Mathematical modelling of LiFePO4 cathodes

LiFePO4 is a commercially available battery material with good theoretical discharge capacity, excellent cycle life and increased safety compared with competing Li-ion chemistries. It has been the focus of considerable experimental and theoretical scrutiny in the past decade, resulting in LiFePO4 cathodes that perform well at high discharge rates. This scrutiny has raised several questions about the behaviour of LiFePO4 material during charge and discharge. In contrast to many other battery chemistries that intercalate homogeneously, LiFePO4 can phase-separate into highly and lowly lithiated phases, with intercalation proceeding by advancing an interface between these two phases. The main objective of this thesis is to construct mathematical models of LiFePO4 cathodes that can be validated against experimental discharge curves. This is in an attempt to understand some of the multi-scale dynamics of LiFePO4 cathodes that can be difficult to determine experimentally. The first section of this thesis constructs a three-scale mathematical model of LiFePO4 cathodes that uses a simple Stefan problem (which has been used previously in the literature) to describe the assumed phase-change. LiFePO4 crystals have been observed agglomerating in cathodes to form a porous collection of crystals and this morphology motivates the use of three size-scales in the model. The multi-scale model developed validates well against experimental data and this validated model is then used to examine the role of manufacturing parameters (including the agglomerate radius) on battery performance. The remainder of the thesis is concerned with investigating phase-field models as a replacement for the aforementioned Stefan problem. Phase-field models have recently been used in LiFePO4 and are a far more accurate representation of experimentally observed crystal-scale behaviour. They are based around the Cahn-Hilliard-reaction (CHR) IBVP, a fourth-order PDE with electrochemical (flux) boundary conditions that is very stiff and possesses multiple time and space scales. Numerical solutions to the CHR IBVP can be difficult to compute and hence a least-squares based Finite Volume Method (FVM) is developed for discretising both the full CHR IBVP and the more traditional Cahn-Hilliard IBVP. Phase-field models are subject to two main physicality constraints and the numerical scheme presented performs well under these constraints. This least-squares based FVM is then used to simulate the discharge of individual crystals of LiFePO4 in two dimensions. This discharge is subject to isotropic Li+ diffusion, based on experimental evidence that suggests the normally orthotropic transport of Li+ in LiFePO4 may become more isotropic in the presence of lattice defects. Numerical investigation shows that two-dimensional Li+ transport results in crystals that phase-separate, even at very high discharge rates. This is very different from results shown in the literature, where phase-separation in LiFePO4 crystals is suppressed during discharge with orthotropic Li+ transport. Finally, the three-scale cathodic model used at the beginning of the thesis is modified to simulate modern, high-rate LiFePO4 cathodes. High-rate cathodes typically do not contain (large) agglomerates and therefore a two-scale model is developed. The Stefan problem used previously is also replaced with the phase-field models examined in earlier chapters. The results from this model are then compared with experimental data and fit poorly, though a significant parameter regime could not be investigated numerically. Many-particle effects however, are evident in the simulated discharges, which match the conclusions of recent literature. These effects result in crystals that are subject to local currents very different from the discharge rate applied to the cathode, which impacts the phase-separating behaviour of the crystals and raises questions about the validity of using cathodic-scale experimental measurements in order to determine crystal-scale behaviour.

Vision-only autonomous navigation using topometric maps

This paper presents a mapping and navigation system for a mobile robot, which uses vision as its sole sensor modality. The system enables the robot to navigate autonomously, plan paths and avoid obstacles using a vision based topometric map of its environment. The map consists of a globally-consistent pose-graph with a local 3D point cloud attached to each of its nodes. These point clouds are used for direction independent loop closure and to dynamically generate 2D metric maps for locally optimal path planning. Using this locally semi-continuous metric space, the robot performs shortest path planning instead of following the nodes of the graph --- as is done with most other vision-only navigation approaches. The system exploits the local accuracy of visual odometry in creating local metric maps, and uses pose graph SLAM, visual appearance-based place recognition and point clouds registration to create the topometric map. The ability of the framework to sustain vision-only navigation is validated experimentally, and the system is provided as open-source software.

Towards persistent visual navigation using SMART

In this paper, we present SMART (Sequence Matching Across Route Traversals): a vision- based place recognition system that uses whole image matching techniques and odometry information to improve the precision-recall performance, latency and general applicability of the SeqSLAM algorithm. We evaluate the system’s performance on challenging day and night journeys over several kilometres at widely varying vehicle velocities from 0 to 60 km/h, compare performance to the current state-of- the-art SeqSLAM algorithm, and provide parameter studies that evaluate the effectiveness of each system component. Using 30-metre sequences, SMART achieves place recognition performance of 81% recall at 100% precision, outperforming SeqSLAM, and is robust to significant degradations in odometry.

Predator Crown-of-Thorns Starfish (Acanthaster planci) Outbreak, Mass Mortality of Corals, and Cascading Effects on Reef Fish and Benthic Communities

Outbreaks of the coral-killing seastar Acanthaster planci are intense disturbances that can decimate coral reefs. These events consist of the emergence of large swarms of the predatory seastar that feed on reef-building corals, often leading to widespread devastation of coral populations. While cyclic occurrences of such outbreaks are reported from many tropical reefs throughout the Indo-Pacific, their causes are hotly debated, and the spatio-temporal dynamics of the outbreaks and impacts to reef communities remain unclear. Based on observations of a recent event around the island of Moorea, French Polynesia, we show that Acanthaster outbreaks are methodic, slow-paced, and diffusive biological disturbances. Acanthaster outbreaks on insular reef systems like Moorea's appear to originate from restricted areas confined to the ocean-exposed base of reefs. Elevated Acanthaster densities then progressively spread to adjacent and shallower locations by migrations of seastars in aggregative waves that eventually affect the entire reef system. The directional migration across reefs appears to be a search for prey as reef portions affected by dense seastar aggregations are rapidly depleted of living corals and subsequently left behind. Coral decline on impacted reefs occurs by the sequential consumption of species in the order of Acanthaster feeding preferences. Acanthaster outbreaks thus result in predictable alteration of the coral community structure. The outbreak we report here is among the most intense and devastating ever reported. Using a hierarchical, multi-scale approach, we also show how sessile benthic communities and resident coral-feeding fish assemblages were subsequently affected by the decline of corals. By elucidating the processes involved in an Acanthaster outbreak, our study contributes to comprehending this widespread disturbance and should thus benefit targeted management actions for coral reef ecosystems.

Brain-inspired sensor fusion for navigating robots

Current state of the art robot mapping and navigation systems produce impressive performance under a narrow range of robot platform, sensor and environmental conditions, in contrast to animals such as rats that produce “good enough” maps that enable them to function under an incredible range of situations. In this paper we present a rat-inspired featureless sensor-fusion system that assesses the usefulness of multiple sensor modalities based on their utility and coherence for place recognition, without knowledge as to the type of sensor. We demonstrate the system on a Pioneer robot in indoor and outdoor environments with abrupt lighting changes. Through dynamic weighting of the sensors, the system is able to perform correct place recognition and mapping where the static sensor weighting approach fails.

RatSLAM : using models of rodent hippocampus for robot navigation and beyond

We describe recent biologically-inspired mapping research incorporating brain-based multi-sensor fusion and calibration processes and a new multi-scale, homogeneous mapping framework. We also review the interdisciplinary approach to the development of the RatSLAM robot mapping and navigation system over the past decade and discuss the insights gained from combining pragmatic modelling of biological processes with attempts to close the loop back to biology. Our aim is to encourage the pursuit of truly interdisciplinary approaches to robotics research by providing successful case studies.

Autonomous multisensor calibration and closed-loop fusion for SLAM

The vast majority of current robot mapping and navigation systems require specific well-characterized sensors that may require human-supervised calibration and are applicable only in one type of environment. Furthermore, if a sensor degrades in performance, either through damage to itself or changes in environmental conditions, the effect on the mapping system is usually catastrophic. In contrast, the natural world presents robust, reasonably well-characterized solutions to these problems. Using simple movement behaviors and neural learning mechanisms, rats calibrate their sensors for mapping and navigation in an incredibly diverse range of environments and then go on to adapt to sensor damage and changes in the environment over the course of their lifetimes. In this paper, we introduce similar movement-based autonomous calibration techniques that calibrate place recognition and self-motion processes as well as methods for online multisensor weighting and fusion. We present calibration and mapping results from multiple robot platforms and multisensory configurations in an office building, university campus, and forest. With moderate assumptions and almost no prior knowledge of the robot, sensor suite, or environment, the methods enable the bio-inspired RatSLAM system to generate topologically correct maps in the majority of experiments.

A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.

Pulsed i-PVD of dielectric nanodot arrays using a nanoporous template

The results of multi-scale numerical simulations of pulsed i-PVD template-assisted nanofabrication of ZnO nanodot arrays on a silicon substrate are presented. The ratios and spatial distributions of the ion fluxes deposited on the lateral and bottom surfaces of the nanopores are computed as a function of the external bias and plasma parameters. The results show that the pulsed bias plays a significant role in the ion current distribution inside the nanopores. The results of numerical experiments of this work suggest that by finely adjusting the pulse voltage, the pulse duration and the duty cycle of the external pulsed bias, the nanopore clogging can be successfully avoided during the deposition and the shapes of the deposited ZnO nanodots can be effectively controlled. A figure is presented.

Nanostructures of various dimensionalities from plasma and neutral fluxes

A complex multi-scale model and numerical simulations are used to demonstrate, by simulating the development of patterns of nanotips, nanowalls, nanoislands and nanovoids of a characteristic size of 5-100 nm, a greater degree of determinism in the formation of various nanostructures by using the low-density, low-temperature plasma-based processes. It is shown that in the plasma, in contrast to the neutral gas-based processes, one can synthesize nanostructures of various dimensionalities and shapes with a larger surface density, desired geometrical parameters and narrower size distribution functions. This effect is mainly attributed to strong ion focusing by irregular electric fields in the nanopatterns, which effectively redistributes the influxes of plasma-generated building units and thus provides a selective control of their delivery to the growing nanostructures.

Vision-based simultaneous localization and mapping in changing outdoor environments

For robots operating in outdoor environments, a number of factors, including weather, time of day, rough terrain, high speeds, and hardware limitations, make performing vision-based simultaneous localization and mapping with current techniques infeasible due to factors such as image blur and/or underexposure, especially on smaller platforms and low-cost hardware. In this paper, we present novel visual place-recognition and odometry techniques that address the challenges posed by low lighting, perceptual change, and low-cost cameras. Our primary contribution is a novel two-step algorithm that combines fast low-resolution whole image matching with a higher-resolution patch-verification step, as well as image saliency methods that simultaneously improve performance and decrease computing time. The algorithms are demonstrated using consumer cameras mounted on a small vehicle in a mixed urban and vegetated environment and a car traversing highway and suburban streets, at different times of day and night and in various weather conditions. The algorithms achieve reliable mapping over the course of a day, both when incrementally incorporating new visual scenes from different times of day into an existing map, and when using a static map comprising visual scenes captured at only one point in time. Using the two-step place-recognition process, we demonstrate for the first time single-image, error-free place recognition at recall rates above 50% across a day-night dataset without prior training or utilization of image sequences. This place-recognition performance enables topologically correct mapping across day-night cycles.

Multiscale features and information extraction of online strain for long-span bridges

The strain data acquired from structural health monitoring (SHM) systems play an important role in the state monitoring and damage identification of bridges. Due to the environmental complexity of civil structures, a better understanding of the actual strain data will help filling the gap between theoretical/laboratorial results and practical application. In the study, the multi-scale features of strain response are first revealed after abundant investigations on the actual data from two typical long-span bridges. Results show that, strain types at the three typical temporal scales of 10^5, 10^2 and 10^0 sec are caused by temperature change, trains and heavy trucks, and have their respective cut-off frequency in the order of 10^-2, 10^-1 and 10^0 Hz. Multi-resolution analysis and wavelet shrinkage are applied for separating and extracting these strain types. During the above process, two methods for determining thresholds are introduced. The excellent ability of wavelet transform on simultaneously time-frequency analysis leads to an effective information extraction. After extraction, the strain data will be compressed at an attractive ratio. This research may contribute to a further understanding of actual strain data of long-span bridges; also, the proposed extracting methodology is applicable on actual SHM systems.

Automated sensory data alignment for environmental and epidermal change monitoring

In this paper we present research adapting a state of the art condition-invariant robotic place recognition algorithm to the role of automated inter- and intra-image alignment of sensor observations of environmental and skin change over time. The approach involves inverting the typical criteria placed upon navigation algorithms in robotics; we exploit rather than attempt to fix the limited camera viewpoint invariance of such algorithms, showing that approximate viewpoint repetition is realistic in a wide range of environments and medical applications. We demonstrate the algorithms automatically aligning challenging visual data from a range of real-world applications: ecological monitoring of environmental change, aerial observation of natural disasters including flooding, tsunamis and bushfires and tracking wound recovery and sun damage over time and present a prototype active guidance system for enforcing viewpoint repetition. We hope to provide an interesting case study for how traditional research criteria in robotics can be inverted to provide useful outcomes in applied situations.

Spatial disaggregation of land systems mapping in the Burnett catchment (South-East Queensland)

This project examined the potential for historical mapping of land resources to be upgraded to meet current requirements for natural resource management. The methods of spatial disaggregation used to improve the scale of mapping were novel and provide a method to rapidly improve existing information. The thesis investigated the potential to use digital soil mapping techniques and the multi-scale identification of areas within historical land systems mapping to provide enhanced information to support modern natural resource management needs. This was undertaken in the Burnett Catchment of South-East Queensland.

The navigation and visualisation of environmental audio using zooming spectrograms

Acoustic recordings play an increasingly important role in monitoring terrestrial and aquatic environments. However, rapid advances in technology make it possible to accumulate thousands of hours of recordings, more than ecologists can ever listen to. Our approach to this big-data challenge is to visualize the content of long-duration audio recordings on multiple scales, from minutes, hours, days to years. The visualization should facilitate navigation and yield ecologically meaningful information prior to listening to the audio. To construct images, we calculate acoustic indices, statistics that describe the distribution of acoustic energy and reflect content of ecological interest. We combine various indices to produce false-color spectrogram images that reveal acoustic content and facilitate navigation. The technical challenge we investigate in this work is how to navigate recordings that are days or even months in duration. We introduce a method of zooming through multiple temporal scales, analogous to Google Maps. However, the “landscape” to be navigated is not geographical and not therefore intrinsically visual, but rather a graphical representation of the underlying audio. We describe solutions to navigating spectrograms that range over three orders of magnitude of temporal scale. We make three sets of observations: 1. We determine that at least ten intermediate scale steps are required to zoom over three orders of magnitude of temporal scale; 2. We determine that three different visual representations are required to cover the range of temporal scales; 3. We present a solution to the problem of maintaining visual continuity when stepping between different visual representations. Finally, we demonstrate the utility of the approach with four case studies.