Link to the University of Pittsburgh Homepage
Link to the University Library System Homepage Link to the Contact Us Form

Computational Approaches to Efficiently Maximize Solution Capabilities and Quantify Uncertainty for Inverse Problems in Mechanics

Notghi, Bahram (2015) Computational Approaches to Efficiently Maximize Solution Capabilities and Quantify Uncertainty for Inverse Problems in Mechanics. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

Primary Text

Download (1MB) | Preview


Computational approaches to solve inverse problems can provide generalized frameworks for treating and distinguishing between the various contributions to a system response, while providing physically meaningful solutions that can be applied to predict future behaviors. However, there are several common challenges when using any computational inverse mechanics technique for applications such as material characterization. These challenges are typically connected to the inherent ill-posedness of the inverse problems, which can lead to a nonexistent solution, non-unique solutions, and/or prohibitive computational expense.

Toward reducing the effects of inverse problem ill-posedness and improving the capability to accurately and efficiently estimate inverse problem solutions, a suite of computational tools was developed and evaluated. First, an approach to NDT design to maximize the capabilities to use computational inverse solution techniques for material characterization and damage identification in structural components, and more generally in solid continua, is presented. The approach combines a novel set of objective functions to maximize test sensitivity and simultaneously minimize test information redundancy to determine optimal NDT parameters. The NDT design approach is shown to provide measurement data that leads to consistent and significant improvement in the ability to accurately inversely characterize variations in the Young's modulus distributions for simulated test cases in comparison to alternate NDT designs. Next, an extension of the NDT design approach is presented, which includes a technique to address potential system uncertainty and add robustness to the resulting NDT design, again in the context of material characterization. The robust NDT design approach uses collocation techniques to approximate the modified objective functionals that not only maximize the test sensitivity and minimize the test information redundancy, but now also maximize the test robustness to system uncertainty. The capability of this probabilistic NDT design method to provide consistent improvement in the ability to accurately inversely characterize variations in the Young's modulus distributions for cases where systems have uncertain parameters, such as uncertain boundary condition features, is again shown with numerically simulated examples. Lastly, an approach is presented to more directly address the computational expense of solving an inverse problem, particularly for those problems with significant system uncertainties. The sparse grid method is used as the foundation of this solution approach to create a computationally efficient polynomial approximation (i.e., surrogate model) of the system response with respect to both deterministic and uncertain parameters to be used in the inverse problem solution process. More importantly, a novel generally applicable algorithm is integrated for adaptive generation of a data ensemble, which is then used to create a reduced-order model (ROM) to estimate the desired system response. In particular, the approach builds the ROM to accurately estimate the system response within the expected range of the deterministic and uncertain parameters, to then be used in place of the traditional full order modeling (i.e., standard finite element analysis) in constructing the surrogate model for the inverse solution procedure. This computationally efficient approach is shown through simulated examples involving both solid mechanics and heat transfer to provide accurate solution estimates to inverse problems for systems represented by stochastic partial differential equations with a fraction of the typical computational cost.


Social Networking:
Share |


Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Notghi, Bahramban32@pitt.eduBAN32
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairBrigham, Johnbrigham@pitt.eduBRIGHAM
Committee MemberBunger, Andrew P.bunger@pitt.eduBUNGER
Committee MemberRizzo, Piervincenzopir3@pitt.eduPIR3
Committee MemberBielak, Jacobo
Date: 28 January 2015
Date Type: Publication
Defense Date: 24 July 2014
Approval Date: 28 January 2015
Submission Date: 23 July 2014
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 112
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: Inverse problem, Uncertainty quantification, ill-posedness, Computational expense and Reduced order modeling
Date Deposited: 28 Jan 2015 20:06
Last Modified: 15 Nov 2016 14:22


Monthly Views for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item