Student Number : 9807515F - MSc Dissertation - School of Computational and Applied Mathematics - Faculty of Science / Statistical and algebraic techniques of subspace tracking were tested for filtering the earth’s response from airborne magnetic field gradients in order to discriminate the relatively small response (dipole) of objects on the earth’s surface, such as UXO. Filtering the data was not very effective with these methods but a subspace was found in the data for the magnitude of the magnetic moment of the dipole. This subspace is easily obtained using the singular value decomposition and can be used for an approximate location, without depth estimation, as well as the relative size of the dipole.

<p>Inom processindustrin finns en etablerad reglerhierarki där basreglering sker med PID-regulatorer och där avancerad, multivariabel styrning sköts av MPC-programvara. Steget mellan dessa två nivåer kan upplevas som stort. För mindre och snabba multivariabla processer undvikes helst en multivariabel ansats, med försämrad reglering som följd. På Preem AB har detta upplevts som ett problem. Syftet med examensarbetet har varit att utveckla en alternativ, multivariabel styrstrategi för en process med ett mindre antal reglerstorheter som interagerar. Detta har gjorts genom en utveckling av en LQG-regulator i styrsystemet DeltaV.</p><p>För att implementera en regulator i ett styrsystem måste hänsyn tas till en rad faktorer, såsom hantering av olika körlägen, bortfall av signaler, integratoruppvridning, kommunikation med slavregulatorer och inte minst operatörernas gränssnitt för hantering av regulatorn. Att sedan utveckla en regulator för en process kräver bland annat stegförsök, analys och anpassning av stegtestdata, modellidentifiering, framtagning av trimningskonstanter, testning av styrstrategi i simulerad miljö och idrifttagning. Den typen av frågeställningar addresseras i rapporten.</p><p>Examensarbetet visar att det finns en plats för LQG-regulatorn i processindustrin för en viss typ av problem. Den utvecklade regulatorn har implementerats på en avsvavlingsprocess på Preems oljeraffenaderi i Lysekil med lyckat resultat. Oscillationer i processen, som tidvis påverkat produktionen av propen, har kunnat reduceras.</p> / <p>Process control in process industry is done in a hierarchy in which PID controllers are used for basic control and MPC software is used for advanced, multivariable process control. The implementation of multivariable control using MPC software is a major undertaking and development of such controllers for small and fast multivariable processes is therefore avoided. To achieve better control for such processes, a simpler approach to multivariable control is often sought. The purpose of this masters thesis is to develop an alternative, multivariable control strategy for processes with a smaller number of interacting control variables. This is achieved by developing an LQG-controller in the DCS DeltaV at Preem AB.</p><p>Implementation of such a controller in a DCS requires that consideration is given to a number of factors, including handling of different modes, loss of signals, reset windup, communication with slave controllers and construction of operator interface. To develop a controller for a specific process also requires step testing, model identification, tuning of the controller parameters, simulation of the control strategy and commissioning. Solutions to such issues are addressed in this report.</p><p>The thesis shows that  LQG-controllers can be useful in process industry for some niche applications. The LQG-controller has successfully been applied to a desulphurisation process at Preem's oil refinery in Lysekil, where oscillations affecting the production of propylene have been reduced.</p>

In system identification, the choice of model structure is important and it is sometimes desirable to use a flexible model structure that is able to approximate a wide range of systems. One such model structure is the Wiener class of systems, that is, systems where the input enters a linear time-invariant subsystem followed by a time-invariant nonlinearity. Given a sequence of input and output pairs, the system identification problem is often formulated as the minimization of the mean-square prediction error. Here, the prediction error has a nonlinear dependence on the parameters of the linear subsystem and the nonlinearity. Unfortunately, this formulation of the estimation problem is often nonconvex, with several local minima, and it is therefore difficult to guarantee that a local search algorithm will be able to find the global optimum. In the first part of this thesis, we consider the application of dimension reduction methods to the problem of estimating the impulse response of the linear part of a system in the Wiener class. For example, by applying the inverse regression approach to dimension reduction, the impulse response estimation problem can be cast as a principal components problem, where the reformulation is based on simple nonparametric estimates of certain conditional moments. The inverse regression approach can be shown to be consistent under restrictions on the distribution of the input signal provided that the true linear subsystem has a finite impulse response. Furthermore, a forward approach to dimension reduction is also considered, where the time-invariant nonlinearity is approximated by a local linear model. In this setting, the impulse response estimation problem can be posed as a rank-reduced linear least-squares problem and a convex relaxation can be derived. Thereafter, we consider the extension of the subspace identification approach to include linear time-invariant rational models. It turns out that only minor structural modifications are needed and already available implementations can be used. Furthermore, other a priori information regarding the structure of the system can incorporated, including a certain class of linear gray-box structures. The proposed extension is not restricted to the discrete-time case and can be used to estimate continuous-time models. The final topic in this thesis is the estimation of discrete-time models containing polynomial nonlinearities. In the continuous-time case, a constructive algorithm based on differential algebra has previously been used to prove that such model structures are globally identifiable if and only if they can be written as a linear regression model. Thus, if we are able to transform the nonlinear model structure into a linear regression model, the parameter estimation problem can be solved with standard methods. Motivated by the above and the fact that most system identification problems involve sampled data, a discrete-time version of the algorithm is developed. This algorithm is closely related to the continuous-time version and enables the handling of noise signals without differentiations.

Inom processindustrin finns en etablerad reglerhierarki där basreglering sker med PID-regulatorer och där avancerad, multivariabel styrning sköts av MPC-programvara. Steget mellan dessa två nivåer kan upplevas som stort. För mindre och snabba multivariabla processer undvikes helst en multivariabel ansats, med försämrad reglering som följd. På Preem AB har detta upplevts som ett problem. Syftet med examensarbetet har varit att utveckla en alternativ, multivariabel styrstrategi för en process med ett mindre antal reglerstorheter som interagerar. Detta har gjorts genom en utveckling av en LQG-regulator i styrsystemet DeltaV. För att implementera en regulator i ett styrsystem måste hänsyn tas till en rad faktorer, såsom hantering av olika körlägen, bortfall av signaler, integratoruppvridning, kommunikation med slavregulatorer och inte minst operatörernas gränssnitt för hantering av regulatorn. Att sedan utveckla en regulator för en process kräver bland annat stegförsök, analys och anpassning av stegtestdata, modellidentifiering, framtagning av trimningskonstanter, testning av styrstrategi i simulerad miljö och idrifttagning. Den typen av frågeställningar addresseras i rapporten. Examensarbetet visar att det finns en plats för LQG-regulatorn i processindustrin för en viss typ av problem. Den utvecklade regulatorn har implementerats på en avsvavlingsprocess på Preems oljeraffenaderi i Lysekil med lyckat resultat. Oscillationer i processen, som tidvis påverkat produktionen av propen, har kunnat reduceras. / Process control in process industry is done in a hierarchy in which PID controllers are used for basic control and MPC software is used for advanced, multivariable process control. The implementation of multivariable control using MPC software is a major undertaking and development of such controllers for small and fast multivariable processes is therefore avoided. To achieve better control for such processes, a simpler approach to multivariable control is often sought. The purpose of this masters thesis is to develop an alternative, multivariable control strategy for processes with a smaller number of interacting control variables. This is achieved by developing an LQG-controller in the DCS DeltaV at Preem AB. Implementation of such a controller in a DCS requires that consideration is given to a number of factors, including handling of different modes, loss of signals, reset windup, communication with slave controllers and construction of operator interface. To develop a controller for a specific process also requires step testing, model identification, tuning of the controller parameters, simulation of the control strategy and commissioning. Solutions to such issues are addressed in this report. The thesis shows that  LQG-controllers can be useful in process industry for some niche applications. The LQG-controller has successfully been applied to a desulphurisation process at Preem's oil refinery in Lysekil, where oscillations affecting the production of propylene have been reduced.

There are a lot of difficulties that have to be overcome in the speaker-independent (S.I.) phrase recognition system . And the feasibility of accurate ,real-time and robust system pose of the greatest challenges in the system. In this thesis ,the speaker-independent phase recognition system is based on Hidden Markov Model (HMM). HMM has been proved to be of great value in many applications, notably in speech recognition. HMM is a stochastic approach which characterizes many of the variability in speech signal. It applys the state-of-the-art approach to Automatic Speech Recognition .

DNA Microarrays are one of the latest breakthroughs in experimental molecular biology and have opened the possibility of creating datasets of molecular information to represent many systems of biological or clinical interest. Clustering techniques have been proven to be helpful to understand gene function, gene regulation, cellular processes, and subtypes of cells. Investigations show that more often than not, several genes contribute to a disease, which motivates researchers to identify a subset of genes whose expression levels are similar under a subset of conditions. Most of the subspace clustering models define similarity among different objects by distances over either all or only a subset of the dimensions. However, strong correlations may still exist among a set of objects, even if they are far apart from each other as measured by the distance functions. Many techniques, such as pCluster and zCluster, have been proposed to find subspace clusters with the coherence expression of a subset of genes on a subset of conditions. However, both of them contain the time-consuming steps, which are constructing gene-pair MDSs and distributing the gene information in each node of a prefix tree. Therefore, in this thesis, we propose a Large Itemset-Based Clustering (LISC) algorithm to improve the disadvantages of the pCluster and zCluster algorithms. First, we avoid to construct the gene-pair MDSs. We only construct the condition-pair MDSs to reduce the processing time. Second, we transform the task of mining the possible maximal gene sets into the mining problem of the large itemsets from the condition-pair MDSs. We make use of the concept of the large itemset which is used in mining association rules, where a large itemset is represented as a set of items appearing in a sufficient number of transactions. Since we are only interested in the subspace cluster with gene sets as large as possible, it is desirable to pay attention to those gene sets which have reasonably large support from the condition-pair MDSs. In other words, we want to find the large itemsets from the condition-pair MDSs; therefore, we obtain the gene set with respect to enough condition-pairs. In this step, we efficiently use the revised version of FP-tree structure, which has been shown to be one of the most efficient data structures for mining large itemsets, to find the large itemsets of gene sets from the condition-pair MDSs. Thus, we can avoid the complex distributing operation and reduce the search space dramatically by using the FP-tree structure. Finally, we develop an algorithm to construct the final clusters from the gene set and the condition--pair after searching the FP-tree. Since we are interested in the clusters which are large enough and not belong to any other clusters, we alternately combine or extend the gene sets and the condition sets to construct the interesting subspace clusters as large as possible. From our simulation results, we show that our proposed algorithm needs shorter processing time than those previous proposed algorithms, since they need to construct gene-pair MDSs.

In this paper, the property of Curvelet transforms for preconditioning the migration and normal operators is investigated. These operators belong to the class of Fourier integral operators and pseudo-differential operators, respectively. The effect of this preconditioner is shown in term of improvement of sparsity, convergence rate, number of iteration for the Krylov-subspace solver and clustering of singular(eigen) values. The migration operator, which we employed in this work is the common-offset Kirchoff-Born migration.

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The structure and geometry of subspaces of a given Banach space is among the most fundamental questions in Functional Analysis. In 1961, Kadec and Pelczyński pioneered a field of study by analyzing the structures of subspaces and basic sequences in L_p[0,1] under a naturally occurring restriction of p, 2 < p <\infty. They proved that any infinite-dimensional subspace X\subset L_p[0,1] for 2<p<\infty must either be isomorphic to l_2 and complemented in L_p or must contain a complemented subspace which is isomorphic to l_p. Many works since have studied the relationships between the sides of this dichotomy, chiefly by weakening hypotheses on side of the equation to gain stronger assumptions on the other. In this way, Johnson and Odell were able to show in 1974 that if X contains no further subspace which is isomorphic to l_2, then it must embed into l_p. Kalton and Werner further strengthened this result in 1993 by showing that such an embedding must be almost isometric. We start by analyzing the tools and definitions originally introduced in 1961 and define a natural extension to these methods. By analyzing this extension, we provide a constructive and streamlined reproving of Kalton and Werner's theorem: Let X be an infinite dimensional subspace of L_p[0,1] for 2<p<\infty. Then, either X contains a subspace which is isomorphic to l_2, or for every \varepsilon>\ 0, X embeds into l_p with constant 1 + \varepsilon.