Heterogeneous Material Characterization Using Incomplete and Complete Data with Application to Soft Solids

This dissertation proposes and develops novel features into the existing inverse algorithms for characterizing nonhomogeneous material properties of soft solids. Firstly, a new feature that material properties are defined as a piece-wise constant in each element has been implemented in the inverse program. Secondly, to reduce boundary sensitivity of the solution to the inverse problem in elasticity, we modify the objective function using a spatially weighted displacement correlation term. Compared to the conventional objective function, the new formulation performs well in preserving stiffness contrast between the inclusion and background. Then, we present an approach to estimate the nonhomogeneous elastic property distribution using only boundary displacement datasets. We further improve this approach by using force indentation measurements to quantitatively map the elastic properties and analyze the sensitivity of this approach to a variety of factors, e.g., the location and size of the inclusion. Furthermore, we present a method to quantitatively determine the shear modulus distribution using full-field displacements with partially known material properties on the boundary and without any traction or force information. We test its performance using two different types of regularization: total variation diminishing (TVD) and total contrast diminishing (TCD) regularizations. We observe that TCD regularization is capable of mapping the absolute shear modulus distribution, while TVD regularization fails to achieve this. Furthermore, we investigate the feasibility of using the linear elastic inverse solver to solve inverse problems for nonlinear elasticity for large deformations. We conclude that the linear elastic approximation will overestimate the stiffness contrast between the inclusion and background. We also extend the inverse strategy to map the orthotropic linear elastic parameter distributions. The reconstructions reveal that this method performs well in the presence of low displacement noise levels, while performing poorly with 3% noise. Finally, a feature that maps the viscoelastic behavior of solids using harmonic displacement data has been implemented and tested. In summary, these new features not only strengthen our understanding in solving the inverse problem for inhomogeneous material property characterization, but also provide a potential technique to characterize nonhomogeneous material properties of soft tissues nondestructively that could be useful in clinical practice

End-to-end Learning for Short Text Expansion

Effectively making sense of short texts is a critical task for many real world applications such as search engines, social media services, and recommender systems. The task is particularly challenging as a short text contains very sparse information, often too sparse for a machine learning algorithm to pick up useful signals. A common practice for analyzing short text is to first expand it with external information, which is usually harvested from a large collection of longer texts. In literature, short text expansion has been done with all kinds of heuristics. We propose an end-to-end solution that automatically learns how to expand short text to optimize a given learning task. A novel deep memory network is proposed to automatically find relevant information from a collection of longer documents and reformulate the short text through a gating mechanism. Using short text classification as a demonstrating task, we show that the deep memory network significantly outperforms classical text expansion methods with comprehensive experiments on real world data sets.Comment: KDD'201

Subharmonic Solutions of Second Order Subquadratic Hamiltonian Systems with Potential Changing Sign

AbstractWith the aid of some symplectic transformations, the existence of subharmonic solutions of the second order Hamiltonian system −ẍ=Vx(t,x) is considered, where the potential V is subquadratic in x as |x| goes to infinity and can change sign with respect to t

Characterizing the elastic property distribution of soft materials nondestructively

Soft materials have the advantage that their subsurface structure may be imaged utilizing imaging modalities such as ultrasound, magnetic resonance imaging, computed tomography (CT) scans, and optical coherence tomography. In recent decades subsurface displacement fields were successfully measured using these imaging modalities. These displacement fields are of time-harmonic, transient, or quasi-static nature and can be used to solve an inverse problem in elasticity to determine the elastic material property distribution within the region of interest of the soft material. One important application area is in the detection and diagnosis of diseased tissues, such as breast tumors. This can be done as tumors are often stiffer than their background tissue, and based on the stiffness contrast they can be visualized and distinguished from their surrounding healthy tissues. We will present the solution of the inverse problem in finite elasticity for quasi-static displacement fields. Here, the quasi-static displacement fields may be determined by taking a sequence of ultrasound images while slowly compressing the tissue with the ultrasound transducer. From this sequence of ultrasound images one may determine the displacement fields utilizing well-developed cross-correlation techniques. We solve the inverse problem iteratively by posing it as a constrained optimization problem, where the difference between a measured and computed displacement field is minimized in the L-2 norm and in the presence of Tikhonov regularization. The computed displacement field satisfies the constraint, which are the equations of equilibrium and solved using finite element methods for the current estimate of the elastic property distribution. We model the material to be hyperelastic with a strain energy density function of exponential form and two elastic property parameters: the shear modulus describes the linear elastic behavior, whereas the nonlinear elastic property describes the rate at which the material is stiffening at large strains [1]. In addition, we assume that the material is isotropic and incompressible. This method has been tested on hypothetical data and breast tumor patients [2] and proofed to be robust in the presence of noisy displacement data to recover the tumors. However, this method appears to be sensitive to the applied boundary conditions, i.e., the solution of the inverse problem for uniform boundary compression appears to be different than applying a linearly changing boundary compression. Obviously, the solution of the inverse problem lacks uniqueness with respect to changing boundary conditions. We realize that the uniqueness issue here is primarily because of the formulation of the displacement correlation term in the objective function. We provide a new formulation and show that this leads to a “more unique” solution of the inverse problem and improves the overall contrast. REFERENCES [1] Goenezen, S., Barbone, P., and Oberai, A.A., Solution of the nonlinear elasticity imaging inverse problem: the incompressible case. Computer Methods in Applied Mechanics and Engineering. 2011, 200(13–16), 1406–1420. [2] Goenezen, S., Dord, J.F., Sink, Z., Barbone, P., Jiang, J., Hall, T.J., and Oberai, A.A., Linear and nonlinear elastic modulus imaging: an application to breast cancer diagnosis. IEEE Trans Med Imaging. 2012, 31(8), 1628–1637