Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

Integrity determination of RTK solutions in precision farming applications

Integrity of Real Time Kinematic (RTK) positioning solutions relates to the confidential level that can be placed in the information provided by the RTK system. It includes the ability of the RTK system to provide timely valid warnings to users when the system must not be used for the intended operation. For instance, in the controlled traffic farming (CTF) system that controls traffic separates wheel beds and root beds, RTK positioning error causes overlap and increases the amount of soil compaction. The RTK system’s integrity capacity can inform users when the actual positional errors of the RTK solutions have exceeded Horizontal Protection Levels (HPL) within a certain Time-To-Alert (TTA) at a given Integrity Risk (IR). The later is defined as the probability that the system claims its normal operational status while actually being in an abnormal status, e.g., the ambiguities being incorrectly fixed and positional errors having exceeded the HPL. The paper studies the required positioning performance (RPP) of GPS positioning system for PA applications such as a CTF system, according to literature review and survey conducted among a number of farming companies. The HPL and IR are derived from these RPP parameters. A RTK-specific rover autonomous integrity monitoring (RAIM) algorithm is developed to determine the system integrity according to real time outputs, such as residual square sum (RSS), HDOP values. A two-station baseline data set is analyzed to demonstrate the concept of RTK integrity and assess the RTK solution continuity, missed detection probability and false alarm probability.

The statistics of refractive error maps : managing wavefront aberration analysis without Zernike polynomials

The refractive error of a human eye varies across the pupil and therefore may be treated as a random variable. The probability distribution of this random variable provides a means for assessing the main refractive properties of the eye without the necessity of traditional functional representation of wavefront aberrations. To demonstrate this approach, the statistical properties of refractive error maps are investigated. Closed-form expressions are derived for the probability density function (PDF) and its statistical moments for the general case of rotationally-symmetric aberrations. A closed-form expression for a PDF for a general non-rotationally symmetric wavefront aberration is difficult to derive. However, for specific cases, such as astigmatism, a closed-form expression of the PDF can be obtained. Further, interpretation of the distribution of the refractive error map as well as its moments is provided for a range of wavefront aberrations measured in real eyes. These are evaluated using a kernel density and sample moments estimators. It is concluded that the refractive error domain allows non-functional analysis of wavefront aberrations based on simple statistics in the form of its sample moments. Clinicians may find this approach to wavefront analysis easier to interpret due to the clinical familiarity and intuitive appeal of refractive error maps.

Setting hospital infection control policy : a decision-making framework incorporating health economics and healthcare epidemiology

Background: Reducing rates of healthcare acquired infection has been identified by the Australian Commission on Safety and Quality in Health Care as a national priority. One of the goals is the prevention of central venous catheter-related bloodstream infection (CR-BSI). At least 3,500 cases of CR-BSI occur annually in Australian hospitals, resulting in unnecessary deaths and costs to the healthcare system between $25.7 and $95.3 million. Two approaches to preventing these infections have been proposed: use of antimicrobial catheters (A-CVCs); or a catheter care and management ‘bundle’. Given finite healthcare budgets, decisions about the optimal infection control policy require consideration of the effectiveness and value for money of each approach. Objectives: The aim of this research is to use a rational economic framework to inform efficient infection control policy relating to the prevention of CR-BSI in the intensive care unit. It addresses three questions relating to decision-making in this area: 1. Is additional investment in activities aimed at preventing CR-BSI an efficient use of healthcare resources? 2. What is the optimal infection control strategy from amongst the two major approaches that have been proposed to prevent CR-BSI? 3. What uncertainty is there in this decision and can a research agenda to improve decision-making in this area be identified? Methods: A decision analytic model-based economic evaluation was undertaken to identify an efficient approach to preventing CR-BSI in Queensland Health intensive care units. A Markov model was developed in conjunction with a panel of clinical experts which described the epidemiology and prognosis of CR-BSI. The model was parameterised using data systematically identified from the published literature and extracted from routine databases. The quality of data used in the model and its validity to clinical experts and sensitivity to modelling assumptions was assessed. Two separate economic evaluations were conducted. The first evaluation compared all commercially available A-CVCs alongside uncoated catheters to identify which was cost-effective for routine use. The uncertainty in this decision was estimated along with the value of collecting further information to inform the decision. The second evaluation compared the use of A-CVCs to a catheter care bundle. We were unable to estimate the cost of the bundle because it is unclear what the full resource requirements are for its implementation, and what the value of these would be in an Australian context. As such we undertook a threshold analysis to identify the cost and effectiveness thresholds at which a hypothetical bundle would dominate the use of A-CVCs under various clinical scenarios. Results: In the first evaluation of A-CVCs, the findings from the baseline analysis, in which uncertainty is not considered, show that the use of any of the four A-CVCs will result in health gains accompanied by cost-savings. The MR catheters dominate the baseline analysis generating 1.64 QALYs and cost-savings of $130,289 per 1.000 catheters. With uncertainty, and based on current information, the MR catheters remain the optimal decision and return the highest average net monetary benefits ($948 per catheter) relative to all other catheter types. This conclusion was robust to all scenarios tested, however, the probability of error in this conclusion is high, 62% in the baseline scenario. Using a value of $40,000 per QALY, the expected value of perfect information associated with this decision is $7.3 million. An analysis of the expected value of perfect information for individual parameters suggests that it may be worthwhile for future research to focus on providing better estimates of the mortality attributable to CR-BSI and the effectiveness of both SPC and CH/SSD (int/ext) catheters. In the second evaluation of the catheter care bundle relative to A-CVCs, the results which do not consider uncertainty indicate that a bundle must achieve a relative risk of CR-BSI of at least 0.45 to be cost-effective relative to MR catheters. If the bundle can reduce rates of infection from 2.5% to effectively zero, it is cost-effective relative to MR catheters if national implementation costs are less than $2.6 million ($56,610 per ICU). If the bundle can achieve a relative risk of 0.34 (comparable to that reported in the literature) it is cost-effective, relative to MR catheters, if costs over an 18 month period are below $613,795 nationally ($13,343 per ICU). Once uncertainty in the decision is considered, the cost threshold for the bundle increases to $2.2 million. Therefore, if each of the 46 Level III ICUs could implement an 18 month catheter care bundle for less than $47,826 each, this approach would be cost effective relative to A-CVCs. However, the uncertainty is substantial and the probability of error in concluding that the bundle is the cost-effective approach at a cost of $2.2 million is 89%. Conclusions: This work highlights that infection control to prevent CR-BSI is an efficient use of healthcare resources in the Australian context. If there is no further investment in infection control, an opportunity cost is incurred, which is the potential for a more efficient healthcare system. Minocycline/rifampicin catheters are the optimal choice of antimicrobial catheter for routine use in Australian Level III ICUs, however, if a catheter care bundle implemented in Australia was as effective as those used in the large studies in the United States it would be preferred over the catheters if it was able to be implemented for less than $47,826 per Level III ICU. Uncertainty is very high in this decision and arises from multiple sources. There are likely greater costs to this uncertainty for A-CVCs, which may carry hidden costs, than there are for a catheter care bundle, which is more likely to provide indirect benefits to clinical practice and patient safety. Research into the mortality attributable to CR-BSI, the effectiveness of SPC and CH/SSD (int/ext) catheters and the cost and effectiveness of a catheter care bundle in Australia should be prioritised to reduce uncertainty in this decision. This thesis provides the economic evidence to inform one area of infection control, but there are many other infection control decisions for which information about the cost-effectiveness of competing interventions does not exist. This work highlights some of the challenges and benefits to generating and using economic evidence for infection control decision-making and provides support for commissioning more research into the cost-effectiveness of infection control.

Estimating interactive coefficients for analysing interactive failures

Engineering assets are often complex systems. In a complex system, components often have failure interactions which lead to interactive failures. A system with interactive failures may lead to an increased failure probability. Hence, one may have to take the interactive failures into account when designing and maintaining complex engineering systems. To address this issue, Sun et al have developed an analytical model for the interactive failures. In this model, the degree of interaction between two components is represented by interactive coefficients. To use this model for failure analysis, the related interactive coefficients must be estimated. However, methods for estimating the interactive coefficients have not been reported. To fill this gap, this paper presents five methods to estimate the interactive coefficients including probabilistic method; failure data based analysis method; laboratory experimental method; failure interaction mechanism based method; and expert estimation method. Examples are given to demonstrate the applications of the proposed methods. Comparisons among these methods are also presented.

Determination of optimal preventive maintenance strategy for serial production lines

A Split System Approach (SSA) based methodology is presented to assist in making optimal Preventive Maintenance decisions for serial production lines. The methodology treats a production line as a complex series system with multiple PM actions over multiple intervals. Both risk related cost and maintenance related cost are factored into the methodology as either deterministic or random variables. This SSA based methodology enables Asset Management (AM) decisions to be optimized considering a variety of factors including failure probability, failure cost, maintenance cost, PM performance, and the type of PM strategy. The application of this new methodology and an evaluation of the effects of these factors on PM decisions are demonstrated using an example. The results of this work show that the performance of a PM strategy can be measured by its Total Expected Cost Index (TECI). The optimal PM interval is dependent on TECI, PM performance and types of PM strategies. These factors are interrelated. Generally it was found that a trade-off between reliability and the number of PM actions needs to be made so that one can minimize Total Expected Cost (TEC) for asset maintenance.

Accelerated computation of cyclic steady state for simulated-moving-bed processes

Industrial applications of the simulated-moving-bed (SMB) chromatographic technology have brought an emergent demand to improve the SMB process operation for higher efficiency and better robustness. Improved process modelling and more-efficient model computation will pave a path to meet this demand. However, the SMB unit operation exhibits complex dynamics, leading to challenges in SMB process modelling and model computation. One of the significant problems is how to quickly obtain the steady state of an SMB process model, as process metrics at the steady state are critical for process design and real-time control. The conventional computation method, which solves the process model cycle by cycle and takes the solution only when a cyclic steady state is reached after a certain number of switching, is computationally expensive. Adopting the concept of quasi-envelope (QE), this work treats the SMB operation as a pseudo-oscillatory process because of its large number of continuous switching. Then, an innovative QE computation scheme is developed to quickly obtain the steady state solution of an SMB model for any arbitrary initial condition. The QE computation scheme allows larger steps to be taken for predicting the slow change of the starting state within each switching. Incorporating with the wavelet-based technique, this scheme is demonstrated to be effective and efficient for an SMB sugar separation process. Moreover, investigations are also carried out on when the computation scheme should be activated and how the convergence of the scheme is affected by a variable stepsize.

An ecological assessment of secondary poisoning risk in the Australian sugarcane industry

Rodenticide use in agriculture can lead to the secondary poisoning of avian predators. Currently the Australian sugarcane industry has two rodenticides, Racumin® and Rattoff®, available for in-crop use but, like many agricultural industries, it lacks an ecologically-based method of determining the potential secondary poisoning risk the use of these rodenticides poses to avian predators. The material presented in this thesis addresses this by: a. determining where predator/prey interactions take place in sugar producing districts; b. quantifying the amount of rodenticide available to avian predators and the probability of encounter; and c. developing a stochastic model that allows secondary poisoning risk under various rodenticide application scenarios to be investigated. Results demonstrate that predator/prey interactions are highly constrained by environmental structure. Rodents used crops that provided high levels of canopy cover and therefore predator protection and poorly utilised open canopy areas. In contrast, raptors over-utilised areas with low canopy cover and low rodent densities, but which provided high accessibility to prey. Given this pattern of habitat use, and that industry baiting protocols preclude rodenticide application in open canopy crops, these results indicate that secondary poisoning can only occur if poisoned rodents leave closed canopy crops and become available for predation in open canopy areas. Results further demonstrate that after in-crop rodenticide application, only a small proportion of rodents available in open areas are poisoned and that these rodents carry low levels of toxicant. Coupled with the low level of rodenticide use in the sugar industry, the high toxic threshold raptors have to these toxicants and the low probability of encountering poisoned rodents, results indicate that the risk of secondary poisoning events occurring is minimal. A stochastic model was developed to investigate the effect of manipulating factors that might influence secondary poisoning hazard in a sugarcane agro-ecosystem. These simulations further suggest that in all but extreme scenarios, the risk of secondary poisoning is also minimal. Collectively, these studies demonstrate that secondary poisoning of avian predators associated with the use of the currently available rodenticides in Australian sugar producing districts is minimal. Further, the ecologically-based method of assessing secondary poisoning risk developed in this thesis has broader applications in other agricultural systems where rodenticide use may pose risks to avian predators.

Object tracking using multiple motion modalities

This paper presents an object tracking system that utilises a hybrid multi-layer motion segmentation and optical flow algorithm. While many tracking systems seek to combine multiple modalities such as motion and depth or multiple inputs within a fusion system to improve tracking robustness, current systems have avoided the combination of motion and optical flow. This combination allows the use of multiple modes within the object detection stage. Consequently, different categories of objects, within motion or stationary, can be effectively detected utilising either optical flow, static foreground or active foreground information. The proposed system is evaluated using the ETISEO database and evaluation metrics and compared to a baseline system utilising a single mode foreground segmentation technique. Results demonstrate a significant improvement in tracking results can be made through the incorporation of the additional motion information.

Dynamic Performance Measures for Object Tracking Systems

Performance evaluation of object tracking systems is typically performed after the data has been processed, by comparing tracking results to ground truth. Whilst this approach is fine when performing offline testing, it does not allow for real-time analysis of the systems performance, which may be of use for live systems to either automatically tune the system or report reliability. In this paper, we propose three metrics that can be used to dynamically asses the performance of an object tracking system. Outputs and results from various stages in the tracking system are used to obtain measures that indicate the performance of motion segmentation, object detection and object matching. The proposed dynamic metrics are shown to accurately indicate tracking errors when visually comparing metric results to tracking output, and are shown to display similar trends to the ETISEO metrics when comparing different tracking configurations.

Impact of cognitive load and frustration on drivers’ speech [Abstract]

Secondary tasks such as cell phone calls or interaction with automated speech dialog systems (SDSs) increase the driver’s cognitive load as well as the probability of driving errors. This study analyzes speech production variations due to cognitive load and emotional state of drivers in real driving conditions. Speech samples were acquired from 24 female and 17 male subjects (approximately 8.5 h of data) while talking to a co-driver and communicating with two automated call centers, with emotional states (neutral, negative) and the number of necessary SDS query repetitions also labeled. A consistent shift in a number of speech production parameters (pitch, first format center frequency, spectral center of gravity, spectral energy spread, and duration of voiced segments) was observed when comparing SDS interaction against co-driver interaction; further increases were observed when considering negative emotion segments and the number of requested SDS query repetitions. A mel frequency cepstral coefficient based Gaussian mixture classifier trained on 10 male and 10 female sessions provided 91% accuracy in the open test set task of distinguishing co-driver interactions from SDS interactions, suggesting—together with the acoustic analysis—that it is possible to monitor the level of driver distraction directly from their speech.