Parallel geostatistics for sparse and dense datasets

Very large spatially-referenced datasets, for example, those derived from satellite-based sensors which sample across the globe or large monitoring networks of individual sensors, are becoming increasingly common and more widely available for use in environmental decision making. In large or dense sensor networks, huge quantities of data can be collected over small time periods. In many applications the generation of maps, or predictions at specific locations, from the data in (near) real-time is crucial. Geostatistical operations such as interpolation are vital in this map-generation process and in emergency situations, the resulting predictions need to be available almost instantly, so that decision makers can make informed decisions and define risk and evacuation zones. It is also helpful when analysing data in less time critical applications, for example when interacting directly with the data for exploratory analysis, that the algorithms are responsive within a reasonable time frame. Performing geostatistical analysis on such large spatial datasets can present a number of problems, particularly in the case where maximum likelihood. Although the storage requirements only scale linearly with the number of observations in the dataset, the computational complexity in terms of memory and speed, scale quadratically and cubically respectively. Most modern commodity hardware has at least 2 processor cores if not more. Other mechanisms for allowing parallel computation such as Grid based systems are also becoming increasingly commonly available. However, currently there seems to be little interest in exploiting this extra processing power within the context of geostatistics. In this paper we review the existing parallel approaches for geostatistics. By recognising that diffeerent natural parallelisms exist and can be exploited depending on whether the dataset is sparsely or densely sampled with respect to the range of variation, we introduce two contrasting novel implementations of parallel algorithms based on approximating the data likelihood extending the methods of Vecchia [1988] and Tresp [2000]. Using parallel maximum likelihood variogram estimation and parallel prediction algorithms we show that computational time can be significantly reduced. We demonstrate this with both sparsely sampled data and densely sampled data on a variety of architectures ranging from the common dual core processor, found in many modern desktop computers, to large multi-node super computers. To highlight the strengths and weaknesses of the diffeerent methods we employ synthetic data sets and go on to show how the methods allow maximum likelihood based inference on the exhaustive Walker Lake data set.

Applications of Reissner's principle to structural dynamics

The analysis and prediction of the dynamic behaviour of s7ructural components plays an important role in modern engineering design. :n this work, the so-called "mixed" finite element models based on Reissnen's variational principle are applied to the solution of free and forced vibration problems, for beam and :late structures. The mixed beam models are obtained by using elements of various shape functions ranging from simple linear to complex cubic and quadratic functions. The elements were in general capable of predicting the natural frequencies and dynamic responses with good accuracy. An isoparametric quadrilateral element with 8-nodes was developed for application to thin plate problems. The element has 32 degrees of freedom (one deflection, two bending and one twisting moment per node) which is suitable for discretization of plates with arbitrary geometry. A linear isoparametric element and two non-conforming displacement elements (4-node and 8-node quadrilateral) were extended to the solution of dynamic problems. An auto-mesh generation program was used to facilitate the preparation of input data required by the 8-node quadrilateral elements of mixed and displacement type. Numerical examples were solved using both the mixed beam and plate elements for predicting a structure's natural frequencies and dynamic response to a variety of forcing functions. The solutions were compared with the available analytical and displacement model solutions. The mixed elements developed have been found to have significant advantages over the conventional displacement elements in the solution of plate type problems. A dramatic saving in computational time is possible without any loss in solution accuracy. With beam type problems, there appears to be no significant advantages in using mixed models.

Bayesian data assimilation

This thesis addresses data assimilation, which typically refers to the estimation of the state of a physical system given a model and observations, and its application to short-term precipitation forecasting. A general introduction to data assimilation is given, both from a deterministic and' stochastic point of view. Data assimilation algorithms are reviewed, in the static case (when no dynamics are involved), then in the dynamic case. A double experiment on two non-linear models, the Lorenz 63 and the Lorenz 96 models, is run and the comparative performance of the methods is discussed in terms of quality of the assimilation, robustness "in the non-linear regime and computational time. Following the general review and analysis, data assimilation is discussed in the particular context of very short-term rainfall forecasting (nowcasting) using radar images. An extended Bayesian precipitation nowcasting model is introduced. The model is stochastic in nature and relies on the spatial decomposition of the rainfall field into rain "cells". Radar observations are assimilated using a Variational Bayesian method in which the true posterior distribution of the parameters is approximated by a more tractable distribution. The motion of the cells is captured by a 20 Gaussian process. The model is tested on two precipitation events, the first dominated by convective showers, the second by precipitation fronts. Several deterministic and probabilistic validation methods are applied and the model is shown to retain reasonable prediction skill at up to 3 hours lead time. Extensions to the model are discussed.

Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques

We consider the problem of stable determination of a harmonic function from knowledge of the solution and its normal derivative on a part of the boundary of the (bounded) solution domain. The alternating method is a procedure to generate an approximation to the harmonic function from such Cauchy data and we investigate a numerical implementation of this procedure based on Fredholm integral equations and Nyström discretization schemes, which makes it possible to perform a large number of iterations (millions) with minor computational cost (seconds) and high accuracy. Moreover, the original problem is rewritten as a fixed point equation on the boundary, and various other direct regularization techniques are discussed to solve that equation. We also discuss how knowledge of the smoothness of the data can be used to further improve the accuracy. Numerical examples are presented showing that accurate approximations of both the solution and its normal derivative can be obtained with much less computational time than in previous works.

A CFD study of biomass pyrolysis in a downer reactor equipped with a novel gas-solid separator-II thermochemical performance and products

A Eulerian-Eulerian CFD model was used to investigate the fast pyrolysis of biomass in a downer reactor equipped with a novel gas-solid separation mechanism. The highly endothermic pyrolysis reaction was assumed to be entirely driven by an inert solid heat carrier (sand). A one-step global pyrolysis reaction, along with the equations describing the biomass drying and heat transfer, was implemented in the hydrodynamic model presented in part I of this study (Fuel Processing Technology, V126, 366-382). The predictions of the gas-solid separation efficiency, temperature distribution, residence time and the pyrolysis product yield are presented and discussed. For the operating conditions considered, the devolatilisation efficiency was found to be above 60% and the yield composition in mass fraction was 56.85% bio-oil, 37.87% bio-char and 5.28% non-condensable gas (NCG). This has been found to agree reasonably well with recent relevant published experimental data. The novel gas-solid separation mechanism allowed achieving greater than 99.9% separation efficiency and < 2 s pyrolysis gas residence time. The model has been found to be robust and fast in terms of computational time, thus has the great potential to aid in future design and optimisation of the biomass fast pyrolysis process.

A comparison of denoising methods for X-ray fluoroscopic images

Fluoroscopic images exhibit severe signal-dependent quantum noise, due to the reduced X-ray dose involved in image formation, that is generally modelled as Poisson-distributed. However, image gray-level transformations, commonly applied by fluoroscopic device to enhance contrast, modify the noise statistics and the relationship between image noise variance and expected pixel intensity. Image denoising is essential to improve quality of fluoroscopic images and their clinical information content. Simple average filters are commonly employed in real-time processing, but they tend to blur edges and details. An extensive comparison of advanced denoising algorithms specifically designed for both signal-dependent noise (AAS, BM3Dc, HHM, TLS) and independent additive noise (AV, BM3D, K-SVD) was presented. Simulated test images degraded by various levels of Poisson quantum noise and real clinical fluoroscopic images were considered. Typical gray-level transformations (e.g. white compression) were also applied in order to evaluate their effect on the denoising algorithms. Performances of the algorithms were evaluated in terms of peak-signal-to-noise ratio (PSNR), signal-to-noise ratio (SNR), mean square error (MSE), structural similarity index (SSIM) and computational time. On average, the filters designed for signal-dependent noise provided better image restorations than those assuming additive white Gaussian noise (AWGN). Collaborative denoising strategy was found to be the most effective in denoising of both simulated and real data, also in the presence of image gray-level transformations. White compression, by inherently reducing the greater noise variance of brighter pixels, appeared to support denoising algorithms in performing more effectively. © 2012 Elsevier Ltd. All rights reserved.

Periodic nonlinear Fourier transform for fiber-optic communications, Part I:theory and numerical methods

In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.

Computational mechanics reveals nanosecond time correlations in molecular dynamics of liquid systems

Statistical complexity, a measure introduced in computational mechanics has been applied to MD simulated liquid water and other molecular systems. It has been found that statistical complexity does not converge in these systems but grows logarithmically without a limit. The coefficient of the growth has been introduced as a new molecular parameter which is invariant for a given liquid system. Using this new parameter extremely long time correlations in the system undetectable by traditional methods are elucidated. The existence of hundreds of picosecond and even nanosecond long correlations in bulk water has been demonstrated. © 2008 Elsevier B.V. All rights reserved.

Modelling financial time series with switching state space models

The deficiencies of stationary models applied to financial time series are well documented. A special form of non-stationarity, where the underlying generator switches between (approximately) stationary regimes, seems particularly appropriate for financial markets. We use a dynamic switching (modelled by a hidden Markov model) combined with a linear dynamical system in a hybrid switching state space model (SSSM) and discuss the practical details of training such models with a variational EM algorithm due to [Ghahramani and Hilton,1998]. The performance of the SSSM is evaluated on several financial data sets and it is shown to improve on a number of existing benchmark methods.

Computational mechanics of molecular systems:quantifying high-dimensional dynamics by distribution of Poincaré recurrence times

A framework that connects computational mechanics and molecular dynamics has been developed and described. As the key parts of the framework, the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore, it is shown that causal states, the constituent parts of the main construct of computational mechanics, the e-machine, define areas of the phase space that are optimal in the sense of transferring information from the micro-variables to the macro-observables. We have demonstrated that, based on the decay of their Poincare´ return times, these areas can be divided into two classes that characterise the separation of the phase space into resonant and chaotic areas. The first class is characterised by predominantly short time returns, typical to quasi-periodic or periodic trajectories. This class includes a countable number of areas corresponding to resonances. The second class includes trajectories with chaotic behaviour characterised by the exponential decay of return times in accordance with the Poincare´ theorem.

Numerically optimized implementations, mitigation and simulations of polarisation mode dispersion in real-time transmission systems

The aim of this thesis is to present numerical investigations of the polarisation mode dispersion (PMD) effect. Outstanding issues on the side of the numerical implementations of PMD are resolved and the proposed methods are further optimized for computational efficiency and physical accuracy. Methods for the mitigation of the PMD effect are taken into account and simulations of transmission system with added PMD are presented. The basic outline of the work focusing on PMD can be divided as follows. At first the widely-used coarse-step method for simulating the PMD phenomenon as well as a method derived from the Manakov-PMD equation are implemented and investigated separately through the distribution of a state of polarisation on the Poincaré sphere, and the evolution of the dispersion of a signal. Next these two methods are statistically examined and compared to well-known analytical models of the probability distribution function (PDF) and the autocorrelation function (ACF) of the PMD phenomenon. Important optimisations are achieved, for each of the aforementioned implementations in the computational level. In addition the ACF of the coarse-step method is considered separately, based on the result which indicates that the numerically produced ACF, exaggerates the value of the correlation between different frequencies. Moreover the mitigation of the PMD phenomenon is considered, in the form of numerically implementing Low-PMD spun fibres. Finally, all the above are combined in simulations that demonstrate the impact of the PMD on the quality factor (Q=factor) of different transmission systems. For this a numerical solver based on the coupled nonlinear Schrödinger equation is created which is otherwise tested against the most important transmission impairments in the early chapters of this thesis.

Perception of concurrent sentences with harmonic or frequency-shifted voiced excitation:performance of human listeners and of computational models based on autocorrelation

Keyword identification in one of two simultaneous sentences is improved when the sentences differ in F0, particularly when they are almost continuously voiced. Sentences of this kind were recorded, monotonised using PSOLA, and re-synthesised to give a range of harmonic ?F0s (0, 1, 3, and 10 semitones). They were additionally re-synthesised by LPC with the LPC residual frequency shifted by 25% of F0, to give excitation with inharmonic but regularly spaced components. Perceptual identification of frequency-shifted sentences showed a similar large improvement with nominal ?F0 as seen for harmonic sentences, although overall performance was about 10% poorer. We compared performance with that of two autocorrelation-based computational models comprising four stages: (i) peripheral frequency selectivity and half-wave rectification; (ii) within-channel periodicity extraction; (iii) identification of the two major peaks in the summary autocorrelation function (SACF); (iv) a template-based approach to speech recognition using dynamic time warping. One model sampled the correlogram at the target-F0 period and performed spectral matching; the other deselected channels dominated by the interferer and performed matching on the short-lag portion of the residual SACF. Both models reproduced the monotonic increase observed in human performance with increasing ?F0 for the harmonic stimuli, but not for the frequency-shifted stimuli. A revised version of the spectral-matching model, which groups patterns of periodicity that lie on a curve in the frequency-delay plane, showed a closer match to the perceptual data for frequency-shifted sentences. The results extend the range of phenomena originally attributed to harmonic processing to grouping by common spectral pattern.

Use of computational fluid dynamics in the design of bubble column reactors

Investigations into the modelling techniques that depict the transport of discrete phases (gas bubbles or solid particles) and model biochemical reactions in a bubble column reactor are discussed here. The mixture model was used to calculate gas-liquid, solid-liquid and gasliquid-solid interactions. Multiphase flow is a difficult phenomenon to capture, particularly in bubble columns where the major driving force is caused by the injection of gas bubbles. The gas bubbles cause a large density difference to occur that results in transient multi-dimensional fluid motion. Standard design procedures do not account for the transient motion, due to the simplifying assumptions of steady plug flow. Computational fluid dynamics (CFD) can assist in expanding the understanding of complex flows in bubble columns by characterising the flow phenomena for many geometrical configurations. Therefore, CFD has a role in the education of chemical and biochemical engineers, providing the examples of flow phenomena that many engineers may not experience, even through experimentation. The performance of the mixture model was investigated for three domains (plane, rectangular and cylindrical) and three flow models (laminar, k-e turbulence and the Reynolds stresses). mThis investigation raised many questions about how gas-liquid interactions are captured numerically. To answer some of these questions the analogy between thermal convection in a cavity and gas-liquid flow in bubble columns was invoked. This involved modelling the buoyant motion of air in a narrow cavity for a number of turbulence schemes. The difference in density was caused by a temperature gradient that acted across the width of the cavity. Multiple vortices were obtained when the Reynolds stresses were utilised with the addition of a basic flow profile after each time step. To implement the three-phase models an alternative mixture model was developed and compared against a commercially available mixture model for three turbulence schemes. The scheme where just the Reynolds stresses model was employed, predicted the transient motion of the fluids quite well for both mixture models. Solid-liquid and then alternative formulations of gas-liquid-solid model were compared against one another. The alternative form of the mixture model was found to perform particularly well for both gas and solid phase transport when calculating two and three-phase flow. The improvement in the solutions obtained was a result of the inclusion of the Reynolds stresses model and differences in the mixture models employed. The differences between the alternative mixture models were found in the volume fraction equation (flux and deviatoric stress tensor terms) and the viscosity formulation for the mixture phase.

Investigation of chaotic mixing in laminar fluid systems by the use of computational fluid dynamics

This work presents significant development into chaotic mixing induced through periodic boundaries and twisting flows. Three-dimensional closed and throughput domains are shown to exhibit chaotic motion under both time periodic and time independent boundary motions, A property is developed originating from a signature of chaos, sensitive dependence to initial conditions, which successfully quantifies the degree of disorder withjn the mixing systems presented and enables comparisons of the disorder throughout ranges of operating parameters, This work omits physical experimental results but presents significant computational investigation into chaotic systems using commercial computational fluid dynamics techniques. Physical experiments with chaotic mixing systems are, by their very nature, difficult to extract information beyond the recognition that disorder does, does not of partially occurs. The initial aim of this work is to observe whether it is possible to accurately simulate previously published physical experimental results through using commercial CFD techniques. This is shown to be possible for simple two-dimensional systems with time periodic wall movements. From this, and subsequent macro and microscopic observations of flow regimes, a simple explanation is developed for how boundary operating parameters affect the system disorder. Consider the classic two-dimensional rectangular cavity with time periodic velocity of the upper and lower walls, causing two opposing streamline motions. The degree of disorder within the system is related to the magnitude of displacement of individual particles within these opposing streamlines. The rationale is then employed in this work to develop and investigate more complex three-dimensional mixing systems that exhibit throughputs and time independence and are therefore more realistic and a significant advance towards designing chaotic mixers for process industries. Domains inducing chaotic motion through twisting flows are also briefly considered. This work concludes by offering possible advancements to the property developed to quantify disorder and suggestions of domains and associated boundary conditions that are expected to produce chaotic mixing.

Time scale analysis for fluidizedbedmeltgranulation-II: binder spreading rate

The spreading time of liquid binder droplet on the surface a primary particle is analyzed for Fluidized Bed Melt Granulation (FBMG). As discussed in the first paper of this series (Chua et al., in press) the droplet spreading rate has been identified as one of the important parameters affecting the probability of particles aggregation in FBMG. In this paper, the binder droplet spreading time has been estimated using Computational Fluid Dynamic modeling (CFD) based on Volume of Fluid approach (VOF). A simplified analytical solution has been developed and tested to explore its validity for predicting the spreading time. For the purpose of models validation, the droplet spreading evolution was recorded using a high speed video camera. Based on the validated model, a generalized correlative equation for binder spreading time is proposed. For the operating conditions considered here, the spreading time for Polyethylene Glycol (PEG1500) binder was found to fall within the range of 10-2 to 10-5 s. The study also included a number of other common binders used in FBMG. The results obtained here will be further used in paper III, where the binder solidification rate is discussed.