The (n+1)/2 rule for dealiasing in the split-step Fourier methods for n-wave interactions

The aim of this letter is to demonstrate that complete removal of spectral aliasing occurring due to finite numerical bandwidth used in the split-step Fourier simulations of nonlinear interactions of optical waves can be achieved by enlarging each dimension of the spectral domain by a factor (n+1)/2, where n is the number of interacting waves. Alternatively, when using low-pass filtering for dealiasing this amounts to the need for filtering a 2/(n+1) fraction of each spectral dimension.

Mathematical methods in power system stability studies

In this thesis various mathematical methods of studying the transient and dynamic stabiIity of practical power systems are presented. Certain long established methods are reviewed and refinements of some proposed. New methods are presented which remove some of the difficulties encountered in applying the powerful stability theories based on the concepts of Liapunov. Chapter 1 is concerned with numerical solution of the transient stability problem. Following a review and comparison of synchronous machine models the superiority of a particular model from the point of view of combined computing time and accuracy is demonstrated. A digital computer program incorporating all the synchronous machine models discussed, and an induction machine model, is described and results of a practical multi-machine transient stability study are presented. Chapter 2 reviews certain concepts and theorems due to Liapunov. In Chapter 3 transient stability regions of single, two and multi~machine systems are investigated through the use of energy type Liapunov functions. The treatment removes several mathematical difficulties encountered in earlier applications of the method. In Chapter 4 a simple criterion for the steady state stability of a multi-machine system is developed and compared with established criteria and a state space approach. In Chapters 5, 6 and 7 dynamic stability and small signal dynamic response are studied through a state space representation of the system. In Chapter 5 the state space equations are derived for single machine systems. An example is provided in which the dynamic stability limit curves are plotted for various synchronous machine representations. In Chapter 6 the state space approach is extended to multi~machine systems. To draw conclusions concerning dynamic stability or dynamic response the system eigenvalues must be properly interpreted, and a discussion concerning correct interpretation is included. Chapter 7 presents a discussion of the optimisation of power system small sjgnal performance through the use of Liapunov functions.

Vibrational methods applied to NDT testing and fluid density measurement

A system for the NDI' testing of the integrity of conposite materials and of adhesive bonds has been developed to meet industrial requirements. The vibration techniques used were found to be applicable to the development of fluid measuring transducers. The vibrational spectra of thin rectangular bars were used for the NDT work. A machined cut in a bar had a significant effect on the spectrum but a genuine crack gave an unambiguous response at high amplitudes. This was the generation of fretting crack noise at frequencies far above that of the drive. A specially designed vibrational decrement meter which, in effect, measures mechanical energy loss enabled a numerical classification of material adhesion to be obtained. This was used to study bars which had been flame or plasma sprayed with a variety of materials. It has become a useful tool in optimising coating methods. A direct industrial application was to classify piston rings of high performance I.C. engines. Each consists of a cast iron ring with a channel into which molybdenum, a good bearing surface, is sprayed. The NDT classification agreed quite well with the destructive test normally used. The techniques and equipment used for the NOT work were applied to the development of the tuning fork transducers investigated by Hassan into commercial density and viscosity devices. Using narrowly spaced, large area tines a thin lamina of fluid is trapped between them. It stores a large fraction of the vibrational energy which, acting as an inertia load reduces the frequency. Magnetostrictive and piezoelectric effects together or in combination enable the fork to be operated through a flange. This allows it to be used in pipeline or 'dipstick' applications. Using a different tine geometry the viscosity loading can be predoninant. This as well as the signal decrement of the density transducer makes a practical viscometer.

Estimating parameters in stochastic systems:a variational Bayesian approach

This work is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variation of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here a new extended framework is derived that is based on a local polynomial approximation of a recently proposed variational Bayesian algorithm. The paper begins by showing that the new extension of this variational algorithm can be used for state estimation (smoothing) and converges to the original algorithm. However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new approach is validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein–Uhlenbeck process, the exact likelihood of which can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz ’63 (3D model). As a special case the algorithm is also applied to the 40 dimensional stochastic Lorenz ’96 system. In our investigation we compare this new approach with a variety of other well known methods, such as the hybrid Monte Carlo, dual unscented Kalman filter, full weak-constraint 4D-Var algorithm and analyse empirically their asymptotic behaviour as a function of observation density or length of time window increases. In particular we show that we are able to estimate parameters in both the drift (deterministic) and the diffusion (stochastic) part of the model evolution equations using our new methods.

Modelling nonlinear stochastic dynamics in financial time series

For analysing financial time series two main opposing viewpoints exist, either capital markets are completely stochastic and therefore prices follow a random walk, or they are deterministic and consequently predictable. For each of these views a great variety of tools exist with which it can be tried to confirm the hypotheses. Unfortunately, these methods are not well suited for dealing with data characterised in part by both paradigms. This thesis investigates these two approaches in order to model the behaviour of financial time series. In the deterministic framework methods are used to characterise the dimensionality of embedded financial data. The stochastic approach includes here an estimation of the unconditioned and conditional return distributions using parametric, non- and semi-parametric density estimation techniques. Finally, it will be shown how elements from these two approaches could be combined to achieve a more realistic model for financial time series.

The application of methods of uncertain reasoning to the biological classification of river water quality

This thesis presents an investigation into the application of methods of uncertain reasoning to the biological classification of river water quality. Existing biological methods for reporting river water quality are critically evaluated, and the adoption of a discrete biological classification scheme advocated. Reasoning methods for managing uncertainty are explained, in which the Bayesian and Dempster-Shafer calculi are cited as primary numerical schemes. Elicitation of qualitative knowledge on benthic invertebrates is described. The specificity of benthic response to changes in water quality leads to the adoption of a sensor model of data interpretation, in which a reference set of taxa provide probabilistic support for the biological classes. The significance of sensor states, including that of absence, is shown. Novel techniques of directly eliciting the required uncertainty measures are presented. Bayesian and Dempster-Shafer calculi were used to combine the evidence provided by the sensors. The performance of these automatic classifiers was compared with the expert's own discrete classification of sampled sites. Variations of sensor data weighting, combination order and belief representation were examined for their effect on classification performance. The behaviour of the calculi under evidential conflict and alternative combination rules was investigated. Small variations in evidential weight and the inclusion of evidence from sensors absent from a sample improved classification performance of Bayesian belief and support for singleton hypotheses. For simple support, inclusion of absent evidence decreased classification rate. The performance of Dempster-Shafer classification using consonant belief functions was comparable to Bayesian and singleton belief. Recommendations are made for further work in biological classification using uncertain reasoning methods, including the combination of multiple-expert opinion, the use of Bayesian networks, and the integration of classification software within a decision support system for water quality assessment.

Numerical and statistical analysis of long-haul undersea optical communication systems

Firstly, we numerically model a practical 20 Gb/s undersea configuration employing the Return-to-Zero Differential Phase Shift Keying data format. The modelling is completed using the Split-Step Fourier Method to solve the Generalised Nonlinear Schrdinger Equation. We optimise the dispersion map and per-channel launch power of these channels and investigate how the choice of pre/post compensation can influence the performance. After obtaining these optimal configurations, we investigate the Bit Error Rate estimation of these systems and we see that estimation based on Gaussian electrical current systems is appropriate for systems of this type, indicating quasi-linear behaviour. The introduction of narrower pulses due to the deployment of quasi-linear transmission decreases the tolerance to chromatic dispersion and intra-channel nonlinearity. We used tools from Mathematical Statistics to study the behaviour of these channels in order to develop new methods to estimate Bit Error Rate. In the final section, we consider the estimation of Eye Closure Penalty, a popular measure of signal distortion. Using a numerical example and assuming the symmetry of eye closure, we see that we can simply estimate Eye Closure Penalty using Gaussian statistics. We also see that the statistics of the logical ones dominates the statistics of the logical ones dominates the statistics of signal distortion in the case of Return-to-Zero On-Off Keying configurations.

A Bayesian perspective on stochastic neurocontrol

Control design for stochastic uncertain nonlinear systems is traditionally based on minimizing the expected value of a suitably chosen loss function. Moreover, most control methods usually assume the certainty equivalence principle to simplify the problem and make it computationally tractable. We offer an improved probabilistic framework which is not constrained by these previous assumptions, and provides a more natural framework for incorporating and dealing with uncertainty. The focus of this paper is on developing this framework to obtain an optimal control law strategy using a fully probabilistic approach for information extraction from process data, which does not require detailed knowledge of system dynamics. Moreover, the proposed control method framework allows handling the problem of input-dependent noise. A basic paradigm is proposed and the resulting algorithm is discussed. The proposed probabilistic control method is for the general nonlinear class of discrete-time systems. It is demonstrated theoretically on the affine class. A nonlinear simulation example is also provided to validate theoretical development.

Finding structures in information networks using the affinity network

This thesis proposes a novel graphical model for inference called the Affinity Network,which displays the closeness between pairs of variables and is an alternative to Bayesian Networks and Dependency Networks. The Affinity Network shares some similarities with Bayesian Networks and Dependency Networks but avoids their heuristic and stochastic graph construction algorithms by using a message passing scheme. A comparison with the above two instances of graphical models is given for sparse discrete and continuous medical data and data taken from the UCI machine learning repository. The experimental study reveals that the Affinity Network graphs tend to be more accurate on the basis of an exhaustive search with the small datasets. Moreover, the graph construction algorithm is faster than the other two methods with huge datasets. The Affinity Network is also applied to data produced by a synchronised system. A detailed analysis and numerical investigation into this dynamical system is provided and it is shown that the Affinity Network can be used to characterise its emergent behaviour even in the presence of noise.

A procedure for the reconstruction of a stochastic stationary temperature field

An iterative procedure is proposed for the reconstruction of a temperature field from a linear stationary heat equation with stochastic coefficients, and stochastic Cauchy data given on a part of the boundary of a bounded domain. In each step, a series of mixed well-posed boundary-value problems are solved for the stochastic heat operator and its adjoint. Well-posedness of these problems is shown to hold and convergence in the mean of the procedure is proved. A discretized version of this procedure, based on a Monte Carlo Galerkin finite-element method, suitable for numerical implementation is discussed. It is demonstrated that the solution to the discretized problem converges to the continuous as the mesh size tends to zero.

Uses of frontier efficiency methodologies and multi-criteria decision making for performance measurement in the energy sector

Guest editorial Ali Emrouznejad is a Senior Lecturer at the Aston Business School in Birmingham, UK. His areas of research interest include performance measurement and management, efficiency and productivity analysis as well as data mining. He has published widely in various international journals. He is an Associate Editor of IMA Journal of Management Mathematics and Guest Editor to several special issues of journals including Journal of Operational Research Society, Annals of Operations Research, Journal of Medical Systems, and International Journal of Energy Management Sector. He is in the editorial board of several international journals and co-founder of Performance Improvement Management Software. William Ho is a Senior Lecturer at the Aston University Business School. Before joining Aston in 2005, he had worked as a Research Associate in the Department of Industrial and Systems Engineering at the Hong Kong Polytechnic University. His research interests include supply chain management, production and operations management, and operations research. He has published extensively in various international journals like Computers & Operations Research, Engineering Applications of Artificial Intelligence, European Journal of Operational Research, Expert Systems with Applications, International Journal of Production Economics, International Journal of Production Research, Supply Chain Management: An International Journal, and so on. His first authored book was published in 2006. He is an Editorial Board member of the International Journal of Advanced Manufacturing Technology and an Associate Editor of the OR Insight Journal. Currently, he is a Scholar of the Advanced Institute of Management Research. Uses of frontier efficiency methodologies and multi-criteria decision making for performance measurement in the energy sector This special issue aims to focus on holistic, applied research on performance measurement in energy sector management and for publication of relevant applied research to bridge the gap between industry and academia. After a rigorous refereeing process, seven papers were included in this special issue. The volume opens with five data envelopment analysis (DEA)-based papers. Wu et al. apply the DEA-based Malmquist index to evaluate the changes in relative efficiency and the total factor productivity of coal-fired electricity generation of 30 Chinese administrative regions from 1999 to 2007. Factors considered in the model include fuel consumption, labor, capital, sulphur dioxide emissions, and electricity generated. The authors reveal that the east provinces were relatively and technically more efficient, whereas the west provinces had the highest growth rate in the period studied. Ioannis E. Tsolas applies the DEA approach to assess the performance of Greek fossil fuel-fired power stations taking undesirable outputs into consideration, such as carbon dioxide and sulphur dioxide emissions. In addition, the bootstrapping approach is deployed to address the uncertainty surrounding DEA point estimates, and provide bias-corrected estimations and confidence intervals for the point estimates. The author revealed from the sample that the non-lignite-fired stations are on an average more efficient than the lignite-fired stations. Maethee Mekaroonreung and Andrew L. Johnson compare the relative performance of three DEA-based measures, which estimate production frontiers and evaluate the relative efficiency of 113 US petroleum refineries while considering undesirable outputs. Three inputs (capital, energy consumption, and crude oil consumption), two desirable outputs (gasoline and distillate generation), and an undesirable output (toxic release) are considered in the DEA models. The authors discover that refineries in the Rocky Mountain region performed the best, and about 60 percent of oil refineries in the sample could improve their efficiencies further. H. Omrani, A. Azadeh, S. F. Ghaderi, and S. Abdollahzadeh presented an integrated approach, combining DEA, corrected ordinary least squares (COLS), and principal component analysis (PCA) methods, to calculate the relative efficiency scores of 26 Iranian electricity distribution units from 2003 to 2006. Specifically, both DEA and COLS are used to check three internal consistency conditions, whereas PCA is used to verify and validate the final ranking results of either DEA (consistency) or DEA-COLS (non-consistency). Three inputs (network length, transformer capacity, and number of employees) and two outputs (number of customers and total electricity sales) are considered in the model. Virendra Ajodhia applied three DEA-based models to evaluate the relative performance of 20 electricity distribution firms from the UK and the Netherlands. The first model is a traditional DEA model for analyzing cost-only efficiency. The second model includes (inverse) quality by modelling total customer minutes lost as an input data. The third model is based on the idea of using total social costs, including the firm’s private costs and the interruption costs incurred by consumers, as an input. Both energy-delivered and number of consumers are treated as the outputs in the models. After five DEA papers, Stelios Grafakos, Alexandros Flamos, Vlasis Oikonomou, and D. Zevgolis presented a multiple criteria analysis weighting approach to evaluate the energy and climate policy. The proposed approach is akin to the analytic hierarchy process, which consists of pairwise comparisons, consistency verification, and criteria prioritization. In the approach, stakeholders and experts in the energy policy field are incorporated in the evaluation process by providing an interactive mean with verbal, numerical, and visual representation of their preferences. A total of 14 evaluation criteria were considered and classified into four objectives, such as climate change mitigation, energy effectiveness, socioeconomic, and competitiveness and technology. Finally, Borge Hess applied the stochastic frontier analysis approach to analyze the impact of various business strategies, including acquisition, holding structures, and joint ventures, on a firm’s efficiency within a sample of 47 natural gas transmission pipelines in the USA from 1996 to 2005. The author finds that there were no significant changes in the firm’s efficiency by an acquisition, and there is a weak evidence for efficiency improvements caused by the new shareholder. Besides, the author discovers that parent companies appear not to influence a subsidiary’s efficiency positively. In addition, the analysis shows a negative impact of a joint venture on technical efficiency of the pipeline company. To conclude, we are grateful to all the authors for their contribution, and all the reviewers for their constructive comments, which made this special issue possible. We hope that this issue would contribute significantly to performance improvement of the energy sector.

Reconstruction of a stationary flow from boundary data using iterative methods

In this paper, three iterative procedures (Landweber-Fridman, conjugate gradient and minimal error methods) for obtaining a stable solution to the Cauchy problem in slow viscous flows are presented and compared. A section is devoted to the numerical investigations of these algorithms. There, we use the boundary element method together with efficient stopping criteria for ceasing the iteration process in order to obtain stable solutions.

Nonlinear integral equation methods for the reconstruction of an acoustically sound-soft obstacle

The problem considered is that of determining the shape of a planar acoustically sound-soft obstacle from knowledge of the far-field pattern for one time-harmonic incident field. Two methods, which are based on the solution of a pair of integral equations representing the incoming wave and the far-field pattern, respectively, are proposed and investigated for finding the unknown boundary. Numerical resultsare included which show that the methods give accurate numerical approximations in relatively few iterations.