Ahmadpoor, Mohammad
(2016)
Reduced-Order Modeling Toward Solving Inverse Problems in Solid Mechanics and Fluid Dynamics.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
Despite great improvements in computing hardware and developments of new methodologies for solving partial differential equations (PDEs), solving PDEs numerically can still be computationally prohibitive for certain applications. This computational difficulty is especially true when the solution of PDEs is tied to characterization, control, design, or other inverse problems in general. Most of the traditional PDE solution strategies, such as the Finite Element Method or Finite Volume Method can require hundreds of thousands of degrees of freedom to accurately capture the behavior of even relatively simple physical system. The computational cost is several orders of magnitude higher for solving optimization problems (a common approach to solve inverse problems), which require obtaining several solution fields. Hence, model order reduction is necessary to enable the solution of such optimization problems with sufficient efficiency to allow practical applicability.
Several approaches have been developed to create accurate reduced-order models (ROMs) of physical systems with dramatically reduced computational expense. Yet, several questions remain as to the optimal approach to create ROMs for a given physical system to ensure suitable accuracy, and even more so in relation to inverse problem applications.
The objective of the present work is to address issues relating to the creation of suitably accurate ROMs that can be utilized for the solution of a variety of computational inverse mechanics problems. This work focuses on ROMs that utilize proper orthogonal decomposition (POD) to create a reduced-order basis for the PDE solution from a set of previously obtained potential solution fields (i.e., snapshots) of the system of interest. First, a generally applicable algorithm is presented to efficiently create accurate ROMs for use in solving inverse problems in material characterization (i.e., nondestructive evaluation). This algorithm is based upon a novel concept for maximizing the diversity of the system snapshots used to create the ROM. Results show that by maximizing the snapshot diversity, the accurate generalization of the resulting ROM is substantially improved, which then improves inverse problem solution capabilities. Then, a comprehensive study is presented of the capability of a set of different approaches for reduced-order modeling (all still using POD) to represent systems involving flow past bluff bodies. One of the relatively unexplored issues when creating ROMs for fluid flows is the accuracy with respect to changes in Reynolds (Re) number. The present work uses the generalized POD technique to create ROMs that are capable of predicting flow field not only at different time levels, but also at different Re numbers.
Finally, the ROM strategies explored for fluid flow were extended to investigate the applicability to optimal flow control problems. The ROM of flow was used along with an optimization technique and adjoint method for gradient calculation to solve a control problem to reduce the drag force in flow past one or more cylinders. Results of the solution of this optimal control problem show that the developed ROMs are capable of solving complex optimization problems with significantly reduced computational expense.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
| Creators | Email | Pitt Username | ORCID  |
|---|
| Ahmadpoor, Mohammad | moa28@pitt.edu | MOA28 | |
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| ETD Committee: |
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| Date: |
15 June 2016 |
| Date Type: |
Publication |
| Defense Date: |
29 March 2016 |
| Approval Date: |
15 June 2016 |
| Submission Date: |
21 April 2016 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
91 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Swanson School of Engineering > Civil and Environmental Engineering |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Reduced Order Model, Proper Orthogonal Decomposition, Inverse Problems, Optimal Control, Flow Control, Turbulent Flow, NDT |
| Date Deposited: |
15 Jun 2016 16:52 |
| Last Modified: |
15 Nov 2016 14:33 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/27796 |
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