一种基于训练数据的迭代改进核函数

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. Sim- ulation 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.     

A moving particle semi‐implicit method for free surface flow: Improvement in inter‐particle force stabilization and consistency restoring

The moving particle semi‐implicit (MPS) method has been widely applied in free surface flows. However, the implementation of MPS remains limited because of compressive instability occurred when the particles are under compressive stress states. This study proposed an inter‐particle force stabilization and consistency restoring MPS (IFS‐CR‐MPS) method to overcome this numerical instability. For inter‐particle force stabilization, a hyperbolic‐shaped quintic kernel function is developed with a non‐negative and smooth second order derivative to satisfy the stability criterion under compressive stress state. Then, a contrastive study is conducted on the contradiction between the common understanding of the conventional MPS hyperbolic‐shaped kernel function and its performance. The result shows that the conventional MPS hyperbolic‐shaped kernel function can easily cause violent repulsive inter‐particle force and then lead to the compressive instability. Therefore, the first order derivative of the modified hyperbolic‐shaped quintic kernel function is recommended as the form of the contribution of the neighbor particles to achieve a more stable inter‐particle repulsive force. For consistency restoring, the Taylor series expansion and the hyperbolic‐shaped quintic kernel are combined to improve the accuracy of the viscosity and pressure calculation. The IFS‐CR‐MPS algorithm is subsequently verified by the inviscid hydrostatic pressure, jet impacting, and viscous droplet impacting problems. These results can be used for choosing kernel function and the contribution of neighbor particles in particle methods. Copyright © 2016 John Wiley & Sons, Ltd.     

An efficient Tabu-search optimized regression for data-driven modeling

In the past decade, data science became trendy and in-demand due to the necessity to capture, process, maintain, analyze and communicate data. Multiple regressions and artificial neural networks are both used for the analysis and handling of data. This work explores the use of meta-heuristic optimization to find optimal regression kernel for data fitting. It is shown that optimizing the regression kernel improve both the fitting and predictive ability of the regression. For instance, Tabu-search optimization is used to find the best least-squares regression kernel for different applications of buckling of straight columns and artificially generated data. Four independent parameters were used as input and a large pool of monomial search domain is initially considered. Different input parameters are also tested and the benefits of using of independent input parameters is shown.     

Development of direct numerical integration methods for one-dimensional integro-differential equations in mechanics

We propose constructive methods for direct numerical integration of one-dimensional singular and hypersingular integro-differential equations for the case in which their solution has an asymptotics of power-law type at the endpoints of the integration interval. The approaches are qualitatively divided into two types, typical of complex and real asymptotics. In the first case, the solution is constructed as an expansion with respect to a finite system of orthogonal polynomials (with the endpoint asymptotics explicitly taken into account), the singular and hypersingular integrals are calculated, the regular (generalized) kernel is replaced by a degenerate kernel of special form, and then the integral containing this kernel is calculated analytically (or by direct numerical computation). The application of the collocation method to the functional equation thus constructed permits obtaining a system of linear algebraic equations for the coefficients of the solution expansion. For the real asymptotics, we develop a direct approach based on the approximation of the unknown function by the Lagrange polynomial (with the endpoint asymptotics taken into account), the use of quadrature formulas of interpolation type, and the construction of a linear algebraic system for the values of the unknown function on a discrete set of points by using the collocation method. We present the results of numerical computations and compare them with the analytic solutions.     

Application of laser ignition on laminar flame front investigation

The first stages of laser-induced spark ignition were investigated as a function of time. Experiments were conducted using a premixed laminar CH₄/air burner. Laser-induced breakdown was achieved by focusing a 532-nm nanosecond pulse from a Q-switched Nd:YAG laser. An anti-reflection coated lens with a focal length of 100 mm was used. The results obtained from an intensified high-speed and PIV CCD camera and a Cassegrain optics system coupled to an ICCD spectrometer provided information about the formation of laser-induced plasma and its transition to a flame kernel and a self-sustaining flame. The localization of the kernel and its time development were reproducible. Two types of flame fronts develop: one that expands against the flow direction, and one that moves with the flow. The initial flame expansion along the laser axis is asymmetric because of the shape of the plasma, different ionization levels inside the plasma, and the shock-wave expansion. Development of the fast flame occurs behind the shock wave induced by the plasma. This is important when laser ignition is used as a flame holder. An ICCD spectrometer coupled to an optical fiber permitted chemiluminescence visualization. The spectrum obtained during the plasma and flame kernel formation defined different stages in flame formation. The results obtained with these two optical techniques were synchronized to obtain the temporal resolution of the flame kernel evolution. Laser-induced ignition of a very lean mixture can be controlled to provide local heat release and extinction in a flame.     

Diagonal form fast multipole boundary element method for 2D acoustic problems based on Burton-Miller boundary integral equation formulation and its applications

This paper describes formulation and implementation of the fast multipole boundary element method (FMBEM) for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the FMBEM are described in details. They are moment calculation, moment to moment translation, moment to local translation, and local to local translation. A data structure for the quad-tree construction is proposed which can facilitate implementation. An analytical moment expression is derived, which is more accurate, stable, and efficient than direct numerical computation. Numerical examples are presented to demonstrate the accuracy and efficiency of the FMBEM, and radiation of a 2D vibration rail mode is simulated using the FMBEM.     

A functional series expansion method for response analysis of non-linear systems subjected to random excitations

A Wiener-Hermite functional series expansion method for response analysis of nonlinear systems under random excitations is presented. The formal procedure for the derivation of the deterministic equations governing the Wiener-Hermite kernel functions is described. A singleterm expansion is used to analyze the non-stationary responses of a damped Duffing oscillator subjected to several modulated white noises. An iterative procedure for evaluating the kernel functions and the mean-square responses of the Duffing oscillator is developed. For several values of non-linearity strength and different damping coefficients the non-stationary variances and autocorrelations of the response are obtained. The results are compared with those found by the digital simulations and the existing methods.     

Determination of mechanical response of non-linear viscoelastic solids based on frechet expansion

This paper deals with the determination of mechanical response of a non-linear viscoelastic solid based on a Fréchet expansion. In the first portion, a modified superposition principle, suggested earlier by various authors, is arrived at from a slightly different point of view. The effect of such a principle on the kernel functions and a geometric interpretation are discussed. In the later portion, the tests required for the experimental determination of the kernel functions are discussed. It is seen that besides the tests suggested by Onaran and Findley for the two-dimensional case, three additional tests are needed for the three-dimensional case to compute the response under constant combined stress.     

Time series prediction using kernel adaptive filter with least mean absolute third loss function

In this paper, a novel kernel adaptive filter, based on the least mean absolute third (LMAT) loss function, is proposed for time series prediction in various noise environments. Combining the benefits of the kernel method and the LMAT loss function, the proposed KLMAT algorithm performs robustly against noises with different probability densities. However, an important limitation of the KLMAT algorithm is a trade-off between the convergence rate and steady-state prediction error imposed by the selection of a certain value for the learning rate. Therefore, a variable learning rate version (VLR–KLMAT algorithm) is also proposed based on a Lorentzian function. We analyze the stability and convergence behavior of the KLMAT algorithm and derive a sufficient condition to predict its learning rate behavior. Moreover, a kernel recursive extension of the KLMAT algorithm is further proposed for performance improvement. Simulation results in the context of time series prediction verify the effectiveness of the proposed algorithms.     

Spread of plasticity from stacked stress concentrations

A large elastic solid containing an infinite sequence of slitlike relaxed cracks with a constant distance of vertical separation is considered. The solid is deforming under plane strain shear conditions (mode II). The plastic relaxation around each of the cracks is represented by a suitable distribution of edge dislocations coplanar with the crack itself, the distribution being determined from a singular integral equation. This equation is solved numerically using an expansion of the non-singular part of the kernel in a series of Chebyshev polynomials. Solutions are obtained for the extent of spread of plasticity from each crack and for the associated dislocation distribution as a function of the crack spacing and the applied load. The results are applied to a brief discussion of the fracture process at stress concentrations using the crack opening displacement criterion.     

A kernel gradient free (KGF) SPH method

The finite particle method (FPM) is a modified SPH method with high order accuracy while retaining the advantages of SPH in modeling problems with free surfaces, moving interfaces, and large deformations. In both SPH and FPM, kernel gradient is necessary in kernel and particle approximation of a field function and its derivatives. In this paper, a new FPM is presented, which only involves kernel function itself in kernel and particle approximation. The kernel gradient is not necessary in the whole computation, and this approach is thus referred to as a kernel gradient free (KGF) SPH method. This is helpful when a kernel function is not differentiable or the resultant kernel gradient is not sufficiently smooth, and thus it is more general in selecting a kernel function. Moreover, different from the original FPM with an asymmetric corrective matrix, in the new FPM, the resultant corrective matrix is symmetric, and this is advantageous in particle approximations. A series of numerical examples have been conducted to show the efficiencies of KGF‐SPH including one‐dimensional mathematical tests of polynomial functions with equal or variable smoothing length and two‐dimensional incompressible fluid flow of shear cavity. It is found that KGF‐SPH is comparable with FPM in accuracy and is flexible as SPH. Copyright © 2015 John Wiley & Sons, Ltd.     

Effects of Turbulence on Self-sustained Combustion in Premixed Flame Kernels: A Direct Numerical Simulation (DNS) Study

The effects of mean flame radius and turbulence on self-sustained combustion of turbulent premixed spherical flames in decaying turbulence have been investigated using three-dimensional direct numerical simulations (DNS) with single step Arrhenius chemistry. Several flame kernels with different initial radius or initial turbulent field have been studied for identical conditions of thermo-chemistry. It has been found that for very small kernel radius the mean displacement speed may become negative leading ultimately to extinction of the flame kernel. A mean negative displacement speed is shown to signify a physical situation where heat transfer from the kernel overcomes the heat release due to combustion. This mechanism is further enhanced by turbulent transport and, based on simulations with different initial turbulent velocity fields, it has been found that self-sustained combustion is adversely affected by higher turbulent velocity fluctuation magnitude and integral length scale. A scaling analysis is performed to estimate the critical radius for self-sustained combustion in premixed flame kernels in a turbulent environment. The scaling analysis is found to be in good agreement with the results of the simulations.     

A Legendre expansion and some exact solutions basic to the McCormack model for binary gas mixtures

A Legendre expansion of the scattering kernel, a conservation condition and some exact solutions are reported for the McCormack kinetic model that is used to describe a binary mixture of rarefied gases.     

一种基于多尺度和改进支持向量机的光纤陀螺温度漂移建模与补偿方法

为了提升光纤陀螺温度漂移模型建模的准确性及补偿的效果,提出了一种基于改进支持向量机的多尺度建模和回归方法。首先分析了造成光纤陀螺温度漂移的关键因素,给出了建模的属性参数和温度试验。然后根据经验模态分解得到的本征模态函数排列熵的变化趋势,得出了回归精度和熵之间的变化关系,进而提出了基于信号分解的多尺度回归方法。为了提高上述多尺度回归算法的适应性,在传统支持向量机的基础上,提出了基于组合核函数的支持向量机回归算法,以适应不同特性的回归数据集。为了进一步提高回归精度,基于降低回归数据复杂度的分段回归思想,在上述多尺度回归的基础上提出了双-多尺度回归,并验证了方法的有效性。最后,将提出的算法以实际的光纤陀螺温度漂移数据进行验证,结果表明,相比于传统的支持向量机和反向传播神经网络具有更好的回归精度,温度漂移模型也更加精确,以均方误差指标为例,回归精度提升了两个数量级。     

基于EEMD和SVR的多自由度结构状态趋势预测

由于工程结构的复杂性和引起结构损伤原因的不确定性,结构早期微弱和潜在的损伤难以识别和预测。为此提出了基于聚类经验模式分解(EEMD)和支持向量机回归(SVR)的结构健康状态趋势预测方法。首先对多自由度结构渐进损伤的加速度振动信号进行聚类经验模式分解(EEMD);再进行希尔伯特变换(HT)计算瞬时频率;然后用回归支持向量机对反映结构健康状态的瞬时频率进行趋势预测。详细分析了各种参数对回归和预测精度的影响,提出了这些参数的选用方法和一般原则。研究表明:该方法具有训练样本少的特点;在采用二阶多项式核函数、回归步长m=3~5、误差惩罚因子C=100、敏感因子ε=0.01时,可以准确地和高精度地预测结构状态趋势,预测精度达到0.24781%。     

物理信息依赖核函数配点法的研究进展

在过去几十年里, 尽管有限元等传统计算方法已被成功用于众多科学与工程领域, 但是其在数值模拟无限域波传播、大尺寸比结构、工程反演和移动边界问题时仍面临计算量大、计算效率低、网格生成困难等计算难题. 本文介绍一类基于物理信息依赖核函数的无网格配点法及其在上述难点问题中的应用. 物理信息依赖核函数配点法的关键在于构建能反映问题微分控制方程物理信息的基函数. 基于这些物理信息依赖核函数, 该方法无需/仅需少量配点对所求微分控制方程进行离散, 即可有效提高计算效率. 本文首先介绍满足常见齐次微分方程的基本解、调和函数、径向Trefftz函数以及T完备函数等典型物理信息依赖核函数. 接着依次介绍非齐次、非均质、非稳态以及隐式微分方程构造物理信息依赖核函数的方法. 随后, 根据所求问题特点, 选用全域配点或局部配点技术, 建立相应的物理信息依赖核函数配点法. 最后, 通过几个典型算例验证所提物理信息依赖核函数配点法的有效性.      

Delayed Fracture of an Aging Viscoelastic Composite under Plane Strain

The theory of delayed fracture of cracked viscoelastic bodies and the method of continued fractions are used to study the problem on the delayed fracture of an unidirectional fibrous composite subjected to uniaxial tension under plane-strain conditions. The aging viscoelastic binder contains a mode I macrocrack, which is parallel to the fibers. The results of a numerical crack-resistance analysis of a composite whose aging properties are described by the Volterra operator with the Maslov–Arutyunyan kernel are presented. A convergence analysis is made of the expansion of an irrational function of the resolvent Volterra operator into a continued fraction.     

基于逐步回归分析的随机响应面法

制约随机响应面法广泛应用的重要原因在于响应面展开式中的待定系数过多,计算效率不高.本文研究建立了改进的随机响应面法.首先,利用Nataf变换将给定边缘累积分布函数的相关随机变量转变为独立标准正态随机变量,进而将结构随机响应量描述为独立标准正态随机变量的混沌多项式展开式;然后,根据线性无关原则选取最优概率配点,并引入逐步回归分析剔除响应面展开项中的次要项,从而大幅减少展开式中的待定系数.算例分析表明,该方法具有较高的计算精度和效率.     

Buckling analysis of cylindrical shells with random geometric imperfections

In this paper the effect of random geometric imperfections on the limit loads of isotropic, thin-walled, cylindrical shells under deterministic axial compression is presented. Therefore, a concept for the numerical prediction of the large scatter in the limit load observed in experiments using direct Monte Carlo simulation technique in context with the Finite Element method is introduced. Geometric imperfections are modeled as a two dimensional, Gaussian stochastic process with prescribed second moment characteristics based on a data bank of measured imperfections. (The initial imperfection data bank at the Delft University of Technology, Part 1. Technical Report LR-290, Department of Aerospace Engineering, Delft University of Technology). In order to generate realizations of geometric imperfections, the estimated covariance kernel is decomposed into an orthogonal series in terms of eigenfunctions with corresponding uncorrelated Gaussian random variables, known as the Karhunen-Loéve expansion. For the determination of the limit load a geometrically non-linear static analysis is carried out using the general purpose code STAGS (STructural Analysis of General Shells, user manual, LMSC P032594, version 3.0, Lockheed Martin Missiles and Space Co., Inc., Palo Alto, CA, USA). As a result of the direct Monte Carlo simulation, second moment characteristics of the limit load are presented. The numerically predicted statistics of the limit load coincide reasonably well with the actual observations, particularly in view of the limited data available, which is reflected in the statistical estimators.