Study On Space-Time Variability Of Geomechanical Parameters With Ensemble Kalman Filter Data Assimilation Method

It is difficult to describe clearly with mathematical method for displacement variation under excavation disturbance in geotechnical engineering, which actual is an uncertainty process and exist objectively in a dynamical stochastic process. Geomechanical parameter is not a certainty value, but a state estimation value in time existing in a stochastic process. So there is a demand for method of stochastic system to solve it. In addition, geomechanical parameter presents great heterogeneity and anisotropy in space, and there is a demand for random field theory to represent it. Therefore, inconsideration of variability of geomechancial parameter in time and space, it is an objective demand and a development trend to incorporate analysis of stochastic system with numerical modeling of geotechnical engineering, and established theory of stochastic back-analysis conforming with practical dynamics in geotechnical engineering, as well as corresponding computational procedure. The ideal and method of sequential data assimilation with ensemble Kalman filter originated from meteorology and oceanography 7is introduced in dissertation, and numerical magnitude and spatial distribution of geomechanical parameter are estimated on basis of observation data distributed in time and space after model incorporated new observation data in process of running. Main research content in dissertation includes the following:1. Geomechanical deformation is treated as a dynamic stochastic system, and displacement observation is looked as the output. Furthermore, ensemble Kalman filter is used as model to describe the system state. The dynamical estimation method coupled ensemble Kalman filter with numerical modeling is presented on basis of stochastic process, which considers time variation property of geomechanical parameter and utilizes displacement observation in time series. Geomechanical parameter is filtered every step during estimation process, then innovation and adjusted value are generated, which reflects the diachronism of geomechanical parameter the truth of deformation in geomechanical media.2. Aim at computing and storing trouble of forecast error covariance matrix of Kalman filter applied in geomechanical parameter estimation, as well as approximating problem of extended Kalman filter applied in nonlinear system, ensemble forecast with Monte Carlo is adopted to estimate forecast error covariance, which implies the statistical error in a set of forecast variable. Thus, new error covariance can be obtained according to difference statistical of forecast value, so it is avoided for computing inaccuracy in process of covariance evolution equation forecasting, as well as storing difficulty of massive data in covariance matrix. Furthermore, singular value decomposition is adopted to compute the Kalman gain matrix. What's more, the ensemble Kalman filter algorithm is incorporated with available numerical simulating software, such as ANSYS, FLAC, FLAC3D, which fuses in situ observation into model forecast. By adjust the model running with observation data, the accumulative error is released. Therefore, the advantages of monitoring and modeling are adequately exerted.3. It is under a dynamical stochastic process for displacement variation under excavation disturbance in geomechanical media, and the measuring displacement is an uncertainty value with error. The dynamical disturbed observation concept is posed, then Monte Carlo simulation is adopted to add Gaussian white noise in observation. At the same time, a priori knowledge is utilized to ensure computational stability and reduce resultant uncertainty in process of dynamical stochastic estimation. Analysis result gives a ensemble of state variable, and also estimates simultaneously the state and parameter value of geomechanical model, which not only can afford the initial value for ensemble prediction, but also can offer the estimated uncertainty, besides the optimal estimation of geomechanical parameter ensemble mean.4. Geomechanical parameter is viewed as zonal variable in terms of geostatistics. Sequentially, variation function is given to describe integral spatial structural variation and local stochastic variation, and theoretical model of variation function is served as mathematical model to depict spatial variation law of geomechanical parameter. Moreover, LU decomposition and Gaussian Sequential Simulation are adopted to construct the random field representing spatial distribution of geomechanical parameter, and then assign to element, which recur veritably the discreteness and fluctuation in random field of geomechanical parameter. The sequential data assimilation method with ensemble Kalman filter is presented to research spatial variation of geomechanical parameter. After gradually fusing dynamical observation data distributed in time and space, the variability in various ensemble realizations decrease step by step, and all approach to the distribution pattern of true field finally. The data assimilation with ensemble Kalman filter integrates observation data and simulation result into various state data sets with consistency of time, space and physics.5. The root mean square error and ensemble spread criteria are put forward to evaluate the data assimilation result. Then, sensitivity is discussed for some influencing factors, such as sampling ensemble size, initial mean of sampling ensemble, dynamical noise ratio, correlative distance, assimilation step, observational number. It is demonstrated that the method of ensemble Kalman filter coupled with numerical modeling is practical and valid.