Advanced chemometric methods: Applicability on industrial data

Recent years have produced great advances in the instrumentation technology. The amount of available data has been increasing due to the simplicity, speed and accuracy of current spectroscopic instruments. Most of these data are, however, meaningless without a proper analysis. This has been one of the reasons for the overgrowing success of multivariate handling of such data. Industrial data is commonly not designed data; in other words, there is no exact experimental design, but rather the data have been collected as a routine procedure during an industrial process. This makes certain demands on the multivariate modeling, as the selection of samples and variables can have an enormous effect. Common approaches in the modeling of industrial data are PCA (principal component analysis) and PLS (projection to latent structures or partial least squares) but there are also other methods that should be considered. The more advanced methods include multi block modeling and nonlinear modeling. In this thesis it is shown that the results of data analysis vary according to the modeling approach used, thus making the selection of the modeling approach dependent on the purpose of the model. If the model is intended to provide accurate predictions, the approach should be different than in the case where the purpose of modeling is mostly to obtain information about the variables and the process. For industrial applicability it is essential that the methods are robust and sufficiently simple to apply. In this way the methods and the results can be compared and an approach selected that is suitable for the intended purpose. Differences in data analysis methods are compared with data from different fields of industry in this thesis. In the first two papers, the multi block method is considered for data originating from the oil and fertilizer industries. The results are compared to those from PLS and priority PLS. The third paper considers applicability of multivariate models to process control for a reactive crystallization process. In the fourth paper, nonlinear modeling is examined with a data set from the oil industry. The response has a nonlinear relation to the descriptor matrix, and the results are compared between linear modeling, polynomial PLS and nonlinear modeling using nonlinear score vectors.

Development and validation of RP-LC and uv spectrophotometric methods to assay bromopride in oral and injectable solutions

A reversed-phase liquid chromatographic (LC) and ultraviolet (UV) spectrophotometric methods were developed and validated for the assay of bromopride in oral and injectable solutions. The methods were validated according to ICH guideline. Both methods were linear in the range between 5-25 μg mL-1 (y = 41837x - 5103.4, r = 0.9996 and y = 0.0284x - 0.0351, r = 1, respectively). The statistical analysis showed no significant difference between the results obtained by the two methods. The proposed methods were found to be simple, rapid, precise, accurate, and sensitive. The LC and UV methods can be used in the routine quantitative analysis of bromopride in oral and injectable solutions.

Design and analysis of a transversal-flux switched-reluctance-linear-machine pole-pair

The Switched Reluctance technology is probably best suited for industrial low-speed or zerospeed applications where the power can be small but the torque or the force in linear movement cases might be relatively high. Because of its simple structure the SR-motor is an interesting alternative for low power applications where pneumatic or hydraulic linear drives are to be avoided. This study analyses the basic parts of an LSR-motor which are the two mover poles and one stator pole and which form the “basic pole pair” in linear-movement transversal-flux switchedreluctance motors. The static properties of the basic pole pair are modelled and the basic design rules are derived. The models developed are validated with experiments. A one-sided one-polepair transversal-flux switched-reluctance-linear-motor prototype is demonstrated and its static properties are measured. The modelling of the static properties is performed with FEM-calculations. Two-dimensional models are accurate enough to model the static key features for the basic dimensioning of LSRmotors. Three-dimensional models must be used in order to get the most accurate calculation results of the static traction force production. The developed dimensioning and modelling methods, which could be systematically validated by laboratory measurements, are the most significant contributions of this thesis.

Automated, adaptive methods for forest inventory

Forest inventories are used to estimate forest characteristics and the condition of forest for many different applications: operational tree logging for forest industry, forest health state estimation, carbon balance estimation, land-cover and land use analysis in order to avoid forest degradation etc. Recent inventory methods are strongly based on remote sensing data combined with field sample measurements, which are used to define estimates covering the whole area of interest. Remote sensing data from satellites, aerial photographs or aerial laser scannings are used, depending on the scale of inventory. To be applicable in operational use, forest inventory methods need to be easily adjusted to local conditions of the study area at hand. All the data handling and parameter tuning should be objective and automated as much as possible. The methods also need to be robust when applied to different forest types. Since there generally are no extensive direct physical models connecting the remote sensing data from different sources to the forest parameters that are estimated, mathematical estimation models are of "black-box" type, connecting the independent auxiliary data to dependent response data with linear or nonlinear arbitrary models. To avoid redundant complexity and over-fitting of the model, which is based on up to hundreds of possibly collinear variables extracted from the auxiliary data, variable selection is needed. To connect the auxiliary data to the inventory parameters that are estimated, field work must be performed. In larger study areas with dense forests, field work is expensive, and should therefore be minimized. To get cost-efficient inventories, field work could partly be replaced with information from formerly measured sites, databases. The work in this thesis is devoted to the development of automated, adaptive computation methods for aerial forest inventory. The mathematical model parameter definition steps are automated, and the cost-efficiency is improved by setting up a procedure that utilizes databases in the estimation of new area characteristics.

Modeling of residual stresses and distortion due to welding in fillet welds

Welding has a growing role in modern world manufacturing. Welding joints are extensively used from pipes to aerospace industries. Prediction of welding residual stresses and distortions is necessary for accurate evaluation of fillet welds in relation to design and safety conditions. Residual stresses may be beneficial or detrimental, depending whether they are tensile or compressive and the loading. They directly affect the fatigue life of the weld by impacting crack growth rate. Beside theoretical background of residual stresses this study calculates residual stresses and deformations due to localized heating by welding process and subsequent rapid cooling in fillet welds. Validated methods are required for this purpose due to complexity of process, localized heating, temperature dependence of material properties and heat source. In this research both empirical and simulation methods were used for the analysis of welded joints. Finite element simulation has become a popular tool of prediction of welding residual stresses and distortion. Three different cases with and without preload have been modeled during this study. Thermal heat load set is used by calculating heat flux from the given heat input energy. First the linear and then nonlinear material behavior model is modeled for calculation of residual stresses. Experimental work is done to calculate the stresses empirically. The results from both the methods are compared to check their reliability. Residual stresses can have a significant effect on fatigue performance of the welded joints made of high strength steel. Both initial residual stress state and subsequent residual stress relaxation need to be considered for accurate description of fatigue behavior. Tensile residual stresses are detrimental and will reduce the fatigue life and compressive residual stresses will increase it. The residual stresses follow the yield strength of base or filler material and the components made of high strength steel are typically thin, where the role of distortion is emphasizing.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

Simulation-Based Finite and Large Sample Tests in Multivariate Regressions.

In the context of multivariate linear regression (MLR) models, it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection. In this paper, we propose a general method for constructing exact tests of possibly nonlinear hypotheses on the coefficients of MLR systems. For the case of uniform linear hypotheses, we present exact distributional invariance results concerning several standard test criteria. These include Wilks' likelihood ratio (LR) criterion as well as trace and maximum root criteria. The normality assumption is not necessary for most of the results to hold. Implications for inference are two-fold. First, invariance to nuisance parameters entails that the technique of Monte Carlo tests can be applied on all these statistics to obtain exact tests of uniform linear hypotheses. Second, the invariance property of the latter statistic is exploited to derive general nuisance-parameter-free bounds on the distribution of the LR statistic for arbitrary hypotheses. Even though it may be difficult to compute these bounds analytically, they can easily be simulated, hence yielding exact bounds Monte Carlo tests. Illustrative simulation experiments show that the bounds are sufficiently tight to provide conclusive results with a high probability. Our findings illustrate the value of the bounds as a tool to be used in conjunction with more traditional simulation-based test methods (e.g., the parametric bootstrap) which may be applied when the bounds are not conclusive.

Finite-Sample Inference Methods for Simultaneous Equations and Models with Unobserved and Generated Regressors

We propose finite sample tests and confidence sets for models with unobserved and generated regressors as well as various models estimated by instrumental variables methods. The validity of the procedures is unaffected by the presence of identification problems or \"weak instruments\", so no detection of such problems is required. We study two distinct approaches for various models considered by Pagan (1984). The first one is an instrument substitution method which generalizes an approach proposed by Anderson and Rubin (1949) and Fuller (1987) for different (although related) problems, while the second one is based on splitting the sample. The instrument substitution method uses the instruments directly, instead of generated regressors, in order to test hypotheses about the \"structural parameters\" of interest and build confidence sets. The second approach relies on \"generated regressors\", which allows a gain in degrees of freedom, and a sample split technique. For inference about general possibly nonlinear transformations of model parameters, projection techniques are proposed. A distributional theory is obtained under the assumptions of Gaussian errors and strictly exogenous regressors. We show that the various tests and confidence sets proposed are (locally) \"asymptotically valid\" under much weaker assumptions. The properties of the tests proposed are examined in simulation experiments. In general, they outperform the usual asymptotic inference methods in terms of both reliability and power. Finally, the techniques suggested are applied to a model of Tobin’s q and to a model of academic performance.

Simulation-Based Finite-and Large-sample Inference Methods in Multivariate Regressions and Seemingly Unrelated Regressions

In the context of multivariate regression (MLR) and seemingly unrelated regressions (SURE) models, it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection. in this paper, we propose finite-and large-sample likelihood-based test procedures for possibly non-linear hypotheses on the coefficients of MLR and SURE systems.

Studies on Some Aspects of Light Beam Propagation Through Certain Nonlinear Media

This thesis deals with the study of light beam propagation through different nonlinear media. Analytical and numerical methods are used to show the formation of solitonS in these media. Basic experiments have also been performed to show the formation of a self-written waveguide in a photopolymer. The variational method is used for the analytical analysis throughout the thesis. Numerical method based on the finite-difference forms of the original partial differential equation is used for the numerical analysis.In Chapter 2, we have studied two kinds of solitons, the (2 + 1) D spatial solitons and the (3 + l)D spatio-temporal solitons in a cubic-quintic medium in the presence of multiphoton ionization.In Chapter 3, we have studied the evolution of light beam through a different kind of nonlinear media, the photorcfractive polymer. We study modulational instability and beam propagation through a photorefractive polymer in the presence of absorption losses. The one dimensional beam propagation through the nonlinear medium is studied using variational and numerical methods. Stable soliton propagation is observed both analytically and numerically.Chapter 4 deals with the study of modulational instability in a photorefractive crystal in the presence of wave mixing effects. Modulational instability in a photorefractive medium is studied in the presence of two wave mixing. We then propose and derive a model for forward four wave mixing in the photorefractive medium and investigate the modulational instability induced by four wave mixing effects. By using the standard linear stability analysis the instability gain is obtained.Chapter 5 deals with the study of self-written waveguides. Besides the usual analytical analysis, basic experiments were done showing the formation of self-written waveguide in a photopolymer system. The formation of a directional coupler in a photopolymer system is studied theoretically in Chapter 6. We propose and study, using the variational approximation as well as numerical simulation, the evolution of a probe beam through a directional coupler formed in a photopolymer system.

Speech Analysis using Modern Techniques of Nonlinear Dynamics

Medical fields requires fast, simple and noninvasive methods of diagnostic techniques. Several methods are available and possible because of the growth of technology that provides the necessary means of collecting and processing signals. The present thesis details the work done in the field of voice signals. New methods of analysis have been developed to understand the complexity of voice signals, such as nonlinear dynamics aiming at the exploration of voice signals dynamic nature. The purpose of this thesis is to characterize complexities of pathological voice from healthy signals and to differentiate stuttering signals from healthy signals. Efficiency of various acoustic as well as non linear time series methods are analysed. Three groups of samples are used, one from healthy individuals, subjects with vocal pathologies and stuttering subjects. Individual vowels/ and a continuous speech data for the utterance of the sentence "iruvarum changatimaranu" the meaning in English is "Both are good friends" from Malayalam language are recorded using a microphone . The recorded audio are converted to digital signals and are subjected to analysis.Acoustic perturbation methods like fundamental frequency (FO), jitter, shimmer, Zero Crossing Rate(ZCR) were carried out and non linear measures like maximum lyapunov exponent(Lamda max), correlation dimension (D2), Kolmogorov exponent(K2), and a new measure of entropy viz., Permutation entropy (PE) are evaluated for all three groups of the subjects. Permutation Entropy is a nonlinear complexity measure which can efficiently distinguish regular and complex nature of any signal and extract information about the change in dynamics of the process by indicating sudden change in its value. The results shows that nonlinear dynamical methods seem to be a suitable technique for voice signal analysis, due to the chaotic component of the human voice. Permutation entropy is well suited due to its sensitivity to uncertainties, since the pathologies are characterized by an increase in the signal complexity and unpredictability. Pathological groups have higher entropy values compared to the normal group. The stuttering signals have lower entropy values compared to the normal signals.PE is effective in charaterising the level of improvement after two weeks of speech therapy in the case of stuttering subjects. PE is also effective in characterizing the dynamical difference between healthy and pathological subjects. This suggests that PE can improve and complement the recent voice analysis methods available for clinicians. The work establishes the application of the simple, inexpensive and fast algorithm of PE for diagnosis in vocal disorders and stuttering subjects.

Design and Synthesis of Donor-Acceptor Low Band Gap Copolymers for Photoconductive and Non-linear Optical Applications

The main focus of the present study was to develop ideal low band gap D-A copolymers for photoconducting and non-linear optical applications. This chapter summarizes the overall research work done. Designed copolymers were synthesized via direct arylation or Suzuki coupling reactions. Copolymers were characterized by theoretical and experimental methods. The suitability of these copolymers in photoconducting and optical limiting devices has been investigated.The results suggest that the copolymers investigated in the present study have a good non-linear optical response and are comparable to or even better than the D-A copolymers reported in the literature and hence could be chosen as ideal candidates with potential applications for non-linear optics. The results also show that the structures of the polymers have great impact on NLO properties. Copolymers studied here exhibits good optical limiting property at 532 nm wavelength due to two-photon absorption (TPA) process. The results revealed that the two copolymers, (P(EDOT-BTSe) and P(PH-TZ)) exhibited strong two-photon absorption and superior optical power limiting properties, which are much better than that of others.

Numerical Methods for the Unsteady Compressible Navier-Stokes Equations

We consider numerical methods for the compressible time dependent Navier-Stokes equations, discussing the spatial discretization by Finite Volume and Discontinuous Galerkin methods, the time integration by time adaptive implicit Runge-Kutta and Rosenbrock methods and the solution of the appearing nonlinear and linear equations systems by preconditioned Jacobian-Free Newton-Krylov, as well as Multigrid methods. As applications, thermal Fluid structure interaction and other unsteady flow problems are considered. The text is aimed at both mathematicians and engineers.

Modelling official and parallel exchange rates in Colombia under alternative regimes: a non-linear approach

We examine the long-run relationship between the parallel and the official exchange rate in Colombia over two regimes; a crawling peg period and a more flexible crawling band one. The short-run adjustment process of the parallel rate is examined both in a linear and a nonlinear context. We find that the change from the crawling peg to the crawling band regime did not affect the long-run relationship between the official and parallel exchange rates, but altered the short-run dynamics. Non-linear adjustment seems appropriate for the first period, mainly due to strict foreign controls that cause distortions in the transition back to equilibrium once disequilibrium occurs