Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

An infinite-horizon robust filter for uncertain hidden Markov Models with conditional relative entropy constraints

We consider a robust filtering problem for uncertain discrete-time, homogeneous, first-order, finite-state hidden Markov models (HMMs). The class of uncertain HMMs considered is described by a conditional relative entropy constraint on measures perturbed from a nominal regular conditional probability distribution given the previous posterior state distribution and the latest measurement. Under this class of perturbations, a robust infinite horizon filtering problem is first formulated as a constrained optimization problem before being transformed via variational results into an unconstrained optimization problem; the latter can be elegantly solved using a risk-sensitive information-state based filtering.

Integrated health prediction of bridge systems using dynamic object oriented Bayesian networks (DOOBNS)

The serviceability and safety of bridges are crucial to people’s daily lives and to the national economy. Every effort should be taken to make sure that bridges function safely and properly as any damage or fault during the service life can lead to transport paralysis, catastrophic loss of property or even casualties. Nonetheless, aggressive environmental conditions, ever-increasing and changing traffic loads and aging can all contribute to bridge deterioration. With often constrained budget, it is of significance to identify bridges and bridge elements that should be given higher priority for maintenance, rehabilitation or replacement, and to select optimal strategy. Bridge health prediction is an essential underpinning science to bridge maintenance optimization, since the effectiveness of optimal maintenance decision is largely dependent on the forecasting accuracy of bridge health performance. The current approaches for bridge health prediction can be categorised into two groups: condition ratings based and structural reliability based. A comprehensive literature review has revealed the following limitations of the current modelling approaches: (1) it is not evident in literature to date that any integrated approaches exist for modelling both serviceability and safety aspects so that both performance criteria can be evaluated coherently; (2) complex system modelling approaches have not been successfully applied to bridge deterioration modelling though a bridge is a complex system composed of many inter-related bridge elements; (3) multiple bridge deterioration factors, such as deterioration dependencies among different bridge elements, observed information, maintenance actions and environmental effects have not been considered jointly; (4) the existing approaches are lacking in Bayesian updating ability to incorporate a variety of event information; (5) the assumption of series and/or parallel relationship for bridge level reliability is always held in all structural reliability estimation of bridge systems. To address the deficiencies listed above, this research proposes three novel models based on the Dynamic Object Oriented Bayesian Networks (DOOBNs) approach. Model I aims to address bridge deterioration in serviceability using condition ratings as the health index. The bridge deterioration is represented in a hierarchical relationship, in accordance with the physical structure, so that the contribution of each bridge element to bridge deterioration can be tracked. A discrete-time Markov process is employed to model deterioration of bridge elements over time. In Model II, bridge deterioration in terms of safety is addressed. The structural reliability of bridge systems is estimated from bridge elements to the entire bridge. By means of conditional probability tables (CPTs), not only series-parallel relationship but also complex probabilistic relationship in bridge systems can be effectively modelled. The structural reliability of each bridge element is evaluated from its limit state functions, considering the probability distributions of resistance and applied load. Both Models I and II are designed in three steps: modelling consideration, DOOBN development and parameters estimation. Model III integrates Models I and II to address bridge health performance in both serviceability and safety aspects jointly. The modelling of bridge ratings is modified so that every basic modelling unit denotes one physical bridge element. According to the specific materials used, the integration of condition ratings and structural reliability is implemented through critical failure modes. Three case studies have been conducted to validate the proposed models, respectively. Carefully selected data and knowledge from bridge experts, the National Bridge Inventory (NBI) and existing literature were utilised for model validation. In addition, event information was generated using simulation to demonstrate the Bayesian updating ability of the proposed models. The prediction results of condition ratings and structural reliability were presented and interpreted for basic bridge elements and the whole bridge system. The results obtained from Model II were compared with the ones obtained from traditional structural reliability methods. Overall, the prediction results demonstrate the feasibility of the proposed modelling approach for bridge health prediction and underpin the assertion that the three models can be used separately or integrated and are more effective than the current bridge deterioration modelling approaches. The primary contribution of this work is to enhance the knowledge in the field of bridge health prediction, where more comprehensive health performance in both serviceability and safety aspects are addressed jointly. The proposed models, characterised by probabilistic representation of bridge deterioration in hierarchical ways, demonstrated the effectiveness and pledge of DOOBNs approach to bridge health management. Additionally, the proposed models have significant potential for bridge maintenance optimization. Working together with advanced monitoring and inspection techniques, and a comprehensive bridge inventory, the proposed models can be used by bridge practitioners to achieve increased serviceability and safety as well as maintenance cost effectiveness.

Motor controller simulation and embedded implementation for a blood pump

This study was a step forward in modeling, simulation and microcontroller implementation of a high performance control algorithm for the motor of a blood pump. The rotor angle is sensed using three Hall effect sensors and an algorithm is developed to obtain better angular resolution from the three signals for better discrete-time updates of the controller. The performance of the system was evaluated in terms of actual and reference speeds, stator currents and power consumption over a range of reference speeds up to 4000 revolutions per minute. The use of fewer low cost Hall effect sensors compared to expensive high resolution sensors could reduce the cost of blood pumps for total artificial hearts.

An Introduction to Constrained Control

An ubiquitous problem in control system design is that the system must operate subject to various constraints. Although the topic of constrained control has a long history in practice, there have been recent significant advances in the supporting theory. In this chapter, we give an introduction to constrained control. In particular, we describe contemporary work which shows that the constrained optimal control problem for discrete-time systems has an interesting geometric structure and a simple local solution. We also discuss issues associated with the output feedback solution to this class of problems, and the implication of these results in the closely related problem of anti-windup. As an application, we address the problem of rudder roll stabilization for ships.

On optimal control of constrained linear systems with imperfect state information and stochastic disturbances

We address the problem of finite horizon optimal control of discrete-time linear systems with input constraints and uncertainty. The uncertainty for the problem analysed is related to incomplete state information (output feedback) and stochastic disturbances. We analyse the complexities associated with finding optimal solutions. We also consider two suboptimal strategies that could be employed for larger optimization horizons.

Enhanced fast handover triggering mechanism for fast proxy mobile IPv6

Handover performance is critical to support real-time traffic applications in wireless network communications. The longer the handover delay is, the longer an Mobile Node (MN) is prevented from sending and receiving any data packet. In real-time network communication applications, such as VoIP and video-conference, a long handover delay is often unacceptable. In order to achieve better handover performance, Fast Proxy Mobile IPv6 (FPMIPv6) has been standardised as an improvement to the original Proxy Mobile IPv6 (PMIPv6) in the Internet Engineering Task Force (IETF). The FPMIPv6 adopts a link layer triggering mechanism to perform two modes of operation: predictive and reactive modes. Using the link layer triggering, the handover performance of the FPMIPv6 can be improved in the predictive mode. However, an unsuccessful predictive handover operation will lead to activation of a reactive handover. In the reactive mode, MNs still experience long handover delays and a large amount of packet loss, which significantly degrade the handover performance of the FPMIPv6. Addressing this problem, this thesis presents an Enhanced Triggering Mechanism (ETM) in the FPMIPv6 to form an enhanced FPMIPv6 (eFPMIPv6). The ETM reduces the most time consuming processes in the reactive handover: the failed Handover Initiate (HO-Initiate) delay and bidirectional tunnel establishment delay. Consequently, the overall handover performance of the FPMIPv6 is enhanced in the eFPMIPv6. To show the advantages of the proposed eFPMIPv6, a theoretical analysis is carried out to mathematically model the performance of PMIPv6, FPMIPv6 and eFPMIPv6. Extensive case studies are conducted to validate the effectiveness of the presented eFPMIPv6 mechanism. They are carried out under various scenarios with changes in network link delay, traffic load, number of hops and MN moving velocity. The case studies show that the proposed mechanism ETM reduces the reactive handover delay, and the presented eFPMIPv6 outperforms the PMIPv6 and FPMIPv6 in terms of the overall handover performance.

Interacting motile agents : taking a mean-field approach beyond monomers and nearest-neighbor steps

We consider a discrete agent-based model on a one-dimensional lattice, where each agent occupies L sites and attempts movements over a distance of d lattice sites. Agents obey a strict simple exclusion rule. A discrete-time master equation is derived using a mean-field approximation and careful probability arguments. In the continuum limit, nonlinear diffusion equations that describe the average agent occupancy are obtained. Averaged discrete simulation data are generated and shown to compare very well with the solution to the derived nonlinear diffusion equations. This framework allows us to approach a lattice-free result using all the advantages of lattice methods. Since different cell types have different shapes and speeds of movement, this work offers insight into population-level behavior of collective cellular motion.

Comparing multilevel and Bayesian spatial random effects survival models to assess geographical inequalities in colorectal cancer survival: a case study

Background Multilevel and spatial models are being increasingly used to obtain substantive information on area-level inequalities in cancer survival. Multilevel models assume independent geographical areas, whereas spatial models explicitly incorporate geographical correlation, often via a conditional autoregressive prior. However the relative merits of these methods for large population-based studies have not been explored. Using a case-study approach, we report on the implications of using multilevel and spatial survival models to study geographical inequalities in all-cause survival. Methods Multilevel discrete-time and Bayesian spatial survival models were used to study geographical inequalities in all-cause survival for a population-based colorectal cancer cohort of 22,727 cases aged 20–84 years diagnosed during 1997–2007 from Queensland, Australia. Results Both approaches were viable on this large dataset, and produced similar estimates of the fixed effects. After adding area-level covariates, the between-area variability in survival using multilevel discrete-time models was no longer significant. Spatial inequalities in survival were also markedly reduced after adjusting for aggregated area-level covariates. Only the multilevel approach however, provided an estimation of the contribution of geographical variation to the total variation in survival between individual patients. Conclusions With little difference observed between the two approaches in the estimation of fixed effects, multilevel models should be favored if there is a clear hierarchical data structure and measuring the independent impact of individual- and area-level effects on survival differences is of primary interest. Bayesian spatial analyses may be preferred if spatial correlation between areas is important and if the priority is to assess small-area variations in survival and map spatial patterns. Both approaches can be readily fitted to geographically enabled survival data from international settings

Destinations: 3 Large Cast Plays for Young People

This book is a collection of three large-cast plays written in response to a very specific problem. My work as a teacher of drama often required me to locate a script that would somehow miraculously work for a cast of unknown number and gender, and most likely uneven skills and enthusiasm, who I hadn’t even met yet. It’s a familiar dilemma for teachers and students of drama in education contexts, at whatever level you’re teaching. I’d first addressed this creative problem with scripts such as Gate 38 (2010). I had tried using scripts that already existed, but found they required such extensive editing to suit the parameters of cast and performance duration that I may as well have been writing them myself. Even in the setting of a closed studio, in altering these plays I felt I was bending the vision of the playwright, and certainly their narrative structure, out of shape. Everyone who’s attempted to stage a performance with a large cast of students in an educational setting knows it takes time to truly connect with a play, its social contexts, themes and characters. It also takes a lot of time to get on top of the practicalities of learning, rehearsing, directing and running a performance with young people. Often the curtain goes up on something unfinished and unstable. I was looking for ways to reduce the complexity of staging a script, while maintaining the potential of this process as a site of rich, enjoyable learning. Two of the plays (Duty Free and Please Be Seated) are comprised of multiple monologues, combined with music-driven ensemble sequences. The monologues enable individuals to develop and polish their own performances, work in small groups, and cut down on the laborious detail of directing naturalistic scenes based in character interaction. The third (Australian Drama) involves a lot of duologues, meaning that its rehearsal process can happily employ that mainstay of the drama classroom: small group work. There’s plenty of room to move in terms of gender-blind casting as well. Please be Seated is mainly young women. The scripts also contain ensemble-based interludes which are non-verbal, music driven, with a choreographic element. They have also springboarded further explorations in form. The ethical and aesthetic complexities of verbatim works; the interaction between music and theatre; and meta-concerns related to the performing of performance: ‘how can the act of acting ‘acted’. The narratives of all three of these plays are deliberately open, enabling the flexible casting and on-the hop editing that large-group, time-poor processes sometimes necessitate. Duty Free is about the overseas ‘adventures’ of young people. Please Be Seated is based in verbatim text about young people falling in and out of love. Australian Drama is about young people in a drama classroom trying to connect with each other and put their own shine on dull fragments of the theatrical canon. The plays were published as a collection in hardcopy and digital editions by Playlab Press in 2015. Please be Seated is a co-write with a large group. These co-author’s names are listed in the publication, and below in ‘additional information’.

A note on Gittins indexes for pharmaceutical research

The Bernoulli/exponential target process is considered. Such processes have been found useful in modelling the search for active compounds in pharmaceutical research. An inequality is presented which improves a result of Gittins (1989), thus providing a better approximation to the Gittins indices which define the optimal search policy.

Insights into students' conceptual understanding using textual analysis: A case study in signal processing

Concept inventory tests are one method to evaluate conceptual understanding and identify possible misconceptions. The multiple-choice question format, offering a choice between a correct selection and common misconceptions, can provide an assessment of students' conceptual understanding in various dimensions. Misconceptions of some engineering concepts exist due to a lack of mental frameworks, or schemas, for these types of concepts or conceptual areas. This study incorporated an open textual response component in a multiple-choice concept inventory test to capture written explanations of students' selections. The study's goal was to identify, through text analysis of student responses, the types and categorizations of concepts in these explanations that had not been uncovered by the distractor selections. The analysis of the textual explanations of a subset of the discrete-time signals and systems concept inventory questions revealed that students have difficulty conceptually explaining several dimensions of signal processing. This contributed to their inability to provide a clear explanation of the underlying concepts, such as mathematical concepts. The methods used in this study evaluate students' understanding of signals and systems concepts through their ability to express understanding in written text. This may present a bias for students with strong written communication skills. This study presents a framework for extracting and identifying the types of concepts students use to express their reasoning when answering conceptual questions.

Output feedback control of networked systems with a stochastic communication protocol

This paper addresses an output feedback control problem for a class of networked control systems (NCSs) with a stochastic communication protocol. Under the scenario that only one sensor is allowed to obtain the communication access at each transmission instant, a stochastic communication protocol is first defined, where the communication access is modelled by a discrete-time Markov chain with partly unknown transition probabilities. Secondly, by use of a network-based output feedback control strategy and a time-delay division method, the closed-loop system is modeled as a stochastic system with multi time-varying delays, where the inherent characteristic of the network delay is well considered to improve the control performance. Then, based on the above constructed stochastic model, two sufficient conditions are derived for ensuring the mean-square stability and stabilization of the system under consideration. Finally, two examples are given to show the effectiveness of the proposed method.

Critical time scales for advection–diffusion–reaction processes

The concept of local accumulation time (LAT) was introduced by Berezhkovskii and coworkers in 2010–2011 to give a finite measure of the time required for the transient solution of a reaction–diffusion equation to approach the steady–state solution (Biophys J. 99, L59 (2010); Phys Rev E. 83, 051906 (2011)). Such a measure is referred to as a critical time. Here, we show that LAT is, in fact, identical to the concept of mean action time (MAT) that was first introduced by McNabb in 1991 (IMA J Appl Math. 47, 193 (1991)). Although McNabb’s initial argument was motivated by considering the mean particle lifetime (MPLT) for a linear death process, he applied the ideas to study diffusion. We extend the work of these authors by deriving expressions for the MAT for a general one–dimensional linear advection–diffusion–reaction problem. Using a combination of continuum and discrete approaches, we show that MAT and MPLT are equivalent for certain uniform–to-uniform transitions; these results provide a practical interpretation for MAT, by directly linking the stochastic microscopic processes to a meaningful macroscopic timescale. We find that for more general transitions, the equivalence between MAT and MPLT does not hold. Unlike other critical time definitions, we show that it is possible to evaluate the MAT without solving the underlying partial differential equation (pde). This makes MAT a simple and attractive quantity for practical situations. Finally, our work explores the accuracy of certain approximations derived using the MAT, showing that useful approximations for nonlinear kinetic processes can be obtained, again without treating the governing pde directly.

Information technology support to improved construction processes : inter-disciplinarity in research and practice

Research and innovation in the built environment is increasingly taking on an inter-disciplinary nature. The built environment industry and professional practice have long adopted multi and inter-disciplinary practices. The application of IT in Construction is moving beyond the automation and replication of discrete mono and multi-disciplinary tasks to replicate and model the improved inter-disciplinary processes of modern design and construction practice. A major long-term research project underway at the University of Salford seeks to develop IT modelling capability to support the design of buildings and facilities that are buildable, maintainable, operable, sustainable, accessible, and have properties of acoustic, thermal and business support performance that are of a high standard. Such an IT modelling tool has been the dream of the research community for a long time. Recent advances in technology are beginning to make such a modelling tool feasible.----- Some of the key problems with its further research and development, and with its ultimate implementation, will be the challenges of multiple research and built environment stakeholders sharing a common vision, language and sense of trust. This paper explores these challenges as a set of research issues that underpin the development of appropriate technology to support realisable advances in construction process improvements.