Predicting the performance of complex structures exposed to harsh thermal environments is a crucial issue in many of today's aerospace and space designs. To predict the thermal stresses a structure might be exposed to, the thermal properties of the independent materials used in the design of the structure need to be known. Therefore, a noninvasive estimation procedure involving Genetic Algorithms was developed to determine the various thermal properties needed to adequately model the Outer Wing Subcomponent (OWS), a structure located at the trailing edge of the High Speed Civil Transport's (HSCT) wing tip. Due to the nature of the nonlinear least-squares estimation method used in this study, both theoretical and experimental temperature histories were required. Several one-dimensional and two-dimensional finite element models of the OWS were developed to compute the transient theoretical temperature histories. The experimental data were obtained from optimized experiments that were run at various surrounding temperature settings to investigate the temperature dependence of the estimated properties. An experimental optimization was performed to provide the most accurate estimates and reduce the confidence intervals. The simultaneous estimation of eight thermal properties, including the volumetric heat capacities and out-of-plane thermal conductivities of the facesheets, the honeycomb, the skins, and the torque tubes, was successfully completed with the one-dimensional model and the results used to evaluate the remaining in-plane thermal conductivities of the facesheets, the honeycomb, the skins, and the torque tubes with the two-dimensional model. Although experimental optimization did not eliminate all correlation between the parameters, the minimization procedure based on the Genetic Algorithm performed extremely well, despite the high degree of correlation and low sensitivity of many of the parameters. / Master of Science

Several biased estimators have been proposed as alternatives to the least squares estimator when multicollinearity is present in the multiple linear regression model. Though the ridge estimator and the principal components estimator have been widely used for such problems, it should be noted that their performances in terms of mean square error are dependent upon the orientation of the unknown parameter vector and the magnitude of σ². By defining the fractional principal components regression model as y̲ = Zα̲ + 𝛜̲ = ZF⁻α_F + 𝛜̲ where α_F = Fα̲ and F⁻ is a generalized inverse of a diagonal matrix P, the resulting estimators of α̲_F, based on various forms of F, are shown to define the class of the fractional principal components estimators. In the fractional principal components framework, several new estimation techniques are developed. The performances of the new estimators are evaluated and compared with other commonly used biased estimators both theoretically and by simulation studies. / Ph. D. / incomplete_metadata

This dissertation develops two new techniques for the identification of parameters in distributed-parameter systems. The first technique identifies the physical parameter distributions such as mass, damping and stiffness. The second technique identifies the modal quantities of self-adjoint distributed-parameter systems. Distributed structures are distributed-parameter systems characterized by mass, damping and stiffness distributions. To identify the distributions, a new identification technique is introduced based on the finite element method. With this approach, the object is to identify "average" values of mass, damping and stiffness distributions over each finite element. This implies that the distributed parameters are identified only approximately, in the same way in which the finite element method approximates the behavior of a structure. It is common practice to represent the motion of a distributed parameter system by a linear combination of the associated modes of vibration. In theory, we have an infinite set of modes although, in practice we are concerned with only a finite linear combination of the modes. The modes of vibration possess certain properties which distinguish them from one another. Indeed, the modes of vibration are uncorrelated in time and orthogonal in space. The modal identification technique introduced in this dissertation uses path these spatial properties. Because both the temporal and spatial properties are used, the method does not encounter problems when the natural frequencies are closely-spaced or repeated. / Ph. D.

Yes / Apigenin (4′,5,7-trihydroxyflavone, APG) has many potential therapeutic benefits; however, its poor aqueous solubility has limited its clinical applications. In this work, a large scale cocrystal screening has been conducted, aiming to discover potential APG cocrystals for enhancement of its solubility and dissolution rate. In order to reduce the number of the experimental screening tests, three computational prescreening tools, i.e., molecular complementarity (MC), hydrogen bond propensity (HBP), and hydrogen bond energy (HBE), were used to provide an initial selection of 47 coformer candidates, leading to the discovery of seven APG cocrystals. Among them, six APG cocrystal structures have been determined by successful growth of single crystals, i.e., apigenin-carbamazepine hydrate 1:1:1 cocrystal, apigenin-1,2-di(pyridin-4-yl)ethane hydrate 1:1:1 cocrystal, apigenin-valerolactam 1:2 cocrystal, apigenin-(dl) proline 1:2 cocrystal, apigenin-(d) proline/(l) proline 1:1 cocrystal. All of the APG cocrystals showed improved dissolution performances with the potential to be formulated into drug products.

In this thesis we develop new mathematical models, using dynamical systems, to represent localized gene delivery of bone morphogenetic protein 2 into bone marrow-derived mesenchymal stem cells and rat calvarial defects. We examine two approaches, using pDNA or cmRNA treatments, respectively, towards the production of calcium deposition and bone regeneration in in vitro and in vivo experiments. We first review the relevant scientific literature and survey existing mathematical representations for similar treatment approaches. We then motivate and develop our new models and determine model parameters from literature, heuristic approaches, and estimation using sparse data. We next conduct a qualitative analysis using dynamical systems theory. Due to the nature of the parameter estimation, it was important that we obtain local and global sensitivity analyses of model outputs to changes in model inputs. Finally we compared results from different treatment protocols. Our model suggests that cmRNA treatments may perform better than pDNA treatments towards bone fracture healing. This work is intended to be a foundation for predictive models of non-viral local gene delivery systems.

Natural attenuation refers to the observed reduction in contaminant concentration via natural processes as contaminants migrate from the source into environmental media. Assessment of the dimensions of contaminant plumes and prediction of their fate requires predictions of the rate of dissolution of contaminants from residual non-aqueous-phase liquids (NAPLs) into the aquifer and the rate of contaminant removal through biodegradation. The available techniques to estimate these parameters do not characterize their confidence intervals by accounting for their relationships to uncertainty in source geometry and hydraulic conductivity distribution. The central idea in this thesis is to develop a flexible modeling approach for characterization of uncertainty in residual NAPL dissolution rate and first-order biodegradation rate by tailoring the estimation of these parameters to distributions of uncertainty in source size and hydraulic conductivity field. The first development in this thesis is related to a distance function approach that characterizes the uncertainty in the areal limits of the source zones. Implementation of the approach for a given monitoring well arrangement results in a unique uncertainty band that meets the requirements of unbiasedness and fairness of the calibrated probabilities. The second development in this thesis is related to a probabilistic model for characterization of uncertainty in the 3D localized distribution of residual NAPL in a real site. A categorical variable is defined based on the available CPT-UVIF data, while secondary data based on soil texture and groundwater table elevation are also incorporated into the model. A cross-validation study shows the importance of incorporation of secondary data in improving the prediction of contaminated and uncontaminated locations. The third development in this thesis is related to the implementation of a Monte Carlo type inverse modeling to develop a screening model used to characterize the confidence intervals in the NAPL dissolution rate and first-order biodegradation rate. The development of the model is based on sequential self-calibration approach, distance-function approach and a gradient-based optimization. It is shown that tailoring the estimation of the transport parameters to joint realizations of source geometry and transmissivity field can effectively reduce the uncertainties in the predicted state variables.

We establish a parameter-dependent pseudo-differential calculus on an infinite cylinder, regarded as a manifold with conical exits to infinity. The parameters are involved in edge-degenerate form, and we formulate the operators in terms of operator-valued amplitude functions.

Inverse problems have gained popularity in statistical research recently. This dissertation consists of two statistical inverse problems: a Bayesian approach to detection of small low emission sources on a large random background, and parameter estimation methods for partial differential equation (PDE) models. Source detection problem arises, for instance, in some homeland security applications. We address the problem of detecting presence and location of a small low emission source inside an object, when the background noise dominates. The goal is to reach the signal-to-noise ratio levels on the order of 10^-3. We develop a Bayesian approach to this problem in two-dimension. The method allows inference not only about the existence of the source, but also about its location. We derive Bayes factors for model selection and estimation of location based on Markov chain Monte Carlo simulation. A simulation study shows that with sufficiently high total emission level, our method can effectively locate the source. Differential equation (DE) models are widely used to model dynamic processes in many fields. The forward problem of solving equations for given parameters that define the DEs has been extensively studied in the past. However, the inverse problem of estimating parameters based on observed state variables is relatively sparse in the statistical literature, and this is especially the case for PDE models. We propose two joint modeling schemes to solve for constant parameters in PDEs: a parameter cascading method and a Bayesian treatment. In both methods, the unknown functions are expressed via basis function expansion. For the parameter cascading method, we develop the algorithm to estimate the parameters and derive a sandwich estimator of the covariance matrix. For the Bayesian method, we develop the joint model for data and the PDE, and describe how the Markov chain Monte Carlo technique is employed to make posterior inference. A straightforward two-stage method is to first fit the data and then to estimate parameters by the least square principle. The three approaches are illustrated using simulated examples and compared via simulation studies. Simulation results show that the proposed methods outperform the two-stage method.

The lymphatic system is responsible for several vital roles in human body, one of which is maintaining fluid and protein balance. There is no central pump in the lymphatic system and the transport of fluid against gravity and adverse pressure gradient is maintained by the extrinsic and intrinsic pumping mechanisms. Any disruption of the lymphatic system due to trauma or injury can lead to edema. There is no cure for lymphedema partly because the knowledge of the function of the lymphatic system is lacking. Thus, a well-developed model of the lymphatic system is crucial to improve our understanding of its function. Here we used a lumped parameter approach to model a chain of lymphangions in series. Equations of conservation of mass, conservation of momentum, and vessel wall force balance were solved for each lymphangion computationally. Due to the lack of knowledge of the parameters describing the system in the literature, more accurate measurements of these parameters should be pursued to advance the model. Because of the difficulty of the isolated vessel and in-situ experiments, we performed a parameter sensitivity analysis to determine the parameters that affect the system most strongly. Our results showed that more accurate estimations of active contractile force and physiologic features of lymphangions, such as length/diameter ratios, should be pursued in future experiments. Also further experiments are required to refine the valve behavior and valve parameters.

Since the development of high-throughput technologies, we can capture large quantities of gene¡¦s expression data from DNA microarray data, so there are some technologies have been proposed to model gene regulatory networks. Gene regulatory networks is mainly used to express the relationship between the genes, but only can express a simple relationship, and can¡¦t clearly show how the operation between genes regulatory. In the simulation method of gene regulation, the mathematical methods are more often used. In the mathematical methods, S-system is the most widely used in non-linear differential equations. When the use of mathematical simulation of gene regulatory networks, there are mainly two aspects¡G(1) deciding on the model structure and (2) estimating the involved parameter values. However, when using S-system simulated the gene regulatory networks, we can only know the gene profiles, and there is no way to know the regulatory relationships between genes, but in order to understand the relationship between genes, we must clearly understand how genes work. Therefore, we propose to encode parameter values to infer the regulatory parameter values between genes. We propose the method of encoding parameter values, and using six artificial genetic datasets, and assuming 100% parameter values are known, 90% known, 70% known, 50% known, 30% known, 10% known. The experimental results show, besides it can infer a high proportion of non-regulation, positive regulation and negative regulation, also can infer more precise parameter values, and also has a clear understanding of the regulatory relationship between genes.