weighting factors, thus to achieve accurate subsidence prediction results. The method is also capable of producing a principal strain pattern and distribution plots over the whole mining area, which can be used as a powerful tool for subsidence effect assessment and future development planning.Almost any values of weighting factors can be adopted so long as the sum of all weighting factors equals a unity. It is recommended to use weighting factors that are consistent with local observational subsidence data. This can be achieved by a trial and error calibration process. In essence, the generalized approach using influence factor in a tabular form without having to establish a mathematical function make the calibration process more flexible, thus to achieve better analytical results.It should be noted that there is a major difference between subsidence profile function method and the aforementioned generalized influence function method, although both methods can be expressed in tabular forms. The subsidence profile function method is used to directly define the subsidence profile and deformation characteristics by either tables or mathematical functions. For example, Peng [1] proposed a number of tables for predicting final and dynamic subsidence basins and he also found that a negative exponential function was applicable to the US coalfields. The generalized influence function approach indirectly affects the subsidence profile by making use of allocation of weighting factors. The advantage of such approach over the conventional profile function method is that it can be applied to all types of underground openings including multiple seams, irregular shaped-extractions, and inclined panels [4]. As demonstrated the case study in Section 4, a complex mining configuration can be analysed using the generalised influence function approach and in doing so, it can provide useful results for assessing potential mining effects on existing structures and future developments.6 AcknowledgementThe authors wish to thank the anonymous reviewers of the journal for their constructive critiques and valuable comments which helped to improve this paper.7 References[1] Peng S S, Surface Subsidence Engineering, Society for Mining, Metallurgy and Exploration inc., Littleton, Colorado 1992.[2] Whittaker B N and Reddish D J, Subsidence occurrence, prediction and control. Elsevier, Amsterdam 1989.[3] Ren G, Reddish D J, and Whittaker B N, Mining subsidence and displacement prediction using influence function methods. Mining Science and Technology, 5(1987) 89-104.[4] Ren G, Reddish D J, and Whittaker B N, Mining subsidence and displacement prediction for inclined seams. Mining Science and Technology, 8(1989) 235-252.[5] Sheorey P R, Loui J P, Singh K B, and Singh S K, Ground subsidence observation and a modified influence function method for complete subsidence prediction. International Journal of Rock Mechanics and Mining Sciences, 37 (2000) 801-818.[6] Ren G and Li J, A Study of Angle of Draw in Mining Subsidence Using Numerical Modeling Techniques, Electronic Journal of Geotechnical Engineering, Vol. 13, Bund. F, 2008.[7] Kratzsch H, Mining Subsidence Engineering, Springer-Verlag Berlin 1983, p206-207.[8] Whittaker B N, Reddish D J and Fitzpatrick D, Calculation by computer program of mining subsidence ground strain patterns due to multiple longwall extractions, Mining Science and Technology, 3 (1985) 21-33.Figure 1: 3D illustration of the influence functionK zm i t l i n eFigure 2: 2D illustration of the influence functionFigure 3. Influence factor distributions from various influence functionsRegular calculation gride1e2v2A1e3E1E2Figure 4. Determination of principal strains from regular grids (Reproduced after Whittaker et al. 1985 [8])Figure 5: Equivalent uniform extraction panel in relation to a surface structure.(m)Figure 6: Contours showing the vertical subsidence in metre, and horizontal movement vectors in relationship to the old mine workingFigure 7a: Case Study showing the vertical subsidence and principal strains in relationship to the old mine working, existing structures and proposed developments(Strains in the inserts are not to scale)Figure 8: Subsidence trough shown in 3D (Subsidence magnified by a factor of 500)。