This dissertation addresses the modeling and solution of mixed-integer linear multistage stochastic programming problems involving both endogenous and exogenous uncertain parameters. We propose a composite scenario tree that captures both types of uncertainty, and we exploit its unique structure to derive new theoretical properties that can drastically reduce the number of non-anticipativity constraints (NACs). Since the reduced model is often still intractable, we discuss two special solution approaches. The first is a sequential scenario decomposition heuristic in which we sequentially solve endogenous MILP subproblems to determine the binary investment decisions, fix these decisions to satisfy the first-period and exogenous NACs, and then solve the resulting model to obtain a feasible solution. The second approach is Lagrangean decomposition. We present numerical results for a process network planning problem and an oilfield development planning problem. The results clearly demonstrate the efficiency of the special solution methods over solving the reduced model directly. To further generalize this work, we also propose a graph-theory algorithm for non-anticipativity constraint reduction in problems with arbitrary scenario sets. Finally, in a break from the rest of the thesis, we present the basics of stochastic programming for non-expert users.

This thesis focuses on the construction of optimum designs for the estimation of the variance components in multistage variability models. Variance components are the model parameters that represent the different sources of variability that affect the response of a system. A general and highly detailed way to define the linear mixed effects model is proposed. The extension considers the explicit definition of all the elements needed to construct a model. One key aspect of this formulation is that the random part is stated as a functional that individually determines the form of the design matrices for each random regressor, which gives significant flexibility. Further, the model is strictly divided into the treatment structure and the variability structure. This allows separate definitions of each structure but using the single rationale of combining, with little restrictions, simple design arrangements called factor layouts. To provide flexibility for considering different models, methodology to find and select optimum designs for variance components is presented using MLE and REML estimators and an alternative method known as the dispersion-mean model. Different forms of information matrices for variance components were obtained. This was mainly done for the cases when the information matrix is a function of the ratios of variances. Closed form expressions for balanced designs for random models with 3-stage variability structure, in crossed and nested layouts were found. The nested case was obtained when the information matrix is a function of the variance components. A general expression for the information matrix for the ratios using REML is presented. An approach to using unbalanced models, which requires the use of general formulae, is discussed. Additionally, D-optimality and A-optimality criteria of design optimality are restated for the case of variance components, and a specific version of pseudo-Bayesian criteria is introduced. Algorithms to construct optimum designs for the variance components based on the aforementioned methodologies were defined. These algorithms have been implemented in the R language. The results are communicated using a simple, but highly informative, graphical approach not seen before in this context. The proposed plots convey enough details for the experimenter to make an informed decision about the design to use in practice. An industrial internship allowed some the results herein to be put into practice, although no new research outcomes originated. Nonetheless, this is evidence of the potential for applications. Equally valuable is the experience of providing statistical advice and reporting conclusions to a non statistical audience.

This dissertation introduces desalination processes in general and multistage flash (MSF) and reverse osmosis (RO) in particular. It presents the fundamental and practical aspects of neural networks and provides an overview of their structures, topology, strengths, and limitations. This study includes the neural network applications to prediction problems of large-scale commercial MSF and RO desalination plants in conjunction with statistical techniques to identify the major independent variables to optimize the process performance. In contrast to several recent studies, this work utilizes actual operating data (not simulated) from a large-scale commercial MSF desalination plant (48 million gallonsper day capacity, MGPD) and RO plant (15 MGPD) located in Kuwait and the Kingdom of Saudi Arabia, respectively. We apply Neural Works Professional II/Plus (NeuralWare, 1993) and SAS (SAS Institute Inc., 1996) software to accomplish this task. This dissertation demonstrates how to apply modular and equation-solving approaches for steady-state and dynamic simulations of large-scale commercial MSF desalination plants using ASPEN PLUS (Advanced System for Process Engineering PLUS) and SPEEDUP (Simulation Program for Evaluation and Evolutionary Design of Unsteady Processes) marketed by Aspen Technology, Cambridge, MA. This work illustrates the development of an optimal operating envelope for achieving a stable operation of a commercial MSF desalination plant using the SPEEDUP model. We then discuss model linearization around nominal operating conditions and arrive at pairing schemes for manipulated and controlled variables by interaction analysis. Finally, this dissertation describes our experience in applying a commercial software, DynaPLUS, for combined steady-state and dynamic simulations of a commercial MSF desalination plant. This dissertation is unique and significant in that it reports the first comprehensive study of predictive modeling, simulation, and optimization of large-scale commercial desalination plants. It is the first detailed and comparative study of commercial desalination plants using both artificial intelligence and computer-aided design techniques. The resulting models are able to reproduce accurately the actual operating data and to predict the optimal operating conditions of commercial desalination plants. / Ph. D.

Understanding the effects of uncertainty on modeling has seen an increased focus as engineering disciplines rely more heavily on computational modeling of complex physical processes to predict system performance and make informed engineering decisions. These computational methods often use simplified models and assumptions with models calibrated using uncertain, averaged experimental data. This commonplace method ignores the effects of uncertainty on the variation of modeling output. Qualitatively, uncertainty is the possibility of error existing from experiment to experiment, from model to model, or from experiment to model. Quantitatively, uncertainty quantification (UQ) methodologies seek to determine the how variable an engineering system is when subjected to variation in the factors that control it. Often performed in conjunction, sensitivity analysis (SA) methods seek to describe what model factor contributes the most to variation in model output. UQ and SA methodologies were employed in the analysis of the Modified Embedded Atom Method (MEAM) model for a pure aluminum, a microstructure sensitive fatigue crack growth model for polycarbonate, and the MultiStage Fatigue (MSF) model for AZ31 magnesium alloy. For the MEAM model, local uncertainty and sensitivity measures were investigated for the purpose of improving model calibrations. In polycarbonate fatigue crack growth, a Monte Carlo method is implemented in code and employed to investigate how variations in model input factors effect fatigue crack growth predictions. Lastly, in the analysis of fatigue life predictions with the MSF model for AZ31, the expected fatigue performance range due to variation in experimental parameters is investigated using both Monte Carlo Simple Random Sampling (MCSRS) methods and the estimation of first order effects indices using the Fourier Amplitude Sensitivity Test (FAST) method.

The goal of this study is to investigate the microstructure and microstructure-based fatigue (MSF) model of additively-manufactured (AM) metallic materials. Several challenges associated with different metals produced through additive manufacturing (Laser Enhanced Net Shaping – LENS®) have been addressed experimentally and numerically. Significant research efforts are focused on optimizing the process parameters for AM manufacturing; however, achieving a homogenous, defectree AM product immediately after its fabrication without postabrication processing has not been fully established yet. Thus, in order to adopt AM materials for applications, a thorough understanding of the impact of AM process parameters on the mechanical behavior of AM parts based on their resultant microstructure is required. Therefore, experiments in this study elucidate the effects of process parameters – i.e. laser power, traverse speed and powder feed rate – on the microstructural characteristics and mechanical properties of AM specimens. A majority of fatigue data in the literature are on rotation/bending test of wrought specimens; however, few studies examined the fatigue behavior of AM specimens. So, investigating the fatigue resistance and failure mechanism of AM specimens fabricated via LENS® is crucial. Finally, a microstructure-based MultiStage Fatigue (MSF) model for AM specimens is proposed. For calibration of the model, fatigue experiments were exploited to determine structure-property relations for an AM alloy. Additional modifications to the microstructurally-based MSF Model were implemented based on microstructural analysis of the fracture surfaces – e.g. grain misorientation and grain orientation angles were added to the MSF code.

<p> An optimization study of an intermittent-flow multistage fluidized ion exchange column was performed using a stochastic approximation method. A new type of downcomer, a fluid diode, was designed and employed to alleviate liquid bypassing through the downcomer. The well known ion exchange system, H⁺/Na⁺ exchange on Dowex 50W resin, was used in this work. </p> <p> The volumetric efficiency of the system was optimized with regard to certain column and diode parameters. A maximum volumetric efficiency of 71.8 hr⁻¹ was obtained for the following conditions: </p> <p> average liquid flowrate = 3661 ml/min ; </p> <p> resin flowrate = 56.1 gm/min ; </p> <p> plate spacing 11.43 cm ; </p> <p> lateral diode displacement= 0.794 cm. </p> <p> Experiments have shown that a 78.2% increase in volumetric efficiency was achieved by use of the fluidic diode downcomers. </p> / Thesis / Master of Engineering (ME)

Multistage tests are a widely used and efficient type of test presentation that aims to provide accurate ability estimates while keeping the test relatively short. Multistage tests typically rely on the psychometric framework of item response theory. Violations of item response models and other assumptions underlying a multistage test, such as differential item functioning, can lead to inaccurate ability estimates and unfair measurements. There is a practical need for methods to detect problematic model violations to avoid these issues. This study compares and evaluates three methods for the detection of differential item functioning with regard to continuous person covariates in data from multistage tests: a linear logistic regression test and two adaptations of a recently proposed score-based DIF test. While all tests show a satisfactory Type I error rate, the score-based tests show greater power against three types of DIF effects.

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The research presented in this dissertation is on the development and application of advanced reduced rank adaptive signal processing techniques for high data rate wireless code division multiple access (CDMA) communications systems. This is an important area of research in the field of wireless communications. Current systems are moving towards the use of multiple simultaneous users in a given channel to increase system capacity as well as spatial and/or temporal diversity for improved performance in the presence of multipath and fading channels. Furthermore, to accommodate the demand for higher data rates, fast signal processing algorithms are required, which often translate into blind signal detection and estimation and the desire for optimal, low complexity detection techniques. The research presented here shows how minimum mean square error (MMSE) receivers implemented via the multistage Wiener filter (MWF) can be employed at the receiving end of a CDMA system to perform multiuser detection (MUD) or interference suppression (IS) with no loss in performance and significant signal subspace compression better than any previous reduced rank techniques have shown. This is important for optimizing performance because it implies a reduction in the number of required samples, so it lessens the requirement that the channel be stationary for a time duration long enough to obtain enough samples for an accurate MMSE estimate. The structure of these receivers is derived for synchronous and asynchronous systems for a multipath environment, and then it is shown that implementation of the receiver in a reduced rank subspace results in no loss in performance over full rank methods. It is also shown in some instances that reduced rank exceeds full rank performance. Multiuser detectors are also studied, and the optimal reduced rank detector is shown to be equivalent to a bank of parallel single user detectors performing interference suppression (IS). The performance as a function of rank for parallel and joint multiuser detectors are compared. The research is then extended to include joint space-code (i.e. a joint multiuser detector) and joint space-time processing algorithms which employ receiver diversity for low complexity diversity gain. Non-linear techniques, namely serial interference cancellation (SIC) and parallel interference cancellation (PIC), will also be studied. The conventional matched filter correlator will be replaced by the MWF, thereby incorporating IS at each stage of the interference canceller for improved performance. A closed form expression is derived for the probability of error, and performance gains are evaluated. It will be further shown how the receiver structure can be extended when space-time codes are employed at the transmitter for additional diversity gain with minimal impact on complexity. The MMSE solution is derived and implemented via the MWF with some examples. It is believed that these new techniques will have a significant impact on the design of fourth generation (4G) and beyond cellular CDMA systems. / Ph. D.