Düşey kontrol ağlarında deformasyon analizi

Abstract

Bu çalışmada, düşey kontrol ağlarında yükseklik de­ğişimlerinin saptanması konusu ele alınmıştır. Birinci ve ikinci bölümde, deformasyon analizi kuramının ana hatları, temel tanımları ve uygulama alanları açıklanmış, kontrol ağları ve düşey kontrol ağının dengelenmesi konuları iş­lenmiştir.Deformasyon analizinin temel ilkesi, varsayımlardan mümkün olduğunca kaçınmaktır. Kaçınılmaz olan varsayımlar ise matematik istatistik yöntemlerle test edilirler. Bu nedenle, fiziksel gerçekliği temsil eden, ölçme ve hipo­tezlere dayalı bir fonksiyonel ve stokastik ilişkiler kü­mesi şeklinde tanımlanan "Gauss-Markoff" modelinde yapılan kabullerin ele alınması, sorgulanması ve modelin gerçeğe yakınlığının test edilmesi gerekir. Bu, deformasyon ana­lizinde çok önemlidir. Çünkü model kabullerinde yapılan hatalar deformasyon olarak yorumlanabilmektedir. Varsa­yımların test edilmesinde, hipotez testleri ya da istatis­tik testlerden yararlanılır. Bu yüzden çalışmada, ista­tistik testler ve model testleri genel olarak ele alınmış­tır.Deformasyonlar çeşitli modellere göre değerlendi­rilebilirler. Bu modeller; statik, dinamik ve kinematik modellerdir. Jeodezik uygulamalarda genellikle statik modeller uygulanmaktadır. Sözü edilen modellerden, sta­tik model ve kinematik modelin yükseklik değişimlerinin analizine uygulanması kuramsal olarak açıklanmıştır.Uygulama bölümünde ise, 20 noktadan oluşan bir dü­şey kontrol ağında, statik model ile deformasyon analizi uygulanmış,ağ noktalarındaki anlamlı deformasyonlar be­lirlenmiştir.

In the application of deformation analysis, after the first repetition of the observations, when two sets of observational data are available, a two-epoch analysis is carried out. The models used in this case are classified into three groups: Static, dynamic or kinematic models. The static models provide an obvious point of view and give the results in forms of displacement vectors. The dynamic model links the displacements to their underlying forces. The kinematic models do not include forces, they describe the deformations by means of displacement velocities and accelerations. In a static model two-epoch analysis of a levelling network is applied by defining the following null hypo thesis, Ho: *-l = *-2 H x with the followings, T H= (I -I) - = (-l -2J Provided that the two single epoch adjustments have been performed using the same a priori variance factor cr 2 and have been based on the some geodetic datum the variance is obtained as, j YiT li Yi + v2 p2 v2 s ^ = ° by using the cofactor matrices T V P V 2« ' 2*i S*2 The quadratic form q. is calculated as follows.-xx -x2 <3A = (5l-İ£2)T (2«,+ Q$J + (İ£l-İ£2) The test statistic is given as, T = A/ m so2 with, m=r (CU + Q- ) -*1 -x2 Xll if the following result is obtained T = qAM > p s 2 l-a;m, f o then it is concluded that the null hypothesis (no deforma tion between two epochs) is rejected. When a null hypothesis is rejected, the point which has the maximum height differences between two epochs is considered as responsible for the rejection of the null hypothesis and tested. The process is carried out until the null hypothesis is accepted. In addition to the static model, a kinematic model is also discussed and basic principles and testing procedure, applied in the model, are presented. In the application part of the study, the above mentioned two-epoch analysis in the static model has been carried out for the detection of vertical movements in a control network consisting of twenty points. After the analysis, displacements up to 3.8cm. have been detected. Xlll In the application of deformation analysis, after the first repetition of the observations, when two sets of observational data are available, a two-epoch analysis is carried out. The models used in this case are classified into three groups: Static, dynamic or kinematic models. The static models provide an obvious point of view and give the results in forms of displacement vectors. The dynamic model links the displacements to their underlying forces. The kinematic models do not include forces, they describe the deformations by means of displacement velocities and accelerations. In a static model two-epoch analysis of a levelling network is applied by defining the following null hypo thesis, Ho: *-l = *-2 H x with the followings, T H= (I -I) - = (-l -2J Provided that the two single epoch adjustments have been performed using the same a priori variance factor cr 2 and have been based on the some geodetic datum the variance is obtained as, j YiT li Yi + v2 p2 v2 s ^ = ° by using the cofactor matrices T V P V 2« ' 2*i S*2 The quadratic form q. is calculated as follows.-xx -x2 <3A = (5l-İ£2)T (2«,+ Q$J + (İ£l-İ£2) The test statistic is given as, T = A/ m so2 with, m=r (CU + Q- ) -*1 -x2 Xll if the following result is obtained T = qAM > p s 2 l-a;m, f o then it is concluded that the null hypothesis (no deforma tion between two epochs) is rejected. When a null hypothesis is rejected, the point which has the maximum height differences between two epochs is considered as responsible for the rejection of the null hypothesis and tested. The process is carried out until the null hypothesis is accepted. In addition to the static model, a kinematic model is also discussed and basic principles and testing procedure, applied in the model, are presented. In the application part of the study, the above mentioned two-epoch analysis in the static model has been carried out for the detection of vertical movements in a control network consisting of twenty points. After the analysis, displacements up to 3.8cm. have been detected. Xlll In the application of deformation analysis, after the first repetition of the observations, when two sets of observational data are available, a two-epoch analysis is carried out. The models used in this case are classified into three groups: Static, dynamic or kinematic models. The static models provide an obvious point of view and give the results in forms of displacement vectors. The dynamic model links the displacements to their underlying forces. The kinematic models do not include forces, they describe the deformations by means of displacement velocities and accelerations. In a static model two-epoch analysis of a levelling network is applied by defining the following null hypo thesis, Ho: *-l = *-2 H x with the followings, T H= (I -I) - = (-l -2J Provided that the two single epoch adjustments have been performed using the same a priori variance factor cr 2 and have been based on the some geodetic datum the variance is obtained as, j YiT li Yi + v2 p2 v2 s ^ = ° by using the cofactor matrices T V P V 2« ' 2*i S*2 The quadratic form q. is calculated as follows.-xx -x2 <3A = (5l-İ£2)T (2«,+ Q$J + (İ£l-İ£2) The test statistic is given as, T = A/ m so2 with, m=r (CU + Q- ) -*1 -x2 Xll if the following result is obtained T = qAM > p s 2 l-a;m, f o then it is concluded that the null hypothesis (no deforma tion between two epochs) is rejected. When a null hypothesis is rejected, the point which has the maximum height differences between two epochs is considered as responsible for the rejection of the null hypothesis and tested. The process is carried out until the null hypothesis is accepted. In addition to the static model, a kinematic model is also discussed and basic principles and testing procedure, applied in the model, are presented. In the application part of the study, the above mentioned two-epoch analysis in the static model has been carried out for the detection of vertical movements in a control network consisting of twenty points. After the analysis, displacements up to 3.8cm. have been detected. Xlll In the application of deformation analysis, after the first repetition of the observations, when two sets of observational data are available, a two-epoch analysis is carried out. The models used in this case are classified into three groups: Static, dynamic or kinematic models. The static models provide an obvious point of view and give the results in forms of displacement vectors. The dynamic model links the displacements to their underlying forces. The kinematic models do not include forces, they describe the deformations by means of displacement velocities and accelerations. In a static model two-epoch analysis of a levelling network is applied by defining the following null hypo thesis, Ho: *-l = *-2 H x with the followings, T H= (I -I) - = (-l -2J Provided that the two single epoch adjustments have been performed using the same a priori variance factor cr 2 and have been based on the some geodetic datum the variance is obtained as, j YiT li Yi + v2 p2 v2 s ^ = ° by using the cofactor matrices T V P V 2« ' 2*i S*2 The quadratic form q. is calculated as follows.-xx -x2 <3A = (5l-İ£2)T (2«,+ Q$J + (İ£l-İ£2) The test statistic is given as, T = A/ m so2 with, m=r (CU + Q- ) -*1 -x2 Xll if the following result is obtained T = qAM > p s 2 l-a;m, f o then it is concluded that the null hypothesis (no deforma tion between two epochs) is rejected. When a null hypothesis is rejected, the point which has the maximum height differences between two epochs is considered as responsible for the rejection of the null hypothesis and tested. The process is carried out until the null hypothesis is accepted. In addition to the static model, a kinematic model is also discussed and basic principles and testing procedure, applied in the model, are presented. In the application part of the study, the above mentioned two-epoch analysis in the static model has been carried out for the detection of vertical movements in a control network consisting of twenty points. After the analysis, displacements up to 3.8cm. have been detected.