A geostatistical inverse method of estimating hydraulic parameters of a heterogeneous porous medium at discrete points in space, called pilot points, is presented. In this inverse method the parameter estimation problem is posed as a nonlinear optimization problem with a likelihood based objective function. The likelihood based objective function is expressed in terms of head residuals at head measurement locations in the flow domain, where head residuals are the differences between measured and model-predicted head values. Model predictions of head at each iteration of the optimization problem are obtained by solving a forward problem that is based on nonlocal conditional ensemble mean flow equations. Nonlocal moment equations make possible optimal deterministic predictions of fluid flow in randomly heterogenous porous media as well as assessment of the associated predictive uncertainty. In this work, the nonlocal moment equations are approximated to second order in the standard deviation of log-transformed hydraulic conductivity, and are solved using the finite element method. To enhance computational efficiency, computations are carried out in the complex Laplace-transform space, after which the results are inverted numerically to the real temporal domain for analysis and presentation. Whereas a forward solution can be conditioned on known values of hydraulic parameters, inversion allows further conditioning of the solution on measurements of system state variables, as well as for the estimation of unknown hydraulic parameters. The Levenberg-Marquardt algorithm is used to solve the optimization problem. The inverse method is illustrated through two numerical examples where parameter estimates and the corresponding predictions of system state are conditioned on measurements of head only, and on measurements of head and log-transformed hydraulic conductivity with prior information. An example in which predictions of system state are conditioned only on measurements of log-conductivity is also included for comparison. A fourth example is included in which the estimation of spatially constant specific storage is demonstrated. In all the examples, a superimposed mean uniform and convergent transient flow field through a bounded square domain is used. The examples show that conditioning on measurements of both head and hydraulic parameters with prior information yields more reliable (low uncertainty and good fit) predictions of system state, than when such information is not incorporated into the estimation process.

South Florida has transformed from a natural to a managed ecosystem upon channelization of Kissimmee River and the wetlands in the 1960’s. The drainage has resulted in fast transport of water and nutrient, and subsequently eutrophication of the downstream water bodies. The intervention required: intensive management of the shallow groundwater to balance ecological water requirement; and nutrient removal, namely phosphorus, to minimize eutrophication. The study was set to examine and develop an operational prediction method for groundwater-phosphorus interactions to support the wetlands management. Accordingly, a point scale and a spatio-temporal groundwater level was simulated using sequence based Markovian stochastic analysis and dynamic factor analysis methods respectively. A root mean square error of 0.12m and 0.15m was observed for a point and spatio-temporal groundwater prediction. Soluble and sequestered phosphorus were also simulated at 13% error using a watershed based model called ArcWAM. A spatial analysis on simulated soluble phosphorus and groundwater level indicated similarity of patterns (spatial correlation) 99% of the time. A geographically weighted multivariate analysis of soluble phosphorus using predictors of groundwater level, total phosphorus of surficial water, and distance from Kissimmee River showed a goodness of fit (R2 ) of 0.2 – 0.7. Amongst the factors, the groundwater explained 70% of the soluble phosphorus variability. In summary, an increase in soluble phosphorus was observed with groundwater rise and a decrease during groundwater recession. A reversed relationship was identified for the total phosphorus. Presumably, organic matter in the root zone has contributed to increased soluble phosphorus with the rise in groundwater. On the other hand, solubility of calcium carbonate from the karst aquifers seems to fix and precipitate phosphorus during recession of groundwater. The least sequestration of phosphorus, observed in oversaturated wetlands also suggested that nutrient removal on karst hydrogeology could be risky unless a check is made using vegetation strip to enhance phosphorus uptake. The study concluded that phosphorus could be operationally predicted associated with forecasting of groundwater fluctuation. Further research is recommended to explore factors that could be derived either empirically or from satellite data for prediction of soluble phosphorus at minimum cost.

This thesis examines the statistics and dynamics of turbulent flow structures generated by towing a grid through a tank of water. The structures were made visible by recording the paths of aluminum tracers moving with the water surface. Flow patterns recorded using a time-exposure method were manually analyzed to extract information on the structure statistics. This two-dimensional flow field was found to be composed of closed rotating 'surface eddies', open and largely translational 'river' motion and stagnant regions. Energy distributions of the eddies and rivers were obtained and characterized by Boltzmann type distributions. A newly developed computer-automated structure identification and flow field analysis system was used to study the structure dynamics. The system analyzes digital images obtained from video recordings of the tracer motion. The predominant evolution processes of initial vortex production, eddy pairing, viscous decay and the omega decay were examined. Flow Reynolds numbers, based on bar spacing, of about 10,000 were examined. The structure statistics and dynamics study was performed in order to examine the validity and viability of a new model for turbulence. The model predicts the evolution of a population of structures using rate equations where the rate coefficients are determined by the individual structure dynamics. A summary of the model is presented and contrasted with models based the the Reynolds stresses as well as computational models. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

To operate a production plant, one requires considerable amounts of power. With a wide range of energy sources, the price of electricity changes rapidly throughout the year, and so does the cost of satisfying the electricity demand. Battery technology allows storing energy while the electric power is lower, saving us from purchasing at higher prices. Thus, adding batteries to run plants can significantly reduce production costs. This thesis proposes a method to determine the optimal battery regime and its maximum capacity, minimizing the production plant's energy expenditures. We use stochastic differential equations to model the dynamics of the system. In this way, our spot price mimics the Uruguayan energy system's historical data: a diffusion process represents the electricity demand and a jump-diffusion process - the spot price. We formulate a corresponding stochastic optimal control problem to determine the battery's optimal operation policy and its optimal storage capacity. To solve our stochastic optimal control problem, we obtain the value function by solving the Hamilton-Jacobi-Bellman partial differential equation associated with the system. We discretize the Hamilton-Jacobi-Bellman partial differential equation using finite differences and a time splitting operator technique, providing a stability analysis. Finally, we solve a one-dimensional minimization problem to determine the battery's optimal capacity.

Thesis: Sc. D., Massachusetts Institute of Technology, Department of Civil Engineering, 1975 / Vita. / Bibliography: leaves 213-221. / Sc. D. / Sc. D. Massachusetts Institute of Technology, Department of Civil Engineering

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In this research, a new zeroth-order (non-gradient based) topology optimization methodology for compliance minimization was developed. It is called the Element Exchange Method (EEM). The principal operation in this method is to convert the less effective solid elements into void elements and the more effective void elements into solid elements while maintaining the overall volume fraction constant. The methodology can be integrated with existing FEA codes to determine the stiffness or other structural characteristics of each candidate design during the optimization process. This thesis provides details of the EEM algorithm, the element exchange strategy, checkerboard control, and the convergence criteria. The results for several two- and three-dimensional benchmark problems are presented with comparisons to those found using other stochastic and gradient-based approaches. Although EEM is not as efficient as some gradient-based methods, it is found to be significantly more efficient than many other non-gradient methods reported in the literature such as GA and PSO.

<p> In this thesis a non-parametric normalized stochastic approximation algorithm has been developed for the identification of multivariable systems from noisy data without prior knowledge of the statistics of measurement noise.</p> <p> The system model is first transformed into a special canonical form, then it is formulated in a non-parametric form. The parameters of this model are estimated through a normalized stochastic approximation algorithm. Finally, the system parameters are recovered from these estimates by another transformation.</p> <p> The proposed algorithm is applied to the identification of two simulated systems.</p> <p> Conclusions of this work and suggestions for future work are given.</p> / Thesis / Master of Engineering (MEngr)

<p> A review of Stochastic Approximation and the major contributions to the area is made. A proof of convergence for the algorithm is developed. An optimization is attempted on the rate of convergence problem and the uniqueness problem is faced. An alternative proof of convergence is given as an independent check on the first one. Simulation results are present in light of the theory developed, and conclusions, limitations and recommendations are presented. </p> / Thesis / Master of Engineering (MEngr)

<p> This study is concerned with the multivariable stochastic regulatory control of a pilot plant fixed bed reactor which is interfaced to a minicomputer. The reactor is non-adiabatic with a highly exothermic, gaseous catalytic reaction, involving several independent species. A low order state space model for the reactor is developed starting from the partial differential equations describing the system. A parameter estimation method is developed to fit the model to experimental data. Noise disturbances present in the system are identified using two methods, and two alternative dynamic-stochastic state space models are obtained. Multivariable stochastic feedback control algorithms are derived from these models and are implemented on the reactor in a series of DDC control studies. The control algorithms are compared with each other and with a single loop controller. The best of the multivariable control algorithms is used to regulate the exit concentrations of the various species from the reactor and the results are compared to data.</p> / Thesis / Doctor of Philosophy (PhD)