Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation

In this paper, we consider the variable-order nonlinear fractional diffusion equation View the MathML source where xRα(x,t) is a generalized Riesz fractional derivative of variable order View the MathML source and the nonlinear reaction term f(u,x,t) satisfies the Lipschitz condition |f(u1,x,t)-f(u2,x,t)|less-than-or-equals, slantL|u1-u2|. A new explicit finite-difference approximation is introduced. The convergence and stability of this approximation are proved. Finally, some numerical examples are provided to show that this method is computationally efficient. The proposed method and techniques are applicable to other variable-order nonlinear fractional differential equations.

Noise robust voice activity detection using normal probability testing and time-domain histogram analysis

This paper presents a method of voice activity detection (VAD) suitable for high noise scenarios, based on the fusion of two complementary systems. The first system uses a proposed non-Gaussianity score (NGS) feature based on normal probability testing. The second system employs a histogram distance score (HDS) feature that detects changes in the signal through conducting a template-based similarity measure between adjacent frames. The decision outputs by the two systems are then merged using an open-by-reconstruction fusion stage. Accuracy of the proposed method was compared to several baseline VAD methods on a database created using real recordings of a variety of high-noise environments.

Noise robust voice activity detection using features extracted from the time-domain autocorrelation function

This paper presents a method of voice activity detection (VAD) for high noise scenarios, using a noise robust voiced speech detection feature. The developed method is based on the fusion of two systems. The first system utilises the maximum peak of the normalised time-domain autocorrelation function (MaxPeak). The second zone system uses a novel combination of cross-correlation and zero-crossing rate of the normalised autocorrelation to approximate a measure of signal pitch and periodicity (CrossCorr) that is hypothesised to be noise robust. The score outputs by the two systems are then merged using weighted sum fusion to create the proposed autocorrelation zero-crossing rate (AZR) VAD. Accuracy of AZR was compared to state of the art and standardised VAD methods and was shown to outperform the best performing system with an average relative improvement of 24.8% in half-total error rate (HTER) on the QUT-NOISE-TIMIT database created using real recordings from high-noise environments.

A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.

Cerebral cortex activation mapping upon electrical muscle stimulation by 32-channel time-domain functional near-infrared spectroscopy

The application of different EMS current thresholds on muscle activates not only the muscle but also peripheral sensory axons that send proprioceptive and pain signals to the cerebral cortex. A 32-channel time-domain fNIRS instrument was employed to map regional cortical activities under varied EMS current intensities applied on the right wrist extensor muscle. Eight healthy volunteers underwent four EMS at different current thresholds based on their individual maximal tolerated intensity (MTI), i.e., 10 % < 50 % < 100 % < over 100 % MTI. Time courses of the absolute oxygenated and deoxygenated hemoglobin concentrations primarily over the bilateral sensorimotor cortical (SMC) regions were extrapolated, and cortical activation maps were determined by general linear model using the NIRS-SPM software. The stimulation-induced wrist extension paradigm significantly increased activation of the contralateral SMC region according to the EMS intensities, while the ipsilateral SMC region showed no significant changes. This could be due in part to a nociceptive response to the higher EMS current intensities and result also from increased sensorimotor integration in these cortical regions.

Comparison between electrically-evoked and voluntary wrist movements on sensorimotor and prefrontal cortical activation : A multi-channel time domain fNIRS study

Neuromuscular electrical stimulation (NMES) has been consistently demonstrated to improve skeletal muscle function in neurological populations with movement disorders, such as poststroke and incomplete spinal cord injury (Vanderthommen and Duchateau, 2007). Recent research has documented that rapid, supraspinal central nervous system reorganisation/neuroplastic mechanisms are also implicated during NMES (Chipchase et al., 2011). Functional neuroimaging studies have shown NMES to activate a network of sub-cortical and cortical brain regions, including the sensorimotor (SMC) and prefrontal (PFC) cortex (Blickenstorfer et al., 2009; Han et al., 2003; Muthalib et al., 2012). A relationship between increase in SMC activation with increasing NMES current intensity up to motor threshold has been previously reported using functional MRI (Smith et al., 2003). However, since clinical neurorehabilitation programmes commonly utilise NMES current intensities above the motor threshold and up to the maximum tolerated current intensity (MTI), limited research has determined the cortical correlates of increasing NMES current intensity at or above MTI (Muthalib et al., 2012). In our previous study (Muthalib et al., 2012), we assessed contralateral PFC activation using 1-channel functional near infrared spectroscopy (fNIRS) during NMES of the elbow flexors by increasing current intensity from motor threshold to greater than MTI and showed a linear relationship between NMES current intensity and the level of PFC activation. However, the relationship between NMES current intensity and activation of the motor cortical network, including SMC and PFC, has not been clarified. Moreover, it is of scientific and clinical relevance to know how NMES affects the central nervous system, especially in comparison to voluntary (VOL) muscle activation. Therefore, the aim of this study was to utilise multi-channel time domain fNIRS to compare SMC and PFC activation between VOL and NMESevoked wrist extension movements.

A comparison of finite difference and finite volume methods for solving the space-fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non- classical diffusion or dispersion which is not adequately described by the classical theory of Brownian motion and Fick’s law. We consider a space-fractional advection-dispersion equation based on a fractional Fick’s law. Zhang et al. [Water Resources Research, 43(5)(2007)] considered such an equation with variable coefficients, which they dis- cretised using the finite difference method proposed by Meerschaert and Tadjeran [Journal of Computational and Applied Mathematics, 172(1):65-77 (2004)]. For this method the presence of variable coef- ficients necessitates applying the product rule before discretising the Riemann–Liouville fractional derivatives using standard and shifted Gru ̈nwald formulas, depending on the fractional order. As an alternative, we propose using a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Gru ̈nwald formulas are used to discretise the Riemann–Liouville fractional derivatives at control volume faces, eliminating the need for product rule expansions. We compare the two methods for several case studies, highlighting the convenience of the finite volume approach.

Time-domain hydroelastic analysis of a flexible marine structure using state-space models

This article deals with time-domain hydroelastic analysis of a marine structure. The convolution terms associated with fluid memory effects are replaced by an alternative state-space representation, the parameters of which are obtained by using realization theory. The mathematical model established is validated by comparison to experimental results of a very flexible barge. Two types of time-domain simulations are performed: dynamic response of the initially inert structure to incident regular waves and transient response of the structure after it is released from a displaced condition in still water. The accuracy and the efficiency of the simulations based on the state-space model representations are compared to those that integrate the convolutions.

Effects of wireless sensor network uncertainties on output-only modal analysis employing merged data of multiple tests

The use of Wireless Sensor Networks (WSNs) for vibration-based Structural Health Monitoring (SHM) has become a promising approach due to many advantages such as low cost, fast and flexible deployment. However, inherent technical issues such as data asynchronicity and data loss have prevented these distinct systems from being extensively used. Recently, several SHM-oriented WSNs have been proposed and believed to be able to overcome a large number of technical uncertainties. Nevertheless, there is limited research verifying the applicability of those WSNs with respect to demanding SHM applications like modal analysis and damage identification. Based on a brief review, this paper first reveals that Data Synchronization Error (DSE) is the most inherent factor amongst uncertainties of SHM-oriented WSNs. Effects of this factor are then investigated on outcomes and performance of the most robust Output-only Modal Analysis (OMA) techniques when merging data from multiple sensor setups. The two OMA families selected for this investigation are Frequency Domain Decomposition (FDD) and data-driven Stochastic Subspace Identification (SSI-data) due to the fact that they both have been widely applied in the past decade. Accelerations collected by a wired sensory system on a large-scale laboratory bridge model are initially used as benchmark data after being added with a certain level of noise to account for the higher presence of this factor in SHM-oriented WSNs. From this source, a large number of simulations have been made to generate multiple DSE-corrupted datasets to facilitate statistical analyses. The results of this study show the robustness of FDD and the precautions needed for SSI-data family when dealing with DSE at a relaxed level. Finally, the combination of preferred OMA techniques and the use of the channel projection for the time-domain OMA technique to cope with DSE are recommended.

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.