In this study, transmissivity and storage coefficient of a semi-infinite, confined, homogeneous and isotropic aquifer, where the flow is one-dimensional and linear, are determined using Marquardt algorithm, considering two independent cases: constant drawdown in the adjacent stream / or constant discharge from the aquifer due to pumping at a constant rate. In the first case piezometric head and discharge measurements are utilized. Hydraulic diffusivity, which is the ratio of transmissivity to storage coefficient, is determined from piezometric head measurements / whereas their product is determined from discharge measurements. Then, the two parameters are calculated easily. In the second case piezometric head observations are utilized only and transmissivity and storage coefficient are determined simultaneously. Convergence to true values is very fast for both cases even for poor initial estimates. Three examples, two using synthetic data for both cases and one using actual field data for the second case, are presented. Conventional type-curve matching method is used for comparison of the results. It is observed that the results of Marquardt algorithm are in a reasonable agreement with those of type-curve matching method.

The emperical pseudopotential method in the large basis approach was used to calculate the electronic bandstructures of bulk semiconductor materials and layered semiconductor heterostructures. The crucial continuous atomic form factor potentials needed to carry out such calculations were determined by using Levenberg-Marquardt optimization in order to obtain optimal cubic spline interpolations of the potentials. The optimized potentials were not constrained by any particular functional form (such as a linear combination of Gaussians) and had better convergence properties for the optimization. It was demonstrated that the results obtained in this work could potentially lead to better agreement between calculated and empirically determined band gaps via optimization / Physics / M. Sc. (Physics)

Master of Science / Department of Civil Engineering / David R. Steward / Accurate modeling of the High Plains Aquifer depends on the availability of good data that represents and quantities properties and processes occurring within the aquifer. Thanks to many previous studies there is a wealth of good data available for the High Plains Aquifer but one key component, groundwater-surface water interaction locations and rates, is generally missing. Without these values accurate modeling of the High Plains Aquifer is very difficult to achieve. This thesis presents methods for simplifying the modeling of the High Plains Aquifer using a sloping base method and then applying mathematical optimization techniques to locate and quantify points of groundwater-surface water interaction. The High Plains Aquifer has a base that slopes gently from west to east and is approximated using a one-dimensional stepping base model. The model was run under steady-state predevelopment conditions using readily available GIS data representing aquifer properties such as hydraulic conductivity, bedrock elevation, recharge, and the predevelopment water level. The Levenberg-Marquardt and particle swarm algorithms were implemented to minimize error in the model. The algorithms reduced model error by finding locations in the aquifer of potential groundwater-surface water interaction and then determining the rate of groundwater to surface water exchange at those points that allowed for the best match between the measured predevelopment water level and the simulated water level. Results from the model indicate that groundwater-surface water interaction plays an important role in the overall water balance in the High Plains Aquifer. Findings from the model show strong groundwater-surface water interaction occurring in the northern basin of the aquifer where the water table is relatively shallow and there are many surface water features. In the central and southern basins the interaction is primarily limited to river valleys. Most rivers have baseflow that is a net sink from groundwater.

Thesis (doctoral)--Leopold-Franzens Universität, Innsbruck, 2003.

This thesis examines how to find the best fit to a series of data points when curve fitting using power-exponential models. We describe the different numerical methods such as the Gauss-Newton and Levenberg-Marquardt methods to compare them for solving non-linear least squares of curve fitting using different power-exponential functions. In addition, we show the results of numerical experiments that illustrate the effectiveness of this approach.Furthermore, we show its application to the practical problems by using different sets of data such as death rates and rocket-triggered lightning return strokes based on the transmission line model.

<p>The study of Surface Air Cooled Oil Coolers (SACOC) is motivated by the need for new cooling concepts for compact machinery designs with high thermal load. Installing finned heat exchangers in the bypass duct of a turbofan engine provides an additional cooling source having transonic flow as a heat sink. The characterization of the heat transfer and the aerodynamics of the design are essential to minimize the impact on the overall efficiency of the engine. In the present study, the SACOC is studied numerically and experimentally. Two geometries are tested in a high-speed linear wind tunnel where measurements are taken with multiple sensors and optical techniques. For the heat transfer characterization, an Inverse Heat Conduction Methodology (IHCM) based on a Levenberg-Marquardt Algorithm is developed. The experimental results are matched to numerical simulations using a Reynolds Averaged Navier-Stokes (RANS) solver. Finally, a multi-objective optimization algorithm is coupled <a>with the RANS solver</a> to explore new geometries that maximize the heat transfer and minimize the pressure drop across the studied domain. The 400 profiles generated allow for the identification of the features that have a higher influence on the performance of the fins and six profiles that present large improvements are chosen for further analysis.</p>

A number of non-invasive fault detection and diagnosis (FDD) techniques have been researched and have proven to have worked well in classifying faults in internal combustion engines (ICE) and other mechanical and electrical systems. These techniques are an integral step to creating more robust and accurate methods of determining where or how a fault has or will occur in such systems. These FDD techniques have the potential to not only save time avoiding a tear-down of a costly machine, but could potentially add another layer of safety in detecting and diagnosing a fault much earlier than was possible before. Looking at the previous research methods and the systems they used to acquire this data, it is a natural progression to try and make a system which is able to encapsulate all of these ideologies into one inexpensive module capable of integrating itself into the advanced set of FDD. This thesis follows along with the development of a new wireless sensor that is developed specifically for the use in FDD for ICE and other mechanical systems. A new set of software and firmware is created for the system to be able to be incorporated into previously designed algorithms. After creating and manufacturing the sensor it is put to the test by incorporating it into several Artificial Neural Networks (ANN) and comparing the results to previous experiments done with previous research equipment. Using vibration data acquired from a running engine to train a neural network, the wireless sensor was able to perform equally as well as its expensive counter parts. It proved to have the ability to achieve 100% accuracy in classifying specific engine faults. The performance of three ANN training algorithms, Levenberg-Marquardt (LM), extended Kalman Filter (EKF), and Smooth Variable Structure filter (SVSF), were tested and compared. Adding to the feasibility of a standalone system the wireless sensor was tested in a live environment as a method of instant ICE fault detection. / Thesis / Master of Applied Science (MASc)

Zur Simulation technischer Prozesse ist eine hinreichend genaue Beschreibung des Materialverhaltens notwendig. Die hierfür häufig verwendeten phänomenologischen Ansätze, wie im vorliegenden Fall die HILLsche Fließbedingung, enthalten materialspezifische Parameter, welche nicht direkt messbar sind. Die Identifikation dieser Materialparameter erfolgt in der Regel durch Minimierung eines Fehlerquadratfunktionals, welches Differenzen von Messwerten und zugehörigen numerisch berechneten Vergleichswerten enthält. In diesem Zusammenhang haben sich zur Lösung dieser Minimierungsaufgabe die Trust-Region Verfahren als gut geeignet herausgestellt. Die Aufgabe besteht darin, die verschiedenen Möglichkeiten zur Steuerung eines Trust-Region Verfahrens, im Hinblick auf die Eignung für das vorliegende Identifikationsproblem, zu untersuchen. Dazu werden die Quadratmittelprobleme und deren Lösungsverfahren überblicksmäßig betrachtet. Danach wird näher auf die Trust-Region Verfahren eingegangen, wobei sich im Weiteren auf Verfahren mit positiv definiten Ansätzen für die Hesse-Matrix, den Levenberg-Marquardt Verfahren, beschränkt wird. Danach wird ein solcher Levenberg-Marquardt Algorithmus in verschiedenen Ausführungen implementiert und an dem vorliegenden Identifikationsproblem getestet. Als Ergebnis stellt sich eine gute Kombination aus verschiedenen Teilalgorithmen des Levenberg-Marquardt Algorithmus mit einer hohen Konvergenzgeschwindigkeit heraus, welche für das vorliegende Problem gut geeignet ist.

In this thesis we consider constrained systems of equations. The focus is on local Newton-type methods for the solution of constrained systems which converge locally quadratically under mild assumptions implying neither local uniqueness of solutions nor differentiability of the equation function at solutions. The first aim of this thesis is to improve existing local convergence results of the constrained Levenberg-Marquardt method. To this end, we describe a general Newton-type algorithm. Then we prove local quadratic convergence of this general algorithm under the same four assumptions which were recently used for the local convergence analysis of the LP-Newton method. Afterwards, we show that, besides the LP-Newton method, the constrained Levenberg-Marquardt method can be regarded as a special realization of the general Newton-type algorithm and therefore enjoys the same local convergence properties. Thus, local quadratic convergence of a nonsmooth constrained Levenberg-Marquardt method is proved without requiring conditions implying the local uniqueness of solutions. As already mentioned, we use four assumptions for the local convergence analysis of the general Newton-type algorithm. The second aim of this thesis is a detailed discussion of these convergence assumptions for the case that the equation function of the constrained system is piecewise continuously differentiable. Some of the convergence assumptions seem quite technical and difficult to check. Therefore, we look for sufficient conditions which are still mild but which seem to be more familiar. We will particularly prove that the whole set of the convergence assumptions holds if some set of local error bound conditions is satisfied and in addition the feasible set of the constrained system excludes those zeros of the selection functions which are not zeros of the equation function itself, at least in a sufficiently small neighborhood of some fixed solution. We apply our results to constrained systems arising from complementarity systems, i.e., systems of equations and inequalities which contain complementarity constraints. Our new conditions are discussed for a suitable reformulation of the complementarity system as constrained system of equations by means of the minimum function. In particular, it will turn out that the whole set of the convergence assumptions is actually implied by some set of local error bound conditions. In addition, we provide a new constant rank condition implying the whole set of the convergence assumptions. Particularly, we provide adapted formulations of our new conditions for special classes of complementarity systems. We consider Karush-Kuhn-Tucker (KKT) systems arising from optimization problems, variational inequalities, or generalized Nash equilibrium problems (GNEPs) and Fritz-John (FJ) systems arising from GNEPs. Thus, we obtain for each problem class conditions which guarantee local quadratic convergence of the general Newton-type algorithm and its special realizations to a solution of the particular problem. Moreover, we prove for FJ systems of GNEPs that generically some full row rank condition is satisfied at any solution of the FJ system of a GNEP. The latter condition implies the whole set of the convergence assumptions if the functions which characterize the GNEP are sufficiently smooth. Finally, we describe an idea for a possible globalization of our Newton-type methods, at least for the case that the constrained system arises from a certain smooth reformulation of the KKT system of a GNEP. More precisely, a hybrid method is presented whose local part is the LP-Newton method. The hybrid method turns out to be, under appropriate conditions, both globally and locally quadratically convergent.

Master’s thesis describes adaptive optimal controller design which change parameters of algorithm based on the system information regard for optimal criterion. Generally, the optimal controller solves the problem of minimum states vector. Problems of desired value and steady-state error are solved by variation in optimization algorithm.