Theses and Dissertations
This collection includes both ASU Theses and Dissertations, submitted by graduate students, and the Barrett, Honors College theses submitted by undergraduate students.
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- All Subjects: Multi-Bay Structures
- All Subjects: stochastic reconstruction
Description
This investigation develops small-size reduced order models (ROMs) that provide an accurate prediction of the response of only part of a structure, referred to as component-centric ROMs. Four strategies to construct such ROMs are presented, the first two of which are based on the Craig-Bampton Method and start with a set of modes for the component of interest (the β component). The response in the rest of the structure (the α component) induced by these modes is then determined and optimally represented by applying a Proper Orthogonal Decomposition strategy using Singular Value Decomposition. These first two methods are effectively basis reductions techniques of the CB basis. An approach based on the “Global - Local” Method generates the “global” modes by “averaging” the mass property over α and β comp., respectively (to extract a “coarse” model of α and β) and the “local” modes orthogonal to the “global” modes to add back necessary “information” for β. The last approach adopts as basis for the entire structure its linear modes which are dominant in the β component response. Then, the contributions of other modes in this part of the structure are approximated in terms of those of the dominant modes with close natural frequencies and similar mode shapes in the β component. In this manner, the non-dominant modal contributions are “lumped” onto the dominant ones, to reduce the number of modes for a prescribed accuracy. The four approaches are critically assessed on the structural finite element model of a 9-bay panel with the modal lumping-based method leading to the smallest sized ROMs. Therefore, it is extended to the nonlinear geometric situation and first recast as a rotation of the modal basis to achieve unobservable modes. In the linear case, these modes completely disappear from the formulation owing to orthogonality. In the nonlinear case, however, the generalized coordinates of these modes are still present in the nonlinear terms of the observable modes. A closure-type algorithm is then proposed to eliminate the unobserved generalized coordinates. This approach, its accuracy and computational savings, was demonstrated on a simple beam model and the 9-bay panel model.
ContributorsWang, Yuting (Author) / Mignolet, Marc P (Thesis advisor) / Jiang, Hanqing (Committee member) / Liu, Yongming (Committee member) / Oswald, Jay (Committee member) / Rajan, Subramaniam D. (Committee member) / Spottswood, Stephen M (Committee member) / Arizona State University (Publisher)
Created2017
Description
An accurate knowledge of the complex microstructure of a heterogeneous material is crucial for quantitative structure-property relations establishment and its performance prediction and optimization. X-ray tomography has provided a non-destructive means for microstructure characterization in both 3D and 4D (i.e., structural evolution over time). Traditional reconstruction algorithms like filtered-back-projection (FBP) method or algebraic reconstruction techniques (ART) require huge number of tomographic projections and segmentation process before conducting microstructural quantification. This can be quite time consuming and computationally intensive.
In this thesis, a novel procedure is first presented that allows one to directly extract key structural information in forms of spatial correlation functions from limited x-ray tomography data. The key component of the procedure is the computation of a “probability map”, which provides the probability of an arbitrary point in the material system belonging to specific phase. The correlation functions of interest are then readily computed from the probability map. Using effective medium theory, accurate predictions of physical properties (e.g., elastic moduli) can be obtained.
Secondly, a stochastic optimization procedure that enables one to accurately reconstruct material microstructure from a small number of x-ray tomographic projections (e.g., 20 - 40) is presented. Moreover, a stochastic procedure for multi-modal data fusion is proposed, where both X-ray projections and correlation functions computed from limited 2D optical images are fused to accurately reconstruct complex heterogeneous materials in 3D. This multi-modal reconstruction algorithm is proved to be able to integrate the complementary data to perform an excellent optimization procedure, which indicates its high efficiency in using limited structural information.
Finally, the accuracy of the stochastic reconstruction procedure using limited X-ray projection data is ascertained by analyzing the microstructural degeneracy and the roughness of energy landscape associated with different number of projections. Ground-state degeneracy of a microstructure is found to decrease with increasing number of projections, which indicates a higher probability that the reconstructed configurations match the actual microstructure. The roughness of energy landscape can also provide information about the complexity and convergence behavior of the reconstruction for given microstructures and projection number.
In this thesis, a novel procedure is first presented that allows one to directly extract key structural information in forms of spatial correlation functions from limited x-ray tomography data. The key component of the procedure is the computation of a “probability map”, which provides the probability of an arbitrary point in the material system belonging to specific phase. The correlation functions of interest are then readily computed from the probability map. Using effective medium theory, accurate predictions of physical properties (e.g., elastic moduli) can be obtained.
Secondly, a stochastic optimization procedure that enables one to accurately reconstruct material microstructure from a small number of x-ray tomographic projections (e.g., 20 - 40) is presented. Moreover, a stochastic procedure for multi-modal data fusion is proposed, where both X-ray projections and correlation functions computed from limited 2D optical images are fused to accurately reconstruct complex heterogeneous materials in 3D. This multi-modal reconstruction algorithm is proved to be able to integrate the complementary data to perform an excellent optimization procedure, which indicates its high efficiency in using limited structural information.
Finally, the accuracy of the stochastic reconstruction procedure using limited X-ray projection data is ascertained by analyzing the microstructural degeneracy and the roughness of energy landscape associated with different number of projections. Ground-state degeneracy of a microstructure is found to decrease with increasing number of projections, which indicates a higher probability that the reconstructed configurations match the actual microstructure. The roughness of energy landscape can also provide information about the complexity and convergence behavior of the reconstruction for given microstructures and projection number.
ContributorsLi, Hechao (Author) / Jiao, Yang (Thesis advisor) / Chawla, Nikhilesh (Committee member) / Liu, Yongming (Committee member) / Ren, Yi (Committee member) / Mu, Bin (Committee member) / Arizona State University (Publisher)
Created2017