Numerical Technique For Evaluation Research Articles

Numerical evaluation of 3D time-harmonic elastodynamic Green's function and its derivatives for anisotropic solids

The paper presents a fast and accurate numerical technique for evaluation of the 3D time-harmonic elastodynamic Green's function and its derivatives for anisotropic solids. Following Wang & Achenbach the Green's function is presented in the form of the sum of singular (static) and regular parts, which are both reduced to integrals over a unit sphere. Singular part and its derivatives are then reduced to the integrals over a unit circle, which can be efficiently (fast and accurately) evaluated using the trapezoid rule, which is exponentially convergent for integrals over the period of a periodic integrand. The regular time-harmonic parts are presented through the double integrals. The outer integral is also efficiently evaluated using the trapezoid rule. A special quadrature is developed for evaluation of the inner integral, which accounts for the highly-oscillating behavior of the integrand. Numerical examples are presented, which shows the advantage of the proposed technique over others.

Series representations of the Volterra function and the Fransén–Robinson constant

The Volterra function μ(t,β,α) was introduced by Vito Volterra in 1916 as the solution to certain integral equations with a logarithmic kernel. Despite the large number of applications of the Volterra function, the only known analytic representations of this function are given in terms of integrals. In this paper we derive several convergent expansion of μ(t,β,α) in terms of incomplete gamma functions. These expansions may be used to implement numerical evaluation techniques for this function. As a particular application, we derive a numerical series representation of the Fransén–Robinson constant F≔μ(1,1,0)=∫0∞1Γ(x)dx. Some numerical examples illustrate the accuracy of the approximations.

Stiffness reconstruction methods for MR elastography.

Assessment of tissue stiffness is desirable for clinicians and researchers, as it is well established that pathophysiological mechanisms often alter the structural properties of tissue. Magnetic resonance elastography (MRE) provides an avenue for measuring tissue stiffness and has a long history of clinical application, including staging liver fibrosis and stratifying breast cancer malignancy. A vital component of MRE consists of the reconstruction algorithms used to derive stiffness from wave‐motion images by solving inverse problems. A large range of reconstruction methods have been presented in the literature, with differing computational expense, required user input, underlying physical assumptions, and techniques for numerical evaluation. These differences, in turn, have led to varying accuracy, robustness, and ease of use. While most reconstruction techniques have been validated against in silico or in vitro phantoms, performance with real data is often more challenging, stressing the robustness and assumptions of these algorithms. This article reviews many current MRE reconstruction methods and discusses the aforementioned differences. The material assumptions underlying the methods are developed and various approaches for noise reduction, regularization, and numerical discretization are discussed. Reconstruction methods are categorized by inversion type, underlying assumptions, and their use in human and animal studies. Future directions, such as alternative material assumptions, are also discussed.

Boundary Element Analysis of Anisotropic Thermomagnetoelectroelastic Solids with 3D Shell-Like Inclusions

Abstract The paper presents novel boundary element technique for analysis of anisotropic thermomagnetoelectroelastic solids containing cracks and thin shell-like soft inclusions. Dual boundary integral equations of heat conduction and thermomagnetoelectroelasticity are derived, which do not contain volume integrals in the absence of distributed body heat and extended body forces. Models of 3D soft thermomagnetoelectroelastic thin inclusions are adopted. The issues on the boundary element solution of obtained equations are discussed. The efficient techniques for numerical evaluation of kernels and singular and hypersingular integrals are discussed. Nonlin-ear polynomial mappings are adopted for smoothing the integrand at the inclusion’s front, which is advantageous for accurate evaluation of field intensity factors. Special shape functions are introduced, which account for a square-root singularity of extended stress and heat flux at the inclusion’s front. Numerical example is presented.

On the Numerical Evaluation of Bandpass Prolates II

We provide a technique for numerical evaluation of certain eigenfunctions of the integral kernel operator corresponding to time truncation of a square-integrable function on the real line to a finite interval, followed by frequency limiting to frequencies in an annular band. When the width of the annulus is small relative to the mean radius of the annulus the method is more accurate than one previously suggested by the authors.

Evaluation of elastic modulus and hardness of highly inhomogeneous materials by nanoindentation

The experimental and numerical techniques for evaluation of mechanical properties of highly inhomogeneous materials are discussed. The techniques are applied to coal as an example of such a material. Characterization of coals is a very difficult task because they are composed of a number of distinct organic entities called macerals and some amount of inorganic substances along with internal pores and cracks. It is argued that to avoid the influence of the pores and cracks, the samples of the materials have to be prepared as very thin and very smooth sections, and the depth-sensing nanoindentation (DSNI) techniques has to be employed rather than the conventional microindentation. It is shown that the use of the modern nanoindentation techniques integrated with transmitted light microscopy is very effective for evaluation of elastic modulus and hardness of coal macerals. However, because the thin sections are glued to the substrate and the glue thickness is approximately equal to the thickness of the section, the conventional DSNI techniques show the effective properties of the section/substrate system rather than the properties of the material. As the first approximation, it is proposed to describe the sample/substrate system using the classic exponential weight function for the dependence of the equivalent elastic contact modulus on the depth of indentation. This simple approach allows us to extract the contact modulus of the material constitutes from the data measured on a region occupied by a specific component of the material. The proposed approach is demonstrated on application to the experimental data obtained by Berkovich nanoindentation with varying maximum depth of indentation.

A Wiener–Hopf based approach to numerical computations in fluctuation theory for Lévy processes

This paper focuses on numerical evaluation techniques related to fluctuation theory for Levy processes; they can be applied in various domains, e.g., in finance in the pricing of so-called barrier options. More specifically, with $$\bar{X}_t:= \sup _{0\le s\le t} X_s$$ denoting the running maximum of the Levy process $$X_t$$ , the aim is to evaluate $$\mathbb{P }(\bar{X}_t \in \mathrm{d}x)$$ for $$t,x>0$$ . The starting point is the Wiener–Hopf factorization, which yields an expression for the transform $$\mathbb E e^{-\alpha \bar{X}_{e(\vartheta )}}$$ of the running maximum at an exponential epoch (with $$\vartheta ^{-1}$$ the mean of this exponential random variable). This expression is first rewritten in a more convenient form, and then it is pointed out how to use Laplace inversion techniques to numerically evaluate $$\mathbb{P }(\bar{X}_t\in \mathrm{d}x).$$ In our experiments we rely on the efficient and accurate algorithm developed in den Iseger (Probab Eng Inf Sci 20:1–44, 2006). We illustrate the performance of the algorithm with various examples: Brownian motion (with drift), a compound Poisson process, and a jump diffusion process. In models with jumps, we are also able to compute the density of the first time a specific threshold is exceeded, jointly with the corresponding overshoot. The paper is concluded by pointing out how our algorithm can be used in order to analyze the Levy process’ concave majorant.

Letter to the Editor: On the Numerical Evaluation of Bandpass Prolates

This letter provides a technique for numerical evaluation of certain eigenfunctions of the integral kernel operator corresponding to time truncation of a square-integrable function to a finite interval, followed by frequency limiting to frequencies in an annular band.

Impact of Unknown Time-varying Fading on the Information Rates of Amplify and Forward Cooperative Systems

We study information rate penalties for single-relay amplify and forward (AF) cooperative communication in the presence of unknown and time-varying fading. The penalty is defined as the gap between the information rate with perfect channel state information and that when the source-destination, source-relay and relay-destination channels are unknown at the receiving nodes. We prove that this gap in the cooperative system is the sum of gaps in the source-destination (single-hop) and source-relay-destination (dual-hop) channels. Under the assumption that the source and destination are mobile and the relay is stationary, we derive a closed-form accurate approximation for the asymptotic penalty of the mobile-to-mobile single-hop channel, which can also be used in computing asymptotic penalties for the mobile-fixed-mobile dual-hop channel. AF relaying induces non-Gaussian noise at the destination and hence, the penalty of the dual-hop channel is computed semi-analytically. We discuss a numerical technique for evaluation of destination noise entropy. One main observation of this paper is that non-negligible amplified relay noise can increase the cooperation information rate penalty of up to 1.5 times, as compared to non-relayed transmission. We provide extensive simulation results that characterize the behavior of penalty and include other mobility models for the source, relay and destination.

New algorithms for the numerical solution of nonlinear Fredholm and Volterra integral equations using Haar wavelets

Two new algorithms based on Haar wavelets are proposed. The first algorithm is proposed for the numerical solution of nonlinear Fredholm integral equations of the second kind, and the second for the numerical solution of nonlinear Volterra integral equations of the second kind. These methods are designed to exploit the special characteristics of Haar wavelets in both one and two dimensions. Formulae for calculating Haar coefficients without solving the system of equations have been derived. These formulae are then used in the proposed numerical methods. In contrast to other numerical methods, the advantage of our method is that it does not involve any intermediate numerical technique for evaluation of the integral present in integral equations. The methods are validated on test problems, and numerical results are compared with those from existing methods in the literature.

Generalized Linear Mixed Models for Longitudinal Data

The study of longitudinal data plays a significant role in medicine, epidemiology and social sciences. Typically, the interest is in the dependence of an outcome variable on the covariates. The Generalized Linear Models (GLMs) were proposed to unify the regression approach for a wide variety of discrete and continuous longitudinal data. The responses (outcomes) in longitudinal data are usually correlated. Hence, we need to use an extension of the GLMs that account for such correlation. This can be done by inclusion of random effects in the linear predictor; that is the Generalized Linear Mixed Models (GLMMs) (also called random effects models). The maximum likelihood estimates (MLE) are obtained for the regression parameters of a logit model, when the traditional assumption of normal random effects is relaxed. In this case a more convenient distribution, such as the lognormal distribution, is used. However, adding non-normal random effects to the GLMM considerably complicates the likelihood estimation. So, the direct numerical evaluation techniques (such as Newton - Raphson) become analytically and computationally tedious. To overcome such problems, we propose and develop a Monte Carlo EM (MCEM) algorithm, to obtain the maximum likelihood estimates. The proposed method is illustrated using a simulated data.

Application of numerical evaluation techniques for interpreting frequency response measurements in power transformers

Frequency response analysis (FRA) is an emerging, powerful non-intrusive condition monitoring and diagnostic tool for verifying the mechanical integrity of power transformers. FRA results are graphical in nature and require trained experts to interpret test results. The work reported discusses numerical-criteria-based evaluation techniques. Persons not familiar with interpreting the FRA results can apply the evaluation criteria. The various criteria help in deriving proper conclusions. By evaluating correlation coefficient (CC), standard deviation and absolute sum of logarithmic error (ASLE) techniques, it is possible to discriminate between defective and non-defective windings. Experimental studies were conducted on two test transformers for axial and radial displacements, and additionally two sets of identical substation transformers. The techniques mentioned above are useful for interpreting frequency responses even in situations when a reference fingerprint was not available. However, it was concluded that if original fingerprints are available, the method gives very reliable indication for diagnosing the faulty winding. In addition, the severity of displacement/deformation can also be concluded from the amount of variation of the parameters from the suggested critical values.

Influence of the level of fit of a density probability function to wind-speed data on the WECS mean power output estimation

Static methods which are based on statistical techniques to estimate the mean power output of a WECS (wind energy conversion system) have been widely employed in the scientific literature related to wind energy. In the static method which we use in this paper, for a given wind regime probability distribution function and a known WECS power curve, the mean power output of a WECS is obtained by resolving the integral, usually using numerical evaluation techniques, of the product of these two functions. In this paper an analysis is made of the influence of the level of fit between an empirical probability density function of a sample of wind speeds and the probability density function of the adjusted theoretical model on the relative error ε made in the estimation of the mean annual power output of a WECS. The mean power output calculated through the use of a quasi-dynamic or chronological method, that is to say using time-series of wind speed data and the power versus wind speed characteristic of the wind turbine, serves as the reference. The suitability of the distributions is judged from the adjusted R 2 statistic ( R a 2 ) . Hourly mean wind speeds recorded at 16 weather stations located in the Canarian Archipelago, an extensive catalogue of wind-speed probability models and two wind turbines of 330 and 800 kW rated power are used in this paper. Among the general conclusions obtained, the following can be pointed out: (a) that the R a 2 statistic might be useful as an initial gross indicator of the relative error made in the mean annual power output estimation of a WECS when a probabilistic method is employed; (b) the relative errors tend to decrease, in accordance with a trend line defined by a second-order polynomial, as R a 2 increases.

Tom Bell Young Author Award Winner 2007Characterisation of hardening performance of quenchants by integrated numerical method

AbstractAn integrated numerical technique for evaluation of hardening performance of cooling media applied for steel quenching is outlined. The newly developed method is based on the specific processing of measured time–temperature samples performed as a result of cooling curve tests. The heat transfer coefficient as a function of surface temperature characterises the heat transfer during cooling and is calculated using an iterative inverse algorithm. The heat transfer coefficient is used for calculation of the microstructural constituents and the hardness profile of cylindrical samples of arbitrary diameter. The hardening performance of media is evaluated by the estimated hardness of specimens obtained by heat treatment.

Damage simulator를 이용한 선박의 손상강도에 관한 연구

A damage analysis simulator, which is applicable for evaluating the residual strength of damaged ship, was developed in this paper. For this process, CDM (Continuum Damage Mechanics) approach has been implemented to the simulator by virtue of the numerical technique for evaluation of crack initiation and/or enlargement. A damage calculation program has been linked with a commercial finite element analysis code (NASTRAN) and a ultimate strength evaluation program (LSAP) in order to assess residual strength of damaged ship. As a results of series calculation for the frigate model, giving the quantitative structural damage to the ultimate strength evaluation, a residual strength with damage is predicted to be at least 70 percentage lower than the case of intact condition. It was found that the proposed technique can be used as a design support tool in the field of simulation based ship design.

Application of genetic algorithms for the extraction of electrical parameters of multicrystalline silicon

The application of the genetic algorithms (GAs) concept in measurements science deals with a fitting procedure used for the numerical prediction of physical parameters from an experimental data curve. In this work, GAs were applied for the extraction of electrical parameters of multicrystalline silicon solar cells. The experimental technique used is the light-beam-induced-current (LBIC). From LBIC measurements, we deduced the values of the diffusion length L and the grain boundary recombination velocity Vr of the minority carriers of the multicrystalline silicon wafers using the fitting procedure. The nonlinear fitting procedure is based on the minimization of the standard deviation of the theoretical LBIC profile from the experimental one. However, this criterion is not convex, and using traditional deterministic optimization algorithms leads to local minima solutions. To overcome this problem, the nonlinear least-square minimization technique was computed with the GAs strategy, increasing the probability of obtaining the best minimum value of the cost function in very reasonable time. The results of the proposed algorithm are presented and compared with the Levenberg–Marquardt algorithm and the Gauss–Newton method. The GAs-based numerical technique was found to be a promising and a powerful technique for numerical evaluation of the electrical parameters of silicon solar cells.

Image-based numerical evaluation techniques in volume holographic memory systems

A simulation technique for a volume holographic memory system based on binary page data is proposed to evaluate quantitative diffraction efficiency, bit error rate, and signal-to-noise ratio. In this simulator, propagation of a signal and reference beams and diffraction at gratings are calculated quantitatively by use of numerical Fresnel propagation and Kogelnik's coupled-wave theory. To apply Kogelnik's wave theory to arbitrary signal and reference beams, both beams at the hologram plane are decomposed into plane waves. Numerical results show good agreement with the exact solution under the Born approximation in a transmission-type volume hologram. We also apply the simulator to reflection-type holographic memory.

Scattering From Natural Soils Modeled by Dielectric Fractal Profiles: The Forward–Backward Approach

The forward-backward (FB) method is an efficient technique for numerical evaluation of electromagnetic scattering from rough surfaces. In its usual formulation, this technique can be only applied to perfectly or highly conducting surfaces. In addition, up to now FB has been employed to compute scattering from surfaces modeled by Gaussian stochastic processes with Gaussian or Pierson-Moscowitz spectra. Accordingly, this technique can be fruitfully used for numerical simulations of scattering from sea surfaces. However, in order to properly deal with natural soil surfaces, extension to the dielectric interface case and to fractal surface models is needed. Extension of the FB method to the dielectric interface case has been recently presented, whereas application to fractal surface models is presented here. Original contribution of the present paper is twofold. First of all, the FB method for dielectric profiles is framed within the theory of iterative methods for the solution of linear systems. In addition, application of the FB method to dielectric band-limited fractional Brownian motion fractal one-dimensional surfaces is explored. Numerical experiments show that, for most of realistic values of dielectric constant and fractal parameters actually encountered for natural soil profiles, the FB method is very rapidly convergent, and its results are in perfect agreement with "exact" ones (i.e. with results of method of moments solved via a direct method).

High-precision entropy values for spanning trees in lattices

Shrock and Wu have given numerical values for the exponential growth rate of the number of spanning trees in Euclidean lattices. We give a new technique for numerical evaluation that gives much more precise values, together with rigorous bounds on the accuracy. In particular, the new values resolve one of their questions.

A novel speed estimation algorithm for induction machines : Derdiyok, A. Electric Power Systems Research, 2003, 64, (1), 73–80

Static methods which are based on statistical techniques to estimate the mean power output of a WECS (wind energy conversion system) have been widely employed in the scientific literature related to wind energy. In the static method which we use in this paper, for a given wind regime probability distribution function and a known WECS power curve, the mean power output of a WECS is obtained by resolving the integral, usually using numerical evaluation techniques, of the product of these two functions. In this paper an analysis is made of the influence of the level of fit between an empirical probability density function of a sample of wind speeds and the probability density function of the adjusted theoretical model on the relative error ε made in the estimation of the mean annual power output of a WECS. The mean power output calculated through the use of a quasi-dynamic or chronological method, that is to say using time-series of wind speed data and the power versus wind speed characteristic of the wind turbine, serves as the reference. The suitability of the distributions is judged from the adjusted R2 statistic (Ra2). Hourly mean wind speeds recorded at 16 weather stations located in the Canarian Archipelago, an extensive catalogue of wind-speed probability models and two wind turbines of 330 and 800 kW rated power are used in this paper.Among the general conclusions obtained, the following can be pointed out: (a) that the Ra2 statistic might be useful as an initial gross indicator of the relative error made in the mean annual power output estimation of a WECS when a probabilistic method is employed; (b) the relative errors tend to decrease, in accordance with a trend line defined by a second-order polynomial, as Ra2 increases.