Geodetic Deformation Analysis as the main part of monitoring projects. Using Adjustments in a Monitoring Network. Dr. I Milev

Transcription

1 Geodetic Deformation Analysis as the main part of monitoring projects Using Adjustments in a Monitoring Network Dr. I Milev

2 Introduction Geodetic measurements (epoch based) Network adjustment Statistical tests for normal distributed values Deformation analysis displacements Permanent measurements Time series* Fourier analysis - FFT/DFT Spectral analysis *finde out the 24 h, Week, Year and other cycles

3 Introduction 12,54 12,55 12,56 12,57 12,58 12,59 12,6 12,61 12,62 12,63 12,

4 Least squares adjustment Using Newton Raphson Method and conjugate gradients are eficient numer ~ 1800 Ical equation solver Geometrical model Stochastically model Reach body movement rotation, Translation, settlement Relative movements causes tensions

5 Least squares adjustment The most common method to manage redundant* data and their distribution is called the least squares adjustment. It is based on the normal distributed values and the law of the error propagation. The least squares adjustment method fits the observations of a network into their functional model with minimizing the sum of squares of residuals. The origin of the least squares method is based on the ideas and developments of Carl Friedrich Gauss and A.M. Legendre. *In engineering, redundancy is the repetition of critical measurements or duplication of critical components of a system with the intention of increasing reliability of the system

6 Network adjustment Deformation analysis Result Benefit Determine per epoch (set of observations) based on the least squares adjustment the network parameters ideally without destroying the inner constraints Most accurate method to compute coordinates/positions Get more precise (accurate) measurement data Receive a statement of reliability Estimate expected accuracy and reliability based on network design Compare the complete network epoch by epoch Most accurate method to detect movements Statistical significance of movements Statistical significance of similar moved group of points Detect unstable reference points Get vectors of significant movements

7 The two-step deformation analysis procedure is explained in the following image and is described on an imaginary dam. The blue triangles are pre-defined stable reference points. The red circles are object points.

8 Setup and pre-define reference points. In this example, both total stations are set up and measure to the pre-defined stable reference points (left diagram) and to the object points (right diagram). The user must select once pre-defined stable reference points. The pre-defined reference points defines the datum of the network. This is the frame.

9 Network adjustment points. Measuring program based on the pre-computed network design. The pre-defined reference points are automatically used together with the network center of gravity to adjust the network. The network adjustment is based on these two components. Every epoch is separately processed.

10 Geometry The complete deformation analysis is based on the assumption of identical network geometry of the reference points and approximate coordinates between the null epoch and the current epoch (=identical datum). In this example the top left reference point was not measured in the epoch 2 e.g. due point obstructions.

11 Geometry To eliminate eventually differences between epochs, the epochs will be automatically transformed on a common base with a socalled S-Transformation before any tests and results are computed. The deformation analysis is based on a valid stochastic model. Before the epochs can be compared and checked for any deformations results it is required to statistically test the epochs with a overall model test using a Fisher distribution. This test is performed automatically.

12 One Two Step Analysis According to the structure of the network a one or two step analysis can be carried out: One step analysis : All points are regarded as reference points ( relative model ). Two step analysis : The network is divided up into reference and object points The reference points are tested of deformations, subsequently the discrepancies of the object points ( relatively to the detected stable reference points ) are subjected to a single point test. As the character of real movements sometimes can not be described by the simple model of single-point-movements, more sophisticated deformation models like block movements, strain, nonlinear trend or others will be added to the deformation module.

13 Paddington Station London UK

14 Paddington Station London UK

15 Paddington Station London UK

16 Paddington Station London UK

17 Paddington Station London UK

18 NY Metro NY_63_Street

19 NY Metro NY_63_Street

20 NY Metro NY_63_Street

21 NY Metro NY_63_Street

22 Analiysis of Deformations - Defan The essential part of the deformation analysis is a global congruency test to determine significant displacements within the reference points. To avoid datum influence on the global congruency test the displacements and the according covariance matrix are transformed on the new datum by a S-transformation.

23 Standard Deviations a priori trigonometrically fixed points in the plane 20mm trigonometrically fixed points for the heights 50mm centring accuracy 2mm directions 8cc distances 4mm + 4ppm zenith angles 20cc height differences 1/s 2 geometrical levelling 2mm GPS measurements in the plane 5mm GPS measurements for the heights 10mm Alignment and tilt measurements

24 Quality Analysis Based on Adjustment Reports The quality of the estimated unknowns is analyzed by computing the following values: - standard deviation of coordinates and additional parameters, - error or confidence regions/ellipses/ellipsoids of points, - relative error or confidence regions/ellipses/ellipsoids between points, - outer reliability measures. The computation of most of these criteria is possible even during the design phase of a network by making a simulated adjustment. Then an optimization of the proposed network is possible considering various criteria for precision and reliability. Furthermore it s relatively simple to add new points and/or to use different types of instruments.

25 Net Quality Analysis Within the Monitoring Adjustment Ssystem the quality of the observations is analyzed by computing the following values : - standard deviation after adjustment, - residuals and normalized residuals, - redundancy numbers, - marginal detectable errors, - information on probable gross errors

26 Final Products of the deformation analisys - settings Automated monitoring mode Manual mode -results Accuracy Reability Quality Significant Movements Defining actions Preserving facts and conditions (measurements) for legal purposes

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34 Thank you for your attention!

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