Yersel fotogrametride analog analog-analitik ve analitik değerlendirme yöntemlerinin yapı konstrüksiyon deneylerinde uygulama olanakları

Abstract

- Ill - Ö Z ET Günümüz koşullarında topoğrafik harita yapı mından tıp araştırmalarına kadar hemen hemen bütün bilim dallarına girmiş olan f ot ogrametr i, genel çizgileriyle havadan veya yerden çekilen resimler üzerinde ölçme, yorumlama ve değerlendirme yapılma sına olanak veren bir bilim dalıdır. Bu bakımdan, çeşitli bilim dallarındaki uygulama alanlarında etüd ve araştırma yapılmasında, amaca uygun hız, ekonomi ve inceliğin elde edilmesinde fotogramet- rinin rolü büyüktür. Bu bilimin temel özelliği, ölçmelerin doğrudan doğruya cisim üzerinde yapılması yerine, cismin üç boyutlu modeli üzerinde yapılmasıdır. Bu dolaylı ölçme özelliğinden yararlanılarak, f o togramet r i, birçok alanda başarı ile uygulanmaktadır. Bu çalışmada, f o togramet r in in uygulama alan larından biri olan yapı kons t rüks iyonlar ı ile ilgi li deformasyon ölçme problemlerinde, çeşitli foto- grametrik yöntemler (analog, analog-anal it ik, ana litik, denenerek, bunların karşılaştırılması yapıl mış, yapı konstrüksiyon deneylerinde hangi incelikle uygula nabileceği araştırılmıştır. Bu amaçla, İ. T. Ü. Yapı Malzemesi Laboratuva- rmda kurulan iki deney düzeninden yararlanılmış tır. Kabuk ve kiriş deneyleri sırasında Wild C40 çift resim çekme makinesi ile çeşitli yükleme adım larında resimler çekilmiştir. Kabuk deneyi sırasın-- IV - da, 4 yükleme adımında, kiriş deneyinde ise 7 yük leme adımında çekilen resimler analog, analog-ana- litik ve analitik yönteme göre değerlendirilmiştir. Resim çekme işlemine geçmeden önce, her iki deney üzerinde gerekli geçiş noktaları, bir çelik şerit metre ve 0.5 mm bölümlü bir cetvelden yarar lanılarak belirlenmiştir. Böyle bir belirlemeye gi dilmesinin nedeni, f ot ograme t r ik nokta belirleme ve deformasyon ölçme işlemlerinde incelik konusunda şimdiye kadar yapılan çalışmalar gözönüne alındığı zaman, bunların büyük bir bölümünde geçiş noktala rının jeodezik ölçmelerle belirlendiği, bunun da ek alet donanımı, büyük zaman ve hesap programı gerek tirmesi nedeniyle f o togramet rik yöntemin ekonomik olma yönünün zedelendiğinin gözlenmesi olmuştur. Bu nedenle, bu çalışmada geçiş noktalarının belirlen mesinde, ek alet ve hesap donanımı gerektirmeyecek, ancak ölçme inceliği düşük olan geçiş noktaları tesisi yönüne gidilmiş ve sonuca ne biçimde etkidi- ği araştırılmıştır. Tek resim ölçmeleri Wild A9 Au tograph ' ma EK 8 elektronik kaydedicisi bağlanarak, çift resim ölçmeleri ve grafik değerlendirmeler ise Wild A40 Autograph ' ı nd a yapılmıştır. Elde edilen veriler, dönüşüm ve demet programları yardımıyla dengelene rek, istenen noktaların uzay koordinatları bulun muş ve her iki yöntemle elde edilen sonuçlar karşı laş t ir ı İmiş t ir. Ayrıca İ.T.Ü. Yapı Malzemesi Labo-- v - ratuvarında deney sırasında deformasyon komparatö- rü ile yapa lan ölçmelerle f otogr amet r ik yöntemle elde edilen deformasyon değerleri karşılaştırıl- mıştır. Geçiş noktalarının belirlenmesinde jeodezik yöntemin kullanılmaması zamandan tasarruf sağlamak ta, fakat özellikle Z doğrultusunda inceliğin düş mesine neden olmaktadır. Çalışma amacına ve istenen inceliğe bağlı olarak her üç f o togramet rik yöntem (analog, analog-anal it ik ve analitik), yapı konstrük- siyon deney ler indeki def ormasyonlar in ve ortaya çı kan çatlakların ölçülmesinde kullanılabilir.

-vı- THE APPLICABILITY IN STRUCTURAL MODEL TESTING OF ANALOG, ANALOG- ANALYTICAL AND ANALYTICAL RESTITUTION METHODS IN CLOSE RANGE PHOTOGRAMMETRY Photogrammetry is the art, science and technique of ? determining geometric and other properties of object's by measurements and observations on the photographs of those objects. The photographs are commonly taken by means of aerial cameras and they are geometrically very close to an ideal central projection. The object is, usually a part of the earth's surface and the measured properties are the position, size and shape of ground features, land use -and other characteristics, all of which are finally presented - graphically on a map. Close range photogrammetry is covered by this definition but lies outside the most frequent use of photo grammetry; the specialised field of map production. Close range means that the distance from object to camera is limited. Some advocate 300 m as a maximum limit, while the minimum distance is a fraction of a millimetre because, when macro-and microscopic photographs are used for measurement, these will both be regarded as falling within the scope of close range photogrammetry. The possibilities of close range photogrammetry as a method for solving a measurement problem depend on a series of factors such as cost, accuracy, effectivenes and availability. In comparison with other measuring techniques in general and in surveying in particular, close range photo grammetry has many advantages. Close range photogrammetry in the industrial field has made significant advances in recent- VI ı - years especially although not exclusively, in the solution of problems in the engineering and allied industries. Although the different branches of engineering manifest many similar problems, it is in the fields of civil and mechanical engineering, particularly mechanical production and fabrication. The aim of this study is to test different photo grammetric methods which are connected with building constructions and to determine the precisions applicable for the solution of specific problems by comparing these methods. The first part of this study covers definition of photogrammetry and its objectives. The second part deals with the historical development of terrestial photogrammetry. In the third part, instruments and restitution' methods is explained. Firstly, cameras are classified and their particular features are noted. Then, mathematical model is formulated. That a mathematical, in any branch of science, should expected to define the functional relation between the measurements and the parameters determined by the measurements was borne in mind. Photogrammetric measurements are examined with geometrical situation to understand mathematical model of the photogrammetric restitution. Interior orientation of a photograph defines the form of the bundle of rays emerging- V 1 1 ı - ' - ?' from, the perspective center to the points, in the object space. It expresses the angular relationship between object space rays on the basis of the location of the image points with respect to the perspective center, co-ordinates of perspective center are needed for determination of camera situation. The orientation which describes altitude of the camera at the moment of exposure, refersto the spatial rela tionship between the object co-ordinate system and the image co-ordinate system. Two of the most common systems for defining the orientation of a photograph are orientation elements are known in a phqtogrammetric restitution in which two photographs are used, there are 2x6+3xn=12x3xn unknowns. Here, the first term is the number of exterior orientation parameters. Second term is the number of object co-ordinates for n object points. Some of the orientation unknowns are obtained from the intersection of rays,. On the other hand, a projection ray includes the following parameters; T y. = (x yc XYZu)d>K ' 1, o o, o o o V *v' Parameters Parameters of image co- Space Scale of inner exterior orien- ordinates object co- factor orientation tation for P^ ordinates object for Pf points object points The below mathematical model of collinearity condition is obtained by expressing the relationship between image (x-, y., 0) and space object. (X., Y., Z.) co-ordinate systems.- IX - = D Ü)<j)K Where D is an orthogonal matrix representing a rotation about perspective center. D has three independent elements which can be the rotations U), cj>, k about X, Y, Z axes respectively and A is scale factor. A can be eliminated. Then we can write the colinearity function as; r..(X.-X ) + r19(Y.-Y ) + r,(Z.-Z )11 i o 1/ i o13 ı o _ ` rQ1(X.-X ) + r00(Y.-Y ) + r0^(Z.-Z ) *o *i `31 `32' 33' and r91(X.-X ) + r00(Y.-Y ) + r``(Z.-Z ) 21 ı oII i o23 ı o _ - c/ r,,(X,-X ) + r00(Y.-Y ) + r`(Z.-Z ) Yo yi` ?31 ?32' 33 This equations are the coplanarity condition. For the case of two photographs, there are two conjugate rays for each object point. Since these two rays originally emanate from the some object point at the time of photography, they must be coplanar in any photogrammetric solution. The corresponding mathematical condition, termed the coplanarity equation, enforces the fact that two camera stations, the two image points, and the object point all line on one and the same plane. In principle, the restitution is reproduction of the geometrical positions of the photographs with analytical or- x - analog projection methods. The procedure becomes simple when the inner orientation elements of photographs are known. Relative orientation and absolute orientation can be carried out on analog plotting instruments. These create a replica of the situation when the photographs were taken. Two projectors represent the cameras and these can be tilted and moved relative to each other. The rays of light joining the image on the photograph to the model point may be light rays in an optical projection instrument, or they may be rods, called space rods, in a mechanical projection instrument. The photographs are viewed stereoscopically and a three dimen sional model is observed. It is common for the projectors to reproduce exactly the geometry of the camera and to have the same principal distance. The photographs must be set in the projectors in the same way as they were taken in the camera and this setting is carried out with the aid of fiducial marks. Relative and absolute orientation then follow special procedures. A reference mark is associated with each photo graph and two marks combine under stereoscopic observation to form a three dimensional mark, known as the floating mark, which can be set onto points of detail. Detail and contours can be traced from model onto a plotting table and X.,Y -,,Z. co-ordinates are obtained from recording of three dimensional model co-ordinates as mentioned in this part by using transformation methods. Three translations and three scale multipliers are linear parameters. They are obtained during these transformations. But, the three rotations make the problem non-linear. In this case, best fitting linear- xı - approximations are used. The relation Dsxj +AX - Xj = 0 = F(y) is choosen as the fundamental equation in this study. Here, D is the transformation matrix, S is the coefficient matrix as x, y, z system, AX is the translation vector as X, Y, Z system, Xj is the co-ordinates of i. point in x system (first system) Xj is the co-ordinates of i- point in X system (second system) The analytical reconstruction of the bundle of rays and of the stereomodels from image co-ordinate readings in comparators or digital plotters open new possibilities for close range applications of photogrammetry, the only limitation being the size of the photograph. Any type of camera with any orientation can now be used. There is no restriction to central projection. The mechanical limitations on model size in the stereo plotter no longer influence the planning of the photography from the point of view of geometry. Corrections for systematic errors in the measuring procedure can be easily effected. The analytical approach can be used in the simple case where the interior and exterior orientations are known. But its advantages and versatility became much more pronounced in the most general case of photogrammetry in which a simultaneous solution incorparates the interior and exterior orientation elements of all photo-? - X 1 I - graphs and the space co-ordinates of object points, all as unknowns. Commonly, in industrial applications, the ratio of object depth to photographing range is too large to be accommodated in the model space of an analogue instrument, thus ruling out of direct plotting. In the analytical approach the accent is on numerical output and the creation of a mathematical model. This mathematical model can, in its simplest form, be simply a sequence of three dimensional co-ordinates of a few discrete points of particular significance in an object or structure which is undergoing some change. For example, in cases of deformation testing, it is often sufficient to take only a number of carefully selected points. Position of the principal point in the bundle adjustment method used in this study is given separetely for every photographs as an auxialary parameter to the basic elements of inner orientation in the computer program. There is a good correlation between distance from the perspective center are used as observations. In relation to the adjustment, the other observations are image co-ordinates and space co-ordinates of pass points. The observations are assumed to show no correlation and therefore, to the image points, pass points and perspective center can be given different weigts. Precision work in close range photogrammetry is given at the last section of this part.- X 1 1 ı - In the fourth part, two different deformation problems are investigated as an example for the practical application of the analog, analog-analytical and analytical methods. The data is obtained from the photogrammetric photo graphs during the shell and girder tests in Structure Labo ratory at the Technical University of Istanbul. These data are handled by using different photogrammetric methods (analog, analog-analytical, analytical). The conclusions are explained by using this information. During both of the tests, Wild C40 stereometric camera was used. Before taking photographs, necessary pass points were obtained with steel tape and a rule with 0,5 mm divisions. Later on, each photograph was measured on Wild A9 Autograph which is connected to EK8 electronic recorder. Stereoscopic measurements and graphical plotting were done on Wild AAO Autograph. The data were adjusted by transformation and bundle adjustment computer programs, space object co-ordinates of testing points were obtained and conclusions of the three methods were compared. In the final part, conclusions of this study are explained. Geodetic measurements were not used in the determination of pass points. On the other hand, this saved time, but it caused a decrease in the precision in the Z direction. Using the photogrammetric methods are helpful in the measurement of deformations in every directions for building constructions tests. These three photogrammetric methods can be used for measuring the deformations of building constructions and the development of cracks. The method can be chosen depending on the aim of the work and the require ments of precision.