Expectation and variation with a virtual die

By the time students reach the middle years they have experienced many chance activities based on dice. Common among these are rolling one die to explore the relationship of frequency and theoretical probability, and rolling two dice and summing the outcomes to consider their probabilities. Although dice may be considered overused by some, the advantage they offer is a familiar context within which to explore much more complex concepts. If the basic chance mechanism of the device is understood, it is possible to enter quickly into an arena of more complex concepts. This is what happened with a two hour activity engaged in by four classes of Grade 6 students in the same school. The activity targeted the concepts of variation and expectation. The teachers held extended discussions with their classes on variation and expectation at the beginning of the activity, with students contributing examples of the two concepts from their own experience. These notions are quite sophisticated for Grade 6, but the underlying concepts describe phenomena that students encounter every day. For example, time varies continuously; sporting results vary from game to game; the maximum temperature varies from day to day. However, there is an expectation about tomorrow’s maximum temperature based on the expert advice from the weather bureau. There may also be an expectation about a sporting result based on the participants’ previous results. It is this juxtaposition that makes life interesting. Variation hence describes the differences we see in phenomena around us. In a scenario displaying variation, expectation describes the effort to characterise or summarise the variation and perhaps make a prediction about the message arising from the scenario. The explicit purpose of the activity described here was to use the familiar scenario of rolling a die to expose these two concepts. Because the students had previously experienced rolling physical dice they knew instinctively about the variation that occurs across many rolls and about the theoretical expectation that each side should “come up” one-sixth of the time. They had observed the instances of the concepts in action, but had not consolidated the underlying terminology to describe it. As the two concepts are so fundamental to understanding statistics, we felt it would be useful to begin building in the familiar environment of rolling a die. Because hand-held dice limit the explorations students can undertake, the classes used the soft-ware TinkerPlots (Konold & Miller, 2011) to simulate rolling a die multiple times.

Practical determination of cane wagon derailment forces for the Australian sugar industry

Derailments are a significant cost to the Australian sugar industry with damage to rail infrastructure and rolling stock in excess of $2 M per annum. Many factors can contribute to cane rail derailments. The more prevalent factors are discussed. Derailment statistics on likely causes for cane rail derailments are presented with the case of empty wagons on the main line being the highest contributor to business cost. Historically, the lateral to vertical wheel load ratio, termed the derailment ratio, has been used to indicate the derailment probability of rolling stock. When the derailment ratio reaches the Nadal limit of 0.81 for cane rail operations, there is a high probability that a derailment will occur. Contributing factors for derailments include the operating forces, the geometric variables of the rolling stock and the geometric deviations of the railway track. These combined, have the capacity to affect the risk of derailment for a cane rail transport operating system. The derailment type that is responsible for creating the most damage to assets and creating mill stops is the flange climb derailment, as these derailments usually occur at speed with a full rake of empty wagons. The typical forces that contribute to the flange climb derailment case for cane rail operations are analysed and a practical derailment model is developed to enable operators to better appreciate the most significant contributing factors to this type of derailment. The paper aims to: (a) improve awareness of the significance of physical operating parameters so that these principles can be included in locomotive driver training and (b) improve awareness of track and wagon variables related to the risk of derailment so that maintainers of the rail system can allocate funds for maintenance more effectively.

A data mining approach for fault diagnosis: An application of anomaly detection algorithm

Rolling-element bearing failures are the most frequent problems in rotating machinery, which can be catastrophic and cause major downtime. Hence, providing advance failure warning and precise fault detection in such components are pivotal and cost-effective. The vast majority of past research has focused on signal processing and spectral analysis for fault diagnostics in rotating components. In this study, a data mining approach using a machine learning technique called anomaly detection (AD) is presented. This method employs classification techniques to discriminate between defect examples. Two features, kurtosis and Non-Gaussianity Score (NGS), are extracted to develop anomaly detection algorithms. The performance of the developed algorithms was examined through real data from a test to failure bearing. Finally, the application of anomaly detection is compared with one of the popular methods called Support Vector Machine (SVM) to investigate the sensitivity and accuracy of this approach and its ability to detect the anomalies in early stages.

Structural, physiological and molecular characterisation of the Australian native resurrection grass Tripogon loliiformis (F.Meull) C.E.Hubb during dehydration and rehydration

There is an urgent need to develop crops that can withstand future climates. Results from this thesis demonstrated that a native Australian resurrection grass exhibits structural, physiological and metabolic strategies to tolerate drying. These strategies may be utilized for the generation of stress tolerant crops.

Characterisation of head-hardened rail steel in terms of cyclic plasticity response and microstructure for improved material modelling

Stress- and strain-controlled tests of heat treated high-strength rail steel (Australian Standard AS1085.1) have been performed in order to improve the characterisation of the said material׳s ratcheting and fatigue wear behaviour. The hardness of the rail head material has also been studied and it has been found that hardness reduces considerably below four-millimetres from the rail top surface. Historically, researchers have used test coupons with circular cross-sections to conduct cyclic load tests. Such test coupons, typically five-millimetres in gauge diameter and ten‐millimetres in grip diameter, are usually taken from the rail head sample. When there is considerable variation of material properties over the cross-section it becomes likely that localised properties of the rail material will be missed. In another case from the literature, disks 47 mm in diameter for a twin-disk rolling contact test machine were obtained directly from the rail sample and used to validate ratcheting and rolling contact fatigue wear models. The question arises: How accurate are such tests, especially when large material property gradients exist? In this research paper, the effects of rail sampling location on the ratcheting behaviour of AS1085.1 rail steel were investigated using rectangular-shaped specimens obtained at four different depths to observe their respective cyclic plasticity behaviour. The microstructural features of the test coupons were also analysed, especially the pearlite inter-lamellar spacing which showed strong correlation with both hardness and cyclic plasticity behaviour of the material. This work ultimately provides new data and testing methodology to aid the selection of valid parameters for material constitutive models to better understand rail surface ratcheting and wear.