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先到百度文库，找一篇此类文档中文的，然后用有道翻译，或是谷歌在线翻译翻成英 文，然后把英文放上面，中文放下面。希望可以帮到你。如果要找标准的PDF格式外文文 献，可以在谷歌，用英文文献名+空格+PDF 这样比较容易找到。 第一是Google搜索，主要是英文，尤其是其学术搜索，意义大。第二，通过各大学图书馆系统，进入几个主流的出版发行集团。第三，利用网络免费储存、电子书系统。尤其是国外多。　1、论文题目：要求准确、简练、醒目、新颖。　　2、目录：目录是论文中主要段落的简表。（短篇论文不必列目录）　　3、提要：是文章主要内容的摘录，要求短、精、完整。字数少可几十字，多不超过三百字为宜。　　4、关键词或主题词：关键词是从论文的题名、提要和正文中选取出来的，是对表述论文的中心内容有实质意义的词汇。关键词是用作机系统标引论文内容特征的词语，便于信息系统汇集，以供读者检索。 每篇论文一般选取3-8个词汇作为关键词，另起一行，排在“提要”的左下方。　　主题词是经过规范化的词，在确定主题词时，要对论文进行主题，依照标引和组配规则转换成主题词表中的规范词语。　　5、论文正文：　　（1）引言：引言又称前言、序言和导言，用在论文的开头。 引言一般要概括地写出作者意图，说明选题的目的和意义, 并指出论文写作的范围。引言要短小精悍、紧扣主题。　　〈2）论文正文：正文是论文的主体，正文应包括论点、论据、 论证过程和结论。主体部分包括以下内容：　　a.提出-论点；　　b.分析问题-论据和论证；　　c.解决问题-论证与步骤；　　d.结论。　　6、一篇论文的参考文献是将论文在和写作中可参考或引证的主要文献资料，列于论文的末尾。参考文献应另起一页，标注方式按《GB7714-87文后参考文献著录规则》进行。　　中文：标题--作者--出版物信息（版地、版者、版期）：作者--标题--出版物信息　　所列参考文献的要求是：　　（1）所列参考文献应是正式出版物，以便读者考证。　　（2）所列举的参考文献要标明序号、著作或文章的标题、作者、出版物信息。　　一，选题要新颖。　　这次我的论文的成功，和高分，得到导师的赞许，都是因为我论文的选题新颖所给我带来的好处。最好涉及护理新领域，以及新进展，这样会给人耳目一新的感觉。　　二，大量文献做基础　　仔细查阅和你论文题目和研究范围相关的文献，大量的文献查阅会你的论文写作铺垫，借鉴别人的思路，和好的语言。而且在写作过程不会觉得语言平乏，当然也要自己一定的语言功底做基矗　　三，一气呵成　　做好充分的准备，不要每天写一些，每天改一些，这样会打断自己的思路，影响文章的连贯。　　四，尽量采用多的专业术语　　可能口语化的表达会给人带来亲切感，但论文是比较专业的形式，是有可能做为文献来查阅和检索的，所以论文语言的专业化，术语化会提升自己论文的水平。　　五，用正规格式书写　　参考正规的论文文献，论文格式。不要因为格式问题，而影响到你论文的质量。　　六，最好在计算机上完成写作过程　　如果有条件最好利用电脑来完成写作过程，好处以下几点：1，节省时间，无论打字的速度慢到什么程度，肯定要比手写的快。2，方便，大量的文献放在手边，一个一个查阅是很不方便的，文献都是用数据库编辑，所以都是在电脑上完成。提前先在电脑上摘要出重点，写出提纲，随时翻阅，方便写作。3，修改编辑，在电脑随时对文章进行修改编辑都是非常的方便。4，随时存档，写一段，存一段，防止突然停电，或者电脑当机。本人就是吃了这个大亏，一个晚上的劳动，差点就全没了，幸亏男友是电脑高手，帮我找回。否则就恨着电脑，哭死算了。　　七，成稿打印好交给导师　　无论你的字写的多么优美，还是按照惯例来，打印出的文字显的正规，而且交流不存在任何的问题，不会让导师因为看不懂你的龙飞凤舞，而低估你的论文。而且干净整洁，女孩子不仅注意自己的形象问题，书面的东西也反映你的修养和气质。　　八，听取导师意见，仔细修改　　导师会给你一些关于你论文建设性的意见，仔细参考，认真修改。毕竟导师是发表过多篇论文，有颇多的经验。
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淘豆网网友近日为您收集整理了关于土木工程毕业设计外文翻译4的文档，希望对您的工作和学习有所帮助。以下是文档介绍：土木工程毕业设计外文翻译4 1356 / JOURNAL OF STRUCTURAL ENGINEERING / NOVEMBER 2000STRUCTURAL HEALTH MONITORING USING STATISTICALPROCESS CONTROLBy Hoon Sohn,1Jerry A. Czarnecki,2and Charles R. Farrar,3P.E., Member, ASCEABSTRACT: This paper poses the process of structural health monitoring in the context of a statistical patternrecognition paradigm. This paper particularly focuses on applying a statistical process control (SPC) techniqueknown as an ‘‘X-bar control chart’’ to vibration-based damage diagnosis. (来源：淘豆网[/p-6536507.html])A control chart provides a statisticalframework for monitoring future measurements and for identifying new data that are inconsistent with past data.First, an autoregressive (AR) model is t to the measured time histories from an undamaged structure. Coef-cients of the AR model are selected as the damage-sensitive features for the subsequent control chart analysis.Next, control limits of the X-bar control chart are constructed based on the features o(来源：淘豆网[/p-6536507.html])btained from the initialstructure. Finally, the AR coefcients of the models t to subsequent new data are monitored relative to thecontrol limits. A statistically signicant number of features outside the control limits indicate a system transitionfrom a healthy state to a damage state. A unique aspect of this study is the coupling of various projectiontechniques such as ponent analysis and linear and quadratic discriminant operators with the SPCin an(来源：淘豆网[/p-6536507.html]) effort to enhance the discrimination between features from the undamaged and damaged structures. bined statistical procedure is applied to vibration test data acquired from a concrete bridge column as thecolumn is progressively damaged. The coupled approach captures a clearer distinction between undamaged anddamaged vibration responses than by applying an SPC alone.INTRODUCTIONMany aerospace, civil, and mechanical engineering systemscontinue to be (来源：淘豆网[/p-6536507.html])used despite aging and the associated potentialfor damage accumulation. Therefore, the ability to monitor thestructural health of these systems is ing increasingly im-portant from economic and life-safety viewpoints. Damageidentication based upon changes in dynamic response is oneof the few methods that monitor changes in the structure on aglobal basis. The basic premise of vibration-based damage de-tection is that changes in the physical properties(来源：淘豆网[/p-6536507.html]), such as re-ductions in stiffness resulting from the onset of cracks or loos-ening of a connection, will cause changes in the measureddynamic response of the structure.Structural health monitoring has received considerable at-tention in the technical literature, where there has been a con-certed effort to develop a rm mathematical and physical foun-dation for this technology. Doebling et al. (1998) presented athorough review of vibration-based stru(来源：淘豆网[/p-6536507.html])ctural health monitor-ing methods. Because all vibration-based damage detectionprocesses rely on experimental data with inherent uncertain-ties, statistical analysis procedures are necessary if one is tostate in a quantiable manner that changes in the vibrationresponse of a structure are indicative of damage as opposedto operational and/or environmental variability. However, mostreferences cited in this review focus on different methods forextractin(来源：淘豆网[/p-6536507.html])g damage-sensitive features from vibration responsemeasurements. Few of the cited references take a statisticalapproach to quantifying the observed changes in these fea-tures.This paper casts the structural health-monitoring problem inthe context of a statistical pattern recognition paradigm. Thisparadigm can be described as a four-part process: (1) Opera-1Postdoctoral Res. Fellow, Engrg. Sci. and Applications Div., Engi-neering Analysis Group, Los (来源：淘豆网[/p-6536507.html])Alamos Nat. Lab., Los Alamos, NM 87545.2PhD Student, Dept. of Civ. and Envir. Engrg., Massachusetts Inst. ofTechnol., Cambridge, MA 02139.3Mat. Behavior Team Leader, Engrg. Sci. and Applications Div., En-gineering Analysis Group, Los Alamos Nat. Lab., Los Alamos, NM.Note. Associate Editor: James H. Garrett. Discussion open until April1, 2001. To extend the closing date one month, a written request mustbe led with the ASCE Manager of Journals. The ma(来源：淘豆网[/p-6536507.html])nuscript for thispaper was submitted for review and possible publication on January 31,2000. This paper is part of the Journal of Structural Engineering, Vol.126, No. 11, November, 2000. ASCE, ISSN /– $.50 per page. Paper No. 22244. (2) data acqui (3) fea-ture extractio and (4) statistical modeldevelopment. In particular, this paper focuses on Parts 3 and4 of (来源：淘豆网[/p-6536507.html])the process, discussed in detail below. More detailed dis-cussion of the statistical pattern recognition paradigm can befound in Farrar and Doebling (1999). The process is illustratedthrough application to time history data measured on undam-aged and subsequently damaged concrete columns. Note thatthe primary objective of this study is to identify the existenceof damage. The localization and quantication of damage arenot addressed in this study.SPATIAL PRESSIONThe distinction between feature extraction and data reduc-tion is not always clear-cut. Feature extraction is the processof identifying damage-sensitive properties from the measuredvibration response, and this process often results in some formof data reduction. pression into feature vectors ofsmall dimension is necessary if accurate estimates of the fea-ture statistical distribution are to be obtained. The need forlow dimensionality in the feature vectors is referred to as the‘‘curse of dimensionality’’ and is discussed in general texts ondensity function estimation (Scott 1992).In this study, ponent analysis (PCA) is usedto perform pression prior to the feature extractionprocess when data from multiple measurement points areavailable. This process transforms the time series from mul-tiple measurement points into a single time series, preservingas much of the relevant information as possible during thedimensionality reduction.If ui(tj) (i = 1, . . . , m and j = 1, . . . , l) denotes the responsetime histories corresponding to m measurement locations andsampled at l time intervals, a vector of the po-nents corresponding to the m measurement locations is formedat a given time tj asTu(t ) = [u (t ) u (t ) u (t )] (1)j 1 j 2 j m jwhere each time history is rst normalized by subtracting itsmean value. Then, the m m covariance matrix amongspatial measurement locations summed over all time samplesis given bylT= u(t )u(t ) (2)j jj=1JOURNAL OF STRUCTURAL ENGINEERING / NOVEMBER 2000 / 1357The eigenvalues i and eigenvectors vi of the covariance ma-trix satisfyv = v (3)i i iHere, an eigenvector vi is also called a ponent.To reduce the m-dimensional vector u(t) into a d-dimensionalvector, xv(t), where d & m, u(t) is projected onto the eigen-vectors corresponding to rst d largest eigenvaluesTx (t) = [v v ] u(t) (4)v 1 dFor the examples presented in the PCA section later in thepaper, all time histories from the measurement points are pro-jected onto the rst ponent.FEATURE EXTRACTIONFeature extraction is the process of identifying damage-sen-sitive properties derived from the measured vibration responsethat allows one to distinguish between the undamaged anddamaged structures. Typically, systematic differences betweentime series from the undamaged and damaged structures arenearly impossible to detect by eye. Therefore, other featuresof the measured data must be examined for damage detection.In this study, the coefcients of autoregressive (AR) modelsare selected as damage sensitive features. The time series froman individual measurement point, or the pressedtime series obtained from PCA, can be used to construct theAR models. In the AR(n) model, the current point in a timeseries is modeled as a bination of the previous npointsny(t) = y(t y) e(t) (5)jj=1where y(t) = ti j = unknown AR coef- and e(t) = random error with zero mean and constantvariance. The values of j are estimated by tting the ARmodel to the time history data using the Yule-Walker method(Brockwell and Davis 1991). A detailed discussion on ARmodel order selection can be found in Box et al. (1994).For the application reported herein, the time signals are di-vided into smaller size time windows, and AR coefcients areestimated from each time window. Following this procedure,a large set of AR coefcients are obtained for subsequent dam-age diagnoses. As mentioned earlier, it is desirable to obtainmany samples of the selected features for statistical analysis.PRESSION FOR FEATURE VECTORDISCRIMINATIONThe preceding section described methods for obtaining ann-dimensional feature space of AR coefcients. In such situ-ation where multidimensional feature vectors exist, severalmonitoring procedures may be employed for feature vectordiscrimination. For example, each AR coefcient can be mon-itored by a variety of statistical procedures, or simultaneousmonitoring of all AR coefcients can be done using multivar-iate statistical procedures. However, for feature vectors with ahigh dimensionality, the rst approach can result in a largeamount of data to be monitored, and the visualization of themultivariate data can be very difcult. In this study the mul-tidimensional feature vectors are projected onto 1D subspaces,and the statistical discrimination procedure is applied to the1D variable. Two transformations, linear and quadratic projec-tions, are presented to maximize the separation in featuresfrom the undamaged and damaged structures.To derive specic linear and quadratic projections, considera situation in which there are only two classes (classes A andB) and multidimensional feature vector x is obtained. Fuku-naga (1990) showed that a decision boundary D(x), based onBayes’ theorem minimizes the probability of error, which isthe probability of misclassication of assigning a new featureto class A when, in fact, it belongs to class B, or vice versa.If classes A and B have normal distributions, the Bayes’decision rule D(x) can be written in a quadratic form (Fuku-naga 1990)TD(x) = x Qx Vx (6)where Q = quadrat and V = linear pro-jection. In the case where the covariance matrices for classesA and B are identical matrices, the classication boundary canbe further simplied to a linear formTD(x) = F x (7)The Q, V, and F matrices will be estimated later in this sec-tion.The decision rule can also be viewed as a projection thatmaps multidimensional space x to 1D space D(x). The presentstudy is particularly interested in dening a transformed fea-ture = D(x) such that the means of two classes are as far aspossible and their variances are the smallest possible after ei-ther quadratic or linear projection. These projections can besought by maximizing the following Fisher criterion (Bishop1995):2 T T(m m ) F (m m )(m m ) FA B A B A Bf = = (8)2 2 TF ( )FA B A Bwhere mA and mB = mean vectors of the classes A and B A and B = covariance mamA and mB = means of the projected feature in classes A andB; and A and B = corresponding standard deviations of thetransformed features, respectively. Furthermore, the momentsof the projected feature are related to those of the multidi-mensional feature vector x as follows:T 2 Tm = F = F F for i = A or B (9a,b)i i i iTaking derivatives of f with respect to F and setting this quan-tity equal to zero, yields the following linear projection(Bishop 1995):1F = 2( ) (m m ) (10)A B A BIt is important to mention that the performance of the linearclassier will not be optimal unless A and B are the same.It is only under the assumption of equal covariance matricesthat the decision role reduces to a linear one. For the test dataemployed in the Application to Concrete Columns section be-low, acceleration data from undamaged and damaged classesare observed to have unequal covariance matrices. Because theBayesian decision boundary is quadratic under the more gen-eral circumstance of unequal covariance matrices betweenclasses, the quadratic transformation yields the best discrimi-nation power. The calculation of the quadratic term Q andlinear term V in (6) putationally more intensive thanthe linear case. However, introducing a new variable yi, whichrepresents the product of two xis, (6) can be linearized in thefollowing form (Fukunaga 1990):n n n n(n 1)/2 nD(x) = q x x v x = a y v x (11)ij i j i i i i i ii=1 j=1 i=1 i=1 i=1where qij and vi = components of Q and V, yirepresents the product of the xjs and ai = corresponding entryin the Q matrix. In addition, n is the order of the AR modelor the dimension of AR coefcients dened in (5).1358 / JOURNAL OF STRUCTURAL ENGINEERING / NOVEMBER 2000Let Y and X denote column vectors of yis and xjs, respec-tively. Now, the following equation analogous to the linearcase can be solved for Q and V by introducing a new variablevector Z = [YTXT]Tand letting E and S be the expected vectorand covariance matrix of Z, respectivelyT 1[a a v v ] = 2[S S ] (E E ) (12)1 n(n 1)/2 1 n A B A BThen ais and vjs can be rearranged to form the Q matrixand V vector. Note that the projection techniques presentedhere are used for a dimensionality reduction purpose as wellas for construction of a discriminant function. That is, the n-dimensional AR coefcient space is projected onto a singlescalar space maximizing the mean differences between twoclasses. Damage diagnosis is conducted on the transformedfeature using the statistical process control (SPC) techniquedescribed in the following section.STATISTICAL MODELING—SPCStatistical model development is concerned with the imple-mentation of the algorithms that analyze the distribution ofextracted features to determine the damage state of the struc-ture. The algorithms used in statistical model development fallinto the three general categories: (1) G (2) and (3) outlier detection. The appropriatealgorithm to use will depend on the ability to perform super-vised or unsupervised learning. Here, supervised learning re-fers to the case where examples of data from damaged andundamaged structures are available. Unsupervised learning re-fers to the case where data are only available from the undam-aged structure. This paper focuses on unsupervised learningmethods.In this study, control chart analysis, which is the -monly used SPC technique and very suitable for automatedcontinuous system monitoring, is applied to the selected fea-tures to investigate the existence of damage in the structure ofinterest. When the system of interest experiences abnormalconditions, the mean and/or variance of the extracted featuresare expected to change. Here an X-bar control chart is em-ployed to monitor the changes of the selected feature meansand to identify samples that are inconsistent with the past datasets. Application of the S control chart, which measures thevariability of the structure over time, to the current test struc-ture is presented in Fugate et al. (2000). Several variations ofthe control charts can be found in Montgomery (1997). Tomonitor the mean variation of the features, the features (i.e.,the AR coefcients or the transformed feature after linear orquadratic projection) are rst arranged in subgroups of size p.The variable ij is the jth feature from the ith subgroup. Thesubgroup size p is often taken to be 4 or 5 (Montgomery1997). If p is chosen too large, a drift present in the individualsubgroup mean may be obscured, or averaged out. An addi-tional motivation for using subgroups, as opposed to individ-ual observations, is that the distribution of the subgroup meanvalues can be reasonably approximated by a normal distribu-tion as a result of central limit theorem.Next, the subgroup mean Xi and standard deviation Si of thefeatures puted for each subgroup (i = 1, . . . , q, whereq is the number of subgroups)X = mean( ); S = std( ) (13a,b)i ij i ijHere, the mean and standard deviation are with respect to pobservations in each subgroup. Finally, an X-bar control chartis constructed by drawing a centerline (CL) at the subgroupmean and two additional horizontal lines corresponding to theupper and lower control limits (UCL and LCL) versus sub-group numbers (or with respect to time). The centerline andtwo control limits are dened as follows:S UCL, LCL = CL Z ; CL = mean (X ) (14a,b)/2 inwhere the calculation of mean is with respect to all subgroups(i = 1, . . . , q); and Z /2 = percentage point of the normaldistribution with zero mean and unit variance such that P[zZ /2] = /2. The variance S2is estimated by averaging thevariance of all subgroups: S2= mean2 2S (S ).i iNote that, if Xi can be approximated by a normal distributiondue to the central limit theorem, the control limits in (14)correspond to a 100(1 )% condence interval. In manypractical situations, the distribution of features may not be ex-actly normal. However, it has been shown that the controllimits based on the normality assumption can often be suc-cessfully used unless the population is extremely nonnormal(Montgomery 1997). If the system experienced damage, thiswould likely be indicated by an unusual number of subgroupmeans outsid a charted value outside thecontrol limits is referred to as an outlier in this paper. Themonitoring of damage occurrence is performed by plotting Xivalues obtained from the new data set along with the previ-ously constructed control limits.APPLICATION TO CONCRETE COLUMNSFaculty, students, and staff at the University of California,Irvine (UCI) performed quasi-static cyclic tests to failure onseismically retrotted, reinforced-concrete bridge columns. Vi-bration tests were performed on the columns at intermittentstages during the static load cycle testing when variousamounts of damage had been accumulated in the columns. Theassociated data obtained from one of the columns are used toinvestigate the applicability of statistical pattern recognitiontechniques to vibration-based damage detection problems.The conguration and dimension of the test column areshown in Fig. 1. The test structure was a 349 cm (137.5 in.)long, 61 cm (24 in.) diameter concrete bridge column that wassubsequently retrotted to a 91 cm (36 in.) diameter column.The column was retrotted by placing forms around the ex-isting column and placing additional concrete within the form.A 61 cm (24 in.2) concrete block, which had been cast inte-grally with the column, extends 46 cm (18 in.) above the topof the circular portion of the column. This block was used toattach the hydraulic actuator to the column for quasi-yclic testing and to attach the ic shaker used forthe vibration tests. The column was bolted to the testing oorin the UCI laboratory during the static cyclic tests and vibra-tion tests. The detail of the test structure can be found at http://ext.lanl.gov/projects/damage id .Test ProcedureA hydraulic actuator was used to apply lateral loads to thetop of the column in a quasi-static cyclic manner. The loadswere rst applied in a force-controlled manner to produce lat-eral deformations at the top of the column corresponding to0.25 yT, 0.5 yT, 0.75 yT, and yT. Here, yT is the lateraldeformation at the top of the column corresponding to thetheoretical rst yield of the longitudinal reinforcement. Thestructure was cycled three times at each of these load levels.Next, a lateral deformation corresponding to the actual rstyield y was estimated based on the observed response. Loadswere then applied in a displacement-controlled manner, againin sets of three cycles, at displacements corresponding to1.5 y, 2.0 y, 2.5 y, etc., until the ultimate capacity of thecolumn was reached.Vibration tests were conducted on the column in its undam-aged state, and after cyclic loading at the subsequent displace-JOURNAL OF STRUCTURAL ENGINEERING / NOVEMBER 2000 / 1359FIG. 1. Column Dimensions and Photograph of Actual Test Structurement levels, y, 1.5 y, 2.5 y, 4.0 y, and 7.0 y. In this study,these vibration tests are referred to as damage levels 0–5, re-spectively. The excitation for the vibration tests was providedby an ic shaker mounted off-axis at the top ofthe structure. The shaker rested on a steel plate attached to thetop square block of the concrete column. Horizontal loadingwas transferred from the shaker to the structure through a fric-tion connection between the shaker and the steel support plate.The shaker was controlled in an open-loop manner while at-tempting to generate a 0–400-Hz uniform random signal. TheRMS voltage level of this signal remained constant during allvibration tests. However, feedback from the column and thedynamics of the mounting plate produced an input signal thatwas not uniform over the specied frequency range.Operational EvaluationOperational evaluation begins to set the limitations on whatwill be monitored and how to perform the monitoring as wellas tailoring the monitoring to unique aspects of the system andunique features of the damage that is to be detected. Becausethe test structure was a laboratory specimen, operational eval-uation was not conducted in a manner that would typically beapplied to an in situ structure. However, because the vibrationtests were not the primary purpose of this investigation, com-promises had to be made regarding the manner in which thevibration tests were conducted. The promise wasassociated with the mounting of the shaker, where it wouldhave been preferable to suspend the shaker from soft supportsand to apply the input at a point location using a stinger. promises are analogous to operational constraints that ur with in situ structures. Environmental variability was notconsidered an issue because the tests were conducted in a lab-oratory setting. The available dynamic measurement hardwareand software placed the only constraints on the data acquisi-tion process.Data Acquisition and CleansingForty accelerometers were mounted on the structure asshown in Fig. 1. These locations were selected based on theinitial desire to measure the global bending and axial and tor-sional modes of the column. Note that at locations 2, 39, and40 the accelerometers had a nominal sensitivity of 10 mV/gand were not sensitive enough for the measurements beingmade. At locations 33–37 the accelerometers had a nominalsensitivity of 100 mV/g. All other channels had accelerometerswith a nominal sensitivity of 1 V/g. An accelerometer on thesliding mass of the shaker provided a measure of the inputforce applied to the column. Analog signals from the accel-erometers were sampled and digitized with mercial dy-namic data acquisition system. Data acquisition parameterswere specied such that 8-s time histories discretized with8,192 points were acquired. No windowing function was ap-plied to these time histories.Antialiasing lters were applied to further cleanse the data.Analog and digital antialiasing lters with cutoff frequenciesof 12.8 kHz and 512 Hz, respectively, were used in this study.Data decimation was also used to cleanse the data. Althoughthe data are sampled at 25.6 kHz, the decimation processyields an effective sampling rate of 1.024 kHz. Finally, analternating current coupling lter that attenuates a signal below2 Hz was applied to remove direct current offsets from thesignal. To eliminate high-frequency noise resulting from otherexperimental activities being conducted in the UCI Laboratory,the raw time series are passed through a seventh-order But-terworth low-pass lter with a cutoff frequency 150 Hz. Thesecleansing processes signicantly improved the quality of data.Feature Extraction and pressionThe PCA, SPC, and projection techniques are illustrated us-ing the vibration test data obtained from the test column shownin Fig. 1. First, the applicability of SPC to the damage diag-nosis problem is demonstrated using a single AR coefcientobtained from individual measurement point. Here, the ARcoefcients are dened as damaged-sensitive features, and thesubsequent control chart analysis is conducted using the ARcoefcient (see Statistical Modeling—X-Bar Control ChartUsing Single AR Coefcient section below). Next, the advan-tage of projection techniques is investigated. Linear and quad-ratic projections are introduced to map multidimensional ARcoefcient space into 1D space to maximize the mean differ-ences between the data sets obtained from the undamaged anddamaged classes (see False-Positive Alarm Testing). SPC anal-yses are then conducted on the transformed single-scale fea-ture. Finally, PCA is carried out to all response time series forspatial dimensionality reduction prior to feature selection andSPC analysis (see PCA section below). That is, all time seriesfrom 39 response points are projected onto the rst principal1360 / JOURNAL OF STRUCTURAL ENGINEERING / NOVEMBER 2000FIG. 2. X-Bar Control Chart Using First AR CoefcientTABLE 1. Outlier Numbers of X-Bar Control Chart Using Different AR CoefcientsAR coefcientDamage Level0 1 2 3 4 51 0/128a0/128 6/128 6/128 2/128 1/ 0/128 6/128 10/128 30/128 23/ 1/128 12/128 31/128 77/128 88/128Total number of outliers 2/384(0.52)1/384(0.26)24/384(6.25)47/384(12.24)109/384(28.39)112/384(29.17)Note: Values in parentheses are percentages.a1/128 indicates that a single outlier exists out of 128 sample data ponent of the covariance matrix of the time series. Thesubsequent feature selection and SPC analyses are performedbased on this single time series, which is a binationof the 39 measured time series.Statistical Modeling—X-Bar Control Chart UsingSingle AR CoefcientThe 8,192-point measured time series are rst divided into512 16-point time windows, and AR(3) is t to an individualwindow resulting in 512 sets of AR coefcients. Then, usingsubgroup size 4, 128 (=512/4) subgroup means are obtained.Fig. 2 shows the damage diagnosis results using the rst co-efcient of the AR(3) model. Time histories from measurementpoint 1 shown in Fig. 1 are used for the construction of thecontrol chart. UCL, LCL, and CL denote the upper and lowercontrol limits, and centerline obtained from the time series ofthe undamaged structure. The control limits corresponding toa 99% condence interval are constructed by setting = 0.01in (14). After the construction of the control limits, damagediagnoses using the X-bar chart are performed for subsequentdamage levels 1–5.Note that the extracted feature (the rst AR coefcient inthis case) is standardized prior to the construction of the X-bar control chart: The mean is subtracted from the feature andthe feature is normalized by the standard deviation. Therefore,CL for all gures in this paper corresponds to zero. After es-tablishing the control limits and centerline, features obtainedat each damage level are plotted relative to the control limitsand centerline obtained from the undamaged data. The outliers,which are samples outside the control limits, are indicated bya ‘‘’’ in Fig. 2. The features extracted at each damage levelare also standardized in the same fashion as before. Note thatthe mean and standard deviation estimated from damage level0 are used to normalize data from all of the subsequent damagelevels.The diagnosis results using the other AR coefcients arealso summarized in Table 1. For this particular example, thethird AR coefcient seems most indicative of damage, and therst coefcient is very insensitive to damage. For damage lev-els 0 and 1, the numbers of total outliers out of 384 samplesare 2 and 1, respectively. (There are three AR coefcients and128 samples for each AR coefcient. Therefore, a total of 384samples are obtained.) These are equivalent to 0.52 and 0.26%of outliers. Considering the fact that the constructed controllimits correspond to a 99% condence interval, features ex-JOURNAL OF STRUCTURAL ENGINEERING / NOVEMBER 2000 / 1361TABLE 2. Outlier Numbers of X-Bar Control Chart Using Linear or Quadratic ProjectionProjectionDamage Level0 1 2 3 4 5Linear 1/128a5/128 24/128 125/128 121/128 127/128Quadratic 3/128 3/128 34/128 128/128 127/128 128/128a1/128 indicates that a single outlier exists out of 128 sample data points.FIG. 3. False-Positive Testing Using Linear Projectiontracted from the in-control system can still produce approxi-mately 1% of the outliers without indicating any damage.Therefore, it is not clear if the system experienced any signif-icant damage at damage level 1 based on the analysis of theX-bar control chart using the individual AR coefcient.Statistical Modeling—Control Chart Analysis afterLinear or Quadratic ProjectionNext, the projection techniques are incorporated into the X-bar control chart. As shown in the previous example, some ARcoefcients are more sensitive to damage than others. Fur-thermore, constructing separate control charts for each AR co-efcient would be time consuming. To e these dif-culties, the construction of multiple control charts using anindividual AR coefcient is simplied into a single controlchart using a 1D transformed feature. In the following exam-ples, the 3D AR coefcients are rst projected onto a 1Dspace, and the X-bar chart is constructed based on the trans-formed feature. In general, the projection onto a 1D spaceleads to a loss of information, and classes well separated inthe original multidimensional space may be strongly over-lapped in the projected space. However, by using the Fishercriterion in (8), the projections are determined to maximizethe class separation.Table 2 shows the results of process monitoring after a lin-ear projection. Comparison of Table 1 and Table 2 clearly re-veals the improvement of diagnosis performance. Again, thediagnoses in Table 2 are performed using the time series frommeasurement point 1. Diagnosis results using the other mea-surement points are conducted, and similar performance im-provement is observed. However, the diagnosis results are notpresented because of space limitations. As mentioned earlier,the linear projection may not be the optimal projection in thisexample because the orders of two class covariance matrices(one from the undamaged case and the other from each dam-age level) are quite different. In theory, the quadratic projec-tion is the optimal one in a sense of minimizing the error ofmisclassication. However, no signicant performance differ-ence between linear and quadratic projections is observed inthis example (Table 2).False-Positive Alarm TestingWhile it is desirable to have features sensitive to urrence, the monitoring system also needs to be robustagainst a false-positive indication of damage. A false-positiveindication of damage means that the monitoring system indi-cates damage although no damage is present. To investigatethe robustness of the proposed X-bar control chart against afalse-positive warning of damage, two separate tests are de-signed.In the rst test, the time histories obtained from the undam-aged state of the test structure are divided into two parts. Therst half of the time series is employed to construct the controllimits, and the false-positive testing is carried out using thesecond half of the time series. Note that the original time seriesare 8-s long with 8,192 time points, and each half of the timeseries is 4-s long with 4,096 points. Half of the time series isfurther divided into 256 sets of 16-point time windows, andAR(3) is again t to each time window producing 256 sets ofAR coefcients. Next, as mentioned before, four consecutiveAR coefcients are grouped together resulting in 64 sampleswith subgroup size 4. Fig. 3(a) shows the construction of thecontrol limits using the rst half of the time series, and theuctuation of the features extracted from the rst half timeseries are plotted together. Fig. 3(b) presents the false-positivetesting using the second half of the time series.For the second test, the control limits are established usingthe whole 8-s time histories from the undamaged state of thecolumn, and the false-positive test is conducted using a 2-stime series measured from an independent vibration test of theundamaged column. Fig. 3(c) shows the result of damage di-agnoses when the linear projection is applied. For all the cases,the number of outliers are 2. Therefore, the two sets of testspresented here have demonstrated that the damage diagnosisusing bination of X-bar control chart and projectiontechniques appears to be robust against a false-positive indi-cation of damage for the data studied. Again, similar resultsare obtained using the quadratic projection.PCAIn the previous examples, all damage diagnoses are individ-ually carried out for each measurement points. The PCA con-ducted on the covariance matrix of 39 response time seriesindicates that the responses of 39 measurement points are1362 / JOURNAL OF STRUCTURAL ENGINEERING / NOVEMBER 2000TABLE 3. Damage Diagnosis Results after PCA and Linear/Quadratic ProjectionsProjectionDamage Level0 1 2 3 4 5Linear 1/128a(0.78)7/128(5.47)127/128(99.22)128/128(100.0)120/128(93.75)120/128(93.75)Quadratic 1/128(0.78)7/128(5.47)126/128(98.44)127/128(99.22)121/128(94.53)124/128(96.88)Note: Values in parentheses are percentages.a1/128 indicates that a single outlier exists out of 128 sample data points.FIG. 5. X-Bar Control Chart of AR Coefcients after PCA of All Measurement Points and Linear ProjectionFIG. 4. PCA of Covariance Matrix of 39 Response Pointsclosely correlated. Fig. 4 shows that the rst -ponent alone holds about 30% of the total information. There-fore, in the following examples, raw time series from the 39measurement points are rst projected onto the rst ponent v1 as shown in (4). Then, the subsequent featureextraction and X-bar control chart analyses are performed inthe same fashion as before. Because the linear and quadraticprojections have produced similar results, only the damage di-agnosis results after PCA and the linear projection at eachdamage level are displayed in Fig. 5, in which the outliers areagain indicated by a ‘‘.’’ However, diagnosis results after thequadratic projection are also summarized in Table 3. The re-sults of Table 3 are equivalent to or slightly better than thoseof Table 2 and much better than those of Table 1. That is, PCAcondenses all time series information that is spatially distrib-uted along the column and essfully identies all ve dam-age cases.SUMMARY AND DISCUSSIONA vibration-based damage detection problem is cast in thecontext of statistical pattern recognition. This statistical ap-proach is used to identify the plastic hinge deformation of aconcrete bridge column solely based on the vibration test data.First, the applicability of SPC to the damage diagnosis prob-lem is demonstrated using individual time series from differentmeasurement points. AR models are constructed using themeasured time signals, and damage diagnoses using X-barcontrol charts are performed using an individual AR coefcientas a damage-sensitive feature. The X-bar control chart pro-vides a framework for monitoring changes in the selected fea-ture mean values and for identifying samples that are incon-sistent with the past data sets. Next, linear and quadraticprojections are introduced to map the multidimensional ARcoefcients into a 1D feature space to maximize the differ-ences in the mean values between the two data sets pared. The control chart analysis is then conducted on theJOURNAL OF STRUCTURAL ENGINEERING / NOVEMBER 2000 / 1363transformed 1D feature data. Third, the robustness of the pro-posed approach against a false-positive indication of damageis demonstrated using two separate time histories obtainedfrom the initial test structure. Finally, PCA is carried out onall response time series for spatial dimensionality reductionprior to feature extraction. That is, all time series from multiplemeasurement points are projected onto the rst -ponent of the time series covariance matrix, and the subse-quent feature selection is performed using pressedtime series.The projection techniques improved the performance ofcontrol chart pared to the damage diagnosis usingthe individual AR coefcient. When the projection techniquesand PCA bined, the control charts essfully indi-cated the system response anomaly for all investigated damagelevels by showing a statistically signicant number of outliersoutside the control limits. It should also be noted that thisstudy is carried out in an unsupervised learning mode. Al-though the projection techniques require two separate datasets, no claim is made that they are from two different classes.It is only assumed that there is one data set from the undam-aged class and that the other data set is from an unknown class.The ability to apply unsupervised damage detection techniquesto civil engineering structures is very important because re-sponse data from a similar damaged system are rarely avail-able.In general, the observation of a large number of outliers inthe control chart does not necessarily indicate that the structureis damaged, but only that the system has varied, causing astatistically signicant change in its vibration response. Thisvariability can be caused by a variety of environmental andoperational conditions that the system is subjected to. Becausethe inuence of operational and environmental factors on thedynamic characteristics of the test structure is minimal for thepresented laboratory test, the deterioration of the structure wasassumed to be the main cause of the abnormal changes of thesystem. However, operational and environmental conditionssuch as wind, humidity, intensity, and frequency of trafcloading should be taken into account for applications to in situcivil engineering infrastructures. A novel approach to data nor-malization, combining AR and AR with exogenous inputs(ARX) techniques, is developed to explicitly incorporate theenvironmental and operational conditions into the statisticalpattern recognition paradigm so that the effect of damage onthe vibration response could be discriminated from these ef-fects and to prevent the operational and environmental varia-bility from causing false-positive indications of damage (H.Sohn et al., unpublished paper, 2001).The presented approach is very attractive for the develop-ment of an automated continuous monitoring system becauseof its simplicity, minimum interaction with users, and a seam-less process of continuous data stream analysis. A researcheffort is underway to integrate the proposed diagnosis algo-rithm into a sensing unit through a programmable micropro-cessing chip. The processed data output of these sensing unitscan be further monitored at a central facility using a munication system. Because signal processing and damagediagnosis can be conducted independently at an individual sen-sor level, many issues related to data transmission, such astime synchronization among the multiple sensors, can be sim-plied. Finally, the only output to the end user will be a simpleindication of the structure safety using green, yellow, or redlights. This strategy offers a potential for a signicant break-through in structural health monitoring technology through anintegrated sensing/data interrogation process that has not beenattempted to date.Several issues remain for further study. This study focusesonly on the identication of damage existence. Based on per-sonal conversation with bridge eld engineers, building own-ers, bridge managers, and panies, their utmosturgent need for civil infrastructures is mainly to investigatethe presence of damage. Then, visual inspections or more so-phisticated localized nondestructive diagnosis techniques canbe applied to pinpoint and quantify structural deterioration.The localization and quantication of damage has not beenaddressed in this current study. The extension of this approachto damage localization is addressed in Sohn and Farrar (2000).ACKNOWLEDGMENTSThe funding for this work was provided by the Department of Energy’sEnhanced Surveillance Program and a cooperative research and devel-opment agreement with Kinemetrics Corporation, Pasadena, Calif. Vibra-tion tests on the columns were conducted jointly with Prof. Gerry Pardoenat UCI using Los Alamos National Laboratory’s University of CaliforniaInteraction Funds. CALTRANS provided the primary funds for construc-tion and cyclic testing of the columns.APPENDIX. REFERENCESBishop, C. M. (1995). works for pattern recognition, OxfordUniversity Press, Oxford, U.K.Box, G. E. P., Jenkins, G. M., and Reinsel, G. C. (1994). Time seriesanalysis: Forecasting and control, Prentice-Hall, Englewood Cliffs,N.J.Brockwell, P. J., and Davis, R. A. (1991). Time series: Theory and meth-ods, Springer, New York.Doebling, S. W., Farrar, C. R., Prime, M. B., and Shevitz, D. W. (1998).‘‘A review of damage identication methods that examine changes indynamic properties.’’ Shock and Vibration Dig., 30(2), 91–105.Farrar, C. R., and Doebling, S. W. (1999). ‘‘Vibration-based structuraldamage identication.’’ Philosophical Trans. Royal Soc.: Math., Phys.and Engrg. Sci., London, accepted for publication.Fugate, M. L., Sohn, H., and Farrar, C. R. (2000). ‘‘Vibration-based dam-age detection using statistical process control.’’ Mech. Syst. and SignalProcessing, London, accepted for publication.Fukunaga, K. (1990). Introduction to statistical pattern recognition, Ac-ademic, New York.Montgomery, D. C. (1997). Introduction to statistical quality control,Wiley, New York.Scott, D. W. (1992). Multivariate density estimation: Theory, practice,and visualization, Wiley, New York.Sohn, H., and Farrar, C. R. (2000). ‘‘Time series analyses for locatingdamage sources in vibration systems.’’ Int. Conf. on Noise and Vibra-tion Engrg.Sohn, H., Fugate, M. L., and Farrar, C. R. (2000). ‘‘Damage diagnosisusing statistical process control.’’ Conf. on Recent Adv. in Struct. Dyn.播放器加载中，请稍候...
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土木工程毕业设计外文翻译4 1356 / JOURNAL OF STRUCTURAL ENGINEERING / NOVEMBER 2000STRUCTURAL HEALTH MONITORING USING STATISTICALPROCESS CONTROLBy Hoon Sohn,1Jerry A. Czarnecki,2and Charles R. Farrar,3P.E., Member, ASCEABSTRACT: This paper poses the process of structural health monitoring in the cont...
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