Simulated-annealing-based conditional simulation for the local-scale characterization of heterogeneous aquifers

Simulated-annealing-based conditional simulations provide a flexible means of quantitatively integrating diverse types of subsurface data. Although such techniques are being increasingly used in hydrocarbon reservoir characterization studies, their potential in environmental, engineering and hydrological investigations is still largely unexploited. Here, we introduce a novel simulated annealing (SA) algorithm geared towards the integration of high-resolution geophysical and hydrological data which, compared to more conventional approaches, provides significant advancements in the way that large-scale structural information in the geophysical data is accounted for. Model perturbations in the annealing procedure are made by drawing from a probability distribution for the target parameter conditioned to the geophysical data. This is the only place where geophysical information is utilized in our algorithm, which is in marked contrast to other approaches where model perturbations are made through the swapping of values in the simulation grid and agreement with soft data is enforced through a correlation coefficient constraint. Another major feature of our algorithm is the way in which available geostatistical information is utilized. Instead of constraining realizations to match a parametric target covariance model over a wide range of spatial lags, we constrain the realizations only at smaller lags where the available geophysical data cannot provide enough information. Thus we allow the larger-scale subsurface features resolved by the geophysical data to have much more due control on the output realizations. Further, since the only component of the SA objective function required in our approach is a covariance constraint at small lags, our method has improved convergence and computational efficiency over more traditional methods. Here, we present the results of applying our algorithm to the integration of porosity log and tomographic crosshole georadar data to generate stochastic realizations of the local-scale porosity structure. Our procedure is first tested on a synthetic data set, and then applied to data collected at the Boise Hydrogeophysical Research Site.

Populaation monimuotoisuuden mittaaminen liukulukukoodatuissa evoluutioalgoritmeissa

Diplomityössä esitetään menetelmä populaation monimuotoisuuden mittaamiseen liukulukukoodatuissa evoluutioalgoritmeissa, ja tarkastellaan kokeellisesti sen toimintaa. Evoluutioalgoritmit ovat populaatiopohjaisia menetelmiä, joilla pyritään ratkaisemaan optimointiongelmia. Evoluutioalgoritmeissa populaation monimuotoisuuden hallinta on välttämätöntä, jotta suoritettu haku olisi riittävän luotettavaa ja toisaalta riittävän nopeaa. Monimuotoisuuden mittaaminen on erityisen tarpeellista tutkittaessa evoluutioalgoritmien dynaamista käyttäytymistä. Työssä tarkastellaan haku- ja tavoitefunktioavaruuden monimuotoisuuden mittaamista. Toistaiseksi ei ole ollut olemassa täysin tyydyttäviä monimuotoisuuden mittareita, ja työn tavoitteena on kehittää yleiskäyttöinen menetelmä liukulukukoodattujen evoluutioalgoritmien suhteellisen ja absoluuttisen monimuotoisuuden mittaamiseen hakuavaruudessa. Kehitettyjen mittareiden toimintaa ja käyttökelpoisuutta tarkastellaan kokeellisesti ratkaisemalla optimointiongelmia differentiaalievoluutioalgoritmilla. Toteutettujen mittareiden toiminta perustuu keskihajontojen laskemiseen populaatiosta. Keskihajonnoille suoritetaan skaalaus, joko alkupopulaation tai nykyisen populaation suhteen, riippuen lasketaanko absoluuttista vai suhteellista monimuotoisuutta. Kokeellisessa tarkastelussa havaittiin kehitetyt mittarit toimiviksi ja käyttökelpoisiksi. Tavoitefunktion venyttäminen koordinaattiakseleiden suunnassa ei vaikuta mittarin toimintaan. Myöskään tavoitefunktion kiertäminen koordinaatistossa ei vaikuta mittareiden tuloksiin. Esitetyn menetelmän aikakompleksisuus riippuu lineaarisesti populaation koosta, ja mittarin toiminta on siten nopeaa suuriakin populaatioita käytettäessä. Suhteellinen monimuotoisuus antaa vertailukelpoisia tuloksia riippumatta parametrien lukumäärästä tai populaation koosta.

Analyzing Carbon Trade Permits in Optimization Framework

The threats caused by global warming motivate different stake holders to deal with and control them. This Master's thesis focuses on analyzing carbon trade permits in optimization framework. The studied model determines optimal emission and uncertainty levels which minimize the total cost. Research questions are formulated and answered by using different optimization tools. The model is developed and calibrated by using available consistent data in the area of carbon emission technology and control. Data and some basic modeling assumptions were extracted from reports and existing literatures. The data collected from the countries in the Kyoto treaty are used to estimate the cost functions. Theory and methods of constrained optimization are briefly presented. A two-level optimization problem (individual and between the parties) is analyzed by using several optimization methods. The combined cost optimization between the parties leads into multivariate model and calls for advanced techniques. Lagrangian, Sequential Quadratic Programming and Differential Evolution (DE) algorithm are referred to. The role of inherent measurement uncertainty in the monitoring of emissions is discussed. We briefly investigate an approach where emission uncertainty would be described in stochastic framework. MATLAB software has been used to provide visualizations including the relationship between decision variables and objective function values. Interpretations in the context of carbon trading were briefly presented. Suggestions for future work are given in stochastic modeling, emission trading and coupled analysis of energy prices and carbon permits.

Economic optimization method to design telescope irrigation of multiples outlets

In this study is presented an economic optimization method to design telescope irrigation laterals (multidiameter) with regular spaced outlets. The proposed analytical hydraulic solution was validated by means of a pipeline composed of three different diameters. The minimum acquisition cost of the telescope pipeline was determined by an ideal arrangement of lengths and respective diameters for each one of the three segments. The mathematical optimization method based on the Lagrange multipliers provides a strategy for finding the maximum or minimum of a function subject to certain constraints. In this case, the objective function describes the acquisition cost of pipes, and the constraints are determined from hydraulic parameters as length of irrigation laterals and total head loss permitted. The developed analytical solution provides the ideal combination of each pipe segment length and respective diameter, resulting in a decreased of the acquisition cost.

Contact with friction using the augmented Lagrangian Method: a conditional constrained minimization problem

This work presents a formulation of the contact with friction between elastic bodies. This is a non linear problem due to unilateral constraints (inter-penetration of bodies) and friction. The solution of this problem can be found using optimization concepts, modelling the problem as a constrained minimization problem. The Finite Element Method is used to construct approximation spaces. The minimization problem has the total potential energy of the elastic bodies as the objective function, the non-inter-penetration conditions are represented by inequality constraints, and equality constraints are used to deal with the friction. Due to the presence of two friction conditions (stick and slip), specific equality constraints are present or not according to the current condition. Since the Coulomb friction condition depends on the normal and tangential contact stresses related to the constraints of the problem, it is devised a conditional dependent constrained minimization problem. An Augmented Lagrangian Method for constrained minimization is employed to solve this problem. This method, when applied to a contact problem, presents Lagrange Multipliers which have the physical meaning of contact forces. This fact allows to check the friction condition at each iteration. These concepts make possible to devise a computational scheme which lead to good numerical results.

The Progressivity of Equalization Payments in Federations

We investigate the conditions under which an inequality averse and additively separable welfarist constitution maker would always choose to set up a progressive equalization payments scheme in a federation with local public goods. A progressive equalization payments scheme is defined as a list of per capita net (possibly negative) subsidies - one such net subsidy for every jurisdiction - that are decreasing with respect to jurisdictions per capita wealth. We examine these questions in a setting in which the case for progressivity is a priori the strongest, namely, all citizens have the same utility function for the private and the public goods, inhabitants of a given jurisdiction are all identical, and they are not able to move across jurisdictions. We show that the constitution maker favors a progressive equalization payments scheme for all distributions of wealth and all population sizes if and only if its objective function is additively separable between each jurisdiction’s per capita wealth and number of inhabitants. When interpreted as a mean of order r social welfare function, this condition is shown to be equivalent to additive separability of the individual’s indirect utility function with respect to wealth and the price of the public good. Some implications of this restriction to the case where the individual’s direct utility function is additively separable are also derived.

Design, implementation and application of a generic framework for integrated regional land-use modeling

Land use is a crucial link between human activities and the natural environment and one of the main driving forces of global environmental change. Large parts of the terrestrial land surface are used for agriculture, forestry, settlements and infrastructure. Given the importance of land use, it is essential to understand the multitude of influential factors and resulting land use patterns. An essential methodology to study and quantify such interactions is provided by the adoption of land-use models. By the application of land-use models, it is possible to analyze the complex structure of linkages and feedbacks and to also determine the relevance of driving forces. Modeling land use and land use changes has a long-term tradition. In particular on the regional scale, a variety of models for different regions and research questions has been created. Modeling capabilities grow with steady advances in computer technology, which on the one hand are driven by increasing computing power on the other hand by new methods in software development, e.g. object- and component-oriented architectures. In this thesis, SITE (Simulation of Terrestrial Environments), a novel framework for integrated regional sland-use modeling, will be introduced and discussed. Particular features of SITE are the notably extended capability to integrate models and the strict separation of application and implementation. These features enable efficient development, test and usage of integrated land-use models. On its system side, SITE provides generic data structures (grid, grid cells, attributes etc.) and takes over the responsibility for their administration. By means of a scripting language (Python) that has been extended by language features specific for land-use modeling, these data structures can be utilized and manipulated by modeling applications. The scripting language interpreter is embedded in SITE. The integration of sub models can be achieved via the scripting language or by usage of a generic interface provided by SITE. Furthermore, functionalities important for land-use modeling like model calibration, model tests and analysis support of simulation results have been integrated into the generic framework. During the implementation of SITE, specific emphasis was laid on expandability, maintainability and usability. Along with the modeling framework a land use model for the analysis of the stability of tropical rainforest margins was developed in the context of the collaborative research project STORMA (SFB 552). In a research area in Central Sulawesi, Indonesia, socio-environmental impacts of land-use changes were examined. SITE was used to simulate land-use dynamics in the historical period of 1981 to 2002. Analogous to that, a scenario that did not consider migration in the population dynamics, was analyzed. For the calculation of crop yields and trace gas emissions, the DAYCENT agro-ecosystem model was integrated. In this case study, it could be shown that land-use changes in the Indonesian research area could mainly be characterized by the expansion of agricultural areas at the expense of natural forest. For this reason, the situation had to be interpreted as unsustainable even though increased agricultural use implied economic improvements and higher farmers' incomes. Due to the importance of model calibration, it was explicitly addressed in the SITE architecture through the introduction of a specific component. The calibration functionality can be used by all SITE applications and enables largely automated model calibration. Calibration in SITE is understood as a process that finds an optimal or at least adequate solution for a set of arbitrarily selectable model parameters with respect to an objective function. In SITE, an objective function typically is a map comparison algorithm capable of comparing a simulation result to a reference map. Several map optimization and map comparison methodologies are available and can be combined. The STORMA land-use model was calibrated using a genetic algorithm for optimization and the figure of merit map comparison measure as objective function. The time period for the calibration ranged from 1981 to 2002. For this period, respective reference land-use maps were compiled. It could be shown, that an efficient automated model calibration with SITE is possible. Nevertheless, the selection of the calibration parameters required detailed knowledge about the underlying land-use model and cannot be automated. In another case study decreases in crop yields and resulting losses in income from coffee cultivation were analyzed and quantified under the assumption of four different deforestation scenarios. For this task, an empirical model, describing the dependence of bee pollination and resulting coffee fruit set from the distance to the closest natural forest, was integrated. Land-use simulations showed, that depending on the magnitude and location of ongoing forest conversion, pollination services are expected to decline continuously. This results in a reduction of coffee yields of up to 18% and a loss of net revenues per hectare of up to 14%. However, the study also showed that ecological and economic values can be preserved if patches of natural vegetation are conservated in the agricultural landscape. -----------------------------------------------------------------------

Triangulation by Continuous Embedding

When triangulating a belief network we aim to obtain a junction tree of minimum state space. Searching for the optimal triangulation can be cast as a search over all the permutations of the network's vaeriables. Our approach is to embed the discrete set of permutations in a convex continuous domain D. By suitably extending the cost function over D and solving the continous nonlinear optimization task we hope to obtain a good triangulation with respect to the aformentioned cost. In this paper we introduce an upper bound to the total junction tree weight as the cost function. The appropriatedness of this choice is discussed and explored by simulations. Then we present two ways of embedding the new objective function into continuous domains and show that they perform well compared to the best known heuristic.

Image-Based View Synthesis

We present a new method for rendering novel images of flexible 3D objects from a small number of example images in correspondence. The strength of the method is the ability to synthesize images whose viewing position is significantly far away from the viewing cone of the example images ("view extrapolation"), yet without ever modeling the 3D structure of the scene. The method relies on synthesizing a chain of "trilinear tensors" that governs the warping function from the example images to the novel image, together with a multi-dimensional interpolation function that synthesizes the non-rigid motions of the viewed object from the virtual camera position. We show that two closely spaced example images alone are sufficient in practice to synthesize a significant viewing cone, thus demonstrating the ability of representing an object by a relatively small number of model images --- for the purpose of cheap and fast viewers that can run on standard hardware.

Aplicació d'algoritmes genètics en l'optimització dels processos de fabricació del paper

La creciente preocupación y concienciación de la sociedad respecto el medio ambiente, y en consecuencia la legislación y regulaciones generadas inducen a la modificación de los procesos productivos existentes en la industria química. Las configuraciones iniciales deben modificarse para conseguir una mayor integración de procesos. Para este fin se han creado y desarrollado diferentes metodologías que deben facilitar la tarea a los responsables del rediseño. El desarrollo de una metodología y herramientas complementarias es el principal objetivo de la investigación aquí presentada, especialmente centrada en el desarrollo y la aplicación de una metodología de optimización de procesos. Esta metodología de optimización se aplica sobre configuraciones de proceso existentes y pretende encontrar nuevas configuraciones viables según los objetivos de optimización fijados. La metodología tiene dos partes diferenciadas: la primera se basa en un simulador de procesos comercial y la segunda es la técnica de optimización propiamente dicha. La metodología se inicia con la elaboración de una simulación convenientemente validada que reproduzca el proceso existente, en este caso una papelera no integrada que produce papel estucado de calidad, para impresión. A continuación la técnica de optimización realiza una búsqueda dentro del dominio de los posibles resultados, en busca de los mejores resultados que satisfazcan plenamente los objetivos planteados. Dicha técnica de optimización está basada en los algoritmos genéticos como herramienta de búsqueda, junto a un subprograma basado en técnicas de programación matemática para el cálculo de resultados. Un número reducido de resultados son finalmente escogidos y utilizados para modificar la simulación existente fijando la redistribución de los flujos del proceso. Los resultados de la simulación del proceso determinan en último caso la viabilidad técnica de cada reconfiguración planteada. En el proceso de optimización, los objetivos están definidos en una función objetivo dentro de la técnica de optimización. Dicha función rige la búsqueda de resultados. La función objetivo puede ser individual o una combinación de objetivos. En el presente caso, la función persigue una minimización del consumo de agua y una minimización de la pérdida de materia prima. La optimización se realiza bajo restricciones para alcanzar este objetivo combinado en forma de una solución de compromiso. Producto de la aplicación de esta metodología se han obtenido resultados interesantes que significan una mejora del cierre de circuitos y un ahorro de materia prima, sin comprometer al mismo tiempo la operabilidad del proceso producto ni la calidad del papel.

Approximate Gauss-Newton methods for nonlinear least squares problems

The Gauss–Newton algorithm is an iterative method regularly used for solving nonlinear least squares problems. It is particularly well suited to the treatment of very large scale variational data assimilation problems that arise in atmosphere and ocean forecasting. The procedure consists of a sequence of linear least squares approximations to the nonlinear problem, each of which is solved by an “inner” direct or iterative process. In comparison with Newton’s method and its variants, the algorithm is attractive because it does not require the evaluation of second-order derivatives in the Hessian of the objective function. In practice the exact Gauss–Newton method is too expensive to apply operationally in meteorological forecasting, and various approximations are made in order to reduce computational costs and to solve the problems in real time. Here we investigate the effects on the convergence of the Gauss–Newton method of two types of approximation used commonly in data assimilation. First, we examine “truncated” Gauss–Newton methods where the inner linear least squares problem is not solved exactly, and second, we examine “perturbed” Gauss–Newton methods where the true linearized inner problem is approximated by a simplified, or perturbed, linear least squares problem. We give conditions ensuring that the truncated and perturbed Gauss–Newton methods converge and also derive rates of convergence for the iterations. The results are illustrated by a simple numerical example. A practical application to the problem of data assimilation in a typical meteorological system is presented.

Optimal discrimination and classification of THz spectra in the wavelet domain

In rapid scan Fourier transform spectrometry, we show that the noise in the wavelet coefficients resulting from the filter bank decomposition of the complex insertion loss function is linearly related to the noise power in the sample interferogram by a noise amplification factor. By maximizing an objective function composed of the power of the wavelet coefficients divided by the noise amplification factor, optimal feature extraction in the wavelet domain is performed. The performance of a classifier based on the output of a filter bank is shown to be considerably better than that of an Euclidean distance classifier in the original spectral domain. An optimization procedure results in a further improvement of the wavelet classifier. The procedure is suitable for enhancing the contrast or classifying spectra acquired by either continuous wave or THz transient spectrometers as well as for increasing the dynamic range of THz imaging systems. (C) 2003 Optical Society of America.

A minimum approximate-BER beamforming approach for PSK modulated wireless systems

A beamforming algorithm is introduced based on the general objective function that approximates the bit error rate for the wireless systems with binary phase shift keying and quadrature phase shift keying modulation schemes. The proposed minimum approximate bit error rate (ABER) beamforming approach does not rely on the Gaussian assumption of the channel noise. Therefore, this approach is also applicable when the channel noise is non-Gaussian. The simulation results show that the proposed minimum ABER solution improves the standard minimum mean squares error beamforming solution, in terms of a smaller achievable system's bit error rate.

Application of the entropy technique and genetic algorithms to construction site layout planning of medium-size projects

Genetic algorithms (GAs) have been introduced into site layout planning as reported in a number of studies. In these studies, the objective functions were defined so as to employ the GAs in searching for the optimal site layout. However, few studies have been carried out to investigate the actual closeness of relationships between site facilities; it is these relationships that ultimately govern the site layout. This study has determined that the underlying factors of site layout planning for medium-size projects include work flow, personnel flow, safety and environment, and personal preferences. By finding the weightings on these factors and the corresponding closeness indices between each facility, a closeness relationship has been deduced. Two contemporary mathematical approaches - fuzzy logic theory and an entropy measure - were adopted in finding these results in order to minimize the uncertainty and vagueness of the collected data and improve the quality of the information. GAs were then applied to searching for the optimal site layout in a medium-size government project using the GeneHunter software. The objective function involved minimizing the total travel distance. An optimal layout was obtained within a short time. This reveals that the application of GA to site layout planning is highly promising and efficient.

Conditioning and preconditioning of the variational data assimilation problem

Numerical weather prediction (NWP) centres use numerical models of the atmospheric flow to forecast future weather states from an estimate of the current state. Variational data assimilation (VAR) is used commonly to determine an optimal state estimate that miminizes the errors between observations of the dynamical system and model predictions of the flow. The rate of convergence of the VAR scheme and the sensitivity of the solution to errors in the data are dependent on the condition number of the Hessian of the variational least-squares objective function. The traditional formulation of VAR is ill-conditioned and hence leads to slow convergence and an inaccurate solution. In practice, operational NWP centres precondition the system via a control variable transform to reduce the condition number of the Hessian. In this paper we investigate the conditioning of VAR for a single, periodic, spatially-distributed state variable. We present theoretical bounds on the condition number of the original and preconditioned Hessians and hence demonstrate the improvement produced by the preconditioning. We also investigate theoretically the effect of observation position and error variance on the preconditioned system and show that the problem becomes more ill-conditioned with increasingly dense and accurate observations. Finally, we confirm the theoretical results in an operational setting by giving experimental results from the Met Office variational system.