Time-dependent fractional advection–diffusion equations by an implicit MLS meshless method

Recently, many new applications in engineering and science are governed by a series of fractional partial differential equations (FPDEs). Unlike the normal partial differential equations (PDEs), the differential order in a FPDE is with a fractional order, which will lead to new challenges for numerical simulation, because most existing numerical simulation techniques are developed for the PDE with an integer differential order. The current dominant numerical method for FPDEs is Finite Difference Method (FDM), which is usually difficult to handle a complex problem domain, and also hard to use irregular nodal distribution. This paper aims to develop an implicit meshless approach based on the moving least squares (MLS) approximation for numerical simulation of fractional advection-diffusion equations (FADE), which is a typical FPDE. The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless strong-forms. The stability and convergence related to the time discretization of this approach are then discussed and theoretically proven. Several numerical examples with different problem domains and different 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 the FADE.

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.

High-voltage modular power supply using parallel and series configurations of flyback converter for pulsed power applications

To cover wide range of pulsed power applications, this paper proposes a modularity concept to improve the performance and flexibility of the pulsed power supply. The proposed scheme utilizes the advantage of parallel and series configurations of flyback modules in obtaining high-voltage levels with fast rise time (dv/dt). Prototypes were implemented using 600-V insulated-gate bipolar transistor (IGBT) switches to generate up to 4-kV output pulses with 1-kHz repetition rate for experimentation. To assess the proposed modular approach for higher number of the modules, prototypes were implemented using 1700-V IGBTs switches, based on ten-series modules, and tested up to 20 kV. Conducted experimental results verified the effectiveness of the proposed method

Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

An improved method to detect damage using modal strain energy based damage index

This paper presents two novel concepts to enhance the accuracy of damage detection using the Modal Strain Energy based Damage Index (MSEDI) with the presence of noise in the mode shape data. Firstly, the paper presents a sequential curve fitting technique that reduces the effect of noise on the calculation process of the MSEDI, more effectively than the two commonly used curve fitting techniques; namely, polynomial and Fourier’s series. Secondly, a probability based Generalized Damage Localization Index (GDLI) is proposed as a viable improvement to the damage detection process. The study uses a validated ABAQUS finite-element model of a reinforced concrete beam to obtain mode shape data in the undamaged and damaged states. Noise is simulated by adding three levels of random noise (1%, 3%, and 5%) to the mode shape data. Results show that damage detection is enhanced with increased number of modes and samples used with the GDLI.

Spelling instruction through Etymology : a method of developing spelling lists for older students

The purpose of this study was to investigate whether an approach to developing word lists centred on etymological roots would improve the spelling performance of older primary school students. Participants were 46 students in the last year of primary school in south-east Queensland (31 girls and 15 boys) across three classes, with two classes being assigned to control conditions. Students were evaluated pre- and post-intervention on three dependent measures: British Spelling Test Series spelling, spelling in writing and writing. The results of this intervention revealed improvements in spelling for girls but not for boys. The implications for improved teaching methods are discussed.

A least squares based finite volume method for the Cahn-Hilliard and Cahn-Hilliard-reaction equations

A vertex-centred finite volume method (FVM) for the Cahn-Hilliard (CH) and recently proposed Cahn-Hilliard-reaction (CHR) equations is presented. Information at control volume faces is computed using a high-order least-squares approach based on Taylor series approximations. This least-squares problem explicitly includes the variational boundary condition (VBC) that ensures that the discrete equations satisfy all of the boundary conditions. We use this approach to solve the CH and CHR equations in one and two dimensions and show that our scheme satisfies the VBC to at least second order. For the CH equation we show evidence of conservative, gradient stable solutions, however for the CHR equation, strict gradient-stability is more challenging to achieve.

Maintenance optimisation of a multi-state series-parallel system considering economic dependence and state-dependent inspection intervals

This paper presents a maintenance optimisation method for a multi-state series-parallel system considering economic dependence and state-dependent inspection intervals. The objective function considered in the paper is the average revenue per unit time calculated based on the semi-regenerative theory and the universal generating function (UGF). A new algorithm using the stochastic ordering is also developed in this paper to reduce the search space of maintenance strategies and to enhance the efficiency of optimisation algorithms. A numerical simulation is presented in the study to evaluate the efficiency of the proposed maintenance strategy and optimisation algorithms. The simulation result reveals that maintenance strategies with opportunistic maintenance and state-dependent inspection intervals are more cost-effective when the influence of economic dependence and inspection cost is significant. The study further demonstrates that the optimisation algorithm proposed in this paper has higher computational efficiency than the commonly employed heuristic algorithms.

A method for systematically pooling data in very early stage construction price forecasting

Client owners usually need an estimate or forecast of their likely building costs in advance of detailed design in order to confirm the financial feasibility of their projects. Because of their timing in the project life cycle, these early stage forecasts are characterized by the minimal amount of information available concerning the new (target) project to the point that often only its size and type are known. One approach is to use the mean contract sum of a sample, or base group, of previous projects of a similar type and size to the project for which the estimate is needed. Bernoulli’s law of large numbers implies that this base group should be as large as possible. However, increasing the size of the base group inevitably involves including projects that are less and less similar to the target project. Deciding on the optimal number of base group projects is known as the homogeneity or pooling problem. A method of solving the homogeneity problem is described involving the use of closed form equations to compare three different sampling arrangements of previous projects for their simulated forecasting ability by a cross-validation method, where a series of targets are extracted, with replacement, from the groups and compared with the mean value of the projects in the base groups. The procedure is then demonstrated with 450 Hong Kong projects (with different project types: Residential, Commercial centre, Car parking, Social community centre, School, Office, Hotel, Industrial, University and Hospital) clustered into base groups according to their type and size.

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.

Saturated core high-temperature superconducting fault current limiters as an alternative to conventional series reactors in a distribution grid

Series reactors are used in distribution grids to reduce the short-circuit fault level. Some of the disadvantages of the application of these devices are the voltage drop produced across the reactor and the steep front rise of the transient recovery voltage (TRV), which generally exceeds the rating of the associated circuit breaker. Simulations were performed to compare the characteristics of a saturated core High-Temperature Superconducting Fault Current Limiter (HTS FCL) and a series reactor. The design of the HTS FCL was optimized using the evolutionary algorithm. The resulting Pareto frontier curve of optimum solution is presented in this paper. The results show that the steady-state impedance of an HTS FCL is significantly lower than that of a series reactor for the same level of fault current limiting. Tests performed on a prototype 11 kV HTS FCL confirm the theoretical results. The respective transient recovery voltages (TRV) of the HTS FCL and an air core reactor of comparable fault current limiting capability are also determined. The results show that the saturated core HTS FCL has a significantly lower effect on the rate of rise of the circuit breaker TRV as compared to the air core reactor. The simulations results are validated with shortcircuit test results.

Temporal summation of intrinsically photosensitive retinal ganglion cell (ipRGC) contributions to the human pupil.

Purpose: IpRGCs mediate non-image forming functions including photoentrainment and the pupil light reflex (PLR). Temporal summation increases visual sensitivity and decreases temporal resolution for image forming vision, but the summation properties of nonimage forming vision are unknown. We investigated the temporal summation of inner (ipRGC) and outer (rod/cone) retinal inputs to the PLR. Method: The consensual PLR of the left eye was measured in six participants with normal vision using a Maxwellian view infrared pupillometer. Temporal summation was investigated using a double-pulse protocol (100 ms stimulus pairs; 0–1024 ms inter-stimulus interval, ISI) presented to the dilated fellow right eye (Tropicamide 1%). Stimulus lights (blue λmax = 460 nm; red λmax = 638 nm) biased activity to inneror outer retinal inputs to non-image forming vision. Temporal summation was measured suprathreshold (15.2 log photons.cm−2.s−1 at the cornea) and subthreshold (11.4 log photons.cm−2.s−1 at the cornea). Results: RM-ANOVAs showed the suprathreshold and subthreshold 6 second post illumination pupil response (PIPR: expressed as percentage baseline diameter) did not significantly vary for red or blue stimuli (p > .05). The PIPR for a subthreshold red 16 ms double-pulse control condition did not significantly differ with ISI (p > .05). The maximum constriction amplitude for red and blue 100 ms double- pulse stimuli did not significantly vary with ISI (p > .05). Conclusion: The non-significant changes in suprathreshold PIPR and subthreshold maximum pupil constriction indicate that inner retinal ipRGC inputs and outer retinal photoreceptor inputs to the PLR do not show temporal summation. The results suggest a fundamental difference between the temporal summation characteristics of image forming and non-image forming vision.

Condition-based maintenance optimisation without a predetermined strategy structure for a two-component series system

Most existing research on maintenance optimisation for multi-component systems only considers the lifetime distribution of the components. When the condition-based maintenance (CBM) strategy is adopted for multi-component systems, the strategy structure becomes complex due to the large number of component states and their combinations. Consequently, some predetermined maintenance strategy structures are often assumed before the maintenance optimisation of a multi-component system in a CBM context. Developing these predetermined strategy structure needs expert experience and the optimality of these strategies is often not proofed. This paper proposed a maintenance optimisation method that does not require any predetermined strategy structure for a two-component series system. The proposed method is developed based on the semi-Markov decision process (SMDP). A simulation study shows that the proposed method can identify the optimal maintenance strategy adaptively for different maintenance costs and parameters of degradation processes. The optimal maintenance strategy structure is also investigated in the simulation study, which provides reference for further research in maintenance optimisation of multi-component systems.

Reconstructing 3D x-ray CT images of polymer gel dosimeters using the zero-scan method

In this study x-ray CT has been used to produce a 3D image of an irradiated PAGAT gel sample, with noise-reduction achieved using the ‘zero-scan’ method. The gel was repeatedly CT scanned and a linear fit to the varying Hounsfield unit of each pixel in the 3D volume was evaluated across the repeated scans, allowing a zero-scan extrapolation of the image to be obtained. To minimise heating of the CT scanner’s x-ray tube, this study used a large slice thickness (1 cm), to provide image slices across the irradiated region of the gel, and a relatively small number of CT scans (63), to extrapolate the zero-scan image. The resulting set of transverse images shows reduced noise compared to images from the initial CT scan of the gel, without being degraded by the additional radiation dose delivered to the gel during the repeated scanning. The full, 3D image of the gel has a low spatial resolution in the longitudinal direction, due to the selected scan parameters. Nonetheless, important features of the dose distribution are apparent in the 3D x-ray CT scan of the gel. The results of this study demonstrate that the zero-scan extrapolation method can be applied to the reconstruction of multiple x-ray CT slices, to provide useful 2D and 3D images of irradiated dosimetry gels.