Verfahren zur echtzeitfähigen Simulation dynamischer Emissionsverläufe ausgewählter Schadstoffe von Ottomotoren

Im Rahmen dieser Arbeit werden Modellbildungsverfahren zur echtzeitfähigen Simulation wichtiger Schadstoffkomponenten im Abgasstrom von Verbrennungsmotoren vorgestellt. Es wird ein ganzheitlicher Entwicklungsablauf dargestellt, dessen einzelne Schritte, beginnend bei der Ver-suchsplanung über die Erstellung einer geeigneten Modellstruktur bis hin zur Modellvalidierung, detailliert beschrieben werden. Diese Methoden werden zur Nachbildung der dynamischen Emissi-onsverläufe relevanter Schadstoffe des Ottomotors angewendet. Die abgeleiteten Emissionsmodelle dienen zusammen mit einer Gesamtmotorsimulation zur Optimierung von Betriebstrategien in Hybridfahrzeugen. Im ersten Abschnitt der Arbeit wird eine systematische Vorgehensweise zur Planung und Erstellung von komplexen, dynamischen und echtzeitfähigen Modellstrukturen aufgezeigt. Es beginnt mit einer physikalisch motivierten Strukturierung, die eine geeignete Unterteilung eines Prozessmodells in einzelne überschaubare Elemente vorsieht. Diese Teilmodelle werden dann, jeweils ausgehend von einem möglichst einfachen nominalen Modellkern, schrittweise erweitert und ermöglichen zum Abschluss eine robuste Nachbildung auch komplexen, dynamischen Verhaltens bei hinreichender Genauigkeit. Da einige Teilmodelle als neuronale Netze realisiert werden, wurde eigens ein Verfah-ren zur sogenannten diskreten evidenten Interpolation (DEI) entwickelt, das beim Training einge-setzt, und bei minimaler Messdatenanzahl ein plausibles, also evidentes Verhalten experimenteller Modelle sicherstellen kann. Zum Abgleich der einzelnen Teilmodelle wurden statistische Versuchs-pläne erstellt, die sowohl mit klassischen DoE-Methoden als auch mittels einer iterativen Versuchs-planung (iDoE ) generiert wurden. Im zweiten Teil der Arbeit werden, nach Ermittlung der wichtigsten Einflussparameter, die Model-strukturen zur Nachbildung dynamischer Emissionsverläufe ausgewählter Abgaskomponenten vor-gestellt, wie unverbrannte Kohlenwasserstoffe (HC), Stickstoffmonoxid (NO) sowie Kohlenmono-xid (CO). Die vorgestellten Simulationsmodelle bilden die Schadstoffkonzentrationen eines Ver-brennungsmotors im Kaltstart sowie in der anschließenden Warmlaufphase in Echtzeit nach. Im Vergleich zur obligatorischen Nachbildung des stationären Verhaltens wird hier auch das dynami-sche Verhalten des Verbrennungsmotors in transienten Betriebsphasen ausreichend korrekt darge-stellt. Eine konsequente Anwendung der im ersten Teil der Arbeit vorgestellten Methodik erlaubt, trotz einer Vielzahl von Prozesseinflussgrößen, auch hier eine hohe Simulationsqualität und Ro-bustheit. Die Modelle der Schadstoffemissionen, eingebettet in das dynamische Gesamtmodell eines Ver-brennungsmotors, werden zur Ableitung einer optimalen Betriebsstrategie im Hybridfahrzeug ein-gesetzt. Zur Lösung solcher Optimierungsaufgaben bieten sich modellbasierte Verfahren in beson-derer Weise an, wobei insbesondere unter Verwendung dynamischer als auch kaltstartfähiger Mo-delle und der damit verbundenen Realitätsnähe eine hohe Ausgabequalität erreicht werden kann.

Modeling, Estimation, and Control of Robot-Soil Interactions

This thesis presents the development of hardware, theory, and experimental methods to enable a robotic manipulator arm to interact with soils and estimate soil properties from interaction forces. Unlike the majority of robotic systems interacting with soil, our objective is parameter estimation, not excavation. To this end, we design our manipulator with a flat plate for easy modeling of interactions. By using a flat plate, we take advantage of the wealth of research on the similar problem of earth pressure on retaining walls. There are a number of existing earth pressure models. These models typically provide estimates of force which are in uncertain relation to the true force. A recent technique, known as numerical limit analysis, provides upper and lower bounds on the true force. Predictions from the numerical limit analysis technique are shown to be in good agreement with other accepted models. Experimental methods for plate insertion, soil-tool interface friction estimation, and control of applied forces on the soil are presented. In addition, a novel graphical technique for inverting the soil models is developed, which is an improvement over standard nonlinear optimization. This graphical technique utilizes the uncertainties associated with each set of force measurements to obtain all possible parameters which could have produced the measured forces. The system is tested on three cohesionless soils, two in a loose state and one in a loose and dense state. The results are compared with friction angles obtained from direct shear tests. The results highlight a number of key points. Common assumptions are made in soil modeling. Most notably, the Mohr-Coulomb failure law and perfectly plastic behavior. In the direct shear tests, a marked dependence of friction angle on the normal stress at low stresses is found. This has ramifications for any study of friction done at low stresses. In addition, gradual failures are often observed for vertical tools and tools inclined away from the direction of motion. After accounting for the change in friction angle at low stresses, the results show good agreement with the direct shear values.

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.

Preconditioning and iterative solution of symmetric indefinite linear systems arising from interior point methods for linear programming

We study the preconditioning of symmetric indefinite linear systems of equations that arise in interior point solution of linear optimization problems. The preconditioning method that we study exploits the block structure of the augmented matrix to design a similar block structure preconditioner to improve the spectral properties of the resulting preconditioned matrix so as to improve the convergence rate of the iterative solution of the system. We also propose a two-phase algorithm that takes advantage of the spectral properties of the transformed matrix to solve for the Newton directions in the interior-point method. Numerical experiments have been performed on some LP test problems in the NETLIB suite to demonstrate the potential of the preconditioning method discussed.

Selection of funding schemes by a borrowing decision model: a Hong Kong case study

In financial decision-making, a number of mathematical models have been developed for financial management in construction. However, optimizing both qualitative and quantitative factors and the semi-structured nature of construction finance optimization problems are key challenges in solving construction finance decisions. The selection of funding schemes by a modified construction loan acquisition model is solved by an adaptive genetic algorithm (AGA) approach. The basic objectives of the model are to optimize the loan and to minimize the interest payments for all projects. Multiple projects being undertaken by a medium-size construction firm in Hong Kong were used as a real case study to demonstrate the application of the model to the borrowing decision problems. A compromise monthly borrowing schedule was finally achieved. The results indicate that Small and Medium Enterprise (SME) Loan Guarantee Scheme (SGS) was first identified as the source of external financing. Selection of sources of funding can then be made to avoid the possibility of financial problems in the firm by classifying qualitative factors into external, interactive and internal types and taking additional qualitative factors including sovereignty, credit ability and networking into consideration. Thus a more accurate, objective and reliable borrowing decision can be provided for the decision-maker to analyse the financial options.

Efficiency of evolutionary algorithms in water network pipe sizing

The pipe sizing of water networks via evolutionary algorithms is of great interest because it allows the selection of alternative economical solutions that meet a set of design requirements. However, available evolutionary methods are numerous, and methodologies to compare the performance of these methods beyond obtaining a minimal solution for a given problem are currently lacking. A methodology to compare algorithms based on an efficiency rate (E) is presented here and applied to the pipe-sizing problem of four medium-sized benchmark networks (Hanoi, New York Tunnel, GoYang and R-9 Joao Pessoa). E numerically determines the performance of a given algorithm while also considering the quality of the obtained solution and the required computational effort. From the wide range of available evolutionary algorithms, four algorithms were selected to implement the methodology: a PseudoGenetic Algorithm (PGA), Particle Swarm Optimization (PSO), a Harmony Search and a modified Shuffled Frog Leaping Algorithm (SFLA). After more than 500,000 simulations, a statistical analysis was performed based on the specific parameters each algorithm requires to operate, and finally, E was analyzed for each network and algorithm. The efficiency measure indicated that PGA is the most efficient algorithm for problems of greater complexity and that HS is the most efficient algorithm for less complex problems. However, the main contribution of this work is that the proposed efficiency ratio provides a neutral strategy to compare optimization algorithms and may be useful in the future to select the most appropriate algorithm for different types of optimization problems.

Reduced gradient method combined with augmented Lagrangian and barrier for the optimal power flow problem

A new approach for solving the optimal power flow (OPF) problem is established by combining the reduced gradient method and the augmented Lagrangian method with barriers and exploring specific characteristics of the relations between the variables of the OPF problem. Computer simulations on IEEE 14-bus and IEEE 30-bus test systems illustrate the method. (c) 2007 Elsevier Inc. All rights reserved.

A discontinuous-Galerkin-based immersed boundary method with non-homogeneous boundary conditions and its application to elasticity

We propose a discontinuous-Galerkin-based immersed boundary method for elasticity problems. The resulting numerical scheme does not require boundary fitting meshes and avoids boundary locking by switching the elements intersected by the boundary to a discontinuous Galerkin approximation. Special emphasis is placed on the construction of a method that retains an optimal convergence rate in the presence of non-homogeneous essential and natural boundary conditions. The role of each one of the approximations introduced is illustrated by analyzing an analog problem in one spatial dimension. Finally, extensive two- and three-dimensional numerical experiments on linear and nonlinear elasticity problems verify that the proposed method leads to optimal convergence rates under combinations of essential and natural boundary conditions. (C) 2009 Elsevier B.V. All rights reserved.

Flockning och förtjockning i High-Rate-förtjockare – en jämförelse med konventionell förtjockarteknik och lamellsedimentering.

In the process laboratory of Metso minerals (Sala) AB, continuous tests have been made with a laboratory unit High-Rate thickener. The tests are made in order to compare three methods of thickening techniques of suspended solids. The three techniques are High-Rate thickening, conventional thickening and lamella thickening. The High-Rate and the conventional trials are based on a continuous method, while the lamella thickener is based on batch trials. Because the lamella thickener is based on batch trials and there were some optimization problems with the adding point of the flocculant at the continuous trials, it was not feasible to compare the lamella thickener with the other two thickener types. On the other hand, since the optimization problems were the same for the other two methods there was no problem comparing them. The result of the comparison between the High-Rate thickener and the conventional thickener, was, that the High-Rate thickener manages to work at a higher rise rate with a lower consumption of flocculant than the conventional thickener. Seeing to the unit area that is needed by each thickener it is apparent that the conventional thickener demands a higher unit area than the High-Rate thickener to achieve the same amount of solids in the underflow. It has also been showed that the High-Rate thickener demands a lesser quantity of flocculant at the same amount of suspended solids in the feed than the conventional thickener.

Solving the Vehicle Routing Problem with Genetic ALgorithm and Simulated Annealing

This Thesis Work will concentrate on a very interesting problem, the Vehicle Routing Problem (VRP). In this problem, customers or cities have to be visited and packages have to be transported to each of them, starting from a basis point on the map. The goal is to solve the transportation problem, to be able to deliver the packages-on time for the customers,-enough package for each Customer,-using the available resources- and – of course - to be so effective as it is possible.Although this problem seems to be very easy to solve with a small number of cities or customers, it is not. In this problem the algorithm have to face with several constraints, for example opening hours, package delivery times, truck capacities, etc. This makes this problem a so called Multi Constraint Optimization Problem (MCOP). What’s more, this problem is intractable with current amount of computational power which is available for most of us. As the number of customers grow, the calculations to be done grows exponential fast, because all constraints have to be solved for each customers and it should not be forgotten that the goal is to find a solution, what is best enough, before the time for the calculation is up. This problem is introduced in the first chapter: form its basics, the Traveling Salesman Problem, using some theoretical and mathematical background it is shown, why is it so hard to optimize this problem, and although it is so hard, and there is no best algorithm known for huge number of customers, why is it a worth to deal with it. Just think about a huge transportation company with ten thousands of trucks, millions of customers: how much money could be saved if we would know the optimal path for all our packages.Although there is no best algorithm is known for this kind of optimization problems, we are trying to give an acceptable solution for it in the second and third chapter, where two algorithms are described: the Genetic Algorithm and the Simulated Annealing. Both of them are based on obtaining the processes of nature and material science. These algorithms will hardly ever be able to find the best solution for the problem, but they are able to give a very good solution in special cases within acceptable calculation time.In these chapters (2nd and 3rd) the Genetic Algorithm and Simulated Annealing is described in details, from their basis in the “real world” through their terminology and finally the basic implementation of them. The work will put a stress on the limits of these algorithms, their advantages and disadvantages, and also the comparison of them to each other.Finally, after all of these theories are shown, a simulation will be executed on an artificial environment of the VRP, with both Simulated Annealing and Genetic Algorithm. They will both solve the same problem in the same environment and are going to be compared to each other. The environment and the implementation are also described here, so as the test results obtained.Finally the possible improvements of these algorithms are discussed, and the work will try to answer the “big” question, “Which algorithm is better?”, if this question even exists.

A Genetic Algorithm for Solar Boat

Genetic algorithm has been widely used in different areas of optimization problems. Ithas been combined with renewable energy domain, photovoltaic system, in this thesis.To participate and win the solar boat race, a control program is needed and C++ hasbeen chosen for programming. To implement the program, the mathematic model hasbeen built. Besides, the approaches to calculate the boundaries related to conditionhave been explained. Afterward, the processing of the prediction and real time controlfunction are offered. The program has been simulated and the results proved thatgenetic algorithm is helpful to get the good results but it does not improve the resultstoo much since the particularity of the solar driven boat project such as the limitationof energy production

Confidence in heuristic solutions?

Solutions to combinatorial optimization problems frequently rely on heuristics to minimize an objective function. The optimum is sought iteratively and pre-setting the number of iterations dominates in operations research applications, which implies that the quality of the solution cannot be ascertained. Deterministic bounds offer a mean of ascertaining the quality, but such bounds are available for only a limited number of heuristics and the length of the interval may be difficult to control in an application. A small, almost dormant, branch of the literature suggests using statistical principles to derive statistical bounds for the optimum. We discuss alternative approaches to derive statistical bounds. We also assess their performance by testing them on 40 test p-median problems on facility location, taken from Beasley’s OR-library, for which the optimum is known. We consider three popular heuristics for solving such location problems; simulated annealing, vertex substitution, and Lagrangian relaxation where only the last offers deterministic bounds. Moreover, we illustrate statistical bounds in the location of 71 regional delivery points of the Swedish Post. We find statistical bounds reliable and much more efficient than deterministic bounds provided that the heuristic solutions are sampled close to the optimum. Statistical bounds are also found computationally affordable.

Joint dynamic probabilistic constraints with projected linear decision rules

We consider multistage stochastic linear optimization problems combining joint dynamic probabilistic constraints with hard constraints. We develop a method for projecting decision rules onto hard constraints of wait-and-see type. We establish the relation between the original (in nite dimensional) problem and approximating problems working with projections from di erent subclasses of decision policies. Considering the subclass of linear decision rules and a generalized linear model for the underlying stochastic process with noises that are Gaussian or truncated Gaussian, we show that the value and gradient of the objective and constraint functions of the approximating problems can be computed analytically.

Non-asymptotic confidence bounds for the optimal value of a stochastic program

We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds for the optimal value of the problem which are essentially better than the quality of the corresponding optimal solutions. At the same time, such bounds are more reliable than “standard” confidence bounds obtained through the asymptotic approach. We also discuss bounding the optimal value of MinMax Stochastic Optimization and stochastically constrained problems. We conclude with a small simulation study illustrating the numerical behavior of the proposed bounds.