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Karışık nivelman ağlarında stokastik model araştırması

Başlık çevirisi mevcut değil.

  1. Tez No: 55742
  2. Yazar: M.ZEKİ COŞKUN
  3. Danışmanlar: PROF.DR. ORHAN BAYKAL
  4. Tez Türü: Doktora
  5. Konular: Jeodezi ve Fotogrametri, Geodesy and Photogrammetry
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 1996
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 103

Özet

ÖZET Bu çalışmanın amacı, farklı yöntemlerle ölçülmüş ve“Karışık Nivelman Ağları (Complex Levelling Nets)”olarak adlandırılan nivelman ağlarının dengelenmesinde, ölçülerin doğruluğunu etkileyen önemli hata kaynaklarını ve farklı ölçme yöntemlerini dikkate alan stokastik modellerin oluşturulması ve mevcut fonksiyonel modelleri genişleterek daha uygun modellerin geliştirilmesidir. Tezin ikinci Bölümü'nde nokta yükseklikleri hakkında kısa bilgi verildikten sonra Üçüncü Bölüm'de tigonometrik nivelman, Dördüncü Bölüm'de presizyonlu nivelman, Beşinci Bölüm'de ise vadi geçiş nivelmanı ölçme ve hesap modellerinden söz edilmiş ve yükseklik farklarına ait standart sapmaların hesabı açıklanmıştır. Altıncı Bölüm'de dengelemenin genel prensibleri özetlenerek bilinen fonksiyonel model dışında ölçek faktörünü, çekül sapması ve refraksiyon etkisini içeren genişletilmiş fonksiyonel modeller açıklanmış, karışık nivelman ağlarının dengelenmesinde kullanılabilecek bilinen ve tarafımızdan önerilen stokastik modeller hakkında bilgi verilmiştir. Yedinci Bölüm'de, iki farklı ağda yapılan uygulama sonuçları verilmiş, Sekizinci Bölüm'de ise uygulama sonuçları değerlendirilerek yorumlanmıştır.

Özet (Çeviri)

SUMMARY STOCHASTIC MODELLING FOR COMPLEX LEVELLING NETS The precise levelling is the main tool for the measurement of the national levelling nets. The levelling nets have been applied to many aspects in engineering surveying. For instance;. To determine recent crustal vertical movements. To determine possible vertical deformations in engineering structures (e.g. dams, bridges, tunnels, etc.). To establish high accuracy levelling points that are used for building of engineering structures (e.g. highways, railways, pipelines, etc.). To select the field for atomic electric stations and their control and maintenance. To appreciate the structures and machines which require high accuracy. To determine the geoid. To measure the national levelling nets In those types of applications, the required accuracy is about +0.5mmNkm. Precise levelling may not be used in some cases due to the topography of the land. Instead, trigonometric and valley cross levelling methods are used. In the end, a levelling net measured by different instruments and methods may be obtained. This type of the net is called“complex net”. In the adjustment of the levelling nets, the weights are, in general, the inverse of the levelling line and the inverse of the square of levelling line for the precise and trigonometric levelling respectively. The weights derived from the above approaches may not represent reliable and proper stochastic models (Vanicek and Grafarend 1980). In these types of levelling nets, the accuracy of the observations is different from each other due to the use of different instruments and different observation and computational methods. Therefore, it is very important to define a proper and reliable a-priori stochastic model. Two types of unknowns can be used in the least-square adjustment. One of them is the scale factor and the other is the parameter of refraction and deviation of plumb line. The scale factor can be occurred between precise and the other levelling methods due to the different instruments and differentobservation and computational methods. The equation of the heigh difference between two bencmarks is as follows: Where k is the scale factor. If k is taken as unknown into the adjustment, the equation of residuals becomes the form of 1 l ff?-#,° Hl-H? Where 8k,: Unknown scale factor. If k0 = 1, the equation becomes vv = WJ-Wl-W1!-H?)Skl-H,l-Hf-Ah, The parameter of the refraction and deviation of plumb line are quite effected for the precise, trigonometric and valley cross levelling, especialy in the large area. The scale factor, parameter of the refraction and deviation of plumb line can be taken as unknown in the adjustment. The parameters of the refraction and deviation of plumb line are accepted to be equal in the two corrensponding points. This effect can be taken as a height difference and the equation of residuals then becomes vİJ=SHi-MJ+öh£ı-H°-H';-Ahij Where £hBi is the unknown of the height differences due to the sum of the effect of refraction and deviation of plumb line. Adjustment of levelling nets is performed in two ways: conditional and indirect approaches. In practice, the indirect approach is the most commonly used method. Because, the approach is more suitable to the programming and error estimate. The basic mathematical model is E(l}= Ax Following stochastic models are used in this research. MODEL 1) The basic equation of Pt=C/o* which shows relative accuracy between the weights, can be used for the adjustment of precise, trigonometric and valley cross levelling observations together. MODEL 2) The most commonly used models are XVIP=-L- p=± 'S ' n for precise levelling and s- for trigonometric and valley cross levelling. Where, S is the length of levelling line and n is the number of set-ups of the instrument. MODEL 3) Another stochastic model that is expanded by length of levelling line is p. - - e 2 MODEL 4) If the weights generally depend on the levelling lines. P = ± Sx can be written. In this case the weights are for precise levelling for valley cross levelling for trigonometric levelling XT“ s-t The problem is to determine Xj. There are several ways for determining xj. For instance, the values, xj of the weights can be obtained from the iteration during the adjustment process. Here, the Xj values for a particular method are assumed to be 1 and the values for the other methods are then computed with an iteration process (e.g. xp = 1 for precise levelling). MODEL 5) Using the residuals related to each levelling line derived from the adjustment, the new weights can be computed from the following equation. The adjustment continues until the a-posteriori variance from adjustment equal to the 1. P =± M v? MODEL 6) Using residuals from adjustment, the standardised residuals, xvii0 are performed. The standard deviations for each group o^=- (n-u); Mi 2 2 Tu = ~J » A ^ > Mj is compared with the F value derived from the Fischer table (F Table) for the degrees of freedom (/ = f.=u-\) and the confidence limit (1 - a ). When T < F li,j - rl-a,f”fj the zero hypotesis is valid. When T - T7 2 2 ILj“ 2 > M-a,f”f} ?> A > Mj the stochastic model having ju;- is more superior than the other on the base of homogeneity. xxIn order to classify the stochastic models whose superiorities cannot be defined (i.e. zero hypotesis), the mean accuracy criteria is used. In this case, the zero hypotesis is H0 = E(o°i) = E{o°j) and the alternative hypotesis is and the test magnitude is (7 -

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