Mathematical modelling and control of agitated extraction columns

Liquid-liquid extraction has long been known as a unit operation that plays an important role in industry. This process is well known for its complexity and sensitivity to operation conditions. This thesis presents an attempt to explore the dynamics and control of this process using a systematic approach and state of the art control system design techniques. The process was studied first experimentally under carefully selected. operation conditions, which resembles the ranges employed practically under stable and efficient conditions. Data were collected at steady state conditions using adequate sampling techniques for the dispersed and continuous phases as well as during the transients of the column with the aid of a computer-based online data logging system and online concentration analysis. A stagewise single stage backflow model was improved to mimic the dynamic operation of the column. The developed model accounts for the variation in hydrodynamics, mass transfer, and physical properties throughout the length of the column. End effects were treated by addition of stages at the column entrances. Two parameters were incorporated in the model namely; mass transfer weight factor to correct for the assumption of no mass transfer in the. settling zones at each stage and the backmixing coefficients to handle the axial dispersion phenomena encountered in the course of column operation. The parameters were estimated by minimizing the differences between the experimental and the model predicted concentration profiles at steady state conditions using non-linear optimisation technique. The estimated values were then correlated as functions of operating parameters and were incorporated in·the model equations. The model equations comprise a stiff differential~algebraic system. This system was solved using the GEAR ODE solver. The calculated concentration profiles were compared to those experimentally measured. A very good agreement of the two profiles was achieved within a percent relative error of ±2.S%. The developed rigorous dynamic model of the extraction column was used to derive linear time-invariant reduced-order models that relate the input variables (agitator speed, solvent feed flowrate and concentration, feed concentration and flowrate) to the output variables (raffinate concentration and extract concentration) using the asymptotic method of system identification. The reduced-order models were shown to be accurate in capturing the dynamic behaviour of the process with a maximum modelling prediction error of I %. The simplicity and accuracy of the derived reduced-order models allow for control system design and analysis of such complicated processes. The extraction column is a typical multivariable process with agitator speed and solvent feed flowrate considered as manipulative variables; raffinate concentration and extract concentration as controlled variables and the feeds concentration and feed flowrate as disturbance variables. The control system design of the extraction process was tackled as multi-loop decentralised SISO (Single Input Single Output) as well as centralised MIMO (Multi-Input Multi-Output) system using both conventional and model-based control techniques such as IMC (Internal Model Control) and MPC (Model Predictive Control). Control performance of each control scheme was. studied in terms of stability, speed of response, sensitivity to modelling errors (robustness), setpoint tracking capabilities and load rejection. For decentralised control, multiple loops were assigned to pair.each manipulated variable with each controlled variable according to the interaction analysis and other pairing criteria such as relative gain array (RGA), singular value analysis (SVD). Loops namely Rotor speed-Raffinate concentration and Solvent flowrate Extract concentration showed weak interaction. Multivariable MPC has shown more effective performance compared to other conventional techniques since it accounts for loops interaction, time delays, and input-output variables constraints.

A study of cluster analysis techniques and their applications

This thesis seeks to describe the development of an inexpensive and efficient clustering technique for multivariate data analysis. The technique starts from a multivariate data matrix and ends with graphical representation of the data and pattern recognition discriminant function. The technique also results in distances frequency distribution that might be useful in detecting clustering in the data or for the estimation of parameters useful in the discrimination between the different populations in the data. The technique can also be used in feature selection. The technique is essentially for the discovery of data structure by revealing the component parts of the data. lhe thesis offers three distinct contributions for cluster analysis and pattern recognition techniques. The first contribution is the introduction of transformation function in the technique of nonlinear mapping. The second contribution is the us~ of distances frequency distribution instead of distances time-sequence in nonlinear mapping, The third contribution is the formulation of a new generalised and normalised error function together with its optimal step size formula for gradient method minimisation. The thesis consists of five chapters. The first chapter is the introduction. The second chapter describes multidimensional scaling as an origin of nonlinear mapping technique. The third chapter describes the first developing step in the technique of nonlinear mapping that is the introduction of "transformation function". The fourth chapter describes the second developing step of the nonlinear mapping technique. This is the use of distances frequency distribution instead of distances time-sequence. The chapter also includes the new generalised and normalised error function formulation. Finally, the fifth chapter, the conclusion, evaluates all developments and proposes a new program. for cluster analysis and pattern recognition by integrating all the new features.

Impact of liberalization on efficiency and productivity of sugar industry in Kenya

Purpose – The data used in this study is for the period 1980-2000. Almost midway through this period (in 1992), the Kenyan government liberalized the sugar industry and the role of the market increased, while the government's role with respect to control of prices, imports and other aspects in the sector declined. This exposed the local sugar manufacturers to external competition from other sugar producers, especially from the COMESA region. This study aims to find whether there were any changes in efficiency of production between the two periods (pre and post-liberalization). Design/methodology/approach – The study utilized two methodologies to efficiency estimation: data envelopment analysis (DEA) and the stochastic frontier. DEA uses mathematical programming techniques and does not impose any functional form on the data. However, it attributes all deviation from the mean function to inefficiencies. The stochastic frontier utilizes econometric techniques. Findings – The test for structural differences in the two periods does not show any statistically significant differences between the two periods. However, both methodologies show a decline in efficiency levels from 1992, with the lowest period experienced in 1998. From then on, efficiency levels began to increase. Originality/value – To the best of the authors' knowledge, this is the first paper to use both methodologies in the sugar industry in Kenya. It is shown that in industries where the noise (error) term is minimal (such as manufacturing), the DEA and stochastic frontier give similar results.

A mathematical model for dynamic efficiency using data envelopment analysis

In this paper we propose a data envelopment analysis (DEA) based method for assessing the comparative efficiencies of units operating production processes where input-output levels are inter-temporally dependent. One cause of inter-temporal dependence between input and output levels is capital stock which influences output levels over many production periods. Such units cannot be assessed by traditional or 'static' DEA which assumes input-output correspondences are contemporaneous in the sense that the output levels observed in a time period are the product solely of the input levels observed during that same period. The method developed in the paper overcomes the problem of inter-temporal input-output dependence by using input-output 'paths' mapped out by operating units over time as the basis of assessing them. As an application we compare the results of the dynamic and static model for a set of UK universities. The paper is suggested that dynamic model capture the efficiency better than static model. © 2003 Elsevier Inc. All rights reserved.

Mathematical and numerical modelling of dispersion-managed solitons, autosolitons and self-similar optical pulses

This thesis presents theoretical investigation of three topics concerned with nonlinear optical pulse propagation in optical fibres. The techniques used are mathematical analysis and numerical modelling. Firstly, dispersion-managed (DM) solitons in fibre lines employing a weak dispersion map are analysed by means of a perturbation approach. In the case of small dispersion map strengths the average pulse dynamics is described by a perturbation approach (NLS) equation. Applying a perturbation theory, based on the Inverse Scattering Transform method, an analytic expression for the envelope of the DM soliton is derived. This expression correctly predicts the power enhancement arising from the dispersion management.Secondly, autosoliton transmission in DM fibre systems with periodical in-line deployment of nonlinear optical loop mirrors (NOLMs) is investigated. The use of in-line NOLMs is addressed as a general technique for all-optical passive 2R regeneration of return-to-zero data in high speed transmission system with strong dispersion management. By system optimisation, the feasibility of ultra-long single-channel and wavelength-division multiplexed data transmission at bit-rates ³ 40 Gbit s-1 in standard fibre-based systems is demonstrated. The tolerance limits of the results are defined.Thirdly, solutions of the NLS equation with gain and normal dispersion, that describes optical pulse propagation in an amplifying medium, are examined. A self-similar parabolic solution in the energy-containing core of the pulse is matched through Painlevé functions to the linear low-amplitude tails. The analysis provides a full description of the features of high-power pulses generated in an amplifying medium.

A design environment for deadlock-free concurrent software

Using current software engineering technology, the robustness required for safety critical software is not assurable. However, different approaches are possible which can help to assure software robustness to some extent. For achieving high reliability software, methods should be adopted which avoid introducing faults (fault avoidance); then testing should be carried out to identify any faults which persist (error removal). Finally, techniques should be used which allow any undetected faults to be tolerated (fault tolerance). The verification of correctness in system design specification and performance analysis of the model, are the basic issues in concurrent systems. In this context, modeling distributed concurrent software is one of the most important activities in the software life cycle, and communication analysis is a primary consideration to achieve reliability and safety. By and large fault avoidance requires human analysis which is error prone; by reducing human involvement in the tedious aspect of modelling and analysis of the software it is hoped that fewer faults will persist into its implementation in the real-time environment. The Occam language supports concurrent programming and is a language where interprocess interaction takes place by communications. This may lead to deadlock due to communication failure. Proper systematic methods must be adopted in the design of concurrent software for distributed computing systems if the communication structure is to be free of pathologies, such as deadlock. The objective of this thesis is to provide a design environment which ensures that processes are free from deadlock. A software tool was designed and used to facilitate the production of fault-tolerant software for distributed concurrent systems. Where Occam is used as a design language then state space methods, such as Petri-nets, can be used in analysis and simulation to determine the dynamic behaviour of the software, and to identify structures which may be prone to deadlock so that they may be eliminated from the design before the program is ever run. This design software tool consists of two parts. One takes an input program and translates it into a mathematical model (Petri-net), which is used for modeling and analysis of the concurrent software. The second part is the Petri-net simulator that takes the translated program as its input and starts simulation to generate the reachability tree. The tree identifies `deadlock potential' which the user can explore further. Finally, the software tool has been applied to a number of Occam programs. Two examples were taken to show how the tool works in the early design phase for fault prevention before the program is ever run.

Immunological and biochemical techniques in the analysis of tear proteins

This study is concerned with the analysis of tear proteins, paying particular attention to the state of the tears (e.g. non-stimulated, reflex, closed), created during sampling, and to assess their interactions with hydrogel contact lenses. The work has involved the use of a variety of biochemical and immunological analytical techniques for the measurement of proteins, (a), in tears, (b), on the contact lens, and (c), in the eluate of extracted lenses. Although a diverse range of tear components may contribute to contact lens spoilation, proteins were of particular interest in this study because of their theoretical potential for producing immunological reactions. Although normal host proteins in their natural state are generally not treated as dangerous or non-self, those which undergo denaturation or suffer a conformational change may provoke an excessive and unnecessary immune response. A novel on-lens cell based assay has been developed and exploited in order to study the role of the ubiquitous cell adhesion glycoprotein, vitronectin, in tears and contact lens wear under various parameters. Vitronectin, whose levels are known to increase in the closed eye environment and shown here to increase during contact lens wear, is an important immunoregulatory protein and may be a prominent marker of inflammatory activity. Immunodiffusion assays were developed and optimised for use in tear analysis, and in a series of subsequent studies used for example in the measurement of albumin, lactoferrin, IgA and IgG. The immunodiffusion assays were then applied in the estimation of the closed eye environment; an environment which has been described as sustaining a state of sub-clinical inflammation. The role and presence of a lesser understood and investigated protein, kininogen, was also estimated, in particular, in relation to contact lens wear. Difficulties arise when attempting to extract proteins from the contact lens in order to examine the individual nature of the proteins involved. These problems were partly alleviated with the use of the on-lens cell assay and a UV spectrophotometry assay, which can analyse the lens surface and bulk respectively, the latter yielding only total protein values. Various lens extraction methods were investigated to remove protein from the lens and the most efficient was employed in the analysis of lens extracts. Counter immunoelectrophoresis, an immunodiffusion assay, was then applied to the analysis of albumin, lactoferrin, IgA and IgG in the resultant eluates.

An econometric analysis of international tourism demand in Hong Kong : a cointegration and error correction approach

The purpose of this study is to develop econometric models to better understand the economic factors affecting inbound tourist flows from each of six origin countries that contribute to Hong Kong’s international tourism demand. To this end, we test alternative cointegration and error correction approaches to examine the economic determinants of tourist flows to Hong Kong, and to produce accurate econometric forecasts of inbound tourism demand. Our empirical findings show that permanent income is the most significant determinant of tourism demand in all models. The variables of own price, weighted substitute prices, trade volume, the share price index (as an indicator of changes in wealth in origin countries), and a dummy variable representing the Beijing incident (1989) are also found to be important determinants for some origin countries. The average long-run income and own price elasticity was measured at 2.66 and – 1.02, respectively. It was hypothesised that permanent income is a better explanatory variable of long-haul tourism demand than current income. A novel approach (grid search process) has been used to empirically derive the weights to be attached to the lagged income variable for estimating permanent income. The results indicate that permanent income, estimated with empirically determined relatively small weighting factors, was capable of producing better results than the current income variable in explaining long-haul tourism demand. This finding suggests that the use of current income in previous empirical tourism demand studies may have produced inaccurate results. The share price index, as a measure of wealth, was also found to be significant in two models. Studies of tourism demand rarely include wealth as an explanatory forecasting long-haul tourism demand. However, finding a satisfactory proxy for wealth common to different countries is problematic. This study indicates with the ECM (Error Correction Models) based on the Engle-Granger (1987) approach produce more accurate forecasts than ECM based on Pesaran and Shin (1998) and Johansen (1988, 1991, 1995) approaches for all of the long-haul markets and Japan. Overall, ECM produce better forecasts than the OLS, ARIMA and NAÏVE models, indicating the superiority of the application of a cointegration approach for tourism demand forecasting. The results show that permanent income is the most important explanatory variable for tourism demand from all countries but there are substantial variations between countries with the long-run elasticity ranging between 1.1 for the U.S. and 5.3 for U.K. Price is the next most important variable with the long-run elasticities ranging between -0.8 for Japan and -1.3 for Germany and short-run elasticities ranging between – 0.14 for Germany and -0.7 for Taiwan. The fastest growing market is Mainland China. The findings have implications for policies and strategies on investment, marketing promotion and pricing.

An evaluation of task analysis techniques for industrial process control

The concept of a task is fundamental to the discipline of ergonomics. Approaches to the analysis of tasks began in the early 1900's. These approaches have evolved and developed to the present day, when there is a vast array of methods available. Some of these methods are specific to particular contexts or applications, others more general. However, whilst many of these analyses allow tasks to be examined in detail, they do not act as tools to aid the design process or the designer. The present thesis examines the use of task analysis in a process control context, and in particular the use of task analysis to specify operator information and display requirements in such systems. The first part of the thesis examines the theoretical aspect of task analysis and presents a review of the methods, issues and concepts relating to task analysis. A review of over 80 methods of task analysis was carried out to form a basis for the development of a task analysis method to specify operator information requirements in industrial process control contexts. Of the methods reviewed Hierarchical Task Analysis was selected to provide such a basis and developed to meet the criteria outlined for such a method of task analysis. The second section outlines the practical application and evolution of the developed task analysis method. Four case studies were used to examine the method in an empirical context. The case studies represent a range of plant contexts and types, both complex and more simple, batch and continuous and high risk and low risk processes. The theoretical and empirical issues are drawn together and a method developed to provide a task analysis technique to specify operator information requirements and to provide the first stages of a tool to aid the design of VDU displays for process control.

Damage analysis of bridge structures using vibrational techniques

Much research is currently centred on the detection of damage in structures using vibrational data. The work presented here examined several areas of interest in support of a practical technique for identifying and locating damage within bridge structures using apparent changes in their vibrational response to known excitation. The proposed goals of such a technique included the need for the measurement system to be operated on site by a minimum number of staff and that the procedure should be as non-invasive to the bridge traffic-flow as possible. Initially the research investigated changes in the vibrational bending characteristics of two series of large-scale model bridge-beams in the laboratory and these included ordinary-reinforced and post-tensioned, prestressed designs. Each beam was progressively damaged at predetermined positions and its vibrational response to impact excitation was analysed. For the load-regime utilised the results suggested that the infuced damage manifested itself as a function of the span of a beam rather than a localised area. A power-law relating apparent damage with the applied loading and prestress levels was then proposed, together with a qualitative vibrational measure of structural damage. In parallel with the laboratory experiments a series of tests were undertaken at the sites of a number of highway bridges. The bridges selected had differing types of construction and geometric design including composite-concrete, concrete slab-and-beam, concrete-slab with supporting steel-troughing constructions together with regular-rectangular, skewed and heavily-skewed geometries. Initial investigations were made of the feasibility and reliability of various methods of structure excitation including traffic and impulse methods. It was found that localised impact using a sledge-hammer was ideal for the purposes of this work and that a cartridge `bolt-gun' could be used in some specific cases.

IN VIVO analysis of ocular morphological changes during phakic accommodation

The principal theme of this thesis is the in vivo examination of ocular morphological changes during phakic accommodation, with particular attention paid to the ciliary muscle and crystalline lens. The investigations detailed involved the application of high-resolution imaging techniques to facilitate the acquisition of new data to assist in the clarification of aspects of the accommodative system that were poorly understood. A clinical evaluation of the newly available Grand Seiko Auto Ref/ Keratometer WAM-5500 optometer was undertaken to assess its value in the field of accommodation research. The device was found to be accurate and repeatable compared to subjective refraction, and has the added advantage of allowing dynamic data collection at a frequency of around 5 Hz. All of the subsequent investigations applied the WAM-5500 for determination of refractive error and objective accommodative responses. Anterior segment optical coherence tomography (AS-OCT) based studies examined the morphology and contractile response of youthful and ageing ciliary muscle. Nasal versus temporal asymmetry was identified, with the temporal aspect being both thicker and demonstrating a greater contractile response. The ciliary muscle was longer in terms of both its anterior (r = 0.49, P <0.001) and overall length (r = 0.45, P = 0.02) characteristics, in myopes. The myopic ciliary muscle does not appear to be merely stretched during axial elongation, as no significant relationship between thickness and refractive error was identified. The main contractile responses observed were a thickening of the anterior region and a shortening of the muscle, particularly anteriorly. Similar patterns of response were observed in subjects aged up to 70 years, supporting a lensocentric theory of presbyopia development. Following the discovery of nasal/ temporal asymmetry in ciliary muscle morphology and response, an investigation was conducted to explore whether the regional variations in muscle contractility impacted on lens stability during accommodation. A bespoke programme was developed to analyse AS-OCT images and determine whether lens tilt and decentration varied between the relaxed and accommodated states. No significant accommodative difference in these parameters was identified, implying that any changes in lens stability with accommodation are very slight, as a possible consequence of vitreous support. Novel three-dimensional magnetic resonance imaging (MRI) and analysis techniques were used to investigate changes in lens morphology and ocular conformation during accommodation. An accommodative reduction in lens equatorial diameter provides further evidence to support the Helmholtzian mechanism of accommodation, whilst the observed increase in lens volume challenges the widespread assertion that this structure is incompressible due to its high water content. Wholeeye MRI indicated that the volume of the vitreous chamber remains constant during accommodation. No significant changes in ocular conformation were detected using MRI. The investigations detailed provide further insight into the mechanisms of accommodation and presbyopia, and represent a platform for future work in this field.

Mathematical modelling of patient risks in a hospital environment, using multiple regression analysis

The aim of this research work was primarily to examine the relevance of patient parameters, ward structures, procedures and practices, in respect of the potential hazards of wound cross-infection and nasal colonisation with multiple resistant strains of Staphylococcus aureus, which it is thought might provide a useful indication of a patient's general susceptibility to wound infection. Information from a large cross-sectional survey involving 12,000 patients from some 41 hospitals and 375 wards was collected over a five-year period from 1967-72, and its validity checked before any subsequent analysis was carried out. Many environmental factors and procedures which had previously been thought (but never conclusively proved) to have an influence on wound infection or nasal colonisation rates, were assessed, and subsequently dismissed as not being significant, provided that the standard of the current range of practices and procedures is maintained and not allowed to deteriorate. Retrospective analysis revealed that the probability of wound infection was influenced by the patient's age, duration of pre-operative hospitalisation, sex, type of wound, presence and type of drain, number of patients in ward, and other special risk factors, whilst nasal colonisation was found to be influenced by the patient's age, total duration of hospitalisation, sex, antibiotics, proportion of occupied beds in the ward, average distance between bed centres and special risk factors. A multi-variate regression analysis technique was used to develop statistical models, consisting of variable patient and environmental factors which were found to have a significant influence on the risks pertaining to wound infection and nasal colonisation. A relationship between wound infection and nasal colonisation was then established and this led to the development of a more advanced model for predicting wound infections, taking advantage of the additional knowledge of the patient's state of nasal colonisation prior to operation.