Performance analysis of neural networks for classification of medical images with wavelets as a feature extractor

In this article, we analyze the performance of artificial neural network, in classification of medical images using wavelets as feature extractor. This work classifies the mammographic image, MRI images, CT images, and ultrasound images as either normal or abnormal. We have tested the proposed approach using 50 mammogram images (13 normal and 37 abnormal), 24 MRI brain images (9 normal and 15 abnormal), 33 CT images (11 normal and 22 abnormal), and 20 ultrasound images (6 normal and 14 abnormal). Four kind of neural network models such as BPN (Back Propagation Network), Hopfield, RBF (Radial Basis Function), and PNN (Probabilistic neural network) were chosen for study. To improve diagnostic accuracy, the feature extracted using wavelets such as Harr, Daubechies (db2, db4, and db8), Biorthogonal and Coiflet wavelets are given as input to the neural network models. Good classification percentage of 96% was achieved using the RBF when Daubechies (db4) wavelet based feature extraction was used. We observed that the classification rate is almost high under the RBF neural network for all the dataset considered. © 2015 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 25, 33–40, 2015     

地下管线在空间随机分布的地震作用下的反应

强震作用下地下管线地震反应计算以往多采用波动法求解。这种方法假定地震波为一行进波,沿管线的轴向或成某一角度传播,它只能求得地面运动的相位差引起的管线的变形和内力。有些文献将地震地面运动假定为空间变化的平稳随机过程,用随机振动理论求得管线的地震反应,但不能反映地面运动的非平稳性对管线地震反应的影响。而地面运动的非平稳性,特别是时域非平稳性很可能是产生地下管线变形和内力的最重要原因。根据地面运动的统计模型生成管线轴线上各点的地面运动时程,用级数解法求管道的地震反应。由于这种方法能较好地反映地面运动的时域非平稳性,所以得到的计算结果更真实。     

Two-dimensional Legendre wavelets for solving fractional Poisson equation with Dirichlet boundary conditions

In this paper, the two-dimensional Legendre wavelets are applied for numerical solution of the fractional Poisson equation with Dirichlet boundary conditions. In this way, a new operational matrix of fractional derivative for the Legendre wavelets is derived and then this operational matrix has been employed to obtain the numerical solution of the above-mentioned problem. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifies the problem. The convergence of the two-dimensional Legendre wavelets expansion is investigated. Also the power of this manageable method is illustrated.     

Robust deconvolution of high-frequency ultrasound images using higher-order spectral analysis and wavelets

Deconvolution of high-frequency (30-40 MHz) ultrasonic images of human skin was studied in vivo. Separate one-dimensional (1-D) functions for the axial and lateral profiles were first estimated using higher-order spectral methods. Subsequently, deconvolution was implemented using a regularized inverse Wiener filtering of the wavelet and scaling coefficients that were obtained after a wavelet decomposition of the RF signals. Deconvolution was first performed in the axial direction, then in the lateral direction. The methods were applied to data obtained from the skin of 16 volunteers using three different transducers. Significant improvements in both the axial and lateral resolutions were obtained in all the cases. Features such as hair follicles in the dermis and fingerprints on the surface of the finger were more clearly displayed in the processed images compared to the original images. The results indicate that the deconvolution method using higher-order spectral methods and wavelet analysis could significantly improve the quality of high-frequency ultrasonic skin images.     

Nonparametric factor analysis of residual time series

We introduce a nonparametric smoothing procedure for nonparametric factor analysis of multivariate time series. Our main objective is to develop an adaptive method for estimating a time-varying covariance matrix. The asymptotic properties of the proposed procedures are derived. We present an application based on the residuals from the Fair macromodel of the U.S. economy. We find substantial evidence of time varying second moments and breaks in the contemporaneous correlation structure during the mid 1970's to the early 1980's.     

Multiple timescale spectral analysis

Spectral analysis is a classical tool for the structural analysis of structures subjected to random excitations. The most common application of spectral analysis is the determination of the steady-state second order cumulant of a linear oscillator, under the action of a stationary loading prescribed by means of its power spectral density. There exists however a broad variety of such similar problems, extending the concept to multi degree-of-freedom systems, non Gaussian excitation, slightly nonlinear oscillators or even transient excitations. In this wide class of problems, the cumulants of the response are obtained as the result of the integral of corresponding spectra over the frequency space, which is possibly multidimensional. Application of standard numerical integration techniques may be prohibitive, a reason why the spectral approach is often left aside. Besides, many engineering problems involve a clear timescale separation, usually of those pertaining to the loading and to the mechanical behavior of the system. In these problems, a proper consideration of the timescale separation results in dropping the order of integration by one, at least. This offers the possibility to derive analytical solutions, whenever the order of integration drops to zero, or to make numerical integration competitive. The paper presents this general method, together with some applications in wind and marine engineering.     

A Bayesian approach to sequential monitoring of nonlinear profiles using wavelets

We consider change‐point detection and estimation in sequences of functional observations. This setting often arises when the quality of a process is characterized by such observations, called profiles, and monitoring profiles for changes in structure can be used to ensure the stability of the process over time. While interest in phase II profile monitoring has grown, few methods approach the problem from a Bayesian perspective. We propose a wavelet‐based Bayesian methodology that bases inference on the posterior distribution of the change point without placing restrictive assumptions on the form of profiles. By obtaining an analytic form of this posterior distribution, we allow the proposed method to run online without using Markov chain Monte Carlo (MCMC) approximation. Wavelets, an effective tool for estimating nonlinear signals from noise‐contaminated observations, enable us to flexibly distinguish between sustained changes in profiles and the inherent variability of the process. We analyze observed profiles in the wavelet domain and consider two possible prior distributions for coefficients corresponding to the unknown change in the sequence. These priors, previously applied in the nonparametric regression setting, yield tuning‐free choices of hyperparameters. We present additional considerations for controlling computational complexity over time and their effects on performance. The proposed method significantly outperforms a relevant frequentist competitor on simulated data.     

Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: Theory and algorithm

This paper presents a novel computational approach, the discrete singular convolution (DSC) algorithm, for analysing plate structures. The basic philosophy behind the DSC algorithm for the approximation of functions and their derivatives is studied. Approximations to the delta distribution are constructed as either bandlimited reproducing kernels or approximate reproducing kernels. Unified features of the DSC algorithm for solving differential equations are explored. It is demonstrated that different methods of implementation for the present algorithm, such as global, local, Galerkin, collocation, and finite difference, can be deduced from a single starting point. The use of the algorithm for the vibration analysis of plates with internal supports is discussed. Detailed formulation is given to the treatment of different plate boundary conditions, including simply supported, elastically supported and clamped edges. This work paves the way for applying the DSC approach in the following paper to plates with complex support conditions, which have not been fully addressed in the literature yet. Copyright © 2002 John Wiley & Sons, Ltd.     

A combined approach for goal‐oriented error estimation and adaptivity using operator‐customized finite element wavelets

We describe how wavelets constructed out of finite element interpolation functions provide a simple and convenient mechanism for both goal‐oriented error estimation and adaptivity in finite element analysis. This is done by posing an adaptive refinement problem as one of compactly representing a signal (the solution to the governing partial differential equation) in a multiresolution basis. To compress the solution in an efficient manner, we first approximately compute the details to be added to the solution on a coarse mesh in order to obtain the solution on a finer mesh (the estimation step) and then compute exactly the coefficients corresponding to only those basis functions contributing significantly to a functional of interest (the adaptation step). In this sense, therefore, the proposed approach is unified, since unlike many contemporary error estimation and adaptive refinement methods, the basis functions used for error estimation are the same as those used for adaptive refinement. We illustrate the application of the proposed technique for goal‐oriented error estimation and adaptivity for second and fourth‐order linear, elliptic PDEs and demonstrate its advantages over existing methods. Copyright © 2005 John Wiley & Sons, Ltd.     

Process capability analysis in the presence of autocorrelation

Process capability analysis when observations are autocorrelated is addressed using time series modelling and regression analysis. Through the use of a numerical example, it is shown that the variance estimate obtained from the original data is no longer an appropriate estimate to be considered for conducting process capability analyses. Copyright © 2002 John Wiley & Sons, Ltd.     

希尔伯特-黄谱的端点效应分析及处理方法研究

希尔伯特-黄谱可以将机械振动信号分解为有限的模式，然后以时频方式揭示机械的运行状况；然而，作为希尔伯特-黄谱的两个关键步骤，经验模式分解和希尔伯特变换都被“端点效应”所困扰；该文分析和研究了“端点效应”产生的原因，提出采用时间序列建模与预测方法对信号数据进行延拓，达到消除或改进经验模式分解和希尔伯特变换“端点效应”的目的，从而优化希尔伯特-黄谱。     

AR（p）模型参数的灰色关联度ARGR诊断方法

本文提出了一种以AR(p)参数构成的二次特征量来计算系统各种状态之间灰色关联度的AR-GR新方法。该法综合了AR(户)模型Marple 算法和灰色关联度GR 算法的优点,可用于工程信号的分类处理和设备的监测诊断。用编制的计算机程序对实测信号进行检验,结果表明。该方法具有快速、准确的特点,有广阔的应用前景。     

板带轧机随机干扰模型与ARMA谱分析

板带轧机随机干扰模型不易建模,是制约轧机随机动力特性研究的主要难点之一。基于某铝热连轧机轧制１２３５铝合金的轧制力随机数据,得到平稳、正态、零均值的时间序列,采用时序分析法建立轧制力的ＡＲＭＡ模型及轧机动态干扰功率谱密度模型,分析了轧制力的ＡＲＭＡ谱特性,采用麦夸特法＋通用全局优化算法,得出便于工程应用的轧制力功率谱表达式,构建轧制力随机干扰模型。对轧制力的预报、轧机动刚度的确定及对轧机与轧制过程的随机动态性研究与分析具有一定的意义。     

Kernel principal component analysis and support vector machines for stock price prediction

Technical indicators are used with two heuristic models, kernel principal component analysis and factor analysis in order to identify the most influential inputs for a forecasting model. Multilayer perceptron (MLP) networks and support vector regression (SVR) are used with different inputs. We assume that the future value of a stock price/return depends on the financial indicators although there is no parametric model to explain this relationship, which comes from the technical analysis. Comparison studies show that SVR and MLP networks require different inputs. Furthermore, proposed heuristic models produce better results than the studied data mining methods. In addition to this, we can say that there is no difference between MLP networks and SVR techniques when we compare their mean square error values.     

Meshless and wavelets based complex quadrature of highly oscillatory integrals and the integrals with stationary points

In this paper, we formulate and employ efficient and accurate methods for numerical evaluation of highly oscillatory integrals and integrals having stationary points. Two new approaches using radial basis function (RBF) and wavelets are discussed. The first approach is related to meshless method (MM) which is based on multiquadric (MQ) RBF, and is specially designed for integrands having oscillatory character. This approach stems from the Levin's method. In this procedure, the solution is obtained by solving the corresponding ODE or PDE instead of finding a numerical solution of the integration problem. In situations when the integrand has stationary points, MM fails to deliver. We opt for quadrature rules based on Haar wavelets and hybrid functions. The proposed methods are tested on a number of benchmark tests considered in available literature. The performance of the new methods is compared with the existing methods. Better accuracy of the proposed methods is reported for a variety of problems.     

Time-dependent reliability analysis of flood defences

This paper describes the underlying theory and a practical process for establishing time-dependent reliability models for components in a realistic and complex flood defence system. Though time-dependent reliability models have been applied frequently in, for example, the offshore, structural safety and nuclear industry, application in the safety-critical field of flood defence has to date been limited. The modelling methodology involves identifying relevant variables and processes, characterisation of those processes in appropriate mathematical terms, numerical implementation, parameter estimation and prediction. A combination of stochastic, hierarchical and parametric processes is employed. The approach is demonstrated for selected deterioration mechanisms in the context of a flood defence system. The paper demonstrates that this structured methodology enables the definition of credible statistical models for time-dependence of flood defences in data scarce situations. In the application of those models one of the main findings is that the time variability in the deterioration process tends to be governed the time-dependence of one or a small number of critical attributes. It is demonstrated how the need for further data collection depends upon the relevance of the time-dependence in the performance of the flood defence system.     

改进谐波小波及其在振动信号时频分析中的应用

针对谐波小波在时域衰减速度慢的缺点,对其在频域进行光滑化处理,得到了性质更好的改进谐波小波。由于采用光谱化方法只能得到改进小波在频域的表达式,因而采用基于FFT的算法对它进行计算。针对振动信号一般舸样点较多的特点,采用计算等间隔小波系数的方法以减少计算量。以改进谐波小波对某新型导弹空中点火试验的振动信号进行了时频分析,并采用计算时频图等高图的方法以消除大部分无用的信息,得到了振动信号的高清晰时频图。     

Time-dependent performance evaluation for loss-waiting queues with arbitrary distributions

This paper presents an analytical approach to evaluate queues with time-dependent, generally distributed inter-arrival times, generally distributed service times, and finite buffer capacities. A stationary backlog carryover (SBC) approach is developed to analyse the probability of blocking and other time-dependent performance measures. We further improve the general SBC approach by the analysis of load-dependent period lengths used in the approximation. The numerical study shows that this approach is very accurate for both transient and time-dependent loss-blocking systems.     

Monitoring of Proportional‐Integral Controlled Processes using a Bayesian Time Series Analysis Method

Recently, there has been interest in applying statistical process monitoring methods to processes controlled with feedback controllers in order to eliminate assignable causes and achieve reduced overall variability. In this paper, we propose a Bayesian change‐point method to monitor processes regulated with proportional‐integral controllers. The approach is based on fitting an exponential rise model to the control input actions in response to a step shift and employs a change‐point method to detect the change. Simulation studies show that the proposed method has better run‐length performance in detecting step shifts in controlled processes than Shewhart chart on individuals and special‐cause chart on residuals of time series model. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive wavelets applied to the analysis of nonlinear systems with chaotic dynamics

We consider an approach to the analysis of nonstationary processes based on the application of wavelet basis sets constructed using segments of the analyzed time series. The proposed method is applied to the analysis of time series generated by a nonlinear system with and without noise.