APPLICATION OF RITZ VECTORS TO DAMAGE DETECTION FOR A GRID-TYPE BRIDGE MODEL

Proceedings of the17th International Modal Analysis Conference,Kissimmee,FL,Feb.8-11,1999.

APPLICATION OF RITZ VECTORS TO DAMAGE DETECTION FOR A

GRID-TYPE BRIDGE MODEL

Hoon Sohn and Kincho https://www.wendangku.net/doc/fb6803659.html,w

Department of Civil and Environmental Engineering

Stanford University

Stanford,CA94305-4020

This paper describes an experimental study on the use of Ritz vectors for damage detection of a grid-type bridge model.

A new procedure to extract Ritz vectors from experimental modal analysis is proposed and demonstrated using the test https://www.wendangku.net/doc/fb6803659.html,ing appropriate load patterns,Ritz vectors can be made more sensitive to damage than modal vectors.The results indicate that the use of load-dependent Ritz vectors produce better damage diagnoses than the modal vectors. Damage detection and health monitoring of large-scale struc-tures are important challenges to engineering research.One common approach is to employ the vibration characteristics of a structure to predict the damage locations and to estimate the amount of damage.It has been shown that changes in the modal parameters might not be apparent at an early stage of damage.Also,the uncertainties caused by measure-ment noise,modeling error involved in an analytical model, and environmental changes such as variations in tempera-ture and load conditions can impede reliable identi?cation of damage.Therefore,for reliable damage detection,dam-age would need to cause signi?cant changes in the modal parameters that are beyond the natural variability caused by the effects other than damage.

T o overcome the insensitivity of modal vectors,several al-ternatives have been proposed.Pandey,Biswas,and Sam-man compute the mode shape curvature from the displace-ment mode shape,and demonstrate that the changes in the mode shape curvature can be a good indicator of damage for beam structures.Stubbs,Kim and T opole present a damage index method which measures the decrease of modal strain energy before and after damage occurrence. Y ao,Chang and Lee apply the strain mode shape to iden-tify local damage detection of a braced steel frame structure. The idea is that the force redistribution caused by damage

can be related to the change of the strain mode shape.These methods require the direct measurement of dynamic strains or the derivatives of the measured displacement mode shapes to compute the strain mode shape or mode shape curvature.

However,the noise induced by the measurement of dynamic strains is generally higher than that by typical accelerometer measurement.Furthermore,numerical procedures to com-pute the curvature from the displacement also inevitably pro-duce errors.Ritz vectors(or Lanczos vectors)have been shown very effective for dynamic and earthquake analyses, eigenvalue problems and model reductions.However,very few studies have applied Ritz vectors to damage detection or system identi?cation problems.Recently,Cao and Zimmerman show that it is possible to experimentally ex-tract Ritz vectors from the traditional modal analysis.

In this paper,Ritz vectors are incorporated into the previously proposed Bayesian probabilistic framework and the ap-plicability is investigated using a grid-type bridge model con-structed and tested at the Hyundai Institute of Construction T echnology(HICT),Korea(see Figure1).We also present

a new extraction procedure of Ritz vectors based on a mea-

sured?exibility matrix.The estimated Ritz vectors are then applied to perform the damage diagnosis for the test struc-ture.

The steel bridge test model consists of two parallel girders and six evenly spaced cross beams connecting the two girders as shown in Figure1.The girders are steel rectangular tubes and the cross beams are C-shape https://www.wendangku.net/doc/fb6803659.html,ing impact excitations,we extract Ritz/modal vectors from the vibration response of the test structure.

A SA-390signal analyzer with four channels is used for the

analog to digital conversion of accelerometer signals and the Fast Fourier T ransform(FFT)calculation.Data acquisition pa-rameters are speci?ed such that a frequency response func-1

tion (FRF)in the range of 0to 100Hz could be estimated.

Each spectrum is computed by averaging three 8second long time histories.2048points are sampled for a 8second time period and this sampling rate produces a frequency resolution of 0.125Hz.An exponential window is applied to all measured time histories prior to the FFT calculation.

A Dytran 5801A4impact hammer and three Dytran 3100

B ac-celerometers with a normal sensitivity of 100mV/g are used.The excitation is applied to nodes 3,4and 5as shown in Fig-ure 2.The sensors measure the vertical accelerations at the twelve nodes as indicated in Figure 2.

Note that since the SA-390data acquisition system has only four channels and there are three accelerometers,the ?rst channel is always connected to the input hammer and the remaining three channels are connected to three accelerom-eters.T o complete one set of modal test,the hammer ex-citation is repeated twelve times at one point and the three accelerometers are moved from one set of three nodes to an-other set of three nodes after every three excitations (note that each FRF is computed by averaging the three response time histories,and there are twelve measurement points and three accelerometers).

Damage location 3

The DIAMOND software developed by the Los Alamos Na-tional Laboratory is employed for the extraction of modal pa-rameters.The ERA and rational polynomial techniques are employed to extract the ?rst six natural frequencies and the corresponding modal vectors from the recorded FRFs.

Cao and Zimmerman proposed a procedure to extract Ritz vectors based on the state-space matrices estimated from vi-bration tests.In this section,we present a new extraction pro-cedure of Ritz vectors based on a measured ?exibility matrix.A close look at the analytical generation procedure in Refer-ence 2reveals that the generation of Ritz vectors uses the ?exibility matrix (de?ned here as the inverse of the stiffness matrix)rather than the stiffness matrix itself.

The extraction of Ritz vectors starts with the assumption that

the dynamic loading

can be separated into a spatial load vector

and time function :If the modal vectors are mass-normalized such that

the ?exibility matrix then can be represented with the modal

parameters :

where is the diagonal eigenvalue matrix and is the cor-responding eigenvector (modal vector)matrix.In most exper-imental modal analyses,only a few lower modal frequencies and modal vectors are identi?ed.For this case,the ?exibility matrix is divided into the modal ?exibility ,which is formed from the estimated frequencies and modal vectors,and the residual ?exibility formed from the residual modes :

where the subscript and denote the estimated and resid-ual quantities,respectively.Here,the modal ?exibility matrix is

constructed only from the measured natural frequencies and

modal vectors (

).The residual ?exibility is the contribution of the unmeasured dynamic modes to the full ?exibility matrix.Note that the contribution of lower modes,which are normally estimated in experimental modal analy-ses,are more signi?cant than those of higher modes because the contribution of each mode is inversely proportional to the magnitude of the corresponding natural frequencies.

From the modal?exibility matrix and the analytical mass matrix,the?rst Ritz vector cab be computed as:

where is the spatial load distribution vector de?ned in Equation(1).The?rst Ritz vector is,then,mass-normalized as:

The following Ritz vectors are recursively generated.Assum-ing the mass matrix times the previous Ritz vector as a load,the recurrence relationship computes the next Ritz vec-tor:

The linear independence of Ritz vectors is achieved using the Gram-Schmidt orthogonalization:

Finally,the current Ritz vector is mass-normalized:

It is worth while to compare the?exibility based extraction procedure with the state-space Based procedure proposed by Cao and Zimmerman.Since the spatial load distribu-tion vector in Equation(5)can be assigned arbitrary,the ?exibility based method is able to generate different sets of Ritz vectors.On the other hand,in?uence matrix estimated from the experimental modal analysis retains the information of the actual load pattern used in the modal test.Therefore, the state-space based method only identi?es the Ritz vectors corresponding to the speci?c excitation pattern used in the actual modal testing.Note that both methods require an ap-propriate approximation for the mass matrix.However,since stiffness changes are the main concern of damage detection, the exact estimation of the mass matrix is not necessary.

A?nite element(FE)model is constructed using twenty three-dimensional beam elements.As shown in Figure2,a girder between two nodes or cross beam is modeled as a single member.An elastic modulus of2.0MPa,a mass density of7850kg/m,and a Poisson’s ratio of0.2are speci?ed in this model.Since the accelerometers measure only the vertical movement of the structure,the lateral DOFs are not included in the analytical model.Therefore,each node of an element has two translational DOFs and three rotational DOFs.The model has a total of64DOFs including four rotational DOFs at the boundary.Both ends of the beam are modeled as sim-ple pinned connections.A pinned connection is modeled by a ball bearing with a35mm diameter in the experimental setup. Based on a preliminary vibration test,the boundary conditions appear to be less accurately modeled.The boundary condi-tions are then modi?ed by introducing rotational springs at the rotational DOFs.Furthermore,additional springs are added to the rotational DOFs at both end of the cross beams to sim-ulate the bolted connection between the girders and the cross beams.After these modi?cations,the relative errors of the?rst six natural frequencies between the analytical model and the test structure fall within4%.

Mode Frequency(Hz)Relative

Ana.()Exp.()Error(%) 1st Bending 5.45 5.56 2.06

1st T orsion10.1510.04 1.08

2nd Bending19.1818.64 2.91

2nd T orsion30.6229.44 4.02

3rd Bending41.6142.59 2.31

3rd T orsion54.9757.19 3.88

*error=

T able1compares the values of the analytical and experimen-tal natural frequencies.Here,the experimental frequency() is a mean value of the three frequencies estimated with im-pacts on nodes3,4and5,respectively.Figure3displays the analytical and experimental modal vectors of the?rst six modes.The?rst six Ritz vectors are also computed follow-ing the extraction procedure in Section3.Figure4shows the analytical Ritz vectors and the experimental Ritz vectors with an impulse excitation at node3.The analytical Ritz vec-tors in Figure4are computed by following the procedure in Reference2.It should be noted that the?rst Ritz vector is equivalent to a de?ection pattern observed when a unit load is applied to node3.

As for the scaling of the Ritz or modal vectors,a mass-normalization is conducted.However,since the DOFs of the analytical model do not coincide with the DOFs of the experi-mental Ritz or modal vectors,a reduced analytical mass ma-trix is?rst computed using the Guyan(static)condensation calculation.Then,both the analytical and experimental vec-tors are normalized with respect to the reduced mass matrix. Errors arise from the model reduction are found to be mini-mum since the inertial forces associated with the omitted ro-tational DOFs(slave DOFs)are negligible in this example.

A Bayesian framework is applied to diagnose the damages imposed to the test structure.For an analytical model with substructures,the system stiffness matrix can be

expressed as an assembly of substructure stiffness matrices :

where and is a nondimensional parameter which represents the contribution of the th substructure stiffness to the system stiffness matrix.

A substructure is de?ned as damaged when the value is less than a speci?ed threshold.

When vibration tests are repeated times,the total collec-tion of data sets is denoted as:

Each data set is composed of the Ritz vectors estimated from the th vibration test:

where denotes the th estimated Ritz vector in the th data set.The Ritz vector has components cor-responding to the instrumented DOFs.The variables

and represent the total number of components in a data set,the number of the measured DOFs and the number of the estimated Ritz vectors,respectively.

Let denote a hypothesis for a damage event which can contain any number of substructures as damaged.The initial degree of belief about the hypothesis is represented by a prior https://www.wendangku.net/doc/fb6803659.html,ing Bayes Theorem,the poste-rior probability,after observing the estimated data sets,is given as:

The most likely damaged substructures are the ones included in the hypothesis which has the largest posterior prob-ability,i.e.

Since the objective is to determine the most probable damage hypothesis(event),only the relative posterior probabilities of alternative hypotheses are of interest.We attempt to avoid the explicit expression of a posterior probability

since the precise calculation of is a dif?cult task. T o overcome these dif?culties,we focus on the relative com-parisons of posterior probabilities.

Note that the search of the most likely damage hypothesis in Equation(14)theoretically requires the examination of all possible damage scenarios.We have proposed a branch-and-bound search scheme using bounding heuristics to expe-dite the search without exhaustively examining all the

possible

Case Location1Location2Location3

1 2.0cm(40%)--

2 3.0cm(60%)--

3 3.0cm(60%) 1.5cm(30%)-

4 3.0cm(60%) 2.6cm(52%)-

5 3.0cm(60%) 3.2cm(64%)-

6 3.0cm(60%) 3.2cm(64%) 2.5cm(50%)

*Damage locations1,2&3are shown in Figure2.The?rst

number is the depth of cut and the second number is the ratio

of the cut depth to the height of the beam(5cm).

damage hypotheses.If the damages are localized in a few substructures,the number of damage hypotheses that need to be examined by the branch-and-bound search is relatively small and the search becomes computationally feasible.

Continuous deterioration of stiffness is simulated at three dif-ferent regions of the grid structure and the vibration tests are conducted at six different damage stages as shown in T able2. Figure2shows the three damage locations.First,a single damage is introduced at damage location1(for cases1and 2)and the second damage is formed between nodes12and 13(for cases3,4and5).Finally,damage case6is simulated by adding damage location3.

For each damage location,a crack is introduced by a saw cutting at a distance of30cm from the left node.A typical saw cutting is shown in Figure5.For example,the damage location1in Figure2is formed at30cm left to the node3.The severity of saw cutting in terms of depth(cm)and the ratio of the cut depth to the height of the beam(%)are tabulated as shown in T able2.In addition,T able3summarizes the change of frequencies at each damage stage.

Case Natural Frequency(Hz)

1st2nd3rd4th5th6th

0 5.5610.0418.6429.4442.5957.19

1 5.539.8118.0629.0442.0356.62

2 5.489.6717.2728.5041.1856.18

3 5.379.6017.2427.6940.6155.39

4 5.249.5217.2227.3439.7752.40

5 5.039.3917.1727.1638.5951.64

6 4.969.0116.1826.7037.2949.95

Damage Ritz Vectors Modal Vectors Case Location Rank Rank

122,31(2)2,8,91(29) 222,31(12)2,8,121(46) 32,112,33(9)2,3,813(41) 42,1123(3)2,8,124(12) 52,112,111(1)2,11,121(9) 62,6,112,6,111(1)2,6,111(1)

1.The?rst number is the highest rank of a damage event which

includes all actual damage locations and the second number is the rank of the actual damage event.

2.is a set of the most probable damage locations identi?ed

by the branch-and-bound search.

First,damage diagnosis is conducted using the six estimated modes.For each damage stage,three sets of modal data, which are obtained from the impulse excitation at nodes3, 4and5,are employed for the proposed Bayesian approach. The diagnosis results are summarized in T able4.The?fth column of the table(the column under)shows the most likely damage locations identi?ed by the branch-and-bound search scheme.The?rst number under the title“Rank”de-notes the highest rank among the damage events that in-clude all the actual damage locations and the second number presents the rank of the actual damage event.The diagnosis results reveal that as we approach to the?nal damage stage, the diagnosis employing the modal parameters converges to the actual damage locations.

Second,the same six cases are re-diagnosed using the Ritz vectors generated from different load patterns.A point load is assumed to be applied to the vertical direction of each node and the?rst six Ritz vectors are generated from the load pat-tern.Then,this process is repeated for all twelve vertical DOFs.From these load patterns,a total of72(6Ritz vec-tors/load12load patterns)Ritz vectors are generated.Note that,following the proposed extraction procedure,Ritz vec-tors corresponding to any load pattern can be theoretically ex-tracted with the same amount of test data used to estimate the modal parameters.That is,more information is gained by applying multiple loads.

The diagnosis results using the Ritz vectors are also sum-marized in T able4.For cases1and2,the actual damage event is ranked as the second and twelfth most likely damage event,respectively.In the?rst two cases,damage location1 is included in the most likely damage event estimated by the branch-and-bound search.This is,although the branch-and-bound search fails to pinpoint the actual damage location,the search?nds the actual damage location as one of the most likely damage locations.For case3,the actual damage event is ranked as the ninth most likely event.For case4,the ac-tual damage case is ranked as the third most likely event.For cases5and6,the branch-and-bound search exactly?nds the actual damage events.

Rank Rank Rank

12,342,3,1271,2,3 22,3,45282,12

32,3,1162,492,11

T able5shows the?rst nine most probable damage events identi?ed by the branch-and-bound search for damage case3. The?rst two most probable events only include damage loca-tion1and miss damage location2.However,the third most probable event includes the two damage locations and one ex-tra member3.That is,although the proposed approach ranks the actual damage event as the ninth most probable event, the third most likely event conservatively includes all the ac-tual damage locations.

The results shown in T able4indicates that the Ritz vectors provide better diagnosis results for the six damage cases in-vestigated than the modal vectors.The sensitivity compar-ison shown in Figure6supports the diagnosis results.In Figure6,the sensitivity comparison using the experimental Ritz/modal vectors at different damage stages is conducted. The Ritz vectors are extracted from a point load applied at node3.From Figure6,we conclude that a careful selection of load patterns can make damages more observable.The better sensitivity of Ritz vectors to damage locations and the increased amount of information employing multiple load pat-terns seem to improve the damage diagnosis.

In this paper,load-dependent Ritz vectors are incorporated into the previously proposed Bayesian framework for damage diagnosis.We also describe a new procedure which extracts Ritz vectors based on the measured?exibility matrix.The

formance of Ritz vectors over modal vectors attributes to(1) the better sensitivity of Ritz vectors over modal vectors and (2)the increased amount of information obtained by employ-ing multiple load patterns.

This research is partially sponsored by the National Science Foundation under Grant No.CMS-95261-2.The authors wish to express their sincere thanks to Hyundai Engineering&Con-struction Co.LTD.for inviting the?rst author to participate in the test of the grid-type bridge model,and to Dr.Chuck R. Farrar and Dr.Scott W.Doebling of the Los Alamos National Laboratory for providing the DIAMOND software.

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dependent Ritz vectors in structural damage detection.

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Ritz vectors from dynamic testing data.In Proceedings of the15th International Modal Analysis Conference,pages 1036–1042,Orlando,FL,1997.

[3]S.W.Doebling.Measurement of Structural Flexibility Ma-

trices for Experiments with Incomplete Reciprocity.PhD thesis,Aerospace Engineering Sciences,University of Colorado,Boulder,CO,1995.

[4]S.W.Doebling,C.R.Farrar,M.B.Prime,and D.W.

Shevitz.Damage identi?cation and health monitoring of structural and mechanical systems from changes in their vibration characteristics:A literature review.T echnical

Report LA-13070-MS,Los Alamos National Laboratory, Los Alamos,NM,1996.

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40bridge before and after the introduction of damage.

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Straser.Variability of modal parameters measured on the Alamosa Canyon Bridge.In Proceedings of the15th In-ternational Modal Analysis Conference,pages257–263, Orlando,FL,1997.

T.A-L.Kashangaki,S.W.Smith,and T.W.Lim.Un-derlying modal data issues for detecting damage in truss structures.T echnical Report AIAA-92-2264-CP,Ameri-can Institute of Aeronautics and Astronautics,1992.

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age detection from changes on curvature mode shapes.

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常用介词的用法

分考点1 表示时间的介词 Point 1 at, in, on 的用法 （1）at 的用法 At 表示时间点，用于具体的时刻（几点，正午，午夜，黎明，拂晓，日出，日落等），或把某一时间看作某一时刻的词之前以及某些节假日的词之前。 at 6：00 在6点钟 At noon 在中午 At daybreak 在拂晓 At down 在黎明 At Christmas 在圣诞节 【特别注意】在以下的时间短语中，at 表示时间段。 At dinner time 在（吃）晚饭时 At weekends/ the weekend 在周末 （2）in 的用法 ①表示时间段，与表示较长一段时间的词搭配，如年份，月份，季节，世纪，朝代，还可以用于泛指的上午、下午、傍晚等时间段的词前。 In 2009 在2009年 In April 在四月 In the 1990s 在20世纪90年代 In Tang Dynasty 在唐朝 In the morning在上午 ②后接时间段，用于将来时，表示“在一段时间之后”。 The film will begin in an hour. 电影将于一个小时之后开始。 【特别注意】当时间名词前有this，that，last，next，every，each，some等词修饰时，通常不用任何介词。 This morning 今天上午last year 去年 （3）on 的用法 ①表示在特定的日子、具体的日期、星期几、具体的某一天或某些日子。 On September the first 在9月1号 On National Day 在国庆节 We left the dock on a beautiful afternoon. 我们在一个明媚的下午离开了码头。 ②表示在具体的某一天的上午、下午或晚上（常有前置定语或后置定语修饰）。 On Sunday morning 在星期日的早上 On the night of October 1 在10月1号的晚上 【特别注意】“on +名词或动名词”表示“一...就...”. On my arrival home/ arriving home, I discovered they had gone. 我一到家就发现他们已经离开了。 Point 2 in，after 的用法 In 和after都可以接时间段，表示“在...之后”，但in 常与将来时连用，after 常与过去时连用。 We will meet again in two weeks.

英语介词用法大全

英语介词用法大全 TTA standardization office【TTA 5AB- TTAK 08- TTA 2C】

介词（The Preposition）又叫做前置词，通常置于名词之前。它是一种虚词，不需要重读，在句中不单独作任何句子成分，只表示其后的名词或相当于名词的词语与其他句子成分的关系。中国学生在使用英语进行书面或口头表达时，往往会出现遗漏介词或误用介词的错误，因此各类考试语法的结构部分均有这方面的测试内容。 1. 介词的种类 英语中最常用的介词，按照不同的分类标准可分为以下几类： (1). 简单介词、复合介词和短语介词 ①.简单介词是指单一介词。如： at , in ,of ,by , about , for, from , except , since, near, with 等。②. 复合介词是指由两个简单介词组成的介词。如： Inside, outside , onto, into , throughout, without , as to as for , unpon, except for 等。 ③. 短语介词是指由短语构成的介词。如： In front of , by means o f, on behalf of, in spite of , by way of , in favor of , in regard to 等。 (2). 按词义分类 {1} 表地点（包括动向）的介词。如： About ,above, across, after, along , among, around , at, before, behind, below, beneath, beside, between , beyond ,by, down, from, in, into , near, off, on, over, through, throught, to, towards,, under, up, unpon, with, within , without 等。 {2} 表时间的介词。如： About, after, around , as , at, before , behind , between , by, during, for, from, in, into, of, on, over, past, since, through, throughout, till(until) , to, towards , within 等。 {3} 表除去的介词。如： beside , but, except等。 {4} 表比较的介词。如： As, like, above, over等。 {5} 表反对的介词。如： againt ,with 等。 {6} 表原因、目的的介词。如： for, with, from 等。 {7} 表结果的介词。如： to, with , without 等。 {8} 表手段、方式的介词。如： by, in ,with 等。 {9} 表所属的介词。如： of , with 等。 {10} 表条件的介词。如：

to与for的用法和区别

to与for的用法和区别 一般情况下, to后面常接对象; for后面表示原因与目的为多。 Thank you for helping me. Thanks to all of you. to sb.表示对某人有直接影响比如，食物对某人好或者不好就用to; for表示从意义、价值等间接角度来说，例如对某人而言是重要的，就用for. for和to这两个介词，意义丰富，用法复杂。这里仅就它们主要用法进行比较。 1. 表示各种“目的” 1. What do you study English for? 你为什么要学英语？ 2. She went to france for holiday. 她到法国度假去了。 3. These books are written for pupils. 这些书是为学生些的。 4. hope for the best, prepare for the worst. 作最好的打算，作最坏的准备。 2．对于 1．She has a liking for painting. 她爱好绘画。 2．She had a natural gift for teaching. 她对教学有天赋/ 3．表示赞成同情，用for不用to. 1. Are you for the idea or against it? 你是支持还是反对这个想法？ 2. He expresses sympathy for the common people.. 他表现了对普通老百姓的同情。 3. I felt deeply sorry for my friend who was very ill. 4 for表示因为，由于（常有较活译法） 1 Thank you for coming. 谢谢你来。 2. France is famous for its wines. 法国因酒而出名。 5．当事人对某事的主观看法，对于（某人），对…来说（多和形容词连用）用介词to，不用for.. He said that money was not important to him. 他说钱对他并不重要。 To her it was rather unusual. 对她来说这是相当不寻常的。 They are cruel to animals. 他们对动物很残忍。 6．for和fit, good, bad, useful, suitable 等形容词连用，表示适宜，适合。 Some training will make them fit for the job. 经过一段训练，他们会胜任这项工作的。 Exercises are good for health. 锻炼有益于健康。 Smoking and drinking are bad for health. 抽烟喝酒对健康有害。 You are not suited for the kind of work you are doing. 7. for表示不定式逻辑上的主语，可以用在主语、表语、状语、定语中。 1．It would be best for you to write to him. 2．The simple thing is for him to resign at once. 3．There was nowhere else for me to go. 4．He opened a door and stood aside for her to pass.

项目管理知识体系

项目管理知识体系

2019年3月

目录 1. 项目整体管理 (8) 1.1. 制定项目章程（启动） (8) 1.2. 制订项目管理计划（计划） (8) 1.3. 指导与管理项目执行（执行） (9) 1.4. 监控项目工作（监控） (9) 1.5. 实施整体变更控制（监控） (9) 1.6. 结束项目或阶段（收尾） (10) 2. 项目范围管理 (10) 2.1. 规划范围管理（计划） (11) 2.2. 收集需求（计划） (11) 2.3. 定义范围（计划） (12) 2.4. 创建工作分析结构WBS（计划） (12) 2.5. 确认范围（监控） (13) 2.6. 控制范围（监控） (13) 3. 项目进度管理 (14) 3.1. 规划进度管理（计划） (14) 3.2. 定义活动（计划） (14) 3.3. 排列活动顺序（计划） (14) 3.4. 估算活动资源（计划） (15) 3.5. 估算活动持续时间（计划） (15) 3.6. 制订进度计划（计划） (16)

4. 项目成本管理 (17) 4.1. 规划成本（计划） (17) 4.2. 估算成本（计划） (17) 4.3. 制定预算（计划） (18) 4.4. 控制成本（监控） (18) 5. 项目质量管理 (19) 5.1. 规划质量管理（计划） (19) 5.2. 实施质量保证（执行） (19) 5.3. 质量控制（监控） (20) 6. 项目人力资源管理 (20) 6.1. 规范人力资源管理（计划） (20) 6.2. 组建项目团队（计划） (21) 6.3. 建设项目团队（计划） (21) 6.4. 管理项目团队（执行） (21) 7. 项目沟通管理 (22) 7.1. 规划沟通管理（计划） (22) 7.2. 管理沟通（执行） (22) 控制沟通（监控） (23) 8. 干系人管理 (23) 8.1. 识别干系人（启动） (23) 8.2. 规划干系人管理（计划） (24)

英语介词用法详解

英语常用介词用法与辨析 ■表示方位的介词：in, to, on 1. in 表示在某地范围之内。如： Shanghai is/lies in the east of China. 上海在中国的东部。 2. to 表示在某地范围之外。如： Japan is/lies to the east of China. 日本位于中国的东面。 3. on 表示与某地相邻或接壤。如： Mongolia is/lies on the north of China. 蒙古国位于中国北边。 ■表示计量的介词：at, for, by 1. at表示“以……速度”“以……价格”。如： It flies at about 900 kilometers a hour. 它以每小时900公里的速度飞行。 I sold my car at a high price. 我以高价出售了我的汽车。 2. for表示“用……交换，以……为代价”。如： He sold his car for 500 dollars. 他以五百元把车卖了。 注意：at表示单价(price) ，for表示总钱数。 3. by表示“以……计”，后跟度量单位。如： They paid him by the month. 他们按月给他计酬。 Here eggs are sold by weight. 在这里鸡蛋是按重量卖的。 ■表示材料的介词：of, from, in 1. of成品仍可看出原料。如： This box is made of paper. 这个盒子是纸做的。 2. from成品已看不出原料。如： Wine is made from grapes. 葡萄酒是葡萄酿成的。 3. in表示用某种材料或语言。如： Please fill in the form in pencil first. 请先用铅笔填写这个表格。 They talk in English. 他们用英语交谈(from 。 注意：in指用材料，不用冠词；而with指用工具，要用冠词。请比较：draw in penc il/draw with a pencil。 ■表示工具或手段的介词：by, with, on 1. by用某种方式，多用于交通。如by bus乘公共汽车，by e-mail. 通过电子邮件。

with的用法大全

with的用法大全----四级专项训练with结构是许多英语复合结构中最常用的一种。学好它对学好复合宾语结构、不定式复合结构、动名词复合结构和独立主格结构均能起很重要的作用。本文就此的构成、特点及用法等作一较全面阐述，以帮助同学们掌握这一重要的语法知识。 一、 with结构的构成 它是由介词with或without+复合结构构成，复合结构作介词with或without的复合宾语，复合宾语中第一部分宾语由名词或代词充当，第二部分补足语由形容词、副词、介词短语、动词不定式或分词充当，分词可以是现在分词，也可以是过去分词。With结构构成方式如下： 1. with或without-名词/代词+形容词; 2. with或without-名词/代词+副词; 3. with或without-名词/代词+介词短语; 4. with或without-名词/代词+动词不定式; 5. with或without-名词/代词+分词。 下面分别举例：

1、 She came into the room，with her nose red because of cold.(with+名词+形容词，作伴随状语) 2、 With the meal over ， we all went home.(with+名词+副词，作时间状语) 3、The master was walking up and down with the ruler under his arm。(with+名词+介词短语，作伴随状语。) The teacher entered the classroom with a book in his hand. 4、He lay in the dark empty house，with not a man ，woman or child to say he was kind to me.(with+名词+不定式，作伴随状语) He could not finish it without me to help him.(without+代词 +不定式，作条件状语) 5、She fell asleep with the light burning.(with+名词+现在分词，作伴随状语) 6、Without anything left in the cupboard， she went out to get something to eat.(without+代词+过去分词，作为原因状语) 二、with结构的用法 在句子中with结构多数充当状语，表示行为方式，伴随情况、时间、原因或条件(详见上述例句)。

从0到1搭建数据分析知识体系_光环大数据培训

https://www.wendangku.net/doc/fb6803659.html, 从0到1搭建数据分析知识体系_光环大数据培训 数据分析在运营工作中无处不在，无论是活动复盘、专题报告、项目优化，还是求职面试，数据分析都有一席之地。 对于数据分析，我发现很多运营都有这样一些困惑： 不知道从哪里获取数据; 不知道用什么样的工具; 不清楚分析的方法论和框架; 大部分的数据分析流于形式; …… 其实，数据分析并没有大家想象的那么难，这篇文章总结了一套较为完整的数据分析知识体系，全文共6103个字，全部读完大约需要8分钟。 一、概念——数据和数据分析 其实大家一直都在接触数据和数据分析，但是对于两者具体的定义又很难说清楚。我曾经做过一个调查，问一些运营同学，下面5个选项哪些属于“数据”概念的范围。 大部分人都知道把“4.报表”选上，但是很难有人会认为上面5个选项都是。其实这反映了一个很普遍的现象：很多人都会先入为主，认为数据就是各种表格、各种数字，例如excel报表、各种数据库。其实这是一个错误或者说有偏差的认识，它会使得我们对数据的认识变得很狭隘。 ①什么是数据 数据(data)是描述事物的符号记录，是构成信息或者知识的原始材料。这种哲学层次的定义，让数据的范围极大丰富，也符合目前“大数据”发展的需要。试想一下，现在很多搜索引擎做的“图片识别”、“音频识别”难道不是数据分析的一部分吗? 作为一名互联网企业的运营从业者，我们接触到的数据可能没有那么复杂，但是也有很多类别。

https://www.wendangku.net/doc/fb6803659.html, 从数据的来源来看，可以分为企业外部数据和内部数据。外部数据主要包括社会人口、宏观经济、新闻舆情和市场调研数据;内部数据包括用户行为数据、服务端日志数据、CRM与交易数据。不同数据的获取途径、分析方法、分析目的都不经相同，不同行业、不同企业在实际分析中也都各有偏好。 那么我们常见的“信息”和“数据”有何不同? 数据是信息的载体和表现形式;信息是数据的内涵，信息加载于数据之上。以书本和知识为例，书本属于数据概念范畴，知识属于信息概念范畴;书本是知识的一种载体和表现形式，知识是书本的内涵和升华。 ②什么是数据分析 数据分析是指从数据中提取有用的信息，并指导实践。 这里有两个点需要注意：首先，我们需要提取的是有用的信息，而不是自嗨;其次，这些信息需要用来指导实践，而不是流于形式。 二、思路——方法论和方法 很多新人入门数据分析的时候，要么胡子眉毛一把抓，要么无从下手。这都是缺少分析思路的表现，需要宏观的方法论和微观的方法来指导。 那么方法论和方法有什么区别? 方法论是从宏观角度出发，从管理和业务的角度提出的分析框架，指导我们接下来具体分析的方向。方法是微观的概念，是指我们在具体分析过程中使用的方法。 ①方法论 数据分析的方法论很多，这里我给大家介绍一些常见的框架。 PEST分析法：从政治(Politics)、经济(Economy)、社会(Society)、技术(Technology)四个方面分析内外环境，适用于宏观分析。 SWOT分析法：从优势(Strength)、劣势(Weakness)、机遇(Opportunity)、威胁(Threat)四个方面分析内外环境，适用于宏观分析。 5W2H分析法：从Why、When、Where、What、Who、How、Howmuch7个常见的维度分析问题。 4P理论：经典营销理论，认为产品(Product)、价格(Price)、渠道(Place)

高中英语45个介词的基本用法

——45个基本介词的用法 1、about 【原始含义】 a-b-out “A在B外面” 【引申含义】 [prep] （1）在…到处，在…各处here and there eg: We wandered about the town for an hour or so. He looked about the room. （2）在…附近next to a place eg. She lives about the office. （3）关于in connection with eg: a book about English study I don’t know what you are talking about. [adv] （1）大约close to eg: We left there about 10 o’clock. It costs about 500 dollars. （2）到处，各处 eg: The children were rushing about in the garden. （3）在附近 eg : There is no food about. 【常见搭配】 作介词时的搭配: 一.动词+(about+名词) （1）arrange (about sth) 安排关于某事（2）argue (about sth) 讨论某事 （3）ask (about sth) 询问关于某事（4）boast (about sb/sth) 吹嘘... （5）care (about sb/sth)关心…,对…感兴趣（6）chat(about sth) 谈论某事（7）complain(about sb/sth) 抱怨… （8）dream (about sb/sth) 梦见某人/某物（9）go (about sth) 着手做...；从事...

with用法归纳

with用法归纳 （1）“用……”表示使用工具，手段等。例如： ①We can walk with our legs and feet. 我们用腿脚行走。 ②He writes with a pencil. 他用铅笔写。 （2）“和……在一起”，表示伴随。例如： ①Can you go to a movie with me? 你能和我一起去看电影'>电影吗？ ②He often goes to the library with Jenny. 他常和詹妮一起去图书馆。 （3）“与……”。例如： I’d like to have a talk with you. 我很想和你说句话。 （4）“关于，对于”，表示一种关系或适应范围。例如： What’s wrong with your watch? 你的手表怎么了？ （5）“带有，具有”。例如： ①He’s a tall kid with short hair. 他是个长着一头短发的高个子小孩。 ②They have no money with them. 他们没带钱。 （6）“在……方面”。例如： Kate helps me with my English. 凯特帮我学英语。 （7）“随着，与……同时”。例如： With these words, he left the room. 说完这些话，他离开了房间。 [解题过程] with结构也称为with复合结构。是由with+复合宾语组成。常在句中做状语，表示谓语动作发生的伴随情况、时间、原因、方式等。其构成有下列几种情形： 1.with+名词(或代词)+现在分词 此时，现在分词和前面的名词或代词是逻辑上的主谓关系。 例如:1)With prices going up so fast, we can't afford luxuries. 由于物价上涨很快，我们买不起高档商品。（原因状语） 2)With the crowds cheering, they drove to the palace. 在人群的欢呼声中，他们驱车来到皇宫。（伴随情况） 2.with+名词(或代词)+过去分词 此时，过去分词和前面的名词或代词是逻辑上的动宾关系。

常用介词用法(for to with of)

For的用法 1. 表示“当作、作为”。如: I like some bread and milk for breakfast. 我喜欢把面包和牛奶作为早餐。 What will we have for supper? 我们晚餐吃什么? 2. 表示理由或原因,意为“因为、由于”。如: Thank you for helping me with my English. 谢谢你帮我学习英语。 3. 表示动作的对象或接受者,意为“给……”、“对…… (而言)”。如: Let me pick it up for you. 让我为你捡起来。 Watching TV too much is bad for your health. 看电视太多有害于你的健康。 4. 表示时间、距离,意为“计、达”。如: I usually do the running for an hour in the morning. 我早晨通常跑步一小时。 We will stay there for two days. 我们将在那里逗留两天。 5. 表示去向、目的,意为“向、往、取、买”等。如: Let’s go for a walk. 我们出去散步吧。 I came here for my schoolbag.我来这儿取书包。 I paid twenty yuan for the dictionary. 我花了20元买这本词典。 6. 表示所属关系或用途,意为“为、适于……的”。如: It’s time for school. 到上学的时间了。 Here is a letter for you. 这儿有你的一封信。 7. 表示“支持、赞成”。如: Are you for this plan or against it? 你是支持还是反对这个计划? 8. 用于一些固定搭配中。如: Who are you waiting for? 你在等谁? For example, Mr Green is a kind teacher. 比如,格林先生是一位心地善良的老师。 尽管for 的用法较多，但记住常用的几个就可以了。 to的用法: 一：表示相对，针对 be strange (common, new, familiar, peculiar) to This injection will make you immune to infection. 二：表示对比，比较 1：以-ior结尾的形容词，后接介词to表示比较，如：superior ,inferior,prior,senior,junior 2: 一些本身就含有比较或比拟意思的形容词，如equal，similar，equivalent，analogous A is similar to B in many ways.

DAMADMBOK数据管理知识体系

DAMA-DMBOK 数据管理知识体系职能框架 版本：V3.0.2

目录 1.简介 (3) 1.1.数据管理专业 (3) 1.2.数据管理知识体系（DMBOK） (4) 1.3.DAMA数据管理辞典 (5) 1.4.为什么需要此职能框架？ (5) 1.5.为什么会有 2.0版? (5) 1.6.为什么会有 3.0版? (7) 2.概述 (8) 2.1.数据管理职能 (8) 2.2.环境元素 (11) 3.DAMA-DMBOK职能纲要 (13)

文档简介　 本文档针对DAMA数据管理知识体系（ DMBOK）职能框架的第 3.0.2版进行描述，该框架是由DAMA国际提供的，用于协助对本专业的最佳实践方法进行规范化的工作。 Deborah Henderson DAMA国际教育服务副主席 DAMA基金会主席 Mark Mosley DMBOK编辑修订历史 版本日期作者描述 1.0 2006.3.27 Mark Mosley 由芝加哥分会给DMBOK 委员 会提交的建议书原始草稿。 1.1 2006.4.17 Mark Mosley 改写后的草稿，作为DMBOK 委员会提供给DAMA国际/基金 会的建议版本。 1.2 2006.5.3 Mark Mosley 2006年丹佛会议由DAMA 国 际使用后进行修改。 1.3 2006.6.12 Deborah 部分内容修订。 Henderson 2.0 2007.4.5 Mark Mosley 部分内容修订，以反映2007年 马萨诸塞州波士顿DAMA国际 会议上所做的部分修改。 2.1 2007.11.5 Mark Mosley 部分修订，反映对DMBOK术 语的使用。 3.0 2008.5.5 Mark Mosley 对第9章和第10章进行结构调 整。 3.0.1 2008.6.25 Mark Mosley 修改为详细的活动纲要。 3.0.2 2008.9.10 Mark Mosley 对DW/BI管理的活动纲要进行 微调。

介词with的用法大全

介词with的用法大全 With是个介词，基本的意思是“用”，但它也可以协助构成一个极为多采多姿的句型，在句子中起两种作用；副词与形容词。 with在下列结构中起副词作用： 1.“with+宾语+现在分词或短语”，如： (1) This article deals with common social ills, with particular attention being paid to vandalism. 2.“with+宾语+过去分词或短语”，如： (2) With different techniques used, different results can be obtained. (3) The TV mechanic entered the factory with tools carried in both hands. 3.“with+宾语+形容词或短语”，如： (4) With so much water vapour present in the room, some iron-made utensils have become rusty easily. (5) Every night, Helen sleeps with all the windows open. 4.“with+宾语＋介词短语”，如： (6) With the school badge on his shirt, he looks all the more serious. (7) With the security guard near the gate no bad character could do any thing illegal. 5.“with+宾语＋副词虚词”，如： (8) You cannot leave the machine there with electric power on. (9) How can you lock the door with your guests in? 上面五种“with”结构的副词功能，相当普遍，尤其是在科技英语中。 接着谈“with”结构的形容词功能，有下列五种： 一、“with+宾语+现在分词或短语”，如： (10) The body with a constant force acting on it. moves at constant pace. (11) Can you see the huge box with a long handle attaching to it ? 二、“with+宾语+过去分词或短语” (12) Throw away the container with its cover sealed. (13) Atoms with the outer layer filled with electrons do not form compounds. 三、“with+宾语+形容词或短语”，如： (14) Put the documents in the filing container with all the drawers open.

for和to区别

1.表示各种“目的”，用for （1）What do you study English for 你为什么要学英语？ （2）went to france for holiday. 她到法国度假去了。 （3）These books are written for pupils. 这些书是为学生些的。 （4）hope for the best, prepare for the worst. 作最好的打算，作最坏的准备。 2．“对于”用for （1）She has a liking for painting. 她爱好绘画。 （2）She had a natural gift for teaching. 她对教学有天赋/ 3．表示“赞成、同情”，用for （1）Are you for the idea or against it 你是支持还是反对这个想法？ （2）He expresses sympathy for the common people.. 他表现了对普通老百姓的同情。 （3）I felt deeply sorry for my friend who was very ill. 4. 表示“因为，由于”（常有较活译法），用for （1）Thank you for coming. 谢谢你来。

（2）France is famous for its wines. 法国因酒而出名。 5．当事人对某事的主观看法，“对于（某人），对…来说”，（多和形容词连用），用介词to，不用for. （1）He said that money was not important to him. 他说钱对他并不重要。 （2）To her it was rather unusual. 对她来说这是相当不寻常的。 （3）They are cruel to animals. 他们对动物很残忍。 6．和fit, good, bad, useful, suitable 等形容词连用，表示“适宜，适合”，用for。（1）Some training will make them fit for the job. 经过一段训练，他们会胜任这项工作的。 （2）Exercises are good for health. 锻炼有益于健康。 （3）Smoking and drinking are bad for health. 抽烟喝酒对健康有害。 （4）You are not suited for the kind of work you are doing. 7. 表示不定式逻辑上的主语，可以用在主语、表语、状语、定语中。 （1）It would be best for you to write to him. （2） The simple thing is for him to resign at once.

介词at的基本用法

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初中 英语 介词“with”的用法

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3、说明名词, 表示事物的附属部分或所具有的性质]具有; 带有; 加上; 包括...在内 tea with sugar 加糖的茶水 a country with a long history 历史悠久的国家4 4、表示一致]在...一边, 与...一致; 拥护, 有利于 vote with sb. 投票赞成某人 with的复合结构作独立主格,表示伴随情况时，既可用分词的独立结构，也可用with的复合结构： with +名词(代词)+现在分词/过去分词/形容词/副词/不定式/介词短语。例如： He stood there, his hand raised. = He stood there, with his hand raise.他举手着站在那儿。 典型例题 The murderer was brought in, with his hands ___ behind his back A. being tied B. having tied C. to be tied D. tied 答案D. with +名词(代词)+分词+介词短语结构。当分词表示伴随状况时，其主语常常用

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中国古代中央集权，我们可以建立如下的知识结构体系 中国古代中央集权体制的发展框架

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总结史料分析题与论文题的答题步骤与技巧 史料分析题被很多老师认为是历史高考的小论文，solo论文更被同学们视为噤若寒蝉，但是如果对题目进行归类和分析，我们不难看出这些题目的一些规律和和结构。 所以无论是史料分析题还是论文题有一定的层次感和逻辑性。 第一、观点清晰，通过归纳找出观点的通用性。 如2013年严复对进化论翻译的论文和2014年梁启超评价李鸿章的论文，其实是同一类型的题目，即“作者对西方思想的引进和人物的评价都是作者以引进西方思想与评价近代人物来表达自己思想和理念的目的，使作者的思想带有时代和个人的烙印。” 这种观点可以通过课堂和题目的答案进行归类总结，这样遇到陌生的论文史料就不会捉襟见肘了！ 第二、在论述中一定要做到“论从史出”，也就是俗话说的“引材料”概括归纳。 第三、不同的题目有不同的答题结构，如社会转型的史料分析，总观点往往是通过微观事件折射宏观的社会变迁，然后逐条分析材料展开其具体变化。 再如场景还原题（穿越题），其回答步骤一定要体现利弊和时代的关系，而最后不要忘记作为当时人，一定会对反对派的意见有妥协和让步，或者提出改进的方案。 我们以2013年李鸿章为同文馆辩护为例，可以从以下结构展开： 以后再遇到场景还原辩论题，这个步骤是可以通用的。

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