Insights into performance of pattern search algorithms for high-frequency surface wave analysis

Inversion of high-frequency surface wave dispersion curves is challenging for most local-search methods due to its high nonlinearity and to its multimodality. In this paper, we implemented an investigation to fully exploit and utilize the potentiality of pattern search algorithms and to further enhance their performance for surface wave analysis. We first investigate effects of different inversion strategies, initial mesh size and final mesh size, expansion factor, and contraction factor, as well as inclusion of noise in surface wave data on the performance of the approaches, by three synthetic earth models. Then, a comparative analysis with genetic algorithms is made to further highlight the advantages of the proposed inverse procedure. Finally, the insights issued from this analysis are verified by a real-world example from Henan, China.Results from both synthetic and field data demonstrate: (a) generalized pattern search (GPS) algorithm with the maximal positive basis set 2N vectors works better than GPS algorithm with the minimal positive basis set N+1 vectors; (b) if one gets a suitable initial mesh size by taking some experimentation, then setting expansion factor Λ=1 (i.e., not allow expansions) and contraction factor θ=1/2 can greatly enhance the performance of pattern search algorithms. This is particularly true as the algorithm converges and final mesh size should go to zero; and (c) pattern search algorithms possess stronger immunity with respect to noise and should be considered good not only in terms of accuracy but also in terms of computation effort, especially when compared to the application of genetic algorithms to Rayleigh wave inversion.     

Rayleigh wave dispersion due to spatial (FEM) discretization of a thin elastic solid having non-curved boundary

The grid dispersion for a harmonic Rayleigh wave propagating along a straight boundary of a thin elastic solid, modelled by finite elements, is investigated. It is shown that with an increase of dimensionless wavenumber γ · q, a phase velocity of Rayleigh waves increases from the long wave limit C_R. For sufficiently short waves it follows the dispersion curve referring to quasitransverse waves in an unbounded discretized medium.     

Nonlinear inversion of potential-field data using a hybrid-encoding genetic algorithm

Using a genetic algorithm to solve an inverse problem of complex nonlinear geophysical equations is advantageous because it does not require computer gradients of models or “good” initial models. The multi-point search of a genetic algorithm makes it easier to find the globally optimal solution while avoiding falling into a local extremum. As is the case in other optimization approaches, the search efficiency for a genetic algorithm is vital in finding desired solutions successfully in a multi-dimensional model space. A binary-encoding genetic algorithm is hardly ever used to resolve an optimization problem such as a simple geophysical inversion with only three unknowns. The encoding mechanism, genetic operators, and population size of the genetic algorithm greatly affect search processes in the evolution. It is clear that improved operators and proper population size promote the convergence. Nevertheless, not all genetic operations perform perfectly while searching under either a uniform binary or a decimal encoding system. With the binary encoding mechanism, the crossover scheme may produce more new individuals than with the decimal encoding. On the other hand, the mutation scheme in a decimal encoding system will create new genes larger in scope than those in the binary encoding. This paper discusses approaches of exploiting the search potential of genetic operations in the two encoding systems and presents an approach with a hybrid-encoding mechanism, multi-point crossover, and dynamic population size for geophysical inversion. We present a method that is based on the routine in which the mutation operation is conducted in the decimal code and multi-point crossover operation in the binary code. The mix-encoding algorithm is called the hybrid-encoding genetic algorithm (HEGA). HEGA provides better genes with a higher probability by a mutation operator and improves genetic algorithms in resolving complicated geophysical inverse problems. Another significant result is that final solution is determined by the average model derived from multiple trials instead of one computation due to the randomness in a genetic algorithm procedure. These advantages were demonstrated by synthetic and real-world examples of inversion of potential-field data.     

基于非线性薛定谔方程的高分三号图像内波参数反演

高分三号(GF-3)SAR遥感卫星的发射为内波的深入研究提供了丰富图像资料,利用其高空间分辨率和大幅宽成像的优势,能够对南中国海东沙岛附近的内波开展振幅和波速的高精度反演。采用高阶完全非线性薛定谔方程描述内波,建立反演振幅和波速的模型。收集2017年5月至8月南海东沙岛附近的GF-3遥感图像,探究南海陆坡处内波的振幅和传播速度演变。理论模型计算出的结果与2013年该研究区域的实测数据对比,发现反演振幅大小基本与实测相近。内波自东向西传播过程中,水深变浅,非线性作用增强,频散作用减弱,振幅和传播速度都不断减小。这为定量研究内波的能量输送、耗散以及未来的预报工作提供依据。     

Control-affine neural network approach for nonminimum-phase nonlinear process control

The design of controllers for nonlinear, nonminimum-phase processes is very challenging and remains as one of the more difficult control research problems. Most currently available control algorithms rely implicitly or explicitly upon an inverse of the process. Linear control methods for nonminimum-phase processes are typically based on a decomposition of the process into a minimum-phase and a nonminimum-phase part, and subsequent inversion of the minimum-phase component. A similar scheme for nonlinear systems is still an open problem. In this work, an internal model control strategy employing a minimum-phase model is proposed. The minimum-phase model is first-order, minimum-phase and control-affine but statically equivalent to the original process. Because the model is identified directly from input-output data, a first principles model of the process is not required. The inverse of the process is obtained through analytical inversion of the process model. The proposed control scheme is applied to a van de Vusse reactor and a complex continuous stirred tank bioreactor.     

特征3有限域上的椭圆曲线算法改进

减少求逆运算次数是快速计算椭圆曲线密码的主要方法之一。若采用逐次累加的方法计算特征3有限域上椭圆曲线标量乘法2kP,需要k次求逆运算。本文根据递推归纳、转换求逆为乘法的思想,推导了直接计算2kP的公式,使求逆运算降至1次。从理论上比较了两种计算方法的运算效率:所提出的新算法在k=4时比逐次累加计算量减少1%,并且减少量随着k的增大而增多,在极限情况下可减少约26%。     

The evolution of solitons in coupled resonator optical waveguides and photonic-crystal waveguides

We successfully used the tight binding theory to derive the extended discrete nonlinear Schrödinger equation to describe the soliton propagation and to obtain the soliton propagation criteria (SPC) in the nonlinear photonic-crystal waveguides (PCWs) and coupled resonant optical waveguides (CROWs) containing Kerr media. From these criteria, we obtain the soliton-propagating region of CROWs in different numbers of separated rods and strengths of self-phase modulation (SPM). The defined soliton-propagating regions coincide with the regions of modulation instability in the CROWs. In the PCWs, the positive Kerr coefficient medium needs to be added to support the pulse propagation in low frequency or low wave vector region of the dispersion curve; while negative Kerr effect is for high frequency case. Due to the linear combination of various cosine harmonic functions in the dispersion relations of both CROWs and PCWs, the pulse broadening which is mainly caused by the third-order dispersion at SPC is the lowest at the boundary of dispersion curves. However, due to the different magnitudes of coupling coefficients in CROWs and PCWs, the group velocity, dispersion and strength of SPM in CROWs are all smaller than those in PCWs.     

GPS软件接收机捕获跟踪算法研究与仿真

本文对GPSL1软件接收机的捕获跟踪算法进行了研究。GPS信号的捕获分别采用时域滑动相关捕获方法和频域快速捕获算法，通过分析比较认为频域快速捕获算法计算量大为减少；在GPS信号跟踪中，采用非相干延迟锁定环（DLL），锁相环（PLL）实现对GPS信号的跟踪。     

Iterative inversion of fuzzified neural networks

The inversion of a neural network is a process of computing inputs that produce a given target when fed into the neural network. The inversion algorithm of crisp neural networks is based on the gradient descent search in which a candidate inverse is iteratively refined to decrease the error between its output and the target. In this paper. we derive an inversion algorithm of fuzzified neural networks from that of crisp neural networks. First, we present a framework of learning algorithms of fuzzified neural networks and introduce the idea of adjusting schemes for fuzzy variables. Next, we derive the inversion algorithm of fuzzified neural networks by applying the adjusting scheme for fuzzy variables to total inputs in the input layer. Finally, we make three experiments on the parity-three problem, examine the effect of the size of training sets on the inversion, and investigate how the fuzziness of inputs and targets of training sets affects the inversion     

A genetic algorithm-based search space splitting pattern and its application in hydraulic and coastal engineering problems

This article reports a search space splitting pattern that can be applied to genetic algorithms in order to ensure that the entire search space is investigated. Hence, by keeping the genetic algorithm simple, in a reasonable time and with a high degree of accuracy, the initial solutions can be improved toward the global optimum point. The simplicity of the presented method is an advantage that makes it useful for applied hydraulic and coastal engineering problems. The performance of the proposed method was evaluated by a benchmark optimization problem, Levy No. 5, and three hydraulic and coastal engineering problems: inverse problem of Manning’s equation, the equation of equilibrium beach profiles, and the settling velocity equation of natural sediment particles. The results indicated that the nonlinear complex problems can be solved by the proposed method with a high degree of accuracy. The proposed genetic algorithm-based search space splitting pattern can either be used exclusively or alternatively it can be combined with improved operators in the literature.

     

Fitting smoothing splines to time-indexed,noisy points on nonlinear manifolds

We address the problem of estimating full curves/paths on certain nonlinear manifolds using only a set of time-indexed points, for use in interpolation, smoothing, and prediction of dynamic systems. These curves are analogous to smoothing splines in Euclidean spaces as they are optimal under a similar objective function, which is a weighted sum of a fitting-related (data term) and a regularity-related (smoothing term) cost functions. The search for smoothing splines on manifolds is based on a Palais metric-based steepest-decent algorithm developed in Samir et al. [38]. Using three representative manifolds: the rotation group for pose tracking, the space of symmetric positive-definite matrices for DTI image analysis, and Kendall's shape space for video-based activity recognition, we demonstrate the effectiveness of the proposed algorithm for optimal curve fitting. This paper derives certain geometrical elements, namely the exponential map and its inverse, parallel transport of tangents, and the curvature tensor, on these manifolds, that are needed in the gradient-based search for smoothing splines. These ideas are illustrated using experimental results involving both simulated and real data, and comparing the results to some current algorithms such as piecewise geodesic curves and splines on tangent spaces, including the method by Kume et al. [24].     

Fast hyperbolic Radon transform using chirp-z transform

The hyperbolic Radon transform plays an important role in seismic data processing for its ability to focus seismic events in the transform domain. Traditional algorithms based on direct implementations, however, are inefficient with limited applications for processing large data sets. A new algorithm is presented for fast computation of the hyperbolic Radon transform and its sparse calculations. It uses interpolation procedures to stretch the data along time axis and efficiently computes the summation paths in the new coordinates via the chirp-z transform which is carried out by fast Fourier transform (FFT). The proposed fast algorithm is then used within the deconvolutive form of the Radon transform and iterative sparse algorithms for effective decomposition of CMP gathers with an improved temporal resolution, compared to the traditional Radon transforms. The effectiveness of the new algorithm are confirmed on sparse velocity-stack inversion, primary and multiple separation, high-quality stacking, and automatic velocity model building. The tests show that sparse velocity-stack inversion using the new algorithm is even more efficient than the traditional velocity scan, both in resolution and speed. Furthermore, numerical tests show the superiority of the proposed algorithm over the state-of-the-art fast algorithms, based on butterfly scheme and log-polar convolutions, demanding less computational complexity.     

SINS/GPS组合导航系统仿真研究

以某载体的规划航迹数据为对象,针对捷联、卫星组合导航系统(SINS/GPS)进行了仿真研究。由规划航迹数据计算出载体的比力和角速度信息,输入至惯性测量器件模型,模型输出激励捷联解算模块,得到惯导系统输出参数;同时对规划数据添加观测噪声模拟GPS测量值。采用相对简单的基于半位置、半速度误差的误差方程作为状态方程,以松耦合方式进行集中式Kalman滤波,给出了SINS单独工作与SINS/GPS组合得到的半位置、半速度误差分布。对各状态的观测度进行了研究,确定了不可观测的状态并给出了部分状态可观测度的时间分布。仿真结果表明,方法正确有效,可对SINS/GPS组合导航系统进行算法验证和方案性评估。     

Hidden solitons in the Zabusky–Kruskal experiment: Analysis using the periodic,inverse scattering transform

Recent numerical work on the Zabusky–Kruskal experiment has revealed, amongst other things, the existence of hidden solitons in the wave profile. Here, using Osborne’s nonlinear Fourier analysis, which is based on the periodic, inverse scattering transform, the hidden soliton hypothesis is corroborated, and the exact number of solitons, their amplitudes and their reference level is computed. Other “less nonlinear” oscillation modes, which are not solitons, are also found to have nontrivial energy contributions over certain ranges of the dispersion parameter. In addition, the reference level is found to be a non-monotone function of the dispersion parameter. Finally, in the case of large dispersion, we show that the one-term nonlinear Fourier series yields a very accurate approximate solution in terms of Jacobian elliptic functions.     

Solving inverse problems involving the Navier–Stokes equations discretized by a Lagrange–Galerkin method

In this article, we are investigating the numerical approximation of an inverse problem involving the evolution of a Newtonian viscous incompressible fluid described by the Navier–Stokes equations in 2D. This system is discretized using a low order finite element in space coupled with a Lagrange–Galerkin scheme for the nonlinear advection operator. We introduce a full discrete linearized scheme that is used to compute the gradient of a given cost function by ensuring its consistency. Using gradient based optimization algorithms, we are able to deal with two fluid flow inverse problems, the drag reduction around a moving cylinder and the identification of a far-field velocity using the knowledge of the fluid load on a rectangular bluff body, for both fixed and prescribed moving configurations.     

Direct and inverse problems on nonlinear rods

In this paper a class of models on nonlinear rods, which includes spatial inhomogeneities, varying cross-sectional area and arbitrary memory functions, is considered. The wave splitting technique is applied to provide a formulation suitable for numerical computation of direct and inverse problems. Due to the nonlinearity of the material, there are no well defined characteristics other than the leading edge, so the method of characteristics, highly successful in the computation of linear wave splitting problems, is abandoned. A standard finite difference method is employed for the direct problem, and a shooting method is introduced for the inverse problem. The feasibility of the inverse algorithm is presented in various numerical examples.     

Modeling Software Behavior in Terms of a Formal Life Cycle Curve: Implications for Software Maintenance

In this paper, a formal model of the software manloading pattern, the Rayleigh model, is described and then applied to four Bankers Trust Company (BTCo.) new development projects possessing complete life cycle manloading data (maintenance phase included). To fit the Rayleigh curve to a project's manloading scores, (nonlinear) regression was used to obtain least squares estimates of the Rayleigh parameters, which, in turn, were used to generate the Rayleigh manloading curve. For all four projects, deviation from the Rayleigh curve was small and constant throughout the software development phases (i.e., preliminary design through implementation); however, the Rayleigh curve consistently deviated from the actual manloading during system maintenance, underestimating the amount of maneffort expended. Restricting maintenance maneffort to manpower expended on repair of system faults (``corrective' maintenance) resulted in a single Rayleigh curve that could be applied over the entire BTCo. life cycle. Furthermore, this corrective portion of the maintenance effort could be accurately forecasted from the Rayleigh curve fit to software development. Implications of these findings for software management are discussed.     

基于局部补数-导数模式的光照反转和旋转不变纹理表达

针对现有局部二值模式(Local binary pattern, LBP) 算法对光照反转变化敏感和特征描述力不足的问题, 本文提出一种基于局部补数-导数模式(Local complement and derivative pattern, LCDP) 的纹理表达方法. 其中, 局部补数模式(Local complement pattern, LCP) 用于编码原始图像空间中的近邻差分符号信息, 局部导数模式(Local derivative pattern, LDP) 用于编码不同尺度下(一阶和二阶) 高斯导数空间中的近邻差分幅值信息, 二者对光照反转和图像旋转均具有鲁棒性. 为实现对差分符号和差分幅值的联合统计, 同时维持特征的紧致性, 进一步提出基于均值采样的联合编码方案. 最后, 对联合编码的结果进行多尺度直方图特征表达. 实验表明, 该方法能够有效提高线性和非线性光照反转条件下纹理图像的分类精度.     

自构造RBF神经网络及其参数优化

径向基函数神经网络的构造需要确定每个RBF的中心、宽度和数目。该文利用改进的聚类算法自动构造RBFN,考虑样本的类别属性,根据样本分布自动计算RBF的中心和宽度,并确定RBF的数目。所有的网络参数采用非线性优化算法来优化。通过IRIS分类问题和混沌时间序列预测评价自构建RBFN的性能,验证参数优化效果。结果表明,自构造RBFN不但能够自动确定网络结构,而且具有良好的模式分类和函数逼近能力。通过对网络参数的非线性优化,该算法明显改善了网络性能。     

A numerical study concerning brain stroke detection by microwave imaging systems

In this paper, a numerical study devoted to evaluate the application of a microwave imaging method for brain stroke detection is described. First of all, suitable operating conditions for the imaging system are defined by solving the forward electromagnetic scattering problem with respect to simplified configurations and analyzing the interactions between an illuminating electromagnetic wave at microwave frequencies and the biological tissues inside the head. Then, preliminary inversion results are obtained by applying an imaging procedure based on an iterative Gauss-Newton scheme to a realistic model of the human head. The proposed imaging algorithm is able to deal with the nonlinear and ill-posed problem associated to the integral equations describing the inverse scattering problem. The aim of the inversion procedure is related to the determination of the presence of a hemorrhagic brain stroke by retrieving the distributions of the dielectric parameters of the human tissues inside a slice of the head model.