Automatic Calibration of Finite Element Analysis Based on Geometric Boundary Models from Terrestrial Laser Scanning

摘要

Large amounts of historical infrastructures were constructed shortly after the Second World War in the late 1950s and 1960s. Their applicable life is over 50 years. Many of them are even reaching their life-time while still being in operations. Lots of uncertainties in these structures need to be considered to make decisions whether to extend their useful time. The finite element analysis (FEA) is a standard numerical technique to approximate, predict, and monitor the object reactions from the outside to the internal corresponding to various boundary conditions. How to estimate the historical structures accurately is a significant topic in engineering applications. It contains lots of unknown deformations and non-negligible deviations compared with the originally designed structure. Geometric measurements and reference data can significantly contribute to the FEA. In the projects related to geometric measurements, terrestrial laser scanning (TLS) has become a powerful technique to acquire geometric surface data due to its high precision, non-contact, and rapid measuring speeds. The key challenge lies in the geometric modeling of the point clouds epoch through mathematical approximations to combine the advantage of FEA and TLS. The approximation methods vary from each other, among which the polynomial and B-spline approximations are advanced candidate solutions and applied in this research. To address the above issues, the thesis discusses the current TLS application to solve the boundary problem in the FEA computation and the feasibility and solutions in approximating point clouds to fill the knowledge gap. We compared the difference between the polynomial and B-spline approximation methods. The polynomial function can approximate the scattered points regarding the regular shapes and surfaces with acceptable results, while B-spline can approximate irregular features with deformed details and deviations better by adjusting the control points. The objective is to realize the automatic calibration of the FEA computation based on the geometric boundary modeling with TLS measurements of the structures with unknown deformations and deviations. Therefore, B-spline approximations based on the Gauss-Markov model in both two- and three-dimensional cases are selected as the free-form geometric modeling in the FEA computation. Results in real experiments regarding the arch structure indicate that, before loading experiments, the calibrated FEA geometric model based on TLS data performs more accurately in the actual geometric description than the general simplified model. The calibrated model can describe the irregular and unknown details of the deviations by the actual construction of both upper and lower sides of the arch structure. After the static loading experiments, the FEA computational results based on the B-spline geometry is closer to the corresponding data in the actual experiment than that of the general FEA computation with the simplified geometry. The calibrated FEA computation by TLS brings the benefits that the internal displacement data and the information that cannot be obtained from TLS, e.g. the stress and strain, are explicit and more reliable from FEA to users. The deformation regarding the structure between the FEA computational results and TLS point cloud data is analyzed through the point-to-point and surface-to-surface methods. However, there is a redundant disadvantage due to the repetitions in mesh generations and computations in updating TLS-based geometric models in each loading when carrying out FEA. It is required to refine the grids to meet the various and detailed deformations of the measured geometry, which causes the low efficiency and large computations in the FEA computation. Obviously, it is therefore time-consuming. By this consideration, the convolutional long short-term memory (LSTM) is utilized, which is a deep learning method, to address the efficiency problem in the automatic FEA calibration bas