Numerical modelling of industrial microwave heating

The numerical modelling of electromagnetic waves has been the focus of many research areas in the past. Some specific applications of electromagnetic wave scattering are in the fields of Microwave Heating and Radar Communication Systems. The equations that govern the fundamental behaviour of electromagnetic wave propagation in waveguides and cavities are the Maxwell's equations. In the literature, a number of methods have been employed to solve these equations. Of these methods, the classical Finite-Difference Time-Domain scheme, which uses a staggered time and space discretisation, is the most well known and widely used. However, it is complicated to implement this method on an irregular computational domain using an unstructured mesh. In this work, a coupled method is introduced for the solution of Maxwell's equations. It is proposed that the free-space component of the solution is computed in the time domain, whilst the load is resolved using the frequency dependent electric field Helmholtz equation. This methodology results in a timefrequency domain hybrid scheme. For the Helmholtz equation, boundary conditions are generated from the time dependent free-space solutions. The boundary information is mapped into the frequency domain using the Discrete Fourier Transform. The solution for the electric field components is obtained by solving a sparse-complex system of linear equations. The hybrid method has been tested for both waveguide and cavity configurations. Numerical tests performed on waveguides and cavities for inhomogeneous lossy materials highlight the accuracy and computational efficiency of the newly proposed hybrid computational electromagnetic strategy.

Real-time performance modelling of a sustained attention to response task

Vigilance declines when exposed to highly predictable and uneventful tasks. Monotonous tasks provide little cognitive and motor stimulation and contribute to human errors. This paper aims to model and detect vigilance decline in real time through participant’s reaction times during a monotonous task. A lab-based experiment adapting the Sustained Attention to Response Task (SART) is conducted to quantify the effect of monotony on overall performance. Then relevant parameters are used to build a model detecting hypovigilance throughout the experiment. The accuracy of different mathematical models are compared to detect in real-time – minute by minute - the lapses in vigilance during the task. We show that monotonous tasks can lead to an average decline in performance of 45%. Furthermore, vigilance modelling enables to detect vigilance decline through reaction times with an accuracy of 72% and a 29% false alarm rate. Bayesian models are identified as a better model to detect lapses in vigilance as compared to Neural Networks and Generalised Linear Mixed Models. This modelling could be used as a framework to detect vigilance decline of any human performing monotonous tasks.

Predicting effects of monotony on driver’s vigilance

Monotony has been identified as a contributing factor to road crashes. Drivers’ ability to react to unpredictable events deteriorates when exposed to highly predictable and uneventful driving tasks, such as driving on Australian rural roads, many of which are monotonous by nature. Highway design in particular attempts to reduce the driver’s task to a merely lane-keeping one. Such a task provides little stimulation and is monotonous, thus affecting the driver’s attention which is no longer directed towards the road. Inattention contributes to crashes, especially for professional drivers. Monotony has been studied mainly from the endogenous perspective (for instance through sleep deprivation) without taking into account the influence of the task itself (repetitiveness) or the surrounding environment. The aim and novelty of this thesis is to develop a methodology (mathematical framework) able to predict driver lapses of vigilance under monotonous environments in real time, using endogenous and exogenous data collected from the driver, the vehicle and the environment. Existing approaches have tended to neglect the specificity of task monotony, leaving the question of the existence of a “monotonous state” unanswered. Furthermore the issue of detecting vigilance decrement before it occurs (predictions) has not been investigated in the literature, let alone in real time. A multidisciplinary approach is necessary to explain how vigilance evolves in monotonous conditions. Such an approach needs to draw on psychology, physiology, road safety, computer science and mathematics. The systemic approach proposed in this study is unique with its predictive dimension and allows us to define, in real time, the impacts of monotony on the driver’s ability to drive. Such methodology is based on mathematical models integrating data available in vehicles to the vigilance state of the driver during a monotonous driving task in various environments. The model integrates different data measuring driver’s endogenous and exogenous factors (related to the driver, the vehicle and the surrounding environment). Electroencephalography (EEG) is used to measure driver vigilance since it has been shown to be the most reliable and real time methodology to assess vigilance level. There are a variety of mathematical models suitable to provide a framework for predictions however, to find the most accurate model, a collection of mathematical models were trained in this thesis and the most reliable was found. The methodology developed in this research is first applied to a theoretically sound measure of sustained attention called Sustained Attention Response to Task (SART) as adapted by Michael (2010), Michael and Meuter (2006, 2007). This experiment induced impairments due to monotony during a vigilance task. Analyses performed in this thesis confirm and extend findings from Michael (2010) that monotony leads to an important vigilance impairment independent of fatigue. This thesis is also the first to show that monotony changes the dynamics of vigilance evolution and tends to create a “monotonous state” characterised by reduced vigilance. Personality traits such as being a low sensation seeker can mitigate this vigilance decrement. It is also evident that lapses in vigilance can be predicted accurately with Bayesian modelling and Neural Networks. This framework was then applied to the driving task by designing a simulated monotonous driving task. The design of such task requires multidisciplinary knowledge and involved psychologist Rebecca Michael. Monotony was varied through both the road design and the road environment variables. This experiment demonstrated that road monotony can lead to driving impairment. Particularly monotonous road scenery was shown to have the most impact compared to monotonous road design. Next, this study identified a variety of surrogate measures that are correlated with vigilance levels obtained from the EEG. Such vigilance states can be predicted with these surrogate measures. This means that vigilance decrement can be detected in a car without the use of an EEG device. Amongst the different mathematical models tested in this thesis, only Neural Networks predicted the vigilance levels accurately. The results of both these experiments provide valuable information about the methodology to predict vigilance decrement. Such an issue is quite complex and requires modelling that can adapt to highly inter-individual differences. Only Neural Networks proved accurate in both studies, suggesting that these models are the most likely to be accurate when used on real roads or for further research on vigilance modelling. This research provides a better understanding of the driving task under monotonous conditions. Results demonstrate that mathematical modelling can be used to determine the driver’s vigilance state when driving using surrogate measures identified during this study. This research has opened up avenues for future research and could result in the development of an in-vehicle device predicting driver vigilance decrement. Such a device could contribute to a reduction in crashes and therefore improve road safety.

Forecasting negative effects of monotony and sensation seeking on performance during a vigilance task

The driving task requires sustained attention during prolonged periods, and can be performed in highly predictable or repetitive environments. Such conditions could create hypovigilance and impair performance towards critical events. Identifying such impairment in monotonous conditions has been a major subject of research, but no research to date has attempted to predict it in real-time. This pilot study aims to show that performance decrements due to monotonous tasks can be predicted through mathematical modelling taking into account sensation seeking levels. A short vigilance task sensitive to short periods of lapses of vigilance called Sustained Attention to Response Task is used to assess participants‟ performance. The framework for prediction developed on this task could be extended to a monotonous driving task. A Hidden Markov Model (HMM) is proposed to predict participants‟ lapses in alertness. Driver‟s vigilance evolution is modelled as a hidden state and is correlated to a surrogate measure: the participant‟s reactions time. This experiment shows that the monotony of the task can lead to an important decline in performance in less than five minutes. This impairment can be predicted four minutes in advance with an 86% accuracy using HMMs. This experiment showed that mathematical models such as HMM can efficiently predict hypovigilance through surrogate measures. The presented model could result in the development of an in-vehicle device that detects driver hypovigilance in advance and warn the driver accordingly, thus offering the potential to enhance road safety and prevent road crashes.

Near infrared for non-destructive testing of articular cartilage

The concept of non-destructive testing (NDT) of materials and structures is of immense importance in engineering and medicine. Several NDT methods including electromagnetic (EM)-based e.g. X-ray and Infrared; ultrasound; and S-waves have been proposed for medical applications. This paper evaluates the viability of near infrared (NIR) spectroscopy, an EM method for rapid non-destructive evaluation of articular cartilage. Specifically, we tested the hypothesis that there is a correlation between the NIR spectrum and the physical and mechanical characteristics of articular cartilage such as thickness, stress and stiffness. Intact, visually normal cartilage-on-bone plugs from 2-3yr old bovine patellae were exposed to NIR light from a diffuse reflectance fibre-optic probe and tested mechanically to obtain their thickness, stress, and stiffness. Multivariate statistical analysis-based predictive models relating articular cartilage NIR spectra to these characterising parameters were developed. Our results show that there is a varying degree of correlation between the different parameters and the NIR spectra of the samples with R2 varying between 65 and 93%. We therefore conclude that NIR can be used to determine, nondestructively, the physical and functional characteristics of articular cartilage.

Asset health prediction using condition indicators and operating environment indicators : a case study

Prognostics and asset life prediction is one of research potentials in engineering asset health management. We previously developed the Explicit Hazard Model (EHM) to effectively and explicitly predict asset life using three types of information: population characteristics; condition indicators; and operating environment indicators. We have formerly studied the application of both the semi-parametric EHM and non-parametric EHM to the survival probability estimation in the reliability field. The survival time in these models is dependent not only upon the age of the asset monitored, but also upon the condition and operating environment information obtained. This paper is a further study of the semi-parametric and non-parametric EHMs to the hazard and residual life prediction of a set of resistance elements. The resistance elements were used as corrosion sensors for measuring the atmospheric corrosion rate in a laboratory experiment. In this paper, the estimated hazard of the resistance element using the semi-parametric EHM and the non-parametric EHM is compared to the traditional Weibull model and the Aalen Linear Regression Model (ALRM), respectively. Due to assuming a Weibull distribution in the baseline hazard of the semi-parametric EHM, the estimated hazard using this model is compared to the traditional Weibull model. The estimated hazard using the non-parametric EHM is compared to ALRM which is a well-known non-parametric covariate-based hazard model. At last, the predicted residual life of the resistance element using both EHMs is compared to the actual life data.

Maternal exposure to ambient temperature and the risk of preterm birth and stillbirth in Brisbane, Australia

Almost 10% of all births are preterm and 2.2% are stillbirths globally. Recent research has suggested that environmental factors may be a contributory cause to these adverse birth outcomes. The authors examined the relationship between ambient temperature and preterm birth and stillbirth in Brisbane, Australia between 2005 and 2009 (n = 101,870). They used a Cox proportional hazard model with live birth and stillbirth as competing risks. They also examined if there were periods of the pregnancy where exposure to high temperatures had a greater effect. Exposure to higher ambient temperatures during pregnancy increased the risk of stillbirth. The hazard ratio for stillbirth was 0.3 at 12 °C relative to the reference temperature at 21 °C. The temperature effect was greatest for fetuses of less than 36 weeks of gestation. There was an association between higher temperature and shorter gestation, as the hazard ratio for live birth was 0.96 at 15 °C and 1.02 at 25 °C. This effect was greatest at later gestational ages. The results provide strong evidence of an association between increased temperature and increased risk of stillbirth and shorter gestations.

Krylov subspace approximations for the exponential Euler method: Error estimates and the harmonic Ritz approximant

We study Krylov subspace methods for approximating the matrix-function vector product φ(tA)b where φ(z) = [exp(z) - 1]/z. This product arises in the numerical integration of large stiff systems of differential equations by the Exponential Euler Method, where A is the Jacobian matrix of the system. Recently, this method has found application in the simulation of transport phenomena in porous media within mathematical models of wood drying and groundwater flow. We develop an a posteriori upper bound on the Krylov subspace approximation error and provide a new interpretation of a previously published error estimate. This leads to an alternative Krylov approximation to φ(tA)b, the so-called Harmonic Ritz approximant, which we find does not exhibit oscillatory behaviour of the residual error.

Relationship between physical activity and stiff or painful joints in mid-aged women and older women: a 3-year prospective study

This prospective study examined the association between physical activity and the incidence of self-reported stiff or painful joints (SPJ) among mid-age women and older women over a 3-year period. Data were collected from cohorts of mid-age (48–55 years at Time 1; n = 4,780) and older women (72–79 years at Time 1; n = 3,970) who completed mailed surveys 3 years apart for the Australian Longitudinal Study on Women's Health. Physical activity was measured with the Active Australia questions and categorized based on metabolic equivalent value minutes per week: none (<40 MET.min/week); very low (40 to <300 MET.min/week); low (300 to <600 MET.min/week); moderate (600 to <1,200 MET.min/week); and high (1,200+ MET.min/week). Cohort-specific logistic regression models were used to examine the association between physical activity at Time 1 and SPJ 'sometimes or often' and separately 'often' at Time 2. Respondents reporting SPJ 'sometimes or often' at Time 1 were excluded from analysis. In univariate models, the odds of reporting SPJ 'sometimes or often' were lower for mid-age respondents reporting low (odds ratio (OR) = 0.77, 95% confidence interval (CI) = 0.63–0.94), moderate (OR = 0.82, 95% CI = 0.68–0.99), and high (OR = 0.75, 95% CI = 0.62–0.90) physical activity levels and for older respondents who were moderately (OR = 0.80, 95% CI = 0.65–0.98) or highly active (OR = 0.83, 95% CI = 0.69–0.99) than for those who were sedentary. After adjustment for confounders, these associations were no longer statistically significant. The odds of reporting SPJ 'often' were lower for mid-age respondents who were moderately active (OR = 0.71, 95% CI = 0.52–0.97) than for sedentary respondents in univariate but not adjusted models. Older women in the low (OR = 0.72, 95% CI = 0.55–0.96), moderate (OR = 0.54, 95% CI = 0.39–0.76), and high (OR = 0.61, 95% CI = 0.46–0.82) physical activity categories had lower odds of reporting SPJ 'often' at Time 2 than their sedentary counterparts, even after adjustment for confounders. These results are the first to show a dose–response relationship between physical activity and arthritis symptoms in older women. They suggest that advice for older women not currently experiencing SPJ should routinely include counseling on the importance of physical activity for preventing the onset of these symptoms.

Stochastic modelling of T cell homeostasis for two competing clonotypes via the master equation

Stochastic models for competing clonotypes of T cells by multivariate, continuous-time, discrete state, Markov processes have been proposed in the literature by Stirk, Molina-París and van den Berg (2008). A stochastic modelling framework is important because of rare events associated with small populations of some critical cell types. Usually, computational methods for these problems employ a trajectory-based approach, based on Monte Carlo simulation. This is partly because the complementary, probability density function (PDF) approaches can be expensive but here we describe some efficient PDF approaches by directly solving the governing equations, known as the Master Equation. These computations are made very efficient through an approximation of the state space by the Finite State Projection and through the use of Krylov subspace methods when evolving the matrix exponential. These computational methods allow us to explore the evolution of the PDFs associated with these stochastic models, and bimodal distributions arise in some parameter regimes. Time-dependent propensities naturally arise in immunological processes due to, for example, age-dependent effects. Incorporating time-dependent propensities into the framework of the Master Equation significantly complicates the corresponding computational methods but here we describe an efficient approach via Magnus formulas. Although this contribution focuses on the example of competing clonotypes, the general principles are relevant to multivariate Markov processes and provide fundamental techniques for computational immunology.

Parameter estimation for a phenomenological model of the cardiac action potential

The action potential (ap) of a cardiac cell is made up of a complex balance of ionic currents which flow across the cell membrane in response to electrical excitation of the cell. Biophysically detailed mathematical models of the ap have grown larger in terms of the variables and parameters required to model new findings in subcellular ionic mechanisms. The fitting of parameters to such models has seen a large degree of parameter and module re-use from earlier models. An alternative method for modelling electrically exciteable cardiac tissue is a phenomenological model, which reconstructs tissue level ap wave behaviour without subcellular details. A new parameter estimation technique to fit the morphology of the ap in a four variable phenomenological model is presented. An approximation of a nonlinear ordinary differential equation model is established that corresponds to the given phenomenological model of the cardiac ap. The parameter estimation problem is converted into a minimisation problem for the unknown parameters. A modified hybrid Nelder–Mead simplex search and particle swarm optimization is then used to solve the minimisation problem for the unknown parameters. The successful fitting of data generated from a well known biophysically detailed model is demonstrated. A successful fit to an experimental ap recording that contains both noise and experimental artefacts is also produced. The parameter estimation method’s ability to fit a complex morphology to a model with substantially more parameters than previously used is established.

Aircraft emission reduction through multi-disciplinary flight path optimisation

There is worldwide interest in reducing aircraft emissions. The difficulty of reducing emissions including water vapour, carbon dioxide (CO2) and oxides of nitrogen (NOx) is mainly due from the fact that a commercial aircraft is usually designed for a particular optimal cruise altitude but may be requested or required to operate and deviate at different altitude and speeds to archive a desired or commanded flight plan, resulting in increased emissions. This is a multi- disciplinary problem with multiple trade-offs such as optimising engine efficiency, minimising fuel burnt, minimise emissions while maintaining aircraft separation and air safety. This project presents the coupling of an advanced optimisation technique with mathematical models and algorithms for aircraft emission reduction through flight optimisation. Numerical results show that the method is able to capture a set of useful trade-offs between aircraft range and NOx, and mission fuel consumption and NOx. In addition, alternative cruise operating conditions including Mach and altitude that produce minimum NOx and CO2 (minimum mission fuel weight) are suggested.