An implicit RBF meshless approach for time fractional diffusion equations

This paper aims to develop an implicit meshless approach based on the radial basis function (RBF) for numerical simulation of time fractional diffusion equations. The meshless RBF interpolation is firstly briefed. The discrete equations for two-dimensional time fractional diffusion equation (FDE) are obtained by using the meshless RBF shape functions and the strong-forms of the time FDE. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approach. It has proven that the present meshless formulation is very effective for modeling and simulation of fractional differential equations.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

An advanced meshless method for time fractional diffusion equation

Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations.

Learning hierarchical prototypes of motion time series for interactive systems

Abstract. For interactive systems, recognition, reproduction, and generalization of observed motion data are crucial for successful interaction. In this paper, we present a novel method for analysis of motion data that we refer to as K-OMM-trees. K-OMM-trees combine Ordered Means Models (OMMs) a model-based machine learning approach for time series with an hierarchical analysis technique for very large data sets, the K-tree algorithm. The proposed K-OMM-trees enable unsupervised prototype extraction of motion time series data with hierarchical data representation. After introducing the algorithmic details, we apply the proposed method to a gesture data set that includes substantial inter-class variations. Results from our studies show that K-OMM-trees are able to substantially increase the recognition performance and to learn an inherent data hierarchy with meaningful gesture abstractions.

A reliable real-time transport protocol for control systems over wireless networks

Deploying networked control systems (NCSs) over wireless networks is becoming more and more popular. However, the widely-used transport layer protocols, Transmission Control Protocol (TCP) and User Datagram Protocol (UDP), are not designed for real-time applications. Therefore, they may not be suitable for many NCS application scenarios because of their limitations on reliability and/or delay performance, which real-control systems concern. Considering a typical type of NCSs with periodic and sporadic real-time traffic, this paper proposes a highly reliable transport layer protocol featuring a packet loss-sensitive retransmission mechanism and a prioritized transmission mechanism. The packet loss-sensitive retransmission mechanism is designed to improve the reliability of all traffic flows. And the prioritized transmission mechanism offers differentiated services for periodic and sporadic flows. Simulation results show that the proposed protocol has better reliability than UDP and improved delay performance than TCP over wireless networks, particularly when channel errors and congestions occur.

A reliable real-time transport protocol for networked control systems over wireless networks

Deploying wireless networks in networked control systems (NCSs) has become more and more popular during the last few years. As a typical type of real-time control systems, an NCS is sensitive to long and nondeterministic time delay and packet losses. However, the nature of the wireless channel has the potential to degrade the performance of NCS networks in many aspects, particularly in time delay and packet losses. Transport layer protocols could play an important role in providing both reliable and fast transmission service to fulfill NCS’s real-time transmission requirements. Unfortunately, none of the existing transport protocols, including the Transport Control Protocol (TCP) and the User Datagram Protocol (UDP), was designed for real-time control applications. Moreover, periodic data and sporadic data are two types of real-time data traffic with different priorities in an NCS. Due to the lack of support for prioritized transmission service, the real-time performance for periodic and sporadic data in an NCS network is often degraded significantly, particularly under congested network conditions. To address these problems, a new transport layer protocol called Reliable Real-Time Transport Protocol (RRTTP) is proposed in this thesis. As a UDP-based protocol, RRTTP inherits UDP’s simplicity and fast transmission features. To improve the reliability, a retransmission and an acknowledgement mechanism are designed in RRTTP to compensate for packet losses. They are able to avoid unnecessary retransmission of the out-of-date packets in NCSs, and collisions are unlikely to happen, and small transmission delay can be achieved. Moreover, a prioritized transmission mechanism is also designed in RRTTP to improve the real-time performance of NCS networks under congested traffic conditions. Furthermore, the proposed RRTTP is implemented in the Network Simulator 2 for comprehensive simulations. The simulation results demonstrate that RRTTP outperforms TCP and UDP in terms of real-time transmissions in an NCS over wireless networks.

Integrating real time positioning systems to improve blind lifting and loading crane operations

Mobile/tower cranes are the most essential forms of construction plant in use in the construction industry but are also the subject of several safety issues. Of these, blind lifting has been found to be one of the most hazardous of crane operations. To improve the situation, a real-time monitoring system that integrates the use of a Global Positioning System (GPS) and Radio Frequency Identification (RFID) is developed. This system aims to identify unauthorized work or entrance of personnel within a pre-defined risk zone by obtaining positioning data of both site workers and the crane. The system alerts to the presence of unauthorized workers within a risk zone——currently defined as 3m from the crane. When this happens, the system suspends the power of the crane and a warning signal is generated to the safety management team. In this way the system assists the safety management team to manage the safety of hundreds of workers simultaneously. An onsite trial with debriefing interviews is presented to illustrate and validate the system in use.

Prediction and proactivity in real-time interactive music systems

We advocate for the use of predictive techniques in interactive computer music systems. We suggest that the inclusion of prediction can assist in the design of proactive rather than reactive computational performance partners. We summarize the significant role prediction plays in human musical decisions, and the only modest use of prediction in interactive music systems to date. After describing how we are working toward employing predictive processes in our own metacreation software we reflect on future extensions to these approaches.

A novel real time pricing scheme for demand response in residential distribution systems

Price based technique is one way to handle increase in peak demand and deal with voltage violations in residential distribution systems. This paper proposes an improved real time pricing scheme for residential customers with demand response option. Smart meters and in-home display units are used to broadcast the price and appropriate load adjustment signals. Customers are given an opportunity to respond to the signals and adjust the loads. This scheme helps distribution companies to deal with overloading problems and voltage issues in a more efficient way. Also, variations in wholesale electricity prices are passed on to electricity customers to take collective measure to reduce network peak demand. It is ensured that both customers and utility are benefitted by this scheme.

The velocity synchronous discrete Fourier transform for order tracking in the field of rotating machinery

Diagnostics of rotating machinery has developed significantly in the last decades, and industrial applications are spreading in different sectors. Most applications are characterized by varying velocities of the shaft and in many cases transients are the most critical to monitor. In these variable speed conditions, fault symptoms are clearer in the angular/order domains than in the common time/frequency ones. In the past, this issue was often solved by synchronously sampling data by means of phase locked circuits governing the acquisition; however, thanks to the spread of cheap and powerful microprocessors, this procedure is nowadays rarer; sampling is usually performed at constant time intervals, and the conversion to the order domain is made by means of digital signal processing techniques. In the last decades different algorithms have been proposed for the extraction of an order spectrum from a signal sampled asynchronously with respect to the shaft rotational velocity; many of them (the so called computed order tracking family) use interpolation techniques to resample the signal at constant angular increments, followed by a common discrete Fourier transform to shift from the angular domain to the order domain. A less exploited family of techniques shifts directly from the time domain to the order spectrum, by means of modified Fourier transforms. This paper proposes a new transform, named velocity synchronous discrete Fourier transform, which takes advantage of the instantaneous velocity to improve the quality of its result, reaching performances that can challenge the computed order tracking.

Order tracking for discrete-random separation in variable speed conditions

The transmission path from the excitation to the measured vibration on the surface of a mechanical system introduces a distortion both in amplitude and in phase. Moreover, in variable speed conditions, the amplification/attenuation and the phase shift, due to the transfer function of the mechanical system, varies in time. This phenomenon reduces the effectiveness of the traditionally tachometer based order tracking, compromising the results of a discrete-random separation performed by a synchronous averaging. In this paper, for the first time, the extent of the distortion is identified both in the time domain and in the order spectrum of the signal, highlighting the consequences for the diagnostics of rotating machinery. A particular focus is given to gears, providing some indications on how to take advantage of the quantification of the disturbance to better tune the techniques developed for the compensation of the distortion. The full theoretical analysis is presented and the results are applied to an experimental case.

A finite volume method with linearisation in time for the solution of advection-reaction-diffusion systems

The numerical solution in one space dimension of advection--reaction--diffusion systems with nonlinear source terms may invoke a high computational cost when the presently available methods are used. Numerous examples of finite volume schemes with high order spatial discretisations together with various techniques for the approximation of the advection term can be found in the literature. Almost all such techniques result in a nonlinear system of equations as a consequence of the finite volume discretisation especially when there are nonlinear source terms in the associated partial differential equation models. This work introduces a new technique that avoids having such nonlinear systems of equations generated by the spatial discretisation process when nonlinear source terms in the model equations can be expanded in positive powers of the dependent function of interest. The basis of this method is a new linearisation technique for the temporal integration of the nonlinear source terms as a supplementation of a more typical finite volume method. The resulting linear system of equations is shown to be both accurate and significantly faster than methods that necessitate the use of solvers for nonlinear system of equations.

A runtime integrity monitoring framework for real-time relative positioning systems based on GPS and DSRC

This paper provides a three-layered framework to monitor the positioning performance requirements of Real-time Relative Positioning (RRP) systems of the Cooperative Intelligent Transport Systems (C-ITS) that support Cooperative Collision Warning (CCW) applications. These applications exploit state data of surrounding vehicles obtained solely from the Global Positioning System (GPS) and Dedicated Short-Range Communications (DSRC) units without using other sensors. To this end, the paper argues the need for the GPS/DSRC-based RRP systems to have an autonomous monitoring mechanism, since the operation of CCW applications is meant to augment safety on roads. The advantages of autonomous integrity monitoring are essential and integral to any safety-of-life system. The autonomous integrity monitoring framework proposed necessitates the RRP systems to detect/predict the unavailability of their sub-systems and of the integrity monitoring module itself, and, if available, to account for effects of data link delays and breakages of DSRC links, as well as of faulty measurement sources of GPS and/or integrated augmentation positioning systems, before the information used for safety warnings/alarms becomes unavailable, unreliable, inaccurate or misleading. Hence, a monitoring framework using a tight integration and correlation approach is proposed for instantaneous reliability assessment of the RRP systems. Ultimately, using the proposed framework, the RRP systems will provide timely alerts to users when the RRP solutions cannot be trusted or used for the intended operation.

Real-time decision making by driverless city vehicles : a discrete event driven approach

This thesis addresses the topic of real-time decision making by driverless (autonomous) city vehicles, i.e. their ability to make appropriate driving decisions in non-simplified urban traffic conditions. After addressing the state of research, and explaining the research question, the thesis presents solutions for the subcomponents which are relevant for decision making with respect to information input (World Model), information output (Driving Maneuvers), and the real-time decision making process. TheWorld Model is a software component developed to fulfill the purpose of collecting information from perception and communication subsystems, maintaining an up-to-date view of the vehicle’s environment, and providing the required input information to the Real-Time Decision Making subsystem in a well-defined, and structured way. The real-time decision making process consists of two consecutive stages. While the first decision making stage uses a Petri net to model the safetycritical selection of feasible driving maneuvers, the second stage uses Multiple Criteria Decision Making (MCDM) methods to select the most appropriate driving maneuver, focusing on fulfilling objectives related to efficiency and comfort. The complex task of autonomous driving is subdivided into subtasks, called driving maneuvers, which represent the output (i.e. decision alternatives) of the real-time decision making process. Driving maneuvers are considered as implementations of closed-loop control algorithms, each capable of maneuvering the autonomous vehicle in a specific traffic situation. Experimental tests in both a 3D simulation and real-world experiments attest that the developed approach is suitable to deal with the complexity of real-world urban traffic situations.

Further development of discrete computational techniques for calculation of restricted diffusion propagators in porous media

Magnetic resonance is a well-established tool for structural characterisation of porous media. Features of pore-space morphology can be inferred from NMR diffusion-diffraction plots or the time-dependence of the apparent diffusion coefficient. Diffusion NMR signal attenuation can be computed from the restricted diffusion propagator, which describes the distribution of diffusing particles for a given starting position and diffusion time. We present two techniques for efficient evaluation of restricted diffusion propagators for use in NMR porous-media characterisation. The first is the Lattice Path Count (LPC). Its physical essence is that the restricted diffusion propagator connecting points A and B in time t is proportional to the number of distinct length-t paths from A to B. By using a discrete lattice, the number of such paths can be counted exactly. The second technique is the Markov transition matrix (MTM). The matrix represents the probabilities of jumps between every pair of lattice nodes within a single timestep. The propagator for an arbitrary diffusion time can be calculated as the appropriate matrix power. For periodic geometries, the transition matrix needs to be defined only for a single unit cell. This makes MTM ideally suited for periodic systems. Both LPC and MTM are closely related to existing computational techniques: LPC, to combinatorial techniques; and MTM, to the Fokker-Planck master equation. The relationship between LPC, MTM and other computational techniques is briefly discussed in the paper. Both LPC and MTM perform favourably compared to Monte Carlo sampling, yielding highly accurate and almost noiseless restricted diffusion propagators. Initial tests indicate that their computational performance is comparable to that of finite element methods. Both LPC and MTM can be applied to complicated pore-space geometries with no analytic solution. We discuss the new methods in the context of diffusion propagator calculation in porous materials and model biological tissues.