Durbin Algorithm Research Articles

Contracted Capacity Optimization Problem of Industrial Customers with Risk Assessment

This study developed a risk assessment tool for contract capacity optimization problems using the ant colony optimization and auto-regression model. Based on the historical data of demand consumption, the Least Square algorithm, the Recursive Levinson–Durbin algorithm, and the Burg algorithm were used to derive the auto-regression model. Then, ant colony optimization was used to search for the auto-regression model’s best p-order parameters. To avoid the risk of setting the contract capacity, this paper designed the risk tolerance parameter β to correct the predicted value of the auto-regression model. Ant colony optimization was also used to search for the optimal contract capacity with risk assessment under the two-stage time-of-use and three-stage time-of-use. This study employed an industrial consumer with high voltage power in Taiwan as the research object, used the AR model to estimate the contract capacity under the risk assessment, and cut back electricity usage to reduce the operation cost. The results can be used as a basis to develop an efficient tool for industrial customers to select contract capacities with risks to obtain the best economic benefits.

Context-Aware Lossless and Lossy Compression of Radio Frequency Signals

We propose an algorithm based on linear prediction that can perform both the lossless and near-lossless compression of RF signals. The proposed algorithm is coupled with two signal detection methods to determine the presence of relevant signals and apply varying levels of loss as needed. The first method uses spectrum sensing techniques, while the second one takes advantage of the error computed in each iteration of the Levinson-Durbin algorithm. These algorithms have been integrated as a new pre-processing stage into FAPEC, a data compressor first designed for space missions. We test the lossless algorithm using two different datasets. The first one was obtained from OPS-SAT, an ESA CubeSat, while the second one was obtained using a SDRplay RSPdx in Barcelona, Spain. The results show that our approach achieves compression ratios that are 23% better than gzip (on average) and very similar to those of FLAC, but at higher speeds. We also assess the performance of our signal detectors using the second dataset. We show that high ratios can be achieved thanks to the lossy compression of the segments without any relevant signal.

Fractional analysis of radiative blood transport through a porous channel containing multishaped cobalt nanoparticles: An application to hemodynamics

AbstractIn this work, impacts of dispersing nonspherical shaped cobalt nanoparticles in the blood are analyzed for magnetohydrodynamic radiative transport of blood inside a vertical porous channel. An Oldroyd‐B model is used to feature flow characteristics of blood along with Fourier's principle of heat transmission for the mathematical modeling of the problem. A fractional system is constructed by employing the idea of the Caputo–Fabrizio derivative on subsequent differential equations. The Laplace transform method is adopted to solve the fractional flow and energy equations subject to generalized boundary conditions, which involve time‐dependent functions and , respectively. Instead of promoting the analytic velocity and energy expressions, Zakian's numerical algorithm is operated to achieve the reverse transformation purpose of Laplace domain functions. To certify the obtained solutions, two additional numerical algorithms named Stehfest's algorithm and Durbin's algorithm are inculcated in this study, and comparative illustrations are drawn. For the extensive investigation of shear stress and heat transfer phenomenon, numerical simulations for the coefficient of skin friction and Nusselt number are performed, and outcomes are communicated through various tables. The impacts of shape‐dependent viscosity and other significant parameters on flow patterns are investigated through graphs for multiple motion types of the left channel wall. Meanwhile, the thermal performance of nanofluid is examined for platelet, brick, cylinder, and blade shape nanoparticles, along with other thermal parameters. In addition, some recently reported results and flow profiles for Maxwell, second‐grade, and viscous fluids are deduced graphically as special cases of the current study.

Quasi-static and dynamic response of functionally graded viscoelastic plates

In this study, quasi static and dynamic response of functional graded material (FGM) viscoelastic plates under dynamic loads were investigated. The governing equations of composite plates were obtained with the help of Hamilton’s principle. Afterwards, time dependent partial differential equations were obtained by applying Navier solution method to these valid equations. These equations were transformed into Laplace space in order to solve time dependent partial differential equations. The transformation of the resulting calculations from Laplace domain into the time domain was conducted with the help of Modified Durbin algorithm. The obtained results were compared with various approaches It was shown that the results are in parallel with other approaches’ results, and in full agreement with the results of the finite element method (ANSYS). Then, quasi-static behavior was investigated for viscoelastic FGM because of there is not enough research on this subject. The sensitivity analysis demonstrated that the volume fractions and damping ratios have a significant effect on the quasi-static and dynamic response of viscoelastic FGM plates. The numerical sample results showed that the present method can solve the problem in a highly accurate, efficient, and easily by utilizing the Laplace transform without the use of natural frequencies or mode shapes.

Viscoelastic damped response of laminated composite shells subjected to various dynamic loads

In this study, viscoelastic damped dynamic behaviors of laminated composite shells (LCS) under different dynamic loads were investigated. In order to obtain better numerical stability, the truncated series method was used in the formation of equations governing the system. While deriving the equations governing the system, the z/R terms are usually neglected, whereas only 3 and higher order terms are truncated here. The method of truncated equations has been used for the first time as suggested here to obtain viscoelastic damped behavior of dynamically loaded LCS. The governing equation of composite shells was obtained with the help of Hamilton’s principle. Afterwards, time dependent partial differential equations were obtained by applying Navier solution method to these valid equations. These equations were transformed into Laplace space in order to solve time dependent partial differential equations. The transformation of the resulting calculations from Laplace domain into the time domain was conducted with the help of Modified Durbin algorithm. In addition, one of the goals of this research is to highlight the importance of including the (1+z/R) part in the equations to account for the curvature effect of the shells. The addition of these effects and truncated series method to the equations and the investigation of their effects are the originalities of the present study. The present work obtained values were compared with the results obtained with Newmark’s approach and ANSYS finite element methods. The numerical results showed that the proposed approach is a highly effective and efficient solution that can be easily applied to laminated viscoelastic shell problems.

Mathematical modeling of elastodynamics and cell growth inside a deformable scaffold fitted to the periphery of a bioreactor

A mathematical model is developed for fluid flow, nutrient transport, and cell growth inside a bioreactor with a scaffold at the periphery and lumen at the centerline. The scaffold material is assumed to be deformable. In order to deal with the deformation of the solid phase and fluid phase inside the scaffold, biphasic mixture theory equations are adopted, which are derived from the theory of mixtures. The flow inside the lumen is governed by Stokes equation. Advection–diffusion–reaction equation is used for the mass balance of the nutrient within the scaffold region. Cell growth depends on the nutrient concentration and is expressed by the Contois equation that accounts for contact inhibition. We use lubrication approximation to reduce the system of hydrodynamic and nutrient transport equations. This leads to a coupled system of partial differential equations (PDEs) with time‐dependent variables. Laplace transformation is used to deal with time‐dependent terms, and Durbin's algorithm is used to retrieve the time dependency. We investigate the outreach of nutrients inside the scaffold region, which regulates the growth of cells at a particular time. Based on the available experimental data, we consider relevant reaction kinematics of the cells and observe the corresponding nutrient distribution inside the bioreactor. The factors that affect the nutrient concentration are lumen radius, porosity, and permeability of the scaffold, Thiele modulus, pressure gradient, and so forth. The total mass transfer rate is computed to understand the nutrient distribution across various regions of the bioreactor.

METHOD OF SPECTRAL ANALYSIS OF TRACTION CURRENT OF AC ELECTRIC LOCOMOTIVES

An improved method for spectral analysis of traction current of an Alternating Current (AC) electric locomotive is considered in the article. A new method of spectral analysis considers the change in voltage in the catenary system as a non-deterministic, non-ergodic and non-Gaussian process. It has been established that higher voltage harmonics in the catenary system have a significant negative effect on the operation of non-traction railway consumers of electricity. In addition, electric locomotives operating in the same feeder zone have a mutual influence on each other. Electric railway transport is a source of higher voltage harmonics and strongly distorts the shape of the sinusoidal voltage of the catenary system, which are caused by the higher spectral components of the current in the electric locomotive traction drive circuit. These spectral components of the traction current arise in the traction drive circuit due to the nonlinearity of the current-voltage characteristics of the electronic devices of an electric locomotive, for example, a contact rectifier, a capacitor circuit of traction motors. Reactive power compensators are used in electric locomotives to eliminate components of higher harmonic traction current in the catenary system. Traditionally, spectral analysis in such systems is performed using Fourier methods. However, the determination of the spectral components of the traction current by the Fourier method for constructing a control system for a reactive power compensator is possible only if the process of voltage variation is a deterministic or ergodic Gaussian process. Otherwise, the application of Fourier transform methods will be incorrect. An analysis of the factors that affect voltage changes in the catenary system showed that this process is significantly different from the ergodic Gaussian process. Such factors include the following: the operating mode of the electric locomotives; number and total capacity of electric locomotives in one feeder zone; electric locomotives passing through feeder zones; instability of collection current. Thus, in the case under consideration, the application of the Fourier methods is incorrect for the analysis of the spectral components of the traction current. This affects the quality of compensation of the higher harmonic components of the traction current, and in some cases, the unstable operation of the control system of the active part of the reactive power compensator. Proposed scientific approach is based on the Levinson–Durbin linear prediction algorithm. On the one hand, this allows adapting the control system of the compensator to the voltage parameters of the catenary system. On the other hand, this allows taking into account the operating modes of electric rail vehicle with reactive power compensation. The construction of a compensator control system using the Levinson–Durbin algorithm significantly simplifies thensynchronization scheme of the compensator and power circuits of the traction electric drive of AC electric locomotive. A comparison of the traditional method of spectral analysis, based on the Fast Fourier Transform (FFT), and the method, based on the Levinson–Durbin algorithm, proposed by the authors, showed the high efficiency of the latter.

ГРАНИЧНО-ЭЛЕМЕНТНЫЙ АНАЛИЗ РАСПРОСТРАНЕНИЯ ВОЛН В ПОРОВЯЗКОУПРУГОМ СЛОИСТОМ ПОЛУПРОСТРАНСТВЕ И ПОЛУПРОСТРАНСТВЕ С ПОЛОСТЬЮ

The paper is dedicated to the wave propagation a porous-viscoelastic material. As a mathematical model of a fully saturated poroelastic medium, we consider the Biot model with four basic functions – pore pressure and skeleton movements. The Biot model is supplemented by the principle of elastic and viscoelastic reaction correspondence. The skeleton of a porous material is assumed to be viscoelastic material. A model of a standard viscoelastic solid is spplied to describe the viscoelastic properties of a skeleton. The initial boundary-value problem is reduced to a boundary-value problem by formal application of the Laplace transform. To solve boundary integral equations, the boundary element method is performed. Quadrangular eight-node biquadratic elements are used for boundary element discretization. Numerical integration is carried out according to Gaussian quadrature formulas using algorithms for lowering the order and eliminating features. To obtain a solution in explicit time, numerical inversion of the Laplace transform is applied based on the Durbin algorithm with a variable frequency step. This study is a development of the existing boundary-element technique for solving problems on layered porous-elastic half-spaces. This will allow you to take into account the heterogeneity of the soil in depth. The problem of the action of a vertical force in the form of the Heaviside function on the surface of a layered porous-elastic half-space and a half-space with a cavity is considered. Variants of a homogeneous and heterogeneous half-space are considered. Under the model of heterogeneity we understand the piecewise homogeneous solid. The responses of the boundary displacements on the surface of the half-space are presented. The effect of the viscoelastic material model parameter on the dynamic response of displacements is demonstrated. It is established that the viscosity parameters have a significant effect on the nature of the distribution of parameters of wave processes.

ARMA order model detection using minimum of Kurtosis: application on seismic data

The objective of this study is to find the order and coefficients of non-low-phase causal filters for ARMA (auto regressive moving average) filter model, using the Kurtosis minimization criterion. This method is based on the Kurtosis calculation of the treated sample at the input level and its identification at the output of the ARMA model. For this purpose, the order and coefficients of the AR (auto regressive) part are identified using the Yule-Walker algorithm at order two and then extended to order four. To obtain the MA (moving average) part, the AR components are calculated at first from the ARMA filter by deconvolution. Then, spectrally equivalent and minimum phase (SEMP) MA filter is identified using the Durbin algorithm at second and fourth order. Finally, the correct filter is found when the Kurtosis value of the output ARMA filter reconstituted is the closest to the Kurtosis of introduced signal. The proposed method is then tested on simulated processes and applied to real seismic data to perform blind deconvolution and obtain the reflectivity coefficients of subsoil studied.

Least-squares finite impulse response fixed-lag smoother and filter in linear discrete-time stochastic systems

This paper proposes the least-squares (LS) finite impulse response (FIR) fixed-lag smoother and filter in linear discrete-time wide-sense stationary stochastic systems. The FIR fixed-lag smoothing estimate is given as a linear convolution sum of the impulse response function and the observed values. It is assumed that the signal is observed with additional white noise, which is uncorrelated with the signal process. By solving the simultaneous linear equations transformed from the Wiener–Hopf equation, the optimal impulse response function is obtained. The necessary information of the LS FIR fixed-lag smoothing algorithm is the auto-covariance function of the signal process and the variance of the observation noise process. In particular, this paper proposes the Levinson–Durbin algorithm, which needs less amount of arithmetic operations than the Gauss–Jordan elimination method in the inverse of the Toeplitz matrix, for the optimal impulse response function. From the numerical simulation example, the proposed LS FIR fixed-lag smoother and filter are superior in estimation accuracy to the RLS Wiener FIR estimators.

Dynamic response of curved Timoshenko beams resting on viscoelastic foundation

Curved beams' dynamic behavior on viscoelastic foundation is the subject of the current paper. By rewritten the Timoshenko beams theory formulation for the curved and twisted spatial rods, governing equations are obtained for the circular beams on viscoelastic foundation. Using the complementary functions method (CFM), in Laplace domain, an ordinary differential equation is solved and then those results are transformed to real space by Durbin's algorithm. Verification of the proposed method is illustrated by solving an example by variating foundation parameters.

Transient analysis of axially functionally graded Timoshenko beams with variable cross-section

Abstract The present study goals to analyze transient analysis of axially functionally graded (AFG) Timoshenko beams with variable cross-section. Both the materials and geometrical properties of the AFG tapered beam varying along the longitudinal direction. In the analysis, the influences of rotary inertia and shear deformation are taken into account. Complementary functions method (CFM) is applied to solve the differential equations in Laplace domain. By using the modified Durbin's algorithm, the results are transformed to the time domain. For the verification of the recommended method, numerous problems which were solved in the literature are handled with the developed method and benchmarked with the findings in the literature.

A new Levinson–Durbin based 2-D AR model parameter estimation method

This paper presents a new method for estimating the parameters of quarterplane two dimensional (2-D) autoregressive model based on the Levinson---Durbin algorithm. To achieve this aim, one-dimensional formulations related to Levinson---Durbin algorithm are extended to 2-D case. Online parameter estimation, capability of parameters variation detection, estimation improvement by using new data and less computational requirement are the significant advantages of the proposed method. Because of not involving complex and time consuming matrix computations, the presented method is computationally efficient. Numerical simulations are presented to show the efficiency of the proposed approach.

Forecasting Daily Variations of Stock Index Returns with a Multifractal Model of Realized Volatility

ABSTRACTMultifractal models have recently been introduced as a new type of data‐generating process for asset returns and other financial data. Here we propose an adaptation of this model for realized volatility. We estimate this new model via generalized method of moments and perform forecasting by means of best linear forecasts derived via the Levinson–Durbin algorithm. Its out‐of‐sample performance is compared against other popular time series specifications. Using an intra‐day dataset for five major international stock market indices, we find that the the multifractal model for realized volatility improves upon forecasts of its earlier counterparts based on daily returns and of many other volatility models. While the more traditional RV‐ARFIMA model comes out as the most successful model (in terms of the number of cases in which it has the best forecasts for all combinations of forecast horizons and evaluation criteria), the new model performs often significantly better during the turbulent times of the recent financial crisis. Copyright © 2014 John Wiley & Sons, Ltd.

Calculation of Dynamic Stress Intensity Factor by the Boundary Element - Laplace Transform Method

Using the Laplace transform and freezing time variable, the problem in the time domain into the frequency domain to solve the problem. The establishment of a crack unit model in the frequency domain, and the boundary integral equation and discrete form containing the crack unit has been deduced. While using Durbin algorithm suitable for transient dynamic response of the inverse Laplace transform, the amount of stress intensity factor of a set of transformation parameters corresponding to the frequency domain into a time domain to obtain the dynamic stress intensity factor of time curve, and calculate the stress intensity factor compared to the boundary finite element method has a Laplace transform high precision, easy to save CPU time and data preparation features, we recommend using this method to calculate the dynamic stress intensity factor.

Dynamic Analysis of Shear Flows over a Porous Medium in a Cylindrical Tube

Dynamic responses of a viscous fluid flow introduced under a time dependent pressure gradient in a rigid cylindrical tube subject to deformable porous surface layer have been investigated. The coupling effect of the fluid movement and the deformation of the porous medium in Laplace transform space have been studied. Governing equations are simplified for the solid displacement and the fluid velocity in the porous layer. Using Durbin's algorithm, in transformed domain analytic solutions are obtained, and time dependent variables are considered. Interaction between the solid and the fluid phases in the porous layer and its effects on fluid flow in tube are investigated under steady and unsteady flow conditions when the solid phase is either rigid or deformable. Significant effects of the porous surface layer on the flow in the tube have been observed.

AR model whitening and signal detection based on GLD algorithm in the non-Gaussian reverberation

The paper analyzes the characteristics of shallow sea reverberation such as divergent variance and heavy tails in probability density distribution and matches it to symmetric alpha stable (SαS) distribution. After analyzing the AR model whitening method based on Gaussian distribution and Levinson–Durbin algorithm, the paper proposes and derives the generalized Levinson–Durbin (GLD) algorithm based on covariation theory of alpha stable distribution. The GLD algorithm can estimate the order and parameters of AR SαS model by iterations which are fast and effective in calculating, and then the performance tests by simulations are given. The AR model whitening method using GLD algorithm has a faster speed and a better detection performance than AR Gaussian whitening method in impulsive reverberation. At last the Monte Carlo simulating tests are used to validate the validity of the new method.

EEG based automated detection of auditory loss: A pilot study

Auditory dysfunction is one of the most common deficiencies present in the newborn. Recent studies show that significant bilateral hearing loss is present in ∼1 to 3 per 1000 newborn infants in the well-baby nursery population and in ∼2 to 4 per 1000 infants in the ICU population. The ignorance of hearing screening test at the initial stage will impede speech, language and cognitive development. It has been further noted that direct physician observation as well as parental recognition has not been significantly successful until today in identifying the hearing loss in the first year of life. To overcome such problems, early screening is essential. This paper presents a pilot study on detection of hearing loss by applying electroencephalography (EEG) signals as the key indicator. The effect of auditory evoked potential (AEP) is exploited on EEGs by introducing an external stimulus to the subject’s auditory canal. Two time domain features, spike rhythmicity, autoregressive model using Levinson–Durbin algorithm and frequency domain features such as power spectral density estimation by Burg’s and Yule–Walker methods are applied. Feed forward and feedback neural network models are used to distinguish the stimuli and non-stimuli EEGs. The neural network models are configured optimally by varying the hidden neurons and learning algorithms and their performance are evaluated in terms of specificity, sensitivity and classification accuracy. It can be concluded from the experimental study that the proposed methodology can be applied for neonatal healthcare applications.

A periodic Levinson–Durbin algorithm for entropy maximization

A recursive algorithm is presented for the computation of the first-order and second-order derivatives of the entropy of a periodic autoregressive process with respect to the autocovariances. It is an extension of the periodic Levinson–Durbin algorithm. The algorithm has been developed for use at one of the steps of an entropy maximization method developed by the authors. Numerical examples of entropy maximization by that method are given. An implementation of the algorithm is available as an R package.

RNN based MIMO channel prediction

A new hybrid PSO-EA-DEPSO algorithm based on particle swarm optimization (PSO), evolutionary algorithm (EA), and differential evolution (DE) is presented for training a recurrent neural network (RNN) for multiple-input multiple-output (MIMO) channel prediction. This algorithm is shown to outperform RNN predictors trained off-line by PSO, EA, and DEPSO as well as a linear predictor trained by the Levinson–Durbin algorithm. To explore the effects of channel prediction error at the receiver, new expressions for the received SNR, array gain, and average probability of error are derived and analyzed. These expressions differ from previous results which assume the prediction error is Gaussian and/or independent of the true CSI. The array gain decays with increasing signal-to-noise ratio and is slightly larger for spatially correlated systems. As the prediction error increases in the non-saturation region, the coding gain decreases and the diversity gain remains unaffected.