Modified Kernel Function Research Articles

Phase-field modeling of anisotropic crack propagation based on higher-order nonlocal operator theory

This paper presents a novel higher-order nonlocal operator theory for the phase-field modeling of brittle fracture in anisotropic materials. Incorporating higher order nonlocal operators can enhance the accuracy of the phase-field model by effectively capturing long-range interactions that hold significance in numerous materials. The reproducing kernel particle method is employed to derive a nonlocal differential operator to enhance computational stability and accuracy. Moreover, the proposed method eliminates the need for direct computation of derivatives of the modified kernel function, which avoids the calculation of moment matrix derivatives and improves computational efficiency. The phase-field modeling of polycrystalline materials, considering the anisotropic fracture resistance of each grain, is implemented using this numerical framework. The present method is able to capture different scenarios intergranular and transgranular crack propagation patterns in polycrystalline materials. The proposed method involves a detailed representation of the complex process of crack initiation and propagation in 2D and 3D models of polycrystalline materials.

High-spin Metal Centres in Dipolar EPR Spectroscopy.

The substitution of Mg2+ by Mn2+ in the bacterial DnaB helicase from Helicobacter pylori, an ATP:Mg2+-fuelled protein engine, allows electron paramagnetic resonance (EPR) spectroscopy to be performed on this system. EPR experiments make it possible to monitor nucleotide binding and to estimate the fraction of bound Mn2+ through relaxation measurements. Furthermore, by measuring spin-spin distances we probe the geometry within such multimeric assemblies using ultra-wideband double electron-electron resonance (DEER) and relaxation induced dipolar modulation enhancement (RIDME). The extraction of distance distributions from RIDME experiments on high-spin paramagnetic centres is influenced by the presence of dipolar frequency overtones. We show herein that we can correct for these overtones by using a modified kernel function in Tikhonov regularization analysis routines, and that the overtone coefficients for Mn2+ in the DnaB helicase are practically the same as in the previously studied Mn2+-Mn2+ model compounds.

Fault detection of aircraft based on support vector domain description

To realize intelligent fault detection of aircraft lacking fault samples, a novel fault detection algorithm for aircraft based on Support Vector Domain Description (SVDD) is proposed. The Genetic Algorithm (GA), threshold scaling factor, rapid anomaly detection, modifying kernel function and SVDD model boundary based on equal loss are introduced to the fault detection algorithm. The empirical analyses show that the method has good fault detection ability. The classification accuracy is improved by 5.52% after using the GA. The fault detection time of the SVDD algorithm is improved by 0.4 seconds on average when compared to the red line shutdown system. The accurate classification rate is enhanced by 0.0225, and the number of support vectors is reduced by 1 after adopting the modified kernel function. The fault detection algorithm in this paper provides novel intelligent fault detection technology for aircraft.

Computing distance distributions from dipolar evolution data with overtones: RIDME spectroscopy with Gd(iii)-based spin labels.

Extraction of distance distributions between high-spin paramagnetic centers from relaxation induced dipolar modulation enhancement (RIDME) data is affected by the presence of overtones of dipolar frequencies. As previously proposed, we account for these overtones by using a modified kernel function in Tikhonov regularization analysis. This paper analyzes the performance of such an approach on a series of model compounds with the Gd(iii)-PyMTA complex serving as paramagnetic high-spin label. We describe the calibration of the overtone coefficients for the RIDME kernel, demonstrate the accuracy of distance distributions obtained with this approach, and show that for our series of Gd-rulers RIDME technique provides more accurate distance distributions than Gd(iii)-Gd(iii) double electron-electron resonance (DEER). The analysis of RIDME data including harmonic overtones can be performed using the MATLAB-based program OvertoneAnalysis, which is available as open-source software from the web page of ETH Zurich. This approach opens a perspective for the routine use of the RIDME technique with high-spin labels in structural biology and structural studies of other soft matter.

Financial Distress Prediction Based on Support Vector Machine with a Modified Kernel Function

AbstractFor the financial distress prediction model based on support vector machine, there are no theories concerning how to choose a proper kernel function in a data-dependent way. This paper proposes a method of modified kernel function that can availably enhance classification accuracy. We apply an information-geometric method to modifying a kernel that is based on the structure of the Riemannian geometry induced in the input space by the kernel. A conformal transformation of a kernel from input space to higher-dimensional feature space enlarges volume elements locally near support vectors that are situated around the classification boundary and reduce the number of support vectors. This paper takes the Gaussian radial basis function as the internal kernel. Additionally, this paper combines the above method with the theories of standard regularization and non-dimensionalization to construct the new model. In the empirical analysis section, the paper adopts the financial data of Chinese listed companies. It uses five groups of experiments with different parameters to compare the classification accuracy. We can make the conclusion that the model of modified kernel function can effectively reduce the number of support vectors, and improve the classification accuracy.

Development of a Particle Interaction Kernel for Convection-Diffusion Scalar Transport Equation

In this study we derive a mathematically rigorous kernel function, which accounts for the interaction among particles, within the framework of the particle method, to predict a computationally more accurate solution for the convection-diffusion equation investigated at low as well as high Peclet numbers. Determination of the functional dependence of the kernel function on the distance vector between the particles is therefore a key to the success of the interaction model. The smoothed quantity for a scalar or for a vector at a particle location is mathematically identical to its collocated value provided that the kernel function is chosen as the delta function. Such a kernel is unfortunately not computable in a discrete context. Our guideline for developing the modified kernel function is therefore to make it closer to the delta function as much as possible in cases when diffusion dominates convection. To achieve this goal, we enforce five constraint conditions in a derivation of the kernel function for the pure diffusion equation. In addition, this kernel function has no effect on the particles outside of the disk, which has the user's specified radius r e . To mimic the delta function we demand that the developed kernel function at r = r e should smoothly approach zero. It is also desired to acquire the largest possible value for the kernel function near r = 0. As flow convection prevailingly dominates its diffusion counterpart, particle interaction at the upstream side should be more favorably taken into account to avoid numerical oscillations due to convective instability. We present in this study a two-dimensional upwind kernel function to enhance numerical stability along the flow direction. The proposed upwind kernel function can render an exact solution for the investigated convection-diffusion equation in the limiting one-dimensional case. The proposed particle interaction model featuring the newly developed kernel function is validated through several problems that are amenable to analytical solutions or have available benchmark solutions. Analysis of the stability condition and spatial accuracy order of the proposed particle interaction model are also provided in details.

Development of an upwinding particle interaction kernel for simulating incompressible Navier‐Stokes equations

AbstractIn this study, we are aimed to derive a kernel function, which accounts for the interaction among particles, within the framework of particle method. To get a computationally more accurate solution for the incompressible Navier‐Stokes equations, determination of kernel function is a key to success in the developed interaction model. In the light of the underlying fact that the smoothed quantity for a scalar or a vector at a particle location is mathematically identical to its collocated value provided that the kernel function is chosen as the Dirac delta function, our guideline is to make the modified kernel function closer to the Dirac delta function as much as possible in flow conditions when diffusion dominates convection. As convection prevailingly dominates its diffusion counterpart, particle interaction at the upstream side should be favorably taken into account to avoid numerical oscillations resulting from the convective instability. The proposed particle interaction model featuring with the newly developed kernel function will be validated through several scalar transport and Navier‐Stokes problems which have either analytical or benchmark solutions. The stability condition and the spatial accuracy order of the proposed particle interaction model will be also analyzed in details in this article for the sake of completeness. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012

Incremental SVM based on reserved set for network intrusion detection

We develop an improved incremental SVM algorithm, named RS-ISVM, to deal with network intrusion detection. To reduce the noise generated by feature differences, we propose a modified kernel function U-RBF, with the mean and mean square difference values of feature attributes embedded in kernel function RBF. Then, given the oscillation problem that usually occurs in traditional incremental SVM’s follow-up learning process, we present a reserved set strategy which can keep those samples that are more likely to be the support vectors in the following computation process. Moreover, in order to shorten the training time, a concentric circle method is suggested to be used in selecting samples to form the reserved set. Academic researches and data experiments show that RS-ISVM can ease the oscillation phenomenon in the learning process and achieve pretty good performance, meanwhile, its reliability is relative high.

An iterative modified kernel based on training data

To improve performance of a support vector regression, a new method for a modified kernel function is proposed. In this method, information of all samples is included in the kernel function with conformal mapping. Thus the kernel function is data-dependent. With a random initial parameter, the kernel function is modified repeatedly until a satisfactory result is achieved. Compared with the conventional model, the improved approach does not need to select parameters of the kernel function. Simulation is carried out for the one-dimension continuous function and a case of strong earthquakes. The results show that the improved approach has better learning ability and forecasting precision than the traditional model. With the increase of the iteration number, the figure of merit decreases and converges. The speed of convergence depends on the parameters used in the algorithm.

Investigation of carbon nanotube antennas using thin wire integral equations

Abstract. In this paper the characteristics of small carbon nanotube (CNT) dipole antennas are investigated on the basis of the thin wire Hallén integral equation (IE). A surface impedance model for the CNT is adopted to account for the specific material properties resulting in a modified kernel function for the integral equation. A numerical solution for the IE gives the current distribution along the CNT. From the current distribution the antenna driving point impedance and the antenna efficiency are computed. The presented numerical examples demonstrate the strong dependence of the antenna characteristics on the used material and show the limitations of nanoscale antennas.

An Improved SVM Based on Similarity Metric

A novel support vector machine method for classification is presented in this paper. A modified kernel function based on the similarity metric and Rieman- nian metric is applied to the support vector machine. In general, it is believed that the similarity of homogeneous samples is higher than that of inhomogeneous samples. Therefore, in Riemannian geometry, Riemannian metric can be used to reflect local property of a curve. In order to enlarge the similarity metric of the homogeneous sam- ples or reduce that of the inhomogeneous samples in the feature space, Riemannian metric is used in the kernel function of the SVM. Simulated experiments are performed using the databases including an artificial and the UCI real data. Simulation results show the effectiveness of the proposed algorithm through the comparison with four typical kernel functions without similarity metric.