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.

Modelling and solving train scheduling problems under capacity constraints

Many large coal mining operations in Australia rely heavily on the rail network to transport coal from mines to coal terminals at ports for shipment. Over the last few years, due to the fast growing demand, the coal rail network is becoming one of the worst industrial bottlenecks in Australia. As a result, this provides great incentives for pursuing better optimisation and control strategies for the operation of the whole rail transportation system under network and terminal capacity constraints. This PhD research aims to achieve a significant efficiency improvement in a coal rail network on the basis of the development of standard modelling approaches and generic solution techniques. Generally, the train scheduling problem can be modelled as a Blocking Parallel- Machine Job-Shop Scheduling (BPMJSS) problem. In a BPMJSS model for train scheduling, trains and sections respectively are synonymous with jobs and machines and an operation is regarded as the movement/traversal of a train across a section. To begin, an improved shifting bottleneck procedure algorithm combined with metaheuristics has been developed to efficiently solve the Parallel-Machine Job- Shop Scheduling (PMJSS) problems without the blocking conditions. Due to the lack of buffer space, the real-life train scheduling should consider blocking or hold-while-wait constraints, which means that a track section cannot release and must hold a train until the next section on the routing becomes available. As a consequence, the problem has been considered as BPMJSS with the blocking conditions. To develop efficient solution techniques for BPMJSS, extensive studies on the nonclassical scheduling problems regarding the various buffer conditions (i.e. blocking, no-wait, limited-buffer, unlimited-buffer and combined-buffer) have been done. In this procedure, an alternative graph as an extension of the classical disjunctive graph is developed and specially designed for the non-classical scheduling problems such as the blocking flow-shop scheduling (BFSS), no-wait flow-shop scheduling (NWFSS), and blocking job-shop scheduling (BJSS) problems. By exploring the blocking characteristics based on the alternative graph, a new algorithm called the topological-sequence algorithm is developed for solving the non-classical scheduling problems. To indicate the preeminence of the proposed algorithm, we compare it with two known algorithms (i.e. Recursive Procedure and Directed Graph) in the literature. Moreover, we define a new type of non-classical scheduling problem, called combined-buffer flow-shop scheduling (CBFSS), which covers four extreme cases: the classical FSS (FSS) with infinite buffer, the blocking FSS (BFSS) with no buffer, the no-wait FSS (NWFSS) and the limited-buffer FSS (LBFSS). After exploring the structural properties of CBFSS, we propose an innovative constructive algorithm named the LK algorithm to construct the feasible CBFSS schedule. Detailed numerical illustrations for the various cases are presented and analysed. By adjusting only the attributes in the data input, the proposed LK algorithm is generic and enables the construction of the feasible schedules for many types of non-classical scheduling problems with different buffer constraints. Inspired by the shifting bottleneck procedure algorithm for PMJSS and characteristic analysis based on the alternative graph for non-classical scheduling problems, a new constructive algorithm called the Feasibility Satisfaction Procedure (FSP) is proposed to obtain the feasible BPMJSS solution. A real-world train scheduling case is used for illustrating and comparing the PMJSS and BPMJSS models. Some real-life applications including considering the train length, upgrading the track sections, accelerating a tardy train and changing the bottleneck sections are discussed. Furthermore, the BPMJSS model is generalised to be a No-Wait Blocking Parallel- Machine Job-Shop Scheduling (NWBPMJSS) problem for scheduling the trains with priorities, in which prioritised trains such as express passenger trains are considered simultaneously with non-prioritised trains such as freight trains. In this case, no-wait conditions, which are more restrictive constraints than blocking constraints, arise when considering the prioritised trains that should traverse continuously without any interruption or any unplanned pauses because of the high cost of waiting during travel. In comparison, non-prioritised trains are allowed to enter the next section immediately if possible or to remain in a section until the next section on the routing becomes available. Based on the FSP algorithm, a more generic algorithm called the SE algorithm is developed to solve a class of train scheduling problems in terms of different conditions in train scheduling environments. To construct the feasible train schedule, the proposed SE algorithm consists of many individual modules including the feasibility-satisfaction procedure, time-determination procedure, tune-up procedure and conflict-resolve procedure algorithms. To find a good train schedule, a two-stage hybrid heuristic algorithm called the SE-BIH algorithm is developed by combining the constructive heuristic (i.e. the SE algorithm) and the local-search heuristic (i.e. the Best-Insertion- Heuristic algorithm). To optimise the train schedule, a three-stage algorithm called the SE-BIH-TS algorithm is developed by combining the tabu search (TS) metaheuristic with the SE-BIH algorithm. Finally, a case study is performed for a complex real-world coal rail network under network and terminal capacity constraints. The computational results validate that the proposed methodology would be very promising because it can be applied as a fundamental tool for modelling and solving many real-world scheduling problems.

Monte Carlo modelling of X-ray absorptiometry and its application to body composition studies

This thesis applies Monte Carlo techniques to the study of X-ray absorptiometric methods of bone mineral measurement. These studies seek to obtain information that can be used in efforts to improve the accuracy of the bone mineral measurements. A Monte Carlo computer code for X-ray photon transport at diagnostic energies has been developed from first principles. This development was undertaken as there was no readily available code which included electron binding energy corrections for incoherent scattering and one of the objectives of the project was to study the effects of inclusion of these corrections in Monte Carlo models. The code includes the main Monte Carlo program plus utilities for dealing with input data. A number of geometrical subroutines which can be used to construct complex geometries have also been written. The accuracy of the Monte Carlo code has been evaluated against the predictions of theory and the results of experiments. The results show a high correlation with theoretical predictions. In comparisons of model results with those of direct experimental measurements, agreement to within the model and experimental variances is obtained. The code is an accurate and valid modelling tool. A study of the significance of inclusion of electron binding energy corrections for incoherent scatter in the Monte Carlo code has been made. The results show this significance to be very dependent upon the type of application. The most significant effect is a reduction of low angle scatter flux for high atomic number scatterers. To effectively apply the Monte Carlo code to the study of bone mineral density measurement by photon absorptiometry the results must be considered in the context of a theoretical framework for the extraction of energy dependent information from planar X-ray beams. Such a theoretical framework is developed and the two-dimensional nature of tissue decomposition based on attenuation measurements alone is explained. This theoretical framework forms the basis for analytical models of bone mineral measurement by dual energy X-ray photon absorptiometry techniques. Monte Carlo models of dual energy X-ray absorptiometry (DEXA) have been established. These models have been used to study the contribution of scattered radiation to the measurements. It has been demonstrated that the measurement geometry has a significant effect upon the scatter contribution to the detected signal. For the geometry of the models studied in this work the scatter has no significant effect upon the results of the measurements. The model has also been used to study a proposed technique which involves dual energy X-ray transmission measurements plus a linear measurement of the distance along the ray path. This is designated as the DPA( +) technique. The addition of the linear measurement enables the tissue decomposition to be extended to three components. Bone mineral, fat and lean soft tissue are the components considered here. The results of the model demonstrate that the measurement of bone mineral using this technique is stable over a wide range of soft tissue compositions and hence would indicate the potential to overcome a major problem of the two component DEXA technique. However, the results also show that the accuracy of the DPA( +) technique is highly dependent upon the composition of the non-mineral components of bone and has poorer precision (approximately twice the coefficient of variation) than the standard DEXA measurements. These factors may limit the usefulness of the technique. These studies illustrate the value of Monte Carlo computer modelling of quantitative X-ray measurement techniques. The Monte Carlo models of bone densitometry measurement have:- 1. demonstrated the significant effects of the measurement geometry upon the contribution of scattered radiation to the measurements, 2. demonstrated that the statistical precision of the proposed DPA( +) three tissue component technique is poorer than that of the standard DEXA two tissue component technique, 3. demonstrated that the proposed DPA(+) technique has difficulty providing accurate simultaneous measurement of body composition in terms of a three component model of fat, lean soft tissue and bone mineral,4. and provided a knowledge base for input to decisions about development (or otherwise) of a physical prototype DPA( +) imaging system. The Monte Carlo computer code, data, utilities and associated models represent a set of significant, accurate and valid modelling tools for quantitative studies of physical problems in the fields of diagnostic radiology and radiography.

Modelling of some biological materials using continuum mechanics

Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.

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.

Discrete choice modelling of combined mode and departure time

Typical daily decision-making process of individuals regarding use of transport system involves mainly three types of decisions: mode choice, departure time choice and route choice. This paper focuses on the mode and departure time choice processes and studies different model specifications for a combined mode and departure time choice model. The paper compares different sets of explanatory variables as well as different model structures to capture the correlation among alternatives and taste variations among the commuters. The main hypothesis tested in this paper is that departure time alternatives are also correlated by the amount of delay. Correlation among different alternatives is confirmed by analyzing different nesting structures as well as error component formulations. Random coefficient logit models confirm the presence of the random taste heterogeneity across commuters. Mixed nested logit models are estimated to jointly account for the random taste heterogeneity and the correlation among different alternatives. Results indicate that accounting for the random taste heterogeneity as well as inter-alternative correlation improves the model performance.

Validation of FHWA crash models for rural intersections - Lessons learned

A national-level safety analysis tool is needed to complement existing analytical tools for assessment of the safety impacts of roadway design alternatives. FHWA has sponsored the development of the Interactive Highway Safety Design Model (IHSDM), which is roadway design and redesign software that estimates the safety effects of alternative designs. Considering the importance of IHSDM in shaping the future of safety-related transportation investment decisions, FHWA justifiably sponsored research with the sole intent of independently validating some of the statistical models and algorithms in IHSDM. Statistical model validation aims to accomplish many important tasks, including (a) assessment of the logical defensibility of proposed models, (b) assessment of the transferability of models over future time periods and across different geographic locations, and (c) identification of areas in which future model improvements should be made. These three activities are reported for five proposed types of rural intersection crash prediction models. The internal validation of the model revealed that the crash models potentially suffer from omitted variables that affect safety, site selection and countermeasure selection bias, poorly measured and surrogate variables, and misspecification of model functional forms. The external validation indicated the inability of models to perform on par with model estimation performance. Recommendations for improving the state of the practice from this research include the systematic conduct of carefully designed before-and-after studies, improvements in data standardization and collection practices, and the development of analytical methods to combine the results of before-and-after studies with cross-sectional studies in a meaningful and useful way.

Empirical investigation of interactive highway safety design model accident prediction algorithm : Rural intersections

One major gap in transportation system safety management is the ability to assess the safety ramifications of design changes for both new road projects and modifications to existing roads. To fulfill this need, FHWA and its many partners are developing a safety forecasting tool, the Interactive Highway Safety Design Model (IHSDM). The tool will be used by roadway design engineers, safety analysts, and planners throughout the United States. As such, the statistical models embedded in IHSDM will need to be able to forecast safety impacts under a wide range of roadway configurations and environmental conditions for a wide range of driver populations and will need to be able to capture elements of driving risk across states. One of the IHSDM algorithms developed by FHWA and its contractors is for forecasting accidents on rural road segments and rural intersections. The methodological approach is to use predictive models for specific base conditions, with traffic volume information as the sole explanatory variable for crashes, and then to apply regional or state calibration factors and accident modification factors (AMFs) to estimate the impact on accidents of geometric characteristics that differ from the base model conditions. In the majority of past approaches, AMFs are derived from parameter estimates associated with the explanatory variables. A recent study for FHWA used a multistate database to examine in detail the use of the algorithm with the base model-AMF approach and explored alternative base model forms as well as the use of full models that included nontraffic-related variables and other approaches to estimate AMFs. That research effort is reported. The results support the IHSDM methodology.