Hybrid mathematical and informational modeling of beam-to-column connections

The analysis of steel and composite frames has traditionally been carried out by idealizing beam-to-column connections as either rigid or pinned. Although some advanced analysis methods have been proposed to account for semi-rigid connections, the performance of these methods strongly depends on the proper modeling of connection behavior. The primary challenge of modeling beam-to-column connections is their inelastic response and continuously varying stiffness, strength, and ductility. In this dissertation, two distinct approaches—mathematical models and informational models—are proposed to account for the complex hysteretic behavior of beam-to-column connections. The performance of the two approaches is examined and is then followed by a discussion of their merits and deficiencies. To capitalize on the merits of both mathematical and informational representations, a new approach, a hybrid modeling framework, is developed and demonstrated through modeling beam-to-column connections. Component-based modeling is a compromise spanning two extremes in the field of mathematical modeling: simplified global models and finite element models. In the component-based modeling of angle connections, the five critical components of excessive deformation are identified. Constitutive relationships of angles, column panel zones, and contact between angles and column flanges, are derived by using only material and geometric properties and theoretical mechanics considerations. Those of slip and bolt hole ovalization are simplified by empirically-suggested mathematical representation and expert opinions. A mathematical model is then assembled as a macro-element by combining rigid bars and springs that represent the constitutive relationship of components. Lastly, the moment-rotation curves of the mathematical models are compared with those of experimental tests. In the case of a top-and-seat angle connection with double web angles, a pinched hysteretic response is predicted quite well by complete mechanical models, which take advantage of only material and geometric properties. On the other hand, to exhibit the highly pinched behavior of a top-and-seat angle connection without web angles, a mathematical model requires components of slip and bolt hole ovalization, which are more amenable to informational modeling. An alternative method is informational modeling, which constitutes a fundamental shift from mathematical equations to data that contain the required information about underlying mechanics. The information is extracted from observed data and stored in neural networks. Two different training data sets, analytically-generated and experimental data, are tested to examine the performance of informational models. Both informational models show acceptable agreement with the moment-rotation curves of the experiments. Adding a degradation parameter improves the informational models when modeling highly pinched hysteretic behavior. However, informational models cannot represent the contribution of individual components and therefore do not provide an insight into the underlying mechanics of components. In this study, a new hybrid modeling framework is proposed. In the hybrid framework, a conventional mathematical model is complemented by the informational methods. The basic premise of the proposed hybrid methodology is that not all features of system response are amenable to mathematical modeling, hence considering informational alternatives. This may be because (i) the underlying theory is not available or not sufficiently developed, or (ii) the existing theory is too complex and therefore not suitable for modeling within building frame analysis. The role of informational methods is to model aspects that the mathematical model leaves out. Autoprogressive algorithm and self-learning simulation extract the missing aspects from a system response. In a hybrid framework, experimental data is an integral part of modeling, rather than being used strictly for validation processes. The potential of the hybrid methodology is illustrated through modeling complex hysteretic behavior of beam-to-column connections. Mechanics-based components of deformation such as angles, flange-plates, and column panel zone, are idealized to a mathematical model by using a complete mechanical approach. Although the mathematical model represents envelope curves in terms of initial stiffness and yielding strength, it is not capable of capturing the pinching effects. Pinching is caused mainly by separation between angles and column flanges as well as slip between angles/flange-plates and beam flanges. These components of deformation are suitable for informational modeling. Finally, the moment-rotation curves of the hybrid models are validated with those of the experimental tests. The comparison shows that the hybrid models are capable of representing the highly pinched hysteretic behavior of beam-to-column connections. In addition, the developed hybrid model is successfully used to predict the behavior of a newly-designed connection.

Characterizing neural tissues with mass spectrometry imaging via enhanced computational approaches

Neuropeptides affect the activity of the myriad of neuronal circuits in the brain. They are under tight spatial and chemical control and the dynamics of their release and catabolism directly modify neuronal network activity. Understanding neuropeptide functioning requires approaches to determine their chemical and spatial heterogeneity within neural tissue, but most imaging techniques do not provide the complete information desired. To provide chemical information, most imaging techniques used to study the nervous system require preselection and labeling of the peptides of interest; however, mass spectrometry imaging (MSI) detects analytes across a broad mass range without the need to target a specific analyte. When used with matrix-assisted laser desorption/ionization (MALDI), MSI detects analytes in the mass range of neuropeptides. MALDI MSI simultaneously provides spatial and chemical information resulting in images that plot the spatial distributions of neuropeptides over the surface of a thin slice of neural tissue. Here a variety of approaches for neuropeptide characterization are developed. Specifically, several computational approaches are combined with MALDI MSI to create improved approaches that provide spatial distributions and neuropeptide characterizations. After successfully validating these MALDI MSI protocols, the methods are applied to characterize both known and unidentified neuropeptides from neural tissues. The methods are further adapted from tissue analysis to be able to perform tandem MS (MS/MS) imaging on neuronal cultures to enable the study of network formation. In addition, MALDI MSI has been carried out over the timecourse of nervous system regeneration in planarian flatworms resulting in the discovery of two novel neuropeptides that may be involved in planarian regeneration. In addition, several bioinformatic tools are developed to predict final neuropeptide structures and associated masses that can be compared to experimental MSI data in order to make assignments of neuropeptide identities. The integration of computational approaches into the experimental design of MALDI MSI has allowed improved instrument automation and enhanced data acquisition and analysis. These tools also make the methods versatile and adaptable to new sample types.