Advanced mathematical modelling and experimental investigation of new torque arms for shaft-mounted drives

Shaft-mounted gearboxes are widely used in industry. The torque arm that holds the reactive torque on the housing of the gearbox, if properly positioned creates the reactive force that lifts the gearbox and unloads the bearings of the output shaft. The shortcoming of these torque arms is that if the gearbox is reversed the direction of the reactive force on the torque arm changes to opposite and added to the weight of the gearbox overloads the bearings shortening their operating life. In this paper, a new patented design of torque arms that develop a controlled lifting force and counteract the weight of the gearbox regardless of the direction of the output shaft rotation is described. Several mathematical models of the conventional and new torque arms were developed and verified experimentally on a specially built test rig that enables modelling of the radial compliance of the gearbox bearings and elastic elements of the torque arms. Comparison showed a good agreement between theoretical and experimental results.

New stress and velocity fields for highly frictional granular materials

The idealised theory for the quasi-static flow of granular materials which satisfy the Coulomb-Mohr hypothesis is considered. This theory arises in the limit that the angle of internal friction approaches $\pi/2$, and accordingly these materials may be referred to as being `highly frictional'. In this limit, the stress field for both two-dimensional and axially symmetric flows may be formulated in terms of a single nonlinear second order partial differential equation for the stress angle. To obtain an accompanying velocity field, a flow rule must be employed. Assuming the non-dilatant double-shearing flow rule, a further partial differential equation may be derived in each case, this time for the streamfunction. Using Lie symmetry methods, a complete set of group-invariant solutions is derived for both systems, and through this process new exact solutions are constructed. Only a limited number of exact solutions for gravity driven granular flows are known, so these results are potentially important in many practical applications. The problem of mass flow through a two-dimensional wedge hopper is examined as an illustration.

Lie group symmetry analysis for granular media stress equations

The Airy stress function, although frequently employed in classical linear elasticity, does not receive similar usage for granular media problems. For plane strain quasi-static deformations of a cohesionless Coulomb–Mohr granular solid, a single nonlinear partial differential equation is formulated for the Airy stress function by combining the equilibrium equations with the yield condition. This has certain advantages from the usual approach, in which two stress invariants and a stress angle are introduced, and a system of two partial differential equations is needed to describe the flow. In the present study, the symmetry analysis of differential equations is utilised for our single partial differential equation, and by computing an optimal system of one-dimensional Lie algebras, a complete set of group-invariant solutions is derived. By this it is meant that any group-invariant solution of the governing partial differential equation (provided it can be derived via the classical symmetries method) may be obtained as a member of this set by a suitable group transformation. For general values of the parameters (angle of internal friction and gravity g) it is found there are three distinct classes of solutions which correspond to granular flows considered previously in the literature. For the two limiting cases of high angle of internal friction and zero gravity, the governing partial differential equation admit larger families of Lie point symmetries, and from these symmetries, further solutions are derived, many of which are new. Furthermore, the majority of these solutions are exact, which is rare for granular flow, especially in the case of gravity driven flows.

Range sensor pose estimation

This paper presents a method of recovering the 6 DoF pose (Cartesian position and angular rotation) of a range sensor mounted on a mobile platform. The method utilises point targets in a local scene and optimises over the error between their absolute position and their apparent position as observed by the range sensor. The analysis includes an investigation into the sensitivity and robustness of the method. Practical results were collected using a SICK LRS2100 mounted on a P&H electric mining shovel and present the errors in scan data relative to an independent 3D scan of the scene. A comparison to directly measuring the sensor pose is presented and shows the significant accuracy improvements in scene reconstruction using this pose estimation method.

Empirical Bayes method in the study of traffic safety via heterogeneous negative multinomial model

In the study of traffic safety, expected crash frequencies across sites are generally estimated via the negative binomial model, assuming time invariant safety. Since the time invariant safety assumption may be invalid, Hauer (1997) proposed a modified empirical Bayes (EB) method. Despite the modification, no attempts have been made to examine the generalisable form of the marginal distribution resulting from the modified EB framework. Because the hyper-parameters needed to apply the modified EB method are not readily available, an assessment is lacking on how accurately the modified EB method estimates safety in the presence of the time variant safety and regression-to-the-mean (RTM) effects. This study derives the closed form marginal distribution, and reveals that the marginal distribution in the modified EB method is equivalent to the negative multinomial (NM) distribution, which is essentially the same as the likelihood function used in the random effects Poisson model. As a result, this study shows that the gamma posterior distribution from the multivariate Poisson-gamma mixture can be estimated using the NM model or the random effects Poisson model. This study also shows that the estimation errors from the modified EB method are systematically smaller than those from the comparison group method by simultaneously accounting for the RTM and time variant safety effects. Hence, the modified EB method via the NM model is a generalisable method for estimating safety in the presence of the time variant safety and the RTM effects.

Bolted beam-column moment connections between cold-formed steel members

ABSTRACT Twelve beam-to-column connections between cold-formed steel sections consisting of three beam depths and four connection types were tested in isolation to investigate their behavior based on strength, stiffness and ductility. Resulting moment-rotation curves indicate that the tested connections are efficient moment connections where moment capacities ranged from about 65% to 100% of the connected beam capac-ity. With a moment capacity of greater than 80% of connected beam member capacity, some of the connec-tions can be regarded as full strength connections. Connections also possessed sufficient ductility with rota-tions of 20 mRad at failure although some connections were too ductile with rotations in excess of 30 mRad. Generally, most of the connections possess the strength and ductility to be considered as partial strength con-nections. The ultimate failures of almost all of the connections were due to local buckling of the compression web and flange elements of the beam closest to the connection.

Development of a software model of a heavy vehicle suspension for research

A Simulink Matlab control system of a heavy vehicle suspension has been developed. The aim of the exercise presented in this paper was to develop a Simulink Matlab control system of a heavy vehicle suspension. The objective facilitated by this outcome was the use of a working model of a heavy vehicle (HV) suspension that could be used for future research. A working computer model is easier and cheaper to re-configure than a HV axle group installed on a truck; it presents less risk should something go wrong and allows more scope for variation and sensitivity analysis before embarking on further "real-world" testing. Empirical data recorded as the input and output signals of a heavy vehicle (HV) suspension were used to develop the parameters for computer simulation of a linear time invariant system described by a second-order differential equation of the form: (i.e. a "2nd-order" system). Using the empirical data as an input to the computer model allowed validation of its output compared with the empirical data. The errors ranged from less than 1% to approximately 3% for any parameter, when comparing like-for-like inputs and outputs. The model is presented along with the results of the validation. This model will be used in future research in the QUT/Main Roads project Heavy vehicle suspensions – testing and analysis, particularly so for a theoretical model of a multi-axle HV suspension with varying values of dynamic load sharing. Allowance will need to be made for the errors noted when using the computer models in this future work.

Pressure, oxygen tension and temperature in the periosteal callus during bone healing - An in vivo study in sheep

Adequate blood supply and sufficient mechanical stability are necessary for timely fracture healing. Damage to vessels impairs blood supply; hindering the transport of oxygen which is an essential metabolite for cells involved in repair. The degree of mechanical stability determines the mechanical conditions in the healing tissues. The mechanical conditions can influence tissue differentiation and may also inhibit revascularization. Knowledge of the actual conditions in a healing fracture in vivo is extremely limited. This study aimed to quantify the pressure, oxygen tension and temperature in the external callus during the early phase of bone healing. Six Merino-mix sheep underwent a tibial osteotomy. The tibia was stabilized with a standard mono-lateral external fixator. A multi-parameter catheter was placed adjacent to the osteotomy gap on the medial aspect of the tibia. Measurements of oxygen tension and temperature were performed for ten days post-op. Measurements of pressure were performed during gait on days three and seven. The ground reaction force and the interfragmentary movements were measured simultaneously. The maximum pressure during gait increased (p=0.028) from three (41.3 [29.2-44.1] mm Hg) to seven days (71.8 [61.8-84.8] mm Hg). During the same interval, there was no change (p=0.92) in the peak ground reaction force or in the interfragmentary movement (compression: p=0.59 and axial rotation: p=0.11). Oxygen tension in the haematoma (74.1 mm Hg [68.6-78.5]) was initially high post-op and decreased steadily over the first five days. The temperature increased over the first four days before reaching a plateau at approximately 38.5 degrees C on day four. This study is the first to report pressure, oxygen tension and temperature in the early callus tissues. The magnitude of pressure increased even though weight bearing and IFM remained unchanged. Oxygen tensions were initially high in the haematoma and fell gradually with a low oxygen environment first established after four to five days. This study illustrates that in bone healing the local environment for cells may not be considered constant with regard to oxygen tension, pressure and temperature.

Similarity metrics within a point of view

In vector space based approaches to natural language processing, similarity is commonly measured by taking the angle between two vectors representing words or documents in a semantic space. This is natural from a mathematical point of view, as the angle between unit vectors is, up to constant scaling, the only unitarily invariant metric on the unit sphere. However, similarity judgement tasks reveal that human subjects fail to produce data which satisfies the symmetry and triangle inequality requirements for a metric space. A possible conclusion, reached in particular by Tversky et al., is that some of the most basic assumptions of geometric models are unwarranted in the case of psychological similarity, a result which would impose strong limits on the validity and applicability vector space based (and hence also quantum inspired) approaches to the modelling of cognitive processes. This paper proposes a resolution to this fundamental criticism of of the applicability of vector space models of cognition. We argue that pairs of words imply a context which in turn induces a point of view, allowing a subject to estimate semantic similarity. Context is here introduced as a point of view vector (POVV) and the expected similarity is derived as a measure over the POVV's. Different pairs of words will invoke different contexts and different POVV's. Hence the triangle inequality ceases to be a valid constraint on the angles. We test the proposal on a few triples of words and outline further research.

Real-time evaluation of driver’s alertness on highways

Suburbanisation has been internationally a major phenomenon in the last decades. Suburb-to-suburb routes are nowadays the most widespread road journeys; and this resulted in an increment of distances travelled, particularly on faster suburban highways. The design of highways tends to over-simplify the driving task and this can result in decreased alertness. Driving behaviour is consequently impaired and drivers are then more likely to be involved in road crashes. This is particularly dangerous on highways where the speed limit is high. While effective countermeasures to this decrement in alertness do not currently exist, the development of in-vehicle sensors opens avenues for monitoring driving behaviour in real-time. The aim of this study is to evaluate in real-time the level of alertness of the driver through surrogate measures that can be collected from in-vehicle sensors. Slow EEG activity is used as a reference to evaluate driver's alertness. Data are collected in a driving simulator instrumented with an eye tracking system, a heart rate monitor and an electrodermal activity device (N=25 participants). Four different types of highways (driving scenario of 40 minutes each) are implemented through the variation of the road design (amount of curves and hills) and the roadside environment (amount of buildings and traffic). We show with Neural Networks that reduced alertness can be detected in real-time with an accuracy of 92% using lane positioning, steering wheel movement, head rotation, blink frequency, heart rate variability and skin conductance level. Such results show that it is possible to assess driver's alertness with surrogate measures. Such methodology could be used to warn drivers of their alertness level through the development of an in-vehicle device monitoring in real-time drivers' behaviour on highways, and therefore it could result in improved road safety.

A biomechanical investigation of vertebral staples for fusionless scoliosis correction

Background: Fusionless scoliosis surgery is an early-stage treatment for idiopathic scoliosis which claims potential advantages over current fusion-based surgical procedures. Anterior vertebral stapling using a shape memory alloy staple is one such approach. Despite increasing interest in this technique, little is known about the effects on the spine following insertion, or the mechanism of action of the staple. The purpose of this study was to investigate the biomechanical consequences of staple insertion in the anterior thoracic spine, using in vitro experiments on an immature bovine model. Methods: Individual calf spine thoracic motion segments were tested in flexion, extension, lateral bending and axial rotation. Changes in motion segment rotational stiffness following staple insertion were measured on a series of 14 specimens. Strain gauges were attached to three of the staples in the series to measure forces transmitted through the staple during loading. A micro-CT scan of a single specimen was performed after loading to qualitatively examine damage to the vertebral bone caused by the staple. Findings: Small but statistically significant decreases in bending stiffness occurred in flexion,extension, lateral bending away from the staple, and axial rotation away from the staple. Each strain-gauged staple showed a baseline compressive loading following insertion which was seen to gradually decrease during testing. Post-test micro-CT showed substantial bone and growth plate damage near the staple. Interpretation: Based on our findings it is possible that growth modulation following staple insertion is due to tissue damage rather than sustained mechanical compression of the motion segment.

Shifting : one-inclusion mistake bounds and sample compression

We present new expected risk bounds for binary and multiclass prediction, and resolve several recent conjectures on sample compressibility due to Kuzmin and Warmuth. By exploiting the combinatorial structure of concept class F, Haussler et al. achieved a VC(F)/n bound for the natural one-inclusion prediction strategy. The key step in their proof is a d = VC(F) bound on the graph density of a subgraph of the hypercube—oneinclusion graph. The first main result of this paper is a density bound of n [n−1 <=d-1]/[n <=d] < d, which positively resolves a conjecture of Kuzmin and Warmuth relating to their unlabeled Peeling compression scheme and also leads to an improved one-inclusion mistake bound. The proof uses a new form of VC-invariant shifting and a group-theoretic symmetrization. Our second main result is an algebraic topological property of maximum classes of VC-dimension d as being d contractible simplicial complexes, extending the well-known characterization that d = 1 maximum classes are trees. We negatively resolve a minimum degree conjecture of Kuzmin and Warmuth—the second part to a conjectured proof of correctness for Peeling—that every class has one-inclusion minimum degree at most its VCdimension. Our final main result is a k-class analogue of the d/n mistake bound, replacing the VC-dimension by the Pollard pseudo-dimension and the one-inclusion strategy by its natural hypergraph generalization. This result improves on known PAC-based expected risk bounds by a factor of O(logn) and is shown to be optimal up to an O(logk) factor. The combinatorial technique of shifting takes a central role in understanding the one-inclusion (hyper)graph and is a running theme throughout.

Shifting : one-inclusion mistake bounds and sample compression

We present new expected risk bounds for binary and multiclass prediction, and resolve several recent conjectures on sample compressibility due to Kuzmin and Warmuth. By exploiting the combinatorial structure of concept class F, Haussler et al. achieved a VC(F)/n bound for the natural one-inclusion prediction strategy. The key step in their proof is a d=VC(F) bound on the graph density of a subgraph of the hypercube—one-inclusion graph. The first main result of this report is a density bound of n∙choose(n-1,≤d-1)/choose(n,≤d) < d, which positively resolves a conjecture of Kuzmin and Warmuth relating to their unlabeled Peeling compression scheme and also leads to an improved one-inclusion mistake bound. The proof uses a new form of VC-invariant shifting and a group-theoretic symmetrization. Our second main result is an algebraic topological property of maximum classes of VC-dimension d as being d-contractible simplicial complexes, extending the well-known characterization that d=1 maximum classes are trees. We negatively resolve a minimum degree conjecture of Kuzmin and Warmuth—the second part to a conjectured proof of correctness for Peeling—that every class has one-inclusion minimum degree at most its VC-dimension. Our final main result is a k-class analogue of the d/n mistake bound, replacing the VC-dimension by the Pollard pseudo-dimension and the one-inclusion strategy by its natural hypergraph generalization. This result improves on known PAC-based expected risk bounds by a factor of O(log n) and is shown to be optimal up to a O(log k) factor. The combinatorial technique of shifting takes a central role in understanding the one-inclusion (hyper)graph and is a running theme throughout

Shape discrimination using invariants defined from higher-order spectra

An approach to pattern recognition using invariant parameters based on higher-order spectra is presented. In particular, bispectral invariants are used to classify one-dimensional shapes. The bispectrum, which is translation invariant, is integrated along straight lines passing through the origin in bifrequency space. The phase of the integrated bispectrum is shown to be scale- and amplification-invariant. A minimal set of these invariants is selected as the feature vector for pattern classification. Pattern recognition using higher-order spectral invariants is fast, suited for parallel implementation, and works for signals corrupted by Gaussian noise. The classification technique is shown to distinguish two similar but different bolts given their one-dimensional profiles

Digit recognition using trispectral features

Features derived from the trispectra of DFT magnitude slices are used for multi-font digit recognition. These features are insensitive to translation, rotation, or scaling of the input. They are also robust to noise. Classification accuracy tests were conducted on a common data base of 256× 256 pixel bilevel images of digits in 9 fonts. Randomly rotated and translated noisy versions were used for training and testing. The results indicate that the trispectral features are better than moment invariants and affine moment invariants. They achieve a classification accuracy of 95% compared to about 81% for Hu's (1962) moment invariants and 39% for the Flusser and Suk (1994) affine moment invariants on the same data in the presence of 1% impulse noise using a 1-NN classifier. For comparison, a multilayer perceptron with no normalization for rotations and translations yields 34% accuracy on 16× 16 pixel low-pass filtered and decimated versions of the same data.