The safety control of dams is based on monitoring activities and modelling of registered observations. The statistical hydrostatic-season-time model was originally developed and proposed for analyzing of monitoring data on concrete dams. In some later works, the model was implemented for earth-fill embankment dams. The model admits a simultaneous estimation of hydrostatic load, temperature influences and irreversible deformations. In our study, we analyze long-term coordinate time series of a geodetic point on the crest of a rock-fill embankment dam. Coordinate time series are result of an adjustment of the observations in a permanent geodetic network for different epochs. An optimal model is defined using a multiple linear regression by combined process of exclusion and inclusion of individual parameters. In the process, different statistical parameters are observed. The analyses confirmed that not all parameters are significant. The most interesting and important conclusion of computations can be stated as follows: after inclusion of significant coefficients of the hydrostatic load and long-term trend, the residual time series still expose underlying periodicities. They can be removed by inclusion of at least one parameter of the seasonal term, where the temperature influences (i.e. air, water and soil) are modelled. The influences of the temperature on the dam are not significant in any direction, but the inclusion of the parameters improves the statistical performance of the used model.
Modern electronic tacheometers offer the possibility to capture kinematic processes in real time. In case when the kinematic process is observed with only one measurement system, we have no possibility to perform redundant observations that would enable the accuracy estimation of observations and computed values. The Kalman filter represents a method of advanced geodetic analysis and as such adjusts the redundant data in an optimum way. Incorporating a time component directly into a processing of terrestrial kinematic observations demands good knowledge about the procedure of processing kinematic terrestrial observations and the electronic tacheometer capabilities. For this purpose the developed model of Kalman filter for processing kinematic terrestrial observations-discrete Wiener process acceleration model-was tested on reference trajectory in the Geodetic Laboratory of the Technical University Munich.
For the evaluation of measurement data, different functional and stochastic models can be used. In the case of time series, a Kalman filtering (KF) algorithm can be implemented. In this case, a very well-known stochastic model, which includes statistical tests in the domain of measurements and in the system state domain, is used. Because the output results depend strongly on input model parameters and the normal distribution of residuals is not always fulfilled, it is very important to perform all possible tests on output results. In this contribution, we give a detailed description of the evaluation of the Kalman filter model. We describe indicators of inner confidence, such as controllability and observability, the determinant of state transition matrix and observing the properties of the a posteriori system state covariance matrix and the properties of the Kalman gain matrix. The statistical tests include the convergence of standard deviations of the system state components and normal distribution beside standard tests. Especially, computing controllability and observability matrices and controlling the normal distribution of residuals are not the standard procedures in the implementation of KF. Practical implementation is done on geodetic kinematic observations.
For embankment dams, the modelling of influences in the dam response becomes more difficult if the empirical model cannot be used due to changing external influences. In this work, an attempt at modeling the measured deformations as a dynamic stochastic process is presented. A discrete Wiener process acceleration model (DWPAM), which is based on Kalman filtering, is implemented on geodetically measured displacements of the point on a rock-fill embankment dam. The acceleration is modelled as a zero-mean white sequence. The verification of a filter design and choosing an appropriate value of the process noise intensity scalar is controlled primarily with the compliance of the statistical tests in the domain of measurements and in the system state domain. In the case study, it was shown that the DWPAM can detect statistically significant changes in measured displacements according to the previous behaviour and can be used for the identification of potential anomalies.
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