Bayesian classification of catchments using spatial data: a first step to improved modelling of catchment effects on stream ecological condition

A major challenge facing freshwater ecologists and managers is the development of models that link stream ecological condition to catchment scale effects, such as land use. Previous attempts to make such models have followed two general approaches. The bottom-up approach employs mechanistic models, which can quickly become too complex to be useful. The top-down approach employs empirical models derived from large data sets, and has often suffered from large amounts of unexplained variation in stream condition.

We believe that the lack of success of both modelling approaches may be at least partly explained by scientists considering too wide a breadth of catchment type. Thus, we believe that by stratifying large sets of catchments into groups of similar types prior to modelling, both types of models may be improved. This paper describes preliminary work using a Bayesian classification software package, ‘Autoclass’ (Cheeseman and Stutz 1996) to create classes of catchments within the Murray Darling Basin based on physiographic data.

Autoclass uses a model-based classification method that employs finite mixture modelling and trades off model fit versus complexity, leading to a parsimonious solution. The software provides information on the posterior probability that the classification is ‘correct’ and also probabilities for alternative classifications. The importance of each attribute in defining the individual classes is calculated and presented, assisting description of the classes. Each case is ‘assigned’ to a class based on membership probability, but the probability of membership of other classes is also provided. This feature deals very well with cases that do not fit neatly into a larger class. Lastly, Autoclass requires the user to specify the measurement error of continuous variables.

Catchments were derived from the Australian digital elevation model. Physiographic data werederived from national spatial data sets. There was very little information on measurement errors for the spatial data, and so a conservative error of 5% of data range was adopted for all continuous attributes. The incorporation of uncertainty into spatial data sets remains a research challenge.

The results of the classification were very encouraging. The software found nine classes of catchments in the Murray Darling Basin. The classes grouped together geographically, and followed altitude and latitude gradients, despite the fact that these variables were not included in the classification. Descriptions of the classes reveal very different physiographic environments, ranging from dry and flat catchments (i.e. lowlands), through to wet and hilly catchments (i.e. mountainous areas). Rainfall and slope were two important discriminators between classes. These two attributes, in particular, will affect the ways in which the stream interacts with the catchment, and can thus be expected to modify the effects of land use change on ecological condition. Thus, realistic models of the effects of land use change on streams would differ between the different types of catchments, and sound management practices will differ.

A small number of catchments were assigned to their primary class with relatively low probability. These catchments lie on the boundaries of groups of catchments, with the second most likely class being an adjacent group. The locations of these ‘uncertain’ catchments show that the Bayesian classification dealt well with cases that do not fit neatly into larger classes.

Although the results are intuitive, we cannot yet assess whether the classifications described in this paper would assist the modelling of catchment scale effects on stream ecological condition. It is most likely that catchment classification and modelling will be an iterative process, where the needs of the model are used to guide classification, and the results of classifications used to suggest further refinements to models.

Modelling regular and estimable inverse demand systems : a distance function approach

To be useful for policy simulation in the current climate of rapid structural change, inverse demand systems must remain regular over substanstial variations in quantities. The distance function is a convenient vehicle for generating such systems. It also allows convenient imposition of prior ideas about the structure of preferences required for realistic policy work. While the distance function directly yields Hicksian inverse demand functions via the Shepard-Hanoch lemma, they are usually explicit in the unobservable level of utility (u), but lack a closed-form representation in terms of the observable variables. Note however that the unobservability of u need not hinder estimation. A simple one-dimensional numerical inversion allows the estimation of the distance function via the parameters of the implied Marshallian inverse demand functions. This paper develops the formal theory for using distance functions in this context, and reports on initial trials on the operational feasibility of the method.

Multivariate modelling of variability in sheet metal forming

The inherent variability in incoming material and process conditions in sheet metal forming makes quality control and the maintenance of consistency extremely difficult. A single FEM simulation is successful at predicting the formability for a given system, however lacks the ability to capture the variability in an actual production process due to the numerical deterministic nature. This paper investigates a probabilistic analytical model where the variation of five input parameters and their relationship to the sensitivity of springback in a stamping process is examined. A range of sheet tensions are investigated, simulating different operating windows in an attempt to highlight robust regions where the distribution of springback is small. A series of FEM simulations were also performed, to compare with the findings from the analytical model using AutoForm Sigma v4.04 and to validate the analytical model assumptions.

Results show that an increase in sheet tension not only decreases springback, but more importantly reduces the sensitivity of the process to variation. A relative sensitivity analysis has been performed where the most influential parameters and the changes in sensitivity at various sheet tensions have been investigated. Variation in the material parameters, yield stress and n-value were the most influential causes of springback variation, when compared to process input parameters such as friction, which had a small effect. The probabilistic model presented allows manufacturers to develop a more comprehensive assessment of the success of their forming processes by capturing the effects of inherent variation.

Simulation of contact pressure in sheet metal trimming/blanking process

In the car body stamping process, trim/blank die cutting edges are subjected to very high tribological loads that result in loss of tool material from both the punch and die cutting edges. According to Archard’s wear model, normal contact force and sliding distance directly affects the wear. Therefore, knowledge of the acting forces on local contact areas has a pivotal role towards the prediction of tool wear. This paper presents a finite element modelling approach to determining the contact pressure distribution on the tool cutting edges during a trimming/blanking process. Characteristic areas on sheared edge profile, variation of punch force and high contact pressures affected areas have also been analysed.

Thermodynamic and kinetic modelling hydrogenation of titanium particles and sheets

Use of hydrogen as a temporary alloying element in titanium alloys is an attractive approach to improve the mechanical properties of the materials, enhance processability and thereby reduce manufacturing costs. In this paper, the hydrogen diffusion process and the phase transformation both between titanium particles and in titanium sheets were computationally simulated to analyze the mechanism of hydrogen diffusion in different phases (α-Ti, β-Ti and TiHx). With the simulation based on the thermodynamics and kinetics, quantitative behaviors of the hydrogen diffusion and the phase transformation were analyzed. The simulation results provide an insight into the diffusion process and improve the fundamental understanding of the mechanism of diffusion and phase transformation.

Modelling the public health consequences of cannabis use in Australia

Aims: To detail and validate a simulation model that describes the dynamics of cannabis use, including its probable causal relationships with schizophrenia, road traffic accidents (RTA) and heroin/poly-drug use (HPU).

Methods: A Markov model with 17 health-states was constructed. Annual cycles were used to simulate the initiation of cannabis use, progression in use, reduction and complete remission. The probabilities of transition between health-states were derived from observational data. Following 10-year-old Australian children for 90 years, the model estimated age-specific prevalence for cannabis use. By applying the relative risks according to the extent of cannabis use, the age-specific prevalence of schizophrenia and HPU, and the annual RTA incidence and fatality rate were also estimated. Predictive validity of the model was tested by comparing modelled outputs with data from other credible sources. Sensitivity and scenario analyses were conducted to evaluate technical validity and face validity.

Results: The estimated cannabis use prevalence in individuals aged 10-65 years was 12.2% which comprised 27.4% weekly and 18.0% daily users. The modelled prevalence and age profile were comparable to the reported cross-sectional data. The model also provided good approximations to the prevalence of schizophrenia (Modelled: 4.75/1,000 persons vs Observed: 4.6/1,000 persons), HPU (3.2/1,000 vs 3.1/1,000) and the RTA fatality rate (8.1 per 100,000 vs 8.2 per 100,000). Sensitivity analyses and scenario analysis provided expected and explainable trends.

Conclusions: The validated model provides a valuable tool to assess the likely effectiveness and cost-effectiveness of interventions designed to affect patterns of cannabis use. It can be updated as new data becomes available and/or applied to other countries.

Deep drawing behaviour of ultrafine grained copper : modelling and experiment

Ultrafine grained materials produced by severe plastic deformation methods possess attractive mechanical properties such as high strength compared with traditional coarse grained counterparts and reasonable ductility. Between existing severe plastic deformation methods the Equal Channel Angular Pressing is the most promising for future industrial applications and can produce a variety of ultrafine grained microstructures in materials depending on route, temperature and number of passes during processing. Driven by a rising trend of miniaturisation of parts these materials are promising candidates for microforming processes. Considering that bi-axial deformation of sheet (foil) is the major operation in microforming, the investigation of the influence of the number of ECAP passes on the bi-axial ductility in micro deep drawing test has been examined by experiments and FE simulation in this study. The experiments have showed that high force was required for drawing of the samples processed by ECAP compare to coarse grained materials. The limit drawing ratio of ultrafine grained samples was in the range of 1.9–2.0 with ECAP pass number changing from 1 to 16, while a higher value of 2.2 was obtained for coarse grained copper. However, the notable decrease in tensile ductility with increase in strength was not as pronounced for bi-axial ductility. The FE simulation using standard isotropic hardening model and von Mises yielding criterion confirmed these findings.

Praxis modelling : an evaluation of and extension to feature based modelling

This thesis presents Relation Based Modelling as an extension to the Feature Based Modelling approach to student modelling. Relation Based Modelling dynamically creates new terms allowing the instructional designer to specify a set of primitives and operators from which the modelling system will create the necessary elements. Focal modelling is a new technique devised to manipulate and coordinate the addition of new terms. The thesis presents an evaluation of student modelling systems based on predictive accuracy.

Controller area network (CAN) modelling for automotive body control applications

This research details methods to improve upon current worst-case message response time analysis of CAN networks. Also, through the development of a CAN network model, and using modern simulation software, methods were shown to provide more realistic analyses of both sporadic and periodic messages on CAN networks prior to implementation.

Integrative catchment modelling of land use, turbidity, flow and geology

The thesis outlines and demonstrates the various aspects that contribute towards water quality management systems and the important use of storage/water quality models. The application of models is demonstrated through the functions that modelling components have on sustainable regional development, and through linkage with water quality systems.

Testing and modelling to obtain material behaviour for crash simulations

The thesis focusses on improving the material behaviour models used in vehicle crash simulations by identifying the mechanical properties most important to crash events, reformulating the material models used in crash simulations, and developing new tests to obtain crash-relevant material.

Advanced modelling of forming high strength steels

The thesis presents a novel approach in the multiscale modelling of Advanced High Strength Steels for prediction of the microstructural effects in forming processes. The results are compared with that of experiments and finite element method. The method is proved to be suitable for complexities in the multiphase AHSS.

Water quality modelling of the Barwon Water Supply System

An existing computer model (QUAL2E) was adapted to simulate the flow and water quality of the Barwon Water Supply System, the major water supply system for Geelong. Various water quality parameters were modelled and options reviewed for improving the water quality in this System.

Atomic scale simulation of deformation in magnesium single crystals

The deformation behaviour of magnesium single crystals under plane strain conditions has been examined using molecular dynamics modelling. The simulations were based on an existing atomic potential for magnesium taken from the literature. A strain of 10% was applied at rates of 3x10⁹s^-1 and 3x10⁷s^-1. The simulations predicted the formation of mechanical twins that accommodated extension in the c-axis direction of the hexagonal unit cell. However, the predicted twin is not of the same kind found in magnesium, but is that commonly observed in titanium. It is believed that further analysis of the physical properties predicted by this interatomic potential will shed more light on the atomic processes controlling twinning in Magnesium alloys. It also highlights the need for improvements to the interatomic potential such that more accurate deformation behaviour can be attained.

Microscale modelling of AISI 304 behaviour during hot deformation

This project aimed to model the microstructure evolution during and following hot deformation using a cellular automaton approach. The flow curves, softening kinetics and final microstructures were used as the input data for the post-deformation simulation to elucidate the effect of dynamic recrystallization on the post-deformation softening.