Model updating in structural dynamics: advanced parametrization, optimal regularization, and symmetry considerations

Numerical models are pervasive tools in science and engineering for simulation, design, and assessment of physical systems. In structural engineering, finite element (FE) models are extensively used to predict responses and estimate risk for built structures. While FE models attempt to exactly replicate the physics of their corresponding structures, discrepancies always exist between measured and model output responses. Discrepancies are related to aleatoric uncertainties, such as measurement noise, and epistemic uncertainties, such as modeling errors. Epistemic uncertainties indicate that the FE model may not fully represent the built structure, greatly limiting its utility for simulation and structural assessment. Model updating is used to reduce error between measurement and model-output responses through adjustment of uncertain FE model parameters, typically using data from structural vibration studies. However, the model updating problem is often ill-posed with more unknown parameters than available data, such that parameters cannot be uniquely inferred from the data. This dissertation focuses on two approaches to remedy ill-posedness in FE model updating: parametrization and regularization. Parametrization produces a reduced set of updating parameters to estimate, thereby improving posedness. An ideal parametrization should incorporate model uncertainties, effectively reduce errors, and use as few parameters as possible. This is a challenging task since a large number of candidate parametrizations are available in any model updating problem. To ameliorate this, three new parametrization techniques are proposed: improved parameter clustering with residual-based weighting, singular vector decomposition-based parametrization, and incremental reparametrization. All of these methods utilize local system sensitivity information, providing effective reduced-order parametrizations which incorporate FE model uncertainties. The other focus of this dissertation is regularization, which improves posedness by providing additional constraints on the updating problem, such as a minimum-norm parameter solution constraint. Optimal regularization is proposed for use in model updating to provide an optimal balance between residual reduction and parameter change minimization. This approach links computationally-efficient deterministic model updating with asymptotic Bayesian inference to provide regularization based on maximal model evidence. Estimates are also provided for uncertainties and model evidence, along with an interesting measure of parameter efficiency

ON SYMMETRY: A FRAMEWORK FOR AUTOMATED SYMMETRY DETECTION

Symmetry has weaved itself into almost all fabrics of science, as well as in arts, and has left an indelible imprint on our everyday lives. And, in the same manner, it has pervaded a wide range of areas of computer science, especially computer vision area, and a copious amount of literature has been produced to seek an algorithmic way to identify symmetry in digital data. Notwithstanding decades of endeavor and attempt to have an efficient system that can locate and recover symmetry embedded in real-world images, it is still challenging to fully automate such tasks while maintaining a high level of efficiency. The subject of this thesis is symmetry of imaged objects. Symmetry is one of the non-accidental features of shapes and has long been (maybe mistakenly) speculated as a pre-attentive feature, which improves recognition of quickly presented objects and reconstruction of shapes from incomplete set of measurements. While symmetry is known to provide rich and useful geometric cues to computer vision, it has been barely used as a principal feature for applications because figuring out how to represent and recognize symmetries embedded in objects is a singularly difficult task, both for computer vision and for perceptual psychology. The three main problems addressed in the dissertation are: (i) finding approximate symmetry by identifying the most prominent axis of symmetry out of an entire region, (ii) locating bilaterally symmetrical areas from a scene, and (iii) automating the process of symmetry recovery by solving the problems mentioned above. Perfect symmetries are rare in the extreme in natural images and symmetry perception in humans allows for qualification so that symmetry can be graduated based on the degree of structural deformation or replacement error. There have been many approaches to detect approximate symmetry by searching an optimal solution in a form of an exhaustive exploration of the parameter space or surmising the center of mass. The algorithm set out in this thesis circumvents the computationally intensive operations by using geometric constraints of symmetric images, and assumes no prerequisite knowledge of the barycenter. The results from an extensive set of evaluation experiments on metrics for symmetry distance and a comparison of the performance between the method presented in this thesis and the state of the art approach are demonstrated as well. Many biological vision systems employ a special computational strategy to locate regions of interest based on local image cues while viewing a compound visual scene. The method taken in this thesis is a bottom-up approach that causes the observer favors stimuli based on their saliency, and creates a feature map contingent on symmetry. With the help of summed area tables, the time complexity of the proposed algorithm is linear in the size of the image. The distinguished regions are then delivered to the algorithm described above to uncover approximate symmetry

Investigating human-perceptual properties of "shapes" using 3D shapes and 2D fonts

Shapes are generally used to convey meaning. They are used in video games, films and other multimedia, in diverse ways. 3D shapes may be destined for virtual scenes or represent objects to be constructed in the real-world. Fonts add character to an otherwise plain block of text, allowing the writer to make important points more visually prominent or distinct from other text. They can indicate the structure of a document, at a glance. Rather than studying shapes through traditional geometric shape descriptors, we provide alternative methods to describe and analyse shapes, from a lens of human perception. This is done via the concepts of Schelling Points and Image Specificity. Schelling Points are choices people make when they aim to match with what they expect others to choose but cannot communicate with others to determine an answer. We study whole mesh selections in this setting, where Schelling Meshes are the most frequently selected shapes. The key idea behind image Specificity is that different images evoke different descriptions; but ‘Specific’ images yield more consistent descriptions than others. We apply Specificity to 2D fonts. We show that each concept can be learned and predict them for fonts and 3D shapes, respectively, using a depth image-based convolutional neural network. Results are shown for a range of fonts and 3D shapes and we demonstrate that font Specificity and the Schelling meshes concept are useful for visualisation, clustering, and search applications. Overall, we find that each concept represents similarities between their respective type of shape, even when there are discontinuities between the shape geometries themselves. The ‘context’ of these similarities is in some kind of abstract or subjective meaning which is consistent among different people

Doctor of Philosophy

dissertationShape analysis is a well-established tool for processing surfaces. It is often a first step in performing tasks such as segmentation, symmetry detection, and finding correspondences between shapes. Shape analysis is traditionally employed on well-sampled surfaces where the geometry and topology is precisely known. When the form of the surface is that of a point cloud containing nonuniform sampling, noise, and incomplete measurements, traditional shape analysis methods perform poorly. Although one may first perform reconstruction on such a point cloud prior to performing shape analysis, if the geometry and topology is far from the true surface, then this can have an adverse impact on the subsequent analysis. Furthermore, for triangulated surfaces containing noise, thin sheets, and poorly shaped triangles, existing shape analysis methods can be highly unstable. This thesis explores methods of shape analysis applied directly to such defect-laden shapes. We first study the problem of surface reconstruction, in order to obtain a better understanding of the types of point clouds for which reconstruction methods contain difficulties. To this end, we have devised a benchmark for surface reconstruction, establishing a standard for measuring error in reconstruction. We then develop a new method for consistently orienting normals of such challenging point clouds by using a collection of harmonic functions, intrinsically defined on the point cloud. Next, we develop a new shape analysis tool which is tolerant to imperfections, by constructing distances directly on the point cloud defined as the likelihood of two points belonging to a mutually common medial ball, and apply this for segmentation and reconstruction. We extend this distance measure to define a diffusion process on the point cloud, tolerant to missing data, which is used for the purposes of matching incomplete shapes undergoing a nonrigid deformation. Lastly, we have developed an intrinsic method for multiresolution remeshing of a poor-quality triangulated surface via spectral bisection

A Survey of Surface Reconstruction from Point Clouds

International audienceThe area of surface reconstruction has seen substantial progress in the past two decades. The traditional problem addressed by surface reconstruction is to recover the digital representation of a physical shape that has been scanned, where the scanned data contains a wide variety of defects. While much of the earlier work has been focused on reconstructing a piece-wise smooth representation of the original shape, recent work has taken on more specialized priors to address significantly challenging data imperfections, where the reconstruction can take on different representations – not necessarily the explicit geometry. We survey the field of surface reconstruction, and provide a categorization with respect to priors, data imperfections, and reconstruction output. By considering a holistic view of surface reconstruction, we show a detailed characterization of the field, highlight similarities between diverse reconstruction techniques, and provide directions for future work in surface reconstruction

Digital Image Access & Retrieval

The 33th Annual Clinic on Library Applications of Data Processing, held at the University of Illinois at Urbana-Champaign in March of 1996, addressed the theme of "Digital Image Access & Retrieval." The papers from this conference cover a wide range of topics concerning digital imaging technology for visual resource collections. Papers covered three general areas: (1) systems, planning, and implementation; (2) automatic and semi-automatic indexing; and (3) preservation with the bulk of the conference focusing on indexing and retrieval.published or submitted for publicatio